%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWW337+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 : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 09:06:46 AM UTC 2026
% Result : Theorem 166.35s 166.67s
% Output : Proof 166.59s
% 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_equalityI,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> V_A_2 = V_B_2 ) ),
file('theBenchmark.p',fact_equalityI) ).
fof(fact_order__refl,axiom,
! [V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ),
file('theBenchmark.p',fact_order__refl) ).
fof(fact_hoare__valids__def,axiom,
! [V_tsa_2,V_Ga_2,T_b] :
( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,V_tsa_2)
<=> ! [B_n] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_Ga_2))
=> c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) )
=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2))
=> c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) ) ) ),
file('theBenchmark.p',fact_hoare__valids__def) ).
fof(fact_le__fun__def,axiom,
! [V_g_2,V_f_2,T_b,T_c] :
( class_Orderings_Oord(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
<=> ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ),
file('theBenchmark.p',fact_le__fun__def) ).
fof(fact_le__funD,axiom,
! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
( class_Orderings_Oord(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ),
file('theBenchmark.p',fact_le__funD) ).
fof(fact_le__funE,axiom,
! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
( class_Orderings_Oord(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ),
file('theBenchmark.p',fact_le__funE) ).
fof(fact_subset__refl,axiom,
! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2)),
file('theBenchmark.p',fact_subset__refl) ).
fof(fact_set__eq__subset,axiom,
! [T_b,V_B_2,V_A_2] :
( V_A_2 = V_B_2
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_set__eq__subset) ).
fof(fact_rev__predicate1D,axiom,
! [V_Q_2,T_b,V_x_2,V_P_2] :
( hBOOL(hAPP(V_P_2,V_x_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
=> hBOOL(hAPP(V_Q_2,V_x_2)) ) ),
file('theBenchmark.p',fact_rev__predicate1D) ).
fof(fact_equalityD1,axiom,
! [T_b,V_B_2,V_A_2] :
( V_A_2 = V_B_2
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
file('theBenchmark.p',fact_equalityD1) ).
fof(fact_equalityD2,axiom,
! [T_b,V_B_2,V_A_2] :
( V_A_2 = V_B_2
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
file('theBenchmark.p',fact_equalityD2) ).
fof(fact_predicate1D,axiom,
! [V_x_2,V_Q_2,V_P_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
=> ( hBOOL(hAPP(V_P_2,V_x_2))
=> hBOOL(hAPP(V_Q_2,V_x_2)) ) ),
file('theBenchmark.p',fact_predicate1D) ).
fof(fact_linorder__le__cases,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ),
file('theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_xt1_I6_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ),
file('theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_xt1_I5_J,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> V_x = V_y ) ) ),
file('theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_order__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ),
file('theBenchmark.p',fact_order__trans) ).
fof(fact_order__antisym,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
=> V_x = V_y ) ) ),
file('theBenchmark.p',fact_order__antisym) ).
fof(fact_xt1_I4_J,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
=> ( V_b = V_c
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ),
file('theBenchmark.p',fact_xt1_I4_J) ).
fof(fact_ord__le__eq__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( V_b = V_c
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ),
file('theBenchmark.p',fact_ord__le__eq__trans) ).
fof(fact_xt1_I3_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a = V_b
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ),
file('theBenchmark.p',fact_xt1_I3_J) ).
fof(fact_ord__eq__le__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( V_a = V_b
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ),
file('theBenchmark.p',fact_ord__eq__le__trans) ).
fof(fact_order__antisym__conv,axiom,
! [V_x_2,V_y_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_order__eq__refl,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( V_x = V_y
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ),
file('theBenchmark.p',fact_order__eq__refl) ).
fof(fact_order__eq__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( V_x_2 = V_y_2
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_order__eq__iff) ).
fof(fact_linorder__linear,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ),
file('theBenchmark.p',fact_linorder__linear) ).
fof(fact_equalityE,axiom,
! [T_b,V_B_2,V_A_2] :
( V_A_2 = V_B_2
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ),
file('theBenchmark.p',fact_equalityE) ).
fof(fact_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_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_triples__valid__Suc,axiom,
! [V_n_2,V_tsa_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2))
=> c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),B_x) )
=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2))
=> c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,B_x) ) ),
file('theBenchmark.p',fact_triples__valid__Suc) ).
fof(fact_le__funI,axiom,
! [T_b,V_g_2,V_f_2,T_c] :
( class_Orderings_Oord(T_c)
=> ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) ),
file('theBenchmark.p',fact_le__funI) ).
fof(fact_strict__mono__less__eq,axiom,
! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
( ( class_Orderings_Olinorder(T_b)
& class_Orderings_Oorder(T_c) )
=> ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_strict__mono__less__eq) ).
fof(fact_thin,axiom,
! [V_Ga_2,V_tsa_2,V_G_H_2,T_b] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_tsa_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ),
file('theBenchmark.p',fact_thin) ).
fof(fact_weaken,axiom,
! [V_tsa_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_tsa_2),V_ts_H_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ),
file('theBenchmark.p',fact_weaken) ).
fof(fact_asm,axiom,
! [V_Ga_2,V_tsa_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_Ga_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ),
file('theBenchmark.p',fact_asm) ).
fof(fact_greaterThan__subset__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_greaterThan__subset__iff) ).
fof(fact_lessThan__subset__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_lessThan__subset__iff) ).
fof(fact_atLeast__subset__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_atLeast__subset__iff) ).
fof(fact_atMost__subset__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_atMost__subset__iff) ).
fof(fact_SUP__subset,axiom,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_B_2),V_f_2))) ) ),
file('theBenchmark.p',fact_SUP__subset) ).
fof(fact_cut,axiom,
! [V_Ga_2,V_tsa_2,V_G_H_2,T_b] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_tsa_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_tsa_2) ) ),
file('theBenchmark.p',fact_cut) ).
fof(fact_greaterThan__eq__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_greaterThan__eq__iff) ).
fof(fact_lessThan__eq__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_lessThan__eq__iff) ).
fof(fact_atLeast__eq__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_atLeast__eq__iff) ).
fof(fact_atMost__eq__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_atMost__eq__iff) ).
fof(fact_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_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_strict__mono__eq,axiom,
! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
( ( class_Orderings_Olinorder(T_b)
& class_Orderings_Oorder(T_c) )
=> ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
=> ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_strict__mono__eq) ).
fof(fact_triple__valid__Suc,axiom,
! [V_t,V_n,T_a] :
( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t)
=> c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ),
file('theBenchmark.p',fact_triple__valid__Suc) ).
fof(fact_Suc__n__not__le__n,axiom,
! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)),
file('theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(fact_not__less__eq__eq,axiom,
! [V_n_2,V_m_2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ),
file('theBenchmark.p',fact_not__less__eq__eq) ).
fof(fact_le__Suc__eq,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
<=> ( V_m_2 = hAPP(c_Nat_OSuc,V_n_2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_le__Suc__eq) ).
fof(fact_Suc__le__mono,axiom,
! [V_m_2,V_n_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Nat_OSuc,V_m_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ),
file('theBenchmark.p',fact_Suc__le__mono) ).
fof(fact_le__SucI,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ),
file('theBenchmark.p',fact_le__SucI) ).
fof(fact_le__SucE,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> V_m = hAPP(c_Nat_OSuc,V_n) ) ),
file('theBenchmark.p',fact_le__SucE) ).
fof(fact_Suc__leD,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
file('theBenchmark.p',fact_Suc__leD) ).
fof(fact_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_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_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_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_le__trans,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ),
file('theBenchmark.p',fact_le__trans) ).
fof(fact_le__antisym,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
=> V_m = V_n ) ),
file('theBenchmark.p',fact_le__antisym) ).
fof(fact_lift__Suc__mono__le,axiom,
! [V_n_H_2,V_n_2,V_f_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_n_H_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_n_2)),hAPP(V_f_2,V_n_H_2))) ) ) ),
file('theBenchmark.p',fact_lift__Suc__mono__le) ).
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_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_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_mono__iff__le__Suc,axiom,
! [V_f_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,T_b,V_f_2)
<=> ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n)))) ) ),
file('theBenchmark.p',fact_mono__iff__le__Suc) ).
fof(fact_Suc__le__D,axiom,
! [V_m_H,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_m_H))
=> ? [B_m] : V_m_H = hAPP(c_Nat_OSuc,B_m) ),
file('theBenchmark.p',fact_Suc__le__D) ).
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_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_atLeastLessThan__subset__iff,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ),
file('theBenchmark.p',fact_atLeastLessThan__subset__iff) ).
fof(fact_Compl__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_atLeastatMost__subset__iff,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ),
file('theBenchmark.p',fact_atLeastatMost__subset__iff) ).
fof(fact_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_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_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_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_monoD,axiom,
! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
( ( class_Orderings_Oorder(T_b)
& class_Orderings_Oorder(T_c) )
=> ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ),
file('theBenchmark.p',fact_monoD) ).
fof(fact_mono__Suc,axiom,
c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),
file('theBenchmark.p',fact_mono__Suc) ).
fof(fact_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_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_strict__mono__mono,axiom,
! [V_f_2,T_b,T_c] :
( ( class_Orderings_Oorder(T_b)
& class_Orderings_Oorder(T_c) )
=> ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
=> c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2) ) ),
file('theBenchmark.p',fact_strict__mono__mono) ).
fof(fact_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_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_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_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_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_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_le__imp__neg__le,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))) ) ),
file('theBenchmark.p',fact_le__imp__neg__le) ).
fof(fact_compl__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_ivl__disj__un_I13_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I13_J) ).
fof(fact_ivl__disj__un_I10_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I10_J) ).
fof(fact_compl__eq__compl__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Lattices_Oboolean__algebra(T_b)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_compl__eq__compl__iff) ).
fof(fact_neg__equal__iff__equal,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Ogroup__add(T_b)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
<=> V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_neg__equal__iff__equal) ).
fof(fact_minus__equation__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Ogroup__add(T_b)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
<=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ),
file('theBenchmark.p',fact_minus__equation__iff) ).
fof(fact_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_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_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_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_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_ball__Un,axiom,
! [V_P_2,V_B_2,V_A_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hBOOL(hAPP(V_P_2,B_x)) )
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
=> hBOOL(hAPP(V_P_2,B_x)) )
& ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(V_P_2,B_x)) ) ) ),
file('theBenchmark.p',fact_ball__Un) ).
fof(fact_bex__Un,axiom,
! [V_P_2,V_B_2,V_A_2,T_b] :
( ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
<=> ( ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
| ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ),
file('theBenchmark.p',fact_bex__Un) ).
fof(fact_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__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_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__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_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_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_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_le__supI2,axiom,
! [V_a,V_b,V_x,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ),
file('theBenchmark.p',fact_le__supI2) ).
fof(fact_le__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__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__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_sup__ge2,axiom,
! [V_x,V_y,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ),
file('theBenchmark.p',fact_sup__ge2) ).
fof(fact_inf__sup__ord_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__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_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_mono__Un,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),V_f_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ),
file('theBenchmark.p',fact_mono__Un) ).
fof(fact_Un__mono,axiom,
! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ),
file('theBenchmark.p',fact_Un__mono) ).
fof(fact_Un__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__absorb2,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ),
file('theBenchmark.p',fact_Un__absorb2) ).
fof(fact_Un__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_subset__Un__eq,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
<=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ),
file('theBenchmark.p',fact_subset__Un__eq) ).
fof(fact_Un__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__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__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_mono__sup,axiom,
! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
( ( class_Lattices_Osemilattice__sup(T_b)
& class_Lattices_Osemilattice__sup(T_c) )
=> ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_A_2),V_B_2)))) ) ),
file('theBenchmark.p',fact_mono__sup) ).
fof(fact_ivl__disj__un_I17_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I17_J) ).
fof(fact_ivl__disj__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__un_I8_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I8_J) ).
fof(fact_ivl__disj__un_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_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_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_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_ivl__disj__un_I11_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I11_J) ).
fof(fact_ivl__disj__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__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_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_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_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_image__uminus__atMost,axiom,
! [V_x_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
file('theBenchmark.p',fact_image__uminus__atMost) ).
fof(fact_image__uminus__atLeast,axiom,
! [V_x_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
file('theBenchmark.p',fact_image__uminus__atLeast) ).
fof(fact_image__uminus__lessThan,axiom,
! [V_x_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
file('theBenchmark.p',fact_image__uminus__lessThan) ).
fof(fact_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_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_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_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_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_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__eq__top__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Lattices_Obounded__lattice__top(T_b)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
<=> ( V_y_2 = c_Orderings_Otop__class_Otop(T_b)
& V_x_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ),
file('theBenchmark.p',fact_inf__eq__top__iff) ).
fof(fact_inf_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_inf__sup__ord_I1_J,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ),
file('theBenchmark.p',fact_inf__sup__ord_I1_J) ).
fof(fact_inf__le1,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ),
file('theBenchmark.p',fact_inf__le1) ).
fof(fact_inf__sup__ord_I2_J,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ),
file('theBenchmark.p',fact_inf__sup__ord_I2_J) ).
fof(fact_inf__le2,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ),
file('theBenchmark.p',fact_inf__le2) ).
fof(fact_le__iff__inf,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Lattices_Osemilattice__inf(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
<=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ),
file('theBenchmark.p',fact_le__iff__inf) ).
fof(fact_le__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__infI1,axiom,
! [V_b,V_x,V_a,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ),
file('theBenchmark.p',fact_le__infI1) ).
fof(fact_le__infI2,axiom,
! [V_a,V_x,V_b,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ),
file('theBenchmark.p',fact_le__infI2) ).
fof(fact_inf__absorb1,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ),
file('theBenchmark.p',fact_inf__absorb1) ).
fof(fact_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_le__infI,axiom,
! [V_b,V_a,V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))) ) ) ),
file('theBenchmark.p',fact_le__infI) ).
fof(fact_inf__greatest,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))) ) ) ),
file('theBenchmark.p',fact_inf__greatest) ).
fof(fact_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_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_subset__image__iff,axiom,
! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
<=> ? [B_AA] :
( V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2)) ) ),
file('theBenchmark.p',fact_subset__image__iff) ).
fof(fact_image__mono,axiom,
! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ),
file('theBenchmark.p',fact_image__mono) ).
fof(fact_image__Un,axiom,
! [V_B_2,V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)),
file('theBenchmark.p',fact_image__Un) ).
fof(fact_sup__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_image__uminus__atLeastLessThan,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
file('theBenchmark.p',fact_image__uminus__atLeastLessThan) ).
fof(fact_image__uminus__greaterThanAtMost,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
file('theBenchmark.p',fact_image__uminus__greaterThanAtMost) ).
fof(fact_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_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_mono__Int,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),V_f_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2)))) ),
file('theBenchmark.p',fact_mono__Int) ).
fof(fact_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_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_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_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_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_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_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_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_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_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_compl__inf,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ),
file('theBenchmark.p',fact_compl__inf) ).
fof(fact_compl__sup,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ),
file('theBenchmark.p',fact_compl__sup) ).
fof(fact_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_mono__inf,axiom,
! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
( ( class_Lattices_Osemilattice__inf(T_b)
& class_Lattices_Osemilattice__inf(T_c) )
=> ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2)))) ) ),
file('theBenchmark.p',fact_mono__inf) ).
fof(fact_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_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_Compl__Int,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),
file('theBenchmark.p',fact_Compl__Int) ).
fof(fact_Compl__Un,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),
file('theBenchmark.p',fact_Compl__Un) ).
fof(fact_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__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_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_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_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_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_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_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_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_ivl__disj__un_I5_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I5_J) ).
fof(fact_ivl__disj__un_I6_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I6_J) ).
fof(fact_ivl__disj__un_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_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_atMost__Int__atLeast,axiom,
! [V_n_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_atMost__Int__atLeast) ).
fof(fact_ivl__disj__un_I2_J,axiom,
! [V_u_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ),
file('theBenchmark.p',fact_ivl__disj__un_I2_J) ).
fof(fact_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_hoare__derivs_Oinsert,axiom,
! [V_tsa_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_tsa_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_tsa_2)) ) ),
file('theBenchmark.p',fact_hoare__derivs_Oinsert) ).
fof(fact_derivs__insertD,axiom,
! [V_tsa_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_tsa_2))
=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_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)))) ) ),
file('theBenchmark.p',fact_derivs__insertD) ).
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_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_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_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_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_singleton__inject,axiom,
! [V_b_2,V_a_2,T_b] :
( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
=> V_a_2 = V_b_2 ),
file('theBenchmark.p',fact_singleton__inject) ).
fof(fact_doubleton__eq__iff,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
<=> ( ( V_b_2 = V_c_2
& V_a_2 = V_d_2 )
| ( V_b_2 = V_d_2
& V_a_2 = V_c_2 ) ) ),
file('theBenchmark.p',fact_doubleton__eq__iff) ).
fof(fact_insert__not__empty,axiom,
! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_insert__not__empty) ).
fof(fact_empty__not__insert,axiom,
! [V_A_2,V_a_2,T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2),
file('theBenchmark.p',fact_empty__not__insert) ).
fof(fact_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_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_ball__empty,axiom,
! [V_P_2,T_b,B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
=> hBOOL(hAPP(V_P_2,B_x)) ),
file('theBenchmark.p',fact_ball__empty) ).
fof(fact_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_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__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__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_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_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_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_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_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_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_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_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_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_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_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_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_Compl__UNIV__eq,axiom,
! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Compl__UNIV__eq) ).
fof(fact_Compl__empty__eq,axiom,
! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Compl__empty__eq) ).
fof(fact_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_subset__singletonD,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
=> ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_subset__singletonD) ).
fof(fact_insert__is__Un,axiom,
! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_A_2),
file('theBenchmark.p',fact_insert__is__Un) ).
fof(fact_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_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_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_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_c_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
<=> ( V_b_2 = V_c_2
& V_a_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_atLeastAtMost__singleton__iff) ).
fof(fact_atLeastAtMost__singleton,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_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_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_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_Compl__disjoint2,axiom,
! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Compl__disjoint2) ).
fof(fact_Compl__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_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_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_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_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_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_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_atLeast0LessThan,axiom,
! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2),
file('theBenchmark.p',fact_atLeast0LessThan) ).
fof(fact_atLeast0AtMost,axiom,
! [V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2),
file('theBenchmark.p',fact_atLeast0AtMost) ).
fof(fact_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_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_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_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_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_disjoint__eq__subset__Compl,axiom,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))) ),
file('theBenchmark.p',fact_disjoint__eq__subset__Compl) ).
fof(fact_ivl__disj__int_I15_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I15_J) ).
fof(fact_ivl__disj__int_I4_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I4_J) ).
fof(fact_ivl__disj__int_I2_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I2_J) ).
fof(fact_ivl__disj__int_I16_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I16_J) ).
fof(fact_ivl__disj__int_I8_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I8_J) ).
fof(fact_ivl__disj__int_I7_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I7_J) ).
fof(fact_ivl__disj__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_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_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_all__nat__less,axiom,
! [V_P_2,V_n_2] :
( ! [B_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
=> hBOOL(hAPP(V_P_2,B_m)) )
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)))
=> hBOOL(hAPP(V_P_2,B_x)) ) ),
file('theBenchmark.p',fact_all__nat__less) ).
fof(fact_ex__nat__less,axiom,
! [V_P_2,V_n_2] :
( ? [B_m] :
( hBOOL(hAPP(V_P_2,B_m))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) )
<=> ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) ) ),
file('theBenchmark.p',fact_ex__nat__less) ).
fof(fact_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_greaterThan__Suc,axiom,
! [V_k_2] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
file('theBenchmark.p',fact_greaterThan__Suc) ).
fof(fact_atLeast__Suc,axiom,
! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
file('theBenchmark.p',fact_atLeast__Suc) ).
fof(fact_ivl__disj__int_I6_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I6_J) ).
fof(fact_ivl__disj__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_ivl__disj__int_I1_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I1_J) ).
fof(fact_ivl__disj__int_I9_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I9_J) ).
fof(fact_ivl__disj__int_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_minus__apply,axiom,
! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
( class_Groups_Ominus(T_b)
=> hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ),
file('theBenchmark.p',fact_minus__apply) ).
fof(fact_diff__eq__diff__eq,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Groups_Oab__group__add(T_b)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
=> ( V_a_2 = V_b_2
<=> V_c_2 = V_d_2 ) ) ),
file('theBenchmark.p',fact_diff__eq__diff__eq) ).
fof(fact_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_diff__eq__diff__less__eq,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ),
file('theBenchmark.p',fact_diff__eq__diff__less__eq) ).
fof(fact_diff__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_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_empty__Diff,axiom,
! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_empty__Diff) ).
fof(fact_Diff__empty,axiom,
! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2,
file('theBenchmark.p',fact_Diff__empty) ).
fof(fact_Diff__cancel,axiom,
! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Diff__cancel) ).
fof(fact_Diff__subset,axiom,
! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)),
file('theBenchmark.p',fact_Diff__subset) ).
fof(fact_Diff__mono,axiom,
! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ),
file('theBenchmark.p',fact_Diff__mono) ).
fof(fact_double__diff,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2 ) ),
file('theBenchmark.p',fact_double__diff) ).
fof(fact_Un__Diff__cancel,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
file('theBenchmark.p',fact_Un__Diff__cancel) ).
fof(fact_Un__Diff__cancel2,axiom,
! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2),
file('theBenchmark.p',fact_Un__Diff__cancel2) ).
fof(fact_Un__Diff,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
file('theBenchmark.p',fact_Un__Diff) ).
fof(fact_Diff__Int__distrib,axiom,
! [V_B_2,V_A_2,V_C_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
file('theBenchmark.p',fact_Diff__Int__distrib) ).
fof(fact_Int__Diff,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
file('theBenchmark.p',fact_Int__Diff) ).
fof(fact_Diff__Int__distrib2,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
file('theBenchmark.p',fact_Diff__Int__distrib2) ).
fof(fact_Diff__Int2,axiom,
! [V_B_2,V_C_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2),
file('theBenchmark.p',fact_Diff__Int2) ).
fof(fact_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_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_diff__eq,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ),
file('theBenchmark.p',fact_diff__eq) ).
fof(fact_Diff__insert,axiom,
! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
file('theBenchmark.p',fact_Diff__insert) ).
fof(fact_Diff__insert2,axiom,
! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2),
file('theBenchmark.p',fact_Diff__insert2) ).
fof(fact_insert__Diff__single,axiom,
! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2),
file('theBenchmark.p',fact_insert__Diff__single) ).
fof(fact_Diff__UNIV,axiom,
! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Diff__UNIV) ).
fof(fact_Diff__disjoint,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Diff__disjoint) ).
fof(fact_Diff__triv,axiom,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ),
file('theBenchmark.p',fact_Diff__triv) ).
fof(fact_image__diff__subset,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))),
file('theBenchmark.p',fact_image__diff__subset) ).
fof(fact_Diff__partition,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2 ),
file('theBenchmark.p',fact_Diff__partition) ).
fof(fact_Diff__subset__conv,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))) ),
file('theBenchmark.p',fact_Diff__subset__conv) ).
fof(fact_Diff__Int,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
file('theBenchmark.p',fact_Diff__Int) ).
fof(fact_Diff__Un,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
file('theBenchmark.p',fact_Diff__Un) ).
fof(fact_Un__Diff__Int,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = V_A_2,
file('theBenchmark.p',fact_Un__Diff__Int) ).
fof(fact_ivl__diff,axiom,
! [V_m_2,V_n_2,V_i_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_n_2),V_m_2) ) ),
file('theBenchmark.p',fact_ivl__diff) ).
fof(fact_Compl__eq__Diff__UNIV,axiom,
! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_A_2),
file('theBenchmark.p',fact_Compl__eq__Diff__UNIV) ).
fof(fact_Compl__Diff__eq,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2),
file('theBenchmark.p',fact_Compl__Diff__eq) ).
fof(fact_Diff__eq,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),
file('theBenchmark.p',fact_Diff__eq) ).
fof(fact_Diff__Compl,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
file('theBenchmark.p',fact_Diff__Compl) ).
fof(fact_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_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_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_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_ivl__disj__int_I12_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I12_J) ).
fof(fact_ivl__disj__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_ivl__disj__un_I18_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I18_J) ).
fof(fact_ivl__disj__un_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_ivl__disj__un_I12_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I12_J) ).
fof(fact_ivl__disj__un_I7_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I7_J) ).
fof(fact_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_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_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_all__interval__nat__def,axiom,
! [V_j_2,V_i_2,V_P_2] :
( c_List_Oall__interval__nat(V_P_2,V_i_2,V_j_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)))
=> hBOOL(hAPP(V_P_2,B_x)) ) ),
file('theBenchmark.p',fact_all__interval__nat__def) ).
fof(fact_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_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_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_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_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_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_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__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_linorder__cases,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> ( V_x != V_y
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ),
file('theBenchmark.p',fact_linorder__cases) ).
fof(fact_order__less__asym,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ),
file('theBenchmark.p',fact_order__less__asym) ).
fof(fact_xt1_I10_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ),
file('theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_order__less__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ),
file('theBenchmark.p',fact_order__less__trans) ).
fof(fact_xt1_I2_J,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
=> ( V_b = V_c
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ),
file('theBenchmark.p',fact_xt1_I2_J) ).
fof(fact_ord__less__eq__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> ( V_b = V_c
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ),
file('theBenchmark.p',fact_ord__less__eq__trans) ).
fof(fact_xt1_I1_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a = V_b
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ),
file('theBenchmark.p',fact_xt1_I1_J) ).
fof(fact_ord__eq__less__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( V_a = V_b
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ),
file('theBenchmark.p',fact_ord__eq__less__trans) ).
fof(fact_xt1_I9_J,axiom,
! [V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ),
file('theBenchmark.p',fact_xt1_I9_J) ).
fof(fact_order__less__asym_H,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ),
file('theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> V_y != V_x ) ),
file('theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_order__less__imp__not__eq,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> V_x != V_y ) ),
file('theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_order__less__imp__not__less,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ),
file('theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__not__sym,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ),
file('theBenchmark.p',fact_order__less__not__sym) ).
fof(fact_less__imp__neq,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> V_x != V_y ) ),
file('theBenchmark.p',fact_less__imp__neq) ).
fof(fact_linorder__neqE,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( V_x != V_y
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ),
file('theBenchmark.p',fact_linorder__neqE) ).
fof(fact_linorder__antisym__conv3,axiom,
! [V_x_2,V_y_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_linorder__less__linear,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
| V_x = V_y
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ),
file('theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
<=> ( V_x_2 = V_y_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ),
file('theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_linorder__neq__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( V_x_2 != V_y_2
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_order__less__irrefl,axiom,
! [V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ),
file('theBenchmark.p',fact_order__less__irrefl) ).
fof(fact_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__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_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_Suc__pred,axiom,
! [V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n ),
file('theBenchmark.p',fact_Suc__pred) ).
fof(fact_diff__Suc__less,axiom,
! [V_i,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_i))),V_n)) ),
file('theBenchmark.p',fact_diff__Suc__less) ).
fof(fact_atLeastatMost__psubset__iff,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2))
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ),
file('theBenchmark.p',fact_atLeastatMost__psubset__iff) ).
fof(fact_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_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_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__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_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__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_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_diffs0__imp__equal,axiom,
! [V_n,V_m] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> V_m = V_n ) ),
file('theBenchmark.p',fact_diffs0__imp__equal) ).
fof(fact_diff__self__eq__0,axiom,
! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_diff__self__eq__0) ).
fof(fact_minus__nat_Odiff__0,axiom,
! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
file('theBenchmark.p',fact_minus__nat_Odiff__0) ).
fof(fact_diff__0__eq__0,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_diff__0__eq__0) ).
fof(fact_xt1_I8_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ),
file('theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_order__le__less__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ),
file('theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_xt1_I7_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ),
file('theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_order__less__le__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ),
file('theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_xt1_I11_J,axiom,
! [V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
=> ( V_a != V_b
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ),
file('theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_order__le__neq__trans,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( V_a != V_b
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> ( V_x = V_y
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ),
file('theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_linorder__antisym__conv2,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_order__less__imp__le,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ),
file('theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_leD,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ),
file('theBenchmark.p',fact_leD) ).
fof(fact_xt1_I12_J,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a != V_b
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ),
file('theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_order__neq__le__trans,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a != V_b
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_order__neq__le__trans) ).
fof(fact_linorder__antisym__conv1,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(fact_not__leE,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ),
file('theBenchmark.p',fact_not__leE) ).
fof(fact_leI,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ),
file('theBenchmark.p',fact_leI) ).
fof(fact_order__le__less,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
<=> ( V_x_2 = V_y_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_order__le__less) ).
fof(fact_less__le__not__le,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Opreorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
<=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_less__le__not__le) ).
fof(fact_order__less__le,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
<=> ( V_x_2 != V_y_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_order__less__le) ).
fof(fact_linorder__le__less__linear,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ),
file('theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_linorder__not__le,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_linorder__not__le) ).
fof(fact_linorder__not__less,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_linorder__not__less) ).
fof(fact_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_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__le__mono2,axiom,
! [V_l,V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ),
file('theBenchmark.p',fact_diff__le__mono2) ).
fof(fact_diff__le__mono,axiom,
! [V_l,V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_l)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_l))) ),
file('theBenchmark.p',fact_diff__le__mono) ).
fof(fact_diff__diff__cancel,axiom,
! [V_n,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = V_i ),
file('theBenchmark.p',fact_diff__diff__cancel) ).
fof(fact_eq__diff__iff,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)
<=> V_m_2 = V_n_2 ) ) ),
file('theBenchmark.p',fact_eq__diff__iff) ).
fof(fact_Nat_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_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_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_diff__eq__diff__less,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) ) ) ),
file('theBenchmark.p',fact_diff__eq__diff__less) ).
fof(fact_less__supI1,axiom,
! [V_b,V_a,V_x,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ),
file('theBenchmark.p',fact_less__supI1) ).
fof(fact_less__supI2,axiom,
! [V_a,V_b,V_x,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ),
file('theBenchmark.p',fact_less__supI2) ).
fof(fact_less__infI2,axiom,
! [V_a,V_x,V_b,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ),
file('theBenchmark.p',fact_less__infI2) ).
fof(fact_less__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__minus__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ),
file('theBenchmark.p',fact_less__minus__iff) ).
fof(fact_minus__less__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ),
file('theBenchmark.p',fact_minus__less__iff) ).
fof(fact_neg__less__iff__less,axiom,
! [V_a_2,V_b_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_neg__less__iff__less) ).
fof(fact_subset__psubset__trans,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ),
file('theBenchmark.p',fact_subset__psubset__trans) ).
fof(fact_psubset__subset__trans,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ),
file('theBenchmark.p',fact_psubset__subset__trans) ).
fof(fact_psubset__imp__subset,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
file('theBenchmark.p',fact_psubset__imp__subset) ).
fof(fact_subset__iff__psubset__eq,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
<=> ( V_A_2 = V_B_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_subset__iff__psubset__eq) ).
fof(fact_psubset__eq,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
<=> ( V_A_2 != V_B_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_psubset__eq) ).
fof(fact_gr0I,axiom,
! [V_n] :
( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
file('theBenchmark.p',fact_gr0I) ).
fof(fact_gr__implies__not0,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_gr__implies__not0) ).
fof(fact_less__nat__zero__code,axiom,
! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_less__nat__zero__code) ).
fof(fact_neq0__conv,axiom,
! [V_n_2] :
( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ),
file('theBenchmark.p',fact_neq0__conv) ).
fof(fact_not__less0,axiom,
! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_not__less0) ).
fof(fact_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_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_atLeastLessThan__inj_I2_J,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
=> V_b_2 = V_d_2 ) ) ) ),
file('theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).
fof(fact_atLeastLessThan__inj_I1_J,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
=> V_a_2 = V_c_2 ) ) ) ),
file('theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).
fof(fact_atLeastLessThan__eq__iff,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
=> ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
<=> ( V_b_2 = V_d_2
& V_a_2 = V_c_2 ) ) ) ) ),
file('theBenchmark.p',fact_atLeastLessThan__eq__iff) ).
fof(fact_less__Sup__iff,axiom,
! [V_S_2,V_a_2,T_b] :
( ( class_Orderings_Olinorder(T_b)
& class_Complete__Lattice_Ocomplete__lattice(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) ) ) ),
file('theBenchmark.p',fact_less__Sup__iff) ).
fof(fact_Inf__less__iff,axiom,
! [V_a_2,V_S_2,T_b] :
( ( class_Orderings_Olinorder(T_b)
& class_Complete__Lattice_Ocomplete__lattice(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) ) ) ),
file('theBenchmark.p',fact_Inf__less__iff) ).
fof(fact_strict__mono__imp__inj__on,axiom,
! [V_A_2,V_f_2,T_b,T_c] :
( ( class_Orderings_Olinorder(T_b)
& class_Orderings_Oorder(T_c) )
=> ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
=> c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
file('theBenchmark.p',fact_strict__mono__imp__inj__on) ).
fof(fact_strict__monoD,axiom,
! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
( ( class_Orderings_Oorder(T_b)
& class_Orderings_Oorder(T_c) )
=> ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ),
file('theBenchmark.p',fact_strict__monoD) ).
fof(fact_strict__mono__less,axiom,
! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
( ( class_Orderings_Olinorder(T_b)
& class_Orderings_Oorder(T_c) )
=> ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_strict__mono__less) ).
fof(fact_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_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_diff__is__0__eq,axiom,
! [V_n_2,V_m_2] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_diff__is__0__eq) ).
fof(fact_diff__is__0__eq_H,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_diff__is__0__eq_H) ).
fof(fact_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_neg__less__nonneg,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
file('theBenchmark.p',fact_neg__less__nonneg) ).
fof(fact_neg__less__0__iff__less,axiom,
! [V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
file('theBenchmark.p',fact_neg__less__0__iff__less) ).
fof(fact_neg__0__less__iff__less,axiom,
! [V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
file('theBenchmark.p',fact_neg__0__less__iff__less) ).
fof(fact_less__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_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_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_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__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__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__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_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_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_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_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_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_ex__nat__less__eq,axiom,
! [V_P_2,V_n_2] :
( ? [B_m] :
( hBOOL(hAPP(V_P_2,B_m))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) )
<=> ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) ) ),
file('theBenchmark.p',fact_ex__nat__less__eq) ).
fof(fact_all__nat__less__eq,axiom,
! [V_P_2,V_n_2] :
( ! [B_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
=> hBOOL(hAPP(V_P_2,B_m)) )
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))
=> hBOOL(hAPP(V_P_2,B_x)) ) ),
file('theBenchmark.p',fact_all__nat__less__eq) ).
fof(fact_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_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_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__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_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_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_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_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_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_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_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_the__inv__into__onto,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> hAPP(c_Set_Oimage(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ),
file('theBenchmark.p',fact_the__inv__into__onto) ).
fof(fact_inj__on__the__inv__into,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> c_Fun_Oinj__on(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ),
file('theBenchmark.p',fact_inj__on__the__inv__into) ).
fof(fact_equalityCE,axiom,
! [V_c_2,T_b,V_B_2,V_A_2] :
( V_A_2 = V_B_2
=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) )
=> ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_equalityCE) ).
fof(fact_emptyE,axiom,
! [V_a_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
file('theBenchmark.p',fact_emptyE) ).
fof(fact_insertE,axiom,
! [V_A_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
=> ( V_a_2 != V_b_2
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_insertE) ).
fof(fact_insertCI,axiom,
! [V_b_2,V_B_2,V_a_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
=> V_a_2 = V_b_2 )
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ),
file('theBenchmark.p',fact_insertCI) ).
fof(fact_subsetD,axiom,
! [V_c_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
file('theBenchmark.p',fact_subsetD) ).
fof(fact_UNIV__I,axiom,
! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
file('theBenchmark.p',fact_UNIV__I) ).
fof(fact_image__eqI,axiom,
! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
( V_b_2 = hAPP(V_f_2,V_x_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ),
file('theBenchmark.p',fact_image__eqI) ).
fof(fact_UnE,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
file('theBenchmark.p',fact_UnE) ).
fof(fact_UnCI,axiom,
! [V_A_2,V_B_2,V_c_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_UnCI) ).
fof(fact_IntI,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
file('theBenchmark.p',fact_IntI) ).
fof(fact_IntE,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
file('theBenchmark.p',fact_IntE) ).
fof(fact_DiffI,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
file('theBenchmark.p',fact_DiffI) ).
fof(fact_DiffE,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
file('theBenchmark.p',fact_DiffE) ).
fof(fact_ComplI,axiom,
! [V_A_2,V_c_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ),
file('theBenchmark.p',fact_ComplI) ).
fof(fact_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_UnionI,axiom,
! [V_A_2,V_C_2,V_X_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ) ),
file('theBenchmark.p',fact_UnionI) ).
fof(fact_InterD,axiom,
! [V_X_2,V_C_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ),
file('theBenchmark.p',fact_InterD) ).
fof(fact_InterE,axiom,
! [V_X_2,V_C_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ),
file('theBenchmark.p',fact_InterE) ).
fof(fact_PowI,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ),
file('theBenchmark.p',fact_PowI) ).
fof(fact_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__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_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_psubsetD,axiom,
! [V_c_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
file('theBenchmark.p',fact_psubsetD) ).
fof(fact_nat__less__cases,axiom,
! [V_P_2,V_n_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
=> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
=> ( ( V_m_2 = V_n_2
=> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
=> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
=> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ),
file('theBenchmark.p',fact_nat__less__cases) ).
fof(fact_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_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__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_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_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_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_mem__def,axiom,
! [V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
<=> hBOOL(hAPP(V_A_2,V_x_2)) ),
file('theBenchmark.p',fact_mem__def) ).
fof(fact_eq__mem,axiom,
! [V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
<=> V_x_2 = V_y_2 ),
file('theBenchmark.p',fact_eq__mem) ).
fof(fact_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__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_eqset__imp__iff,axiom,
! [V_x_2,T_b,V_B_2,V_A_2] :
( V_A_2 = V_B_2
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_eqset__imp__iff) ).
fof(fact_eqelem__imp__iff,axiom,
! [V_A_2,T_b,V_y_2,V_x_2] :
( V_x_2 = V_y_2
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ),
file('theBenchmark.p',fact_eqelem__imp__iff) ).
fof(fact_eq__mem__trans,axiom,
! [V_A_2,T_b,V_b_2,V_a_2] :
( V_a_2 = V_b_2
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_eq__mem__trans) ).
fof(fact_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_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_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__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_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__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__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__UNIV,axiom,
! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_vimage__UNIV) ).
fof(fact_vimage__Un,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
file('theBenchmark.p',fact_vimage__Un) ).
fof(fact_vimage__Int,axiom,
! [V_B_2,V_A_2,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__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_all__not__in__conv,axiom,
! [V_A_2,T_b] :
( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
<=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_all__not__in__conv) ).
fof(fact_ex__in__conv,axiom,
! [V_A_2,T_b] :
( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
<=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ex__in__conv) ).
fof(fact_empty__iff,axiom,
! [V_c_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
file('theBenchmark.p',fact_empty__iff) ).
fof(fact_equals0D,axiom,
! [V_a_2,T_b,V_A_2] :
( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
file('theBenchmark.p',fact_equals0D) ).
fof(fact_insertI1,axiom,
! [V_B_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))),
file('theBenchmark.p',fact_insertI1) ).
fof(fact_insert__iff,axiom,
! [V_A_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_insert__iff) ).
fof(fact_insert__ident,axiom,
! [V_B_2,V_A_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
=> ( hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)
<=> V_A_2 = V_B_2 ) ) ),
file('theBenchmark.p',fact_insert__ident) ).
fof(fact_insertI2,axiom,
! [V_b_2,V_B_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ),
file('theBenchmark.p',fact_insertI2) ).
fof(fact_insert__absorb,axiom,
! [V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ),
file('theBenchmark.p',fact_insert__absorb) ).
fof(fact_in__mono,axiom,
! [V_x_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_in__mono) ).
fof(fact_set__rev__mp,axiom,
! [V_B_2,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_set__rev__mp) ).
fof(fact_set__mp,axiom,
! [V_x_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_set__mp) ).
fof(fact_image__iff,axiom,
! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
<=> ? [B_x] :
( V_z_2 = hAPP(V_f_2,B_x)
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_image__iff) ).
fof(fact_imageI,axiom,
! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ),
file('theBenchmark.p',fact_imageI) ).
fof(fact_rev__image__eqI,axiom,
! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( V_b_2 = hAPP(V_f_2,V_x_2)
=> hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ),
file('theBenchmark.p',fact_rev__image__eqI) ).
fof(fact_Un__iff,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ),
file('theBenchmark.p',fact_Un__iff) ).
fof(fact_UnI1,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_UnI1) ).
fof(fact_UnI2,axiom,
! [V_A_2,V_B_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_UnI2) ).
fof(fact_Int__iff,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ),
file('theBenchmark.p',fact_Int__iff) ).
fof(fact_IntD1,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
file('theBenchmark.p',fact_IntD1) ).
fof(fact_IntD2,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ),
file('theBenchmark.p',fact_IntD2) ).
fof(fact_Diff__iff,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
<=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ),
file('theBenchmark.p',fact_Diff__iff) ).
fof(fact_DiffD1,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
file('theBenchmark.p',fact_DiffD1) ).
fof(fact_DiffD2,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ),
file('theBenchmark.p',fact_DiffD2) ).
fof(fact_inj__on__contraD,axiom,
! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( V_x_2 != V_y_2
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
=> hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ),
file('theBenchmark.p',fact_inj__on__contraD) ).
fof(fact_inj__on__iff,axiom,
! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
=> ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ) ),
file('theBenchmark.p',fact_inj__on__iff) ).
fof(fact_inj__onD,axiom,
! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
=> V_x_2 = V_y_2 ) ) ) ),
file('theBenchmark.p',fact_inj__onD) ).
fof(fact_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_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_Compl__iff,axiom,
! [V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
<=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
file('theBenchmark.p',fact_Compl__iff) ).
fof(fact_ComplD,axiom,
! [V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
file('theBenchmark.p',fact_ComplD) ).
fof(fact_ComplE,axiom,
! [V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
file('theBenchmark.p',fact_ComplE) ).
fof(fact_Pow__top,axiom,
! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_A_2))),
file('theBenchmark.p',fact_Pow__top) ).
fof(fact_setsum__empty,axiom,
! [V_f_2,T_c,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ),
file('theBenchmark.p',fact_setsum__empty) ).
fof(fact_setsum_Oempty,axiom,
! [V_g_2,T_c,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ),
file('theBenchmark.p',fact_setsum_Oempty) ).
fof(fact_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_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_singleton__iff,axiom,
! [V_a_2,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
<=> V_b_2 = V_a_2 ),
file('theBenchmark.p',fact_singleton__iff) ).
fof(fact_singletonE,axiom,
! [V_a_2,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
=> V_b_2 = V_a_2 ),
file('theBenchmark.p',fact_singletonE) ).
fof(fact_subset__insert,axiom,
! [V_B_2,V_A_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_subset__insert) ).
fof(fact_insert__subset,axiom,
! [V_B_2,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_insert__subset) ).
fof(fact_insert__image,axiom,
! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(hAPP(c_Set_Oinsert(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) ),
file('theBenchmark.p',fact_insert__image) ).
fof(fact_Int__insert__right,axiom,
! [V_B_2,V_A_2,V_a_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_Int__insert__right) ).
fof(fact_Int__insert__left,axiom,
! [V_B_2,V_C_2,V_a_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ) ),
file('theBenchmark.p',fact_Int__insert__left) ).
fof(fact_Int__insert__right__if0,axiom,
! [V_B_2,V_A_2,V_a_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ),
file('theBenchmark.p',fact_Int__insert__right__if0) ).
fof(fact_Int__insert__left__if0,axiom,
! [V_B_2,V_C_2,V_a_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2) ),
file('theBenchmark.p',fact_Int__insert__left__if0) ).
fof(fact_Int__insert__right__if1,axiom,
! [V_B_2,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
file('theBenchmark.p',fact_Int__insert__right__if1) ).
fof(fact_Int__insert__left__if1,axiom,
! [V_B_2,V_C_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ),
file('theBenchmark.p',fact_Int__insert__left__if1) ).
fof(fact_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_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_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_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_Sup__upper,axiom,
! [V_A_2,V_x_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2))) ) ),
file('theBenchmark.p',fact_Sup__upper) ).
fof(fact_Inf__lower,axiom,
! [V_A_2,V_x_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)),V_x_2)) ) ),
file('theBenchmark.p',fact_Inf__lower) ).
fof(fact_lessThan__iff,axiom,
! [V_k_2,V_i_2,T_b] :
( class_Orderings_Oord(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ),
file('theBenchmark.p',fact_lessThan__iff) ).
fof(fact_atMost__iff,axiom,
! [V_k_2,V_i_2,T_b] :
( class_Orderings_Oord(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ),
file('theBenchmark.p',fact_atMost__iff) ).
fof(fact_Union__upper,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ),
file('theBenchmark.p',fact_Union__upper) ).
fof(fact_Pow__bottom,axiom,
! [V_B_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Set_OPow(T_b),V_B_2))),
file('theBenchmark.p',fact_Pow__bottom) ).
fof(fact_atLeast__iff,axiom,
! [V_k_2,V_i_2,T_b] :
( class_Orderings_Oord(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ),
file('theBenchmark.p',fact_atLeast__iff) ).
fof(fact_PowD,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
file('theBenchmark.p',fact_PowD) ).
fof(fact_Pow__iff,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
file('theBenchmark.p',fact_Pow__iff) ).
fof(fact_greaterThan__iff,axiom,
! [V_k_2,V_i_2,T_b] :
( class_Orderings_Oord(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ),
file('theBenchmark.p',fact_greaterThan__iff) ).
fof(fact_Inter__lower,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2)) ),
file('theBenchmark.p',fact_Inter__lower) ).
fof(fact_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_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_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_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_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_insert__Diff,axiom,
! [V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = V_A_2 ),
file('theBenchmark.p',fact_insert__Diff) ).
fof(fact_Diff__insert__absorb,axiom,
! [V_A_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2 ),
file('theBenchmark.p',fact_Diff__insert__absorb) ).
fof(fact_range__ex1__eq,axiom,
! [V_b_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
<=> ? [B_x] :
( ! [B_y] :
( V_b_2 = hAPP(V_f_2,B_y)
=> B_y = B_x )
& V_b_2 = hAPP(V_f_2,B_x) ) ) ),
file('theBenchmark.p',fact_range__ex1__eq) ).
fof(fact_inj__image__mem__iff,axiom,
! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_inj__image__mem__iff) ).
fof(fact_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_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_ord_OatMost__iff,axiom,
! [V_k_2,V_less__eq_2,V_i_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
<=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ),
file('theBenchmark.p',fact_ord_OatMost__iff) ).
fof(fact_ord_OatLeast__iff,axiom,
! [V_k_2,V_less__eq_2,V_i_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
<=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ),
file('theBenchmark.p',fact_ord_OatLeast__iff) ).
fof(fact_ord_OlessThan__iff,axiom,
! [V_k_2,V_less_2,V_i_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
<=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ),
file('theBenchmark.p',fact_ord_OlessThan__iff) ).
fof(fact_ord_OgreaterThan__iff,axiom,
! [V_k_2,V_less_2,V_i_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
<=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ),
file('theBenchmark.p',fact_ord_OgreaterThan__iff) ).
fof(fact_ord_OatLeastAtMost__iff,axiom,
! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_b,V_less__eq_2,V_l_2,V_u_2)))
<=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
& hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) ) ),
file('theBenchmark.p',fact_ord_OatLeastAtMost__iff) ).
fof(fact_ord_OgreaterThanLessThan__iff,axiom,
! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_b,V_less_2,V_l_2,V_u_2)))
<=> ( hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
& hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) ) ),
file('theBenchmark.p',fact_ord_OgreaterThanLessThan__iff) ).
fof(fact_ord_OatLeastLessThan__iff,axiom,
! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
<=> ( hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
& hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) ) ),
file('theBenchmark.p',fact_ord_OatLeastLessThan__iff) ).
fof(fact_ord_OgreaterThanAtMost__iff,axiom,
! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
<=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
& hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) ) ),
file('theBenchmark.p',fact_ord_OgreaterThanAtMost__iff) ).
fof(fact_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_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_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_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_setsum__diff1,axiom,
! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
( class_Groups_Oab__group__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_setsum__diff1) ).
fof(fact_setsum__diff1__ring,axiom,
! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
( class_Rings_Oring(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ),
file('theBenchmark.p',fact_setsum__diff1__ring) ).
fof(fact_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_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_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_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_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_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_finite__atLeastAtMost,axiom,
! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2))),
file('theBenchmark.p',fact_finite__atLeastAtMost) ).
fof(fact_finite__lessThan,axiom,
! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))),
file('theBenchmark.p',fact_finite__lessThan) ).
fof(fact_finite__atMost,axiom,
! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))),
file('theBenchmark.p',fact_finite__atMost) ).
fof(fact_finite__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_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_c_2,V_a_2] :
( V_a_2 != V_c_2
=> c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_a_2,V_b_2),V_c_2,V_d_2) = c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_c_2,V_d_2),V_a_2,V_b_2) ),
file('theBenchmark.p',fact_fun__upd__twist) ).
fof(fact_fun__upd__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_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_add__left__cancel,axiom,
! [V_c_2,V_b_2,V_a_2,T_b] :
( class_Groups_Ocancel__semigroup__add(T_b)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)
<=> V_b_2 = V_c_2 ) ),
file('theBenchmark.p',fact_add__left__cancel) ).
fof(fact_add__right__cancel,axiom,
! [V_c_2,V_a_2,V_b_2,T_b] :
( class_Groups_Ocancel__semigroup__add(T_b)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)
<=> V_b_2 = V_c_2 ) ),
file('theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__left__imp__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
=> V_b = V_c ) ),
file('theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_add__imp__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Ocancel__ab__semigroup__add(T_a)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
=> V_b = V_c ) ),
file('theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__right__imp__eq,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)
=> V_b = V_c ) ),
file('theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_add__le__cancel__right,axiom,
! [V_b_2,V_c_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_add__le__cancel__right) ).
fof(fact_add__le__cancel__left,axiom,
! [V_b_2,V_a_2,V_c_2,T_b] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_add__le__cancel__left) ).
fof(fact_add__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ),
file('theBenchmark.p',fact_add__right__mono) ).
fof(fact_add__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ),
file('theBenchmark.p',fact_add__left__mono) ).
fof(fact_add__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ),
file('theBenchmark.p',fact_add__mono) ).
fof(fact_add__le__imp__le__right,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ),
file('theBenchmark.p',fact_add__le__imp__le__right) ).
fof(fact_add__le__imp__le__left,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ),
file('theBenchmark.p',fact_add__le__imp__le__left) ).
fof(fact_add__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_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_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__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_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__less__cancel__right,axiom,
! [V_b_2,V_c_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_add__less__cancel__left,axiom,
! [V_b_2,V_a_2,V_c_2,T_b] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_add__less__cancel__left) ).
fof(fact_add__strict__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ),
file('theBenchmark.p',fact_add__strict__right__mono) ).
fof(fact_add__strict__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ),
file('theBenchmark.p',fact_add__strict__left__mono) ).
fof(fact_add__strict__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ),
file('theBenchmark.p',fact_add__strict__mono) ).
fof(fact_add__less__imp__less__right,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ),
file('theBenchmark.p',fact_add__less__imp__less__right) ).
fof(fact_add__less__imp__less__left,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ),
file('theBenchmark.p',fact_add__less__imp__less__left) ).
fof(fact_diff__add__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_b) = V_a ),
file('theBenchmark.p',fact_diff__add__cancel) ).
fof(fact_add__diff__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = V_a ),
file('theBenchmark.p',fact_add__diff__cancel) ).
fof(fact_minus__add__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = V_b ),
file('theBenchmark.p',fact_minus__add__cancel) ).
fof(fact_add__minus__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) = V_b ),
file('theBenchmark.p',fact_add__minus__cancel) ).
fof(fact_minus__add,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) ),
file('theBenchmark.p',fact_minus__add) ).
fof(fact_minus__add__distrib,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ),
file('theBenchmark.p',fact_minus__add__distrib) ).
fof(fact_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_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_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_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__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_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_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_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__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__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__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__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_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_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_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_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_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__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_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_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_diff__add__inverse2,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m,
file('theBenchmark.p',fact_diff__add__inverse2) ).
fof(fact_diff__add__inverse,axiom,
! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_n) = V_m,
file('theBenchmark.p',fact_diff__add__inverse) ).
fof(fact_diff__diff__left,axiom,
! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)),
file('theBenchmark.p',fact_diff__diff__left) ).
fof(fact_diff__cancel,axiom,
! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),
file('theBenchmark.p',fact_diff__cancel) ).
fof(fact_diff__cancel2,axiom,
! [V_n,V_k,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),
file('theBenchmark.p',fact_diff__cancel2) ).
fof(fact_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_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_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_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_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_add__le__less__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ),
file('theBenchmark.p',fact_add__le__less__mono) ).
fof(fact_add__less__le__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ),
file('theBenchmark.p',fact_add__less__le__mono) ).
fof(fact_pos__add__strict,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ),
file('theBenchmark.p',fact_pos__add__strict) ).
fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
file('theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
file('theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(fact_add__pos__pos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ),
file('theBenchmark.p',fact_add__pos__pos) ).
fof(fact_add__neg__neg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('theBenchmark.p',fact_add__neg__neg) ).
fof(fact_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__minus__eq__add,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) ),
file('theBenchmark.p',fact_diff__minus__eq__add) ).
fof(fact_ab__diff__minus,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ),
file('theBenchmark.p',fact_ab__diff__minus) ).
fof(fact_diff__def,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ),
file('theBenchmark.p',fact_diff__def) ).
fof(fact_one__is__add,axiom,
! [V_n_2,V_m_2] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)
<=> ( ( V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('theBenchmark.p',fact_one__is__add) ).
fof(fact_add__is__1,axiom,
! [V_n_2,V_m_2] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('theBenchmark.p',fact_add__is__1) ).
fof(fact_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_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_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_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_less__diff__conv,axiom,
! [V_k_2,V_j_2,V_i_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ),
file('theBenchmark.p',fact_less__diff__conv) ).
fof(fact_add__diff__inverse,axiom,
! [V_n,V_m] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ),
file('theBenchmark.p',fact_add__diff__inverse) ).
fof(fact_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__add__diff__inverse,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ),
file('theBenchmark.p',fact_le__add__diff__inverse) ).
fof(fact_add__diff__assoc,axiom,
! [V_i,V_j,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) ),
file('theBenchmark.p',fact_add__diff__assoc) ).
fof(fact_le__diff__conv2,axiom,
! [V_i_2,V_j_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ),
file('theBenchmark.p',fact_le__diff__conv2) ).
fof(fact_le__add__diff__inverse2,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ),
file('theBenchmark.p',fact_le__add__diff__inverse2) ).
fof(fact_le__imp__diff__is__add,axiom,
! [V_k_2,V_j_2,V_i_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
<=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ),
file('theBenchmark.p',fact_le__imp__diff__is__add) ).
fof(fact_diff__add__assoc,axiom,
! [V_i,V_j,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) ),
file('theBenchmark.p',fact_diff__add__assoc) ).
fof(fact_add__diff__assoc2,axiom,
! [V_i,V_j,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) ),
file('theBenchmark.p',fact_add__diff__assoc2) ).
fof(fact_diff__add__assoc2,axiom,
! [V_i,V_j,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) ),
file('theBenchmark.p',fact_diff__add__assoc2) ).
fof(fact_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_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_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_setsum_Oremove,axiom,
! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ),
file('theBenchmark.p',fact_setsum_Oremove) ).
fof(fact_setsum__diff1_H,axiom,
! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ),
file('theBenchmark.p',fact_setsum__diff1_H) ).
fof(fact_add__nonpos__neg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_add__neg__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('theBenchmark.p',fact_add__neg__nonpos) ).
fof(fact_add__strict__increasing2,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ),
file('theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_add__strict__increasing,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ),
file('theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_add__nonneg__pos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ),
file('theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__pos__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ),
file('theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_nat__diff__split__asm,axiom,
! [V_b_2,V_a_2,V_P_2] :
( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
<=> ~ ( ? [B_d] :
( ~ hBOOL(hAPP(V_P_2,B_d))
& V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
| ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) ) ),
file('theBenchmark.p',fact_nat__diff__split__asm) ).
fof(fact_nat__diff__split,axiom,
! [V_b_2,V_a_2,V_P_2] :
( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
<=> ( ! [B_d] :
( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
=> hBOOL(hAPP(V_P_2,B_d)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
=> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('theBenchmark.p',fact_nat__diff__split) ).
fof(fact_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_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__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_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_setsum__head__upt__Suc,axiom,
! [V_f_2,V_n_2,V_m_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2))) ) ),
file('theBenchmark.p',fact_setsum__head__upt__Suc) ).
fof(fact_setsum__head__Suc,axiom,
! [V_f_2,V_n_2,V_m_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))) ) ),
file('theBenchmark.p',fact_setsum__head__Suc) ).
fof(fact_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_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_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_finite__Inter,axiom,
! [V_M_2,T_b] :
( ? [B_x] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x))
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2)) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ),
file('theBenchmark.p',fact_finite__Inter) ).
fof(fact_finite__Diff,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_finite__Diff) ).
fof(fact_finite__Int,axiom,
! [V_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_finite__imageI,axiom,
! [V_h_2,T_c,V_F_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ),
file('theBenchmark.p',fact_finite__imageI) ).
fof(fact_finite_OinsertI,axiom,
! [V_a_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ),
file('theBenchmark.p',fact_finite_OinsertI) ).
fof(fact_finite_OemptyI,axiom,
! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
file('theBenchmark.p',fact_finite_OemptyI) ).
fof(fact_finite__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_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_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_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__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__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__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_finite__UN,axiom,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ),
file('theBenchmark.p',fact_finite__UN) ).
fof(fact_finite,axiom,
! [V_A_2,T_b] :
( class_Finite__Set_Ofinite(T_b)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
file('theBenchmark.p',fact_finite) ).
fof(fact_finite__code,axiom,
! [V_A_2,T_b] :
( class_Finite__Set_Ofinite(T_b)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
file('theBenchmark.p',fact_finite__code) ).
fof(fact_infinite__UNIV__nat,axiom,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
file('theBenchmark.p',fact_infinite__UNIV__nat) ).
fof(fact_finite_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_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__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_finite__Prod__UNIV,axiom,
! [T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ),
file('theBenchmark.p',fact_finite__Prod__UNIV) ).
fof(fact_finite__Plus__UNIV__iff,axiom,
! [T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ),
file('theBenchmark.p',fact_finite__Plus__UNIV__iff) ).
fof(fact_finite__option__UNIV,axiom,
! [T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool))))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
file('theBenchmark.p',fact_finite__option__UNIV) ).
fof(fact_finite__UNIV,axiom,
! [T_b] :
( class_Finite__Set_Ofinite(T_b)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
file('theBenchmark.p',fact_finite__UNIV) ).
fof(fact_finite__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_finite__UnionD,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ),
file('theBenchmark.p',fact_finite__UnionD) ).
fof(fact_finite__Pow__iff,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
file('theBenchmark.p',fact_finite__Pow__iff) ).
fof(fact_finite__surj,axiom,
! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ),
file('theBenchmark.p',fact_finite__surj) ).
fof(fact_finite__Diff__insert,axiom,
! [V_B_2,V_a_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_finite__Diff__insert) ).
fof(fact_finite__imageD,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
=> ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ),
file('theBenchmark.p',fact_finite__imageD) ).
fof(fact_finite__compl,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ),
file('theBenchmark.p',fact_finite__compl) ).
fof(fact_finite__fun__UNIVD2,axiom,
! [T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ),
file('theBenchmark.p',fact_finite__fun__UNIVD2) ).
fof(fact_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_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_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_folding__one_Oremove,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_F_2,V_A_2) = V_x_2 ) ) ) ) ),
file('theBenchmark.p',fact_folding__one_Oremove) ).
fof(fact_folding__image__simple_Oremove,axiom,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ),
file('theBenchmark.p',fact_folding__image__simple_Oremove) ).
fof(fact_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_setsum_Ounion__inter__neutral,axiom,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_setsum_Ounion__inter__neutral) ).
fof(fact_setsum__Un__zero,axiom,
! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)))
=> hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2)) ) ) ) ),
file('theBenchmark.p',fact_setsum__Un__zero) ).
fof(fact_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_ball__UN,axiom,
! [V_P_2,V_B_2,V_A_2,T_c,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hBOOL(hAPP(V_P_2,B_x)) )
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x)))
=> hBOOL(hAPP(V_P_2,B_xa)) ) ) ),
file('theBenchmark.p',fact_ball__UN) ).
fof(fact_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_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_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_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_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_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_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_folding__one_Oinsert,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_folding__one_Oinsert) ).
fof(fact_folding__one_Oinsert__remove,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_folding__one_Oinsert__remove) ).
fof(fact_folding__image__simple_Oinsert__remove,axiom,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ),
file('theBenchmark.p',fact_folding__image__simple_Oinsert__remove) ).
fof(fact_folding__one_Ounion__inter,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_folding__one_Ounion__inter) ).
fof(fact_folding__one_Ounion__disjoint,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ) ),
file('theBenchmark.p',fact_folding__one_Ounion__disjoint) ).
fof(fact_folding__image__simple_Ounion__disjoint,axiom,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_folding__image__simple_Ounion__disjoint) ).
fof(fact_finite__Union,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
=> ( ! [B_M] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ),
file('theBenchmark.p',fact_finite__Union) ).
fof(fact_Inf__fin_Oremove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 ) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oremove) ).
fof(fact_Sup__fin_Oremove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 ) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oremove) ).
fof(fact_insert__partition,axiom,
! [V_F_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)))
=> ( B_x != B_xa
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),B_xa) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_insert__partition) ).
fof(fact_folding__one_Oclosed,axiom,
! [V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_folding__one_Oclosed) ).
fof(fact_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_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_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_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_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_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_card__eq__UNIV__imp__eq__UNIV,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
=> ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).
fof(fact_card__image,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ),
file('theBenchmark.p',fact_card__image) ).
fof(fact_subset__card__intvl__is__intvl,axiom,
! [V_k_2,V_A_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2)))))
=> V_A_2 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2))) ),
file('theBenchmark.p',fact_subset__card__intvl__is__intvl) ).
fof(fact_card__atLeastLessThan,axiom,
! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2),
file('theBenchmark.p',fact_card__atLeastLessThan) ).
fof(fact_card__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_Inf__fin_Osingleton,axiom,
! [V_x_2,T_b] :
( class_Lattices_Olattice(T_b)
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
file('theBenchmark.p',fact_Inf__fin_Osingleton) ).
fof(fact_Sup__fin_Osingleton,axiom,
! [V_x_2,T_b] :
( class_Lattices_Olattice(T_b)
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
file('theBenchmark.p',fact_Sup__fin_Osingleton) ).
fof(fact_card__greaterThanAtMost,axiom,
! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2),
file('theBenchmark.p',fact_card__greaterThanAtMost) ).
fof(fact_card__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_card__insert__le,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)))) ),
file('theBenchmark.p',fact_card__insert__le) ).
fof(fact_card__mono,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ),
file('theBenchmark.p',fact_card__mono) ).
fof(fact_card__seteq,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
=> V_A_2 = V_B_2 ) ) ),
file('theBenchmark.p',fact_card__seteq) ).
fof(fact_card__image__le,axiom,
! [V_f_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ),
file('theBenchmark.p',fact_card__image__le) ).
fof(fact_inj__on__iff__eq__card,axiom,
! [V_f_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
<=> hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ),
file('theBenchmark.p',fact_inj__on__iff__eq__card) ).
fof(fact_eq__card__imp__inj__on,axiom,
! [V_f_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
=> c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
file('theBenchmark.p',fact_eq__card__imp__inj__on) ).
fof(fact_pigeonhole,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)))
=> ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ),
file('theBenchmark.p',fact_pigeonhole) ).
fof(fact_psubset__card__mono,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ),
file('theBenchmark.p',fact_psubset__card__mono) ).
fof(fact_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_sup__Inf__absorb,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = V_a_2 ) ) ),
file('theBenchmark.p',fact_sup__Inf__absorb) ).
fof(fact_Sup__fin_Oin__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oin__idem) ).
fof(fact_inf__Sup__absorb,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = V_a_2 ) ) ),
file('theBenchmark.p',fact_inf__Sup__absorb) ).
fof(fact_Inf__fin_Oin__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oin__idem) ).
fof(fact_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_Sup__fin__Sup,axiom,
! [V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ),
file('theBenchmark.p',fact_Sup__fin__Sup) ).
fof(fact_Inf__fin__Inf,axiom,
! [V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ),
file('theBenchmark.p',fact_Inf__fin__Inf) ).
fof(fact_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_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__gt__0__iff,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
& V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_card__gt__0__iff) ).
fof(fact_finite__UNIV__card__ge__0,axiom,
! [T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ),
file('theBenchmark.p',fact_finite__UNIV__card__ge__0) ).
fof(fact_card_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ),
file('theBenchmark.p',fact_card_Ounion__inter) ).
fof(fact_card__Un__Int,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
file('theBenchmark.p',fact_card__Un__Int) ).
fof(fact_card__bij__eq,axiom,
! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
=> ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ),
file('theBenchmark.p',fact_card__bij__eq) ).
fof(fact_card__Diff__subset,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ),
file('theBenchmark.p',fact_card__Diff__subset) ).
fof(fact_card__Diff__subset__Int,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_card__Diff__subset__Int) ).
fof(fact_diff__card__le__card__Diff,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ),
file('theBenchmark.p',fact_diff__card__le__card__Diff) ).
fof(fact_card__psubset,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_card__psubset) ).
fof(fact_Sup__fin_Oinsert__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oinsert__idem) ).
fof(fact_Inf__fin_Oinsert__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oinsert__idem) ).
fof(fact_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_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_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_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_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__Un__disjoint,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ),
file('theBenchmark.p',fact_card__Un__disjoint) ).
fof(fact_card__Diff1__le,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ),
file('theBenchmark.p',fact_card__Diff1__le) ).
fof(fact_card__inj__on__le,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ),
file('theBenchmark.p',fact_card__inj__on__le) ).
fof(fact_inj__on__iff__card__le,axiom,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( ? [B_f] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_B_2))
& c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) )
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ),
file('theBenchmark.p',fact_inj__on__iff__card__le) ).
fof(fact_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_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_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_Sup__fin_Oinsert,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oinsert) ).
fof(fact_Inf__fin_Oinsert,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oinsert) ).
fof(fact_Sup__fin_Oinsert__remove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oinsert__remove) ).
fof(fact_Inf__fin_Oinsert__remove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oinsert__remove) ).
fof(fact_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_Inf__fin_Ounion__disjoint,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Ounion__disjoint) ).
fof(fact_Inf__fin_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Ounion__inter) ).
fof(fact_Inf__fin_Oclosed,axiom,
! [V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oclosed) ).
fof(fact_Sup__fin_Oclosed,axiom,
! [V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oclosed) ).
fof(fact_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_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_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_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_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_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_not__one__le__zero,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ),
file('theBenchmark.p',fact_not__one__le__zero) ).
fof(fact_zero__le__one,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ),
file('theBenchmark.p',fact_zero__le__one) ).
fof(fact_zero__less__one,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ),
file('theBenchmark.p',fact_zero__less__one) ).
fof(fact_not__one__less__zero,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ),
file('theBenchmark.p',fact_not__one__less__zero) ).
fof(fact_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_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_Suc__eq__plus1,axiom,
! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('theBenchmark.p',fact_Suc__eq__plus1) ).
fof(fact_Suc__eq__plus1__left,axiom,
! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n),
file('theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(fact_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_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_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_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_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_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,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_card_Oinsert,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ),
file('theBenchmark.p',fact_card_Oinsert) ).
fof(fact_setsum__ub__add__nat,axiom,
! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2)))) ) ),
file('theBenchmark.p',fact_setsum__ub__add__nat) ).
fof(fact_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_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_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_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_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_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_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_ex__least__nat__less,axiom,
! [V_n_2,V_P_2] :
( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(V_P_2,V_n_2))
=> ? [B_k] :
( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
=> ~ hBOOL(hAPP(V_P_2,B_i)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) ) ) ),
file('theBenchmark.p',fact_ex__least__nat__less) ).
fof(fact_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__diff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Rings_Oring__1(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ),
file('theBenchmark.p',fact_Ints__diff) ).
fof(fact_Ints__1,axiom,
! [T_b] :
( class_Rings_Oring__1(T_b)
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ),
file('theBenchmark.p',fact_Ints__1) ).
fof(fact_Ints__minus,axiom,
! [V_a_2,T_b] :
( class_Rings_Oring__1(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Int_Oring__1__class_OInts(T_b))) ) ),
file('theBenchmark.p',fact_Ints__minus) ).
fof(fact_Ints__double__eq__0__iff,axiom,
! [V_a_2,T_b] :
( class_Int_Oring__char__0(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_Ints__double__eq__0__iff) ).
fof(fact_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_finite__empty__induct,axiom,
! [V_P_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(V_P_2,V_A_2))
=> ( ! [B_a,B_A] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
=> ( hBOOL(hAPP(V_P_2,B_A))
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_b),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) )
=> hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ),
file('theBenchmark.p',fact_finite__empty__induct) ).
fof(fact_folding__one__idem_Ounion__idem,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ),
file('theBenchmark.p',fact_folding__one__idem_Ounion__idem) ).
fof(fact_finite__subset__induct,axiom,
! [V_P_2,V_A_2,V_F_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
=> ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
=> ( ! [B_a,B_F] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
=> ( hBOOL(hAPP(V_P_2,B_F))
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
=> hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ),
file('theBenchmark.p',fact_finite__subset__induct) ).
fof(fact_folding__one__idem_Osubset__idem,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ),
file('theBenchmark.p',fact_folding__one__idem_Osubset__idem) ).
fof(fact_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_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_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_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_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__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_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_sgn__pos,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ),
file('theBenchmark.p',fact_sgn__pos) ).
fof(fact_sgn__1__pos,axiom,
! [V_a_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
file('theBenchmark.p',fact_sgn__1__pos) ).
fof(fact_sgn__1__neg,axiom,
! [V_a_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
file('theBenchmark.p',fact_sgn__1__neg) ).
fof(fact_sgn__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_folding__one__idem_Ohom__commute,axiom,
! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
=> ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(V_f_2,B_x),B_y)) = hAPP(hAPP(V_f_2,hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
file('theBenchmark.p',fact_folding__one__idem_Ohom__commute) ).
fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hAPP(V_g_2,B_x) = V_z_2 )
=> hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_folding__image__simple_Ounion__inter__neutral) ).
fof(fact_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_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_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_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_c_2,V_a_2,T_b,T_c] :
( ( class_Orderings_Oord(T_b)
& class_Groups_Ocomm__monoid__add(T_c) )
=> ( V_a_2 = V_c_2
=> ( V_b_2 = V_d_2
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),B_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
=> hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) ) ) ) ),
file('theBenchmark.p',fact_setsum__ivl__cong) ).
fof(fact_eq__number__of,axiom,
! [V_y_2,V_x_2,T_b] :
( ( class_Int_Oring__char__0(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_eq__number__of) ).
fof(fact_number__of__reorient,axiom,
! [V_x_2,V_w_2,T_b] :
( class_Int_Onumber(T_b)
=> ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
<=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ),
file('theBenchmark.p',fact_number__of__reorient) ).
fof(fact_le__number__of,axiom,
! [V_y_2,V_x_2,T_b] :
( ( class_Rings_Olinordered__idom(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_le__number__of) ).
fof(fact_less__number__of,axiom,
! [V_y_2,V_x_2,T_b] :
( ( class_Rings_Olinordered__idom(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_less__number__of) ).
fof(fact_number__of__add,axiom,
! [V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
file('theBenchmark.p',fact_number__of__add) ).
fof(fact_add__number__of__eq,axiom,
! [V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) ),
file('theBenchmark.p',fact_add__number__of__eq) ).
fof(fact_add__number__of__left,axiom,
! [V_z,V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_z) ),
file('theBenchmark.p',fact_add__number__of__left) ).
fof(fact_number__of__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_diff__number__of__eq,axiom,
! [V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ),
file('theBenchmark.p',fact_diff__number__of__eq) ).
fof(fact_number__of__minus,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
file('theBenchmark.p',fact_number__of__minus) ).
fof(fact_arith__simps_I30_J,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ),
file('theBenchmark.p',fact_arith__simps_I30_J) ).
fof(fact_le__number__of__eq__not__less,axiom,
! [V_w_2,V_v_2,T_b] :
( ( class_Orderings_Olinorder(T_b)
& class_Int_Onumber(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2))) ) ),
file('theBenchmark.p',fact_le__number__of__eq__not__less) ).
fof(fact_add__number__of__diff2,axiom,
! [V_w,V_c,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)))),V_c) ),
file('theBenchmark.p',fact_add__number__of__diff2) ).
fof(fact_add__number__of__diff1,axiom,
! [V_c,V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_c) ),
file('theBenchmark.p',fact_add__number__of__diff1) ).
fof(fact_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_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_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_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_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_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_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_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_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_plus__numeral__code_I9_J,axiom,
! [V_w,V_v] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)),
file('theBenchmark.p',fact_plus__numeral__code_I9_J) ).
fof(fact_minus__numeral__code_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_minus__numeral__code_I5_J,axiom,
! [V_w] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)),
file('theBenchmark.p',fact_minus__numeral__code_I5_J) ).
fof(fact_less__number__of__int__code,axiom,
! [V_l_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
file('theBenchmark.p',fact_less__number__of__int__code) ).
fof(fact_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_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_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_int__0__less__1,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('theBenchmark.p',fact_int__0__less__1) ).
fof(fact_int__one__le__iff__zero__less,axiom,
! [V_z_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ),
file('theBenchmark.p',fact_int__one__le__iff__zero__less) ).
fof(fact_zle__diff1__eq,axiom,
! [V_z_2,V_w_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ),
file('theBenchmark.p',fact_zle__diff1__eq) ).
fof(fact_pred__def,axiom,
! [V_k] : c_Int_Opred(V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('theBenchmark.p',fact_pred__def) ).
fof(fact_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_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_zless__add1__eq,axiom,
! [V_z_2,V_w_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
<=> ( V_w_2 = V_z_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ),
file('theBenchmark.p',fact_zless__add1__eq) ).
fof(fact_zless__imp__add1__zle,axiom,
! [V_z,V_w] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z)) ),
file('theBenchmark.p',fact_zless__imp__add1__zle) ).
fof(fact_add1__zle__eq,axiom,
! [V_z_2,V_w_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ),
file('theBenchmark.p',fact_add1__zle__eq) ).
fof(fact_zle__add1__eq__le,axiom,
! [V_z_2,V_w_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ),
file('theBenchmark.p',fact_zle__add1__eq__le) ).
fof(fact_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_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_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_zless__linear,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x))
| V_x = V_y
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) ),
file('theBenchmark.p',fact_zless__linear) ).
fof(fact_zminus__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_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_diff__int__def__symmetric,axiom,
! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w),
file('theBenchmark.p',fact_diff__int__def__symmetric) ).
fof(fact_diff__int__def,axiom,
! [V_w,V_z] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)),
file('theBenchmark.p',fact_diff__int__def) ).
fof(fact_zadd__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__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_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_zadd__commute,axiom,
! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z),
file('theBenchmark.p',fact_zadd__commute) ).
fof(fact_zadd__left__commute,axiom,
! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z)),
file('theBenchmark.p',fact_zadd__left__commute) ).
fof(fact_zadd__assoc,axiom,
! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3)),
file('theBenchmark.p',fact_zadd__assoc) ).
fof(fact_zminus__zadd__distrib,axiom,
! [V_w,V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)),
file('theBenchmark.p',fact_zminus__zadd__distrib) ).
fof(fact_zadd__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__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__refl,axiom,
! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)),
file('theBenchmark.p',fact_zle__refl) ).
fof(fact_zle__linear,axiom,
! [V_w,V_z] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) ),
file('theBenchmark.p',fact_zle__linear) ).
fof(fact_zle__trans,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ),
file('theBenchmark.p',fact_zle__trans) ).
fof(fact_zle__antisym,axiom,
! [V_w,V_z] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
=> V_z = V_w ) ),
file('theBenchmark.p',fact_zle__antisym) ).
fof(fact_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_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_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_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_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_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_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_union__fold__insert,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),V_B_2),V_A_2) ),
file('theBenchmark.p',fact_union__fold__insert) ).
fof(fact_fold__sup__insert,axiom,
! [V_a_2,V_b_2,V_A_2,T_b] :
( class_Lattices_Osemilattice__sup(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2)) ) ),
file('theBenchmark.p',fact_fold__sup__insert) ).
fof(fact_fold__inf__insert,axiom,
! [V_a_2,V_b_2,V_A_2,T_b] :
( class_Lattices_Osemilattice__inf(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)) ) ),
file('theBenchmark.p',fact_fold__inf__insert) ).
fof(fact_sup__Sup__fold__sup,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_B_2),V_A_2) ) ),
file('theBenchmark.p',fact_sup__Sup__fold__sup) ).
fof(fact_inf__Inf__fold__inf,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_B_2),V_A_2) ) ),
file('theBenchmark.p',fact_inf__Inf__fold__inf) ).
fof(fact_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_sup__le__fold__sup,axiom,
! [V_b_2,V_a_2,V_A_2,T_b] :
( class_Lattices_Osemilattice__sup(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2))) ) ) ),
file('theBenchmark.p',fact_sup__le__fold__sup) ).
fof(fact_fold__inf__le__inf,axiom,
! [V_b_2,V_a_2,V_A_2,T_b] :
( class_Lattices_Osemilattice__inf(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2))) ) ) ),
file('theBenchmark.p',fact_fold__inf__le__inf) ).
fof(fact_Sup__fold__sup,axiom,
! [V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),c_Orderings_Obot__class_Obot(T_b)),V_A_2) ) ),
file('theBenchmark.p',fact_Sup__fold__sup) ).
fof(fact_Inf__fold__inf,axiom,
! [V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),c_Orderings_Otop__class_Otop(T_b)),V_A_2) ) ),
file('theBenchmark.p',fact_Inf__fold__inf) ).
fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_a_2),V_A_2) ) ),
file('theBenchmark.p',fact_Sup__fin_Oeq__fold__idem_H) ).
fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_a_2),V_A_2) ) ),
file('theBenchmark.p',fact_Inf__fin_Oeq__fold__idem_H) ).
fof(fact_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__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_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_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__increasing__iff,axiom,
! [V_y_2,V_x_2,V_b_2,T_b] :
( class_Rings_Olinordered__semidom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_power__increasing__iff) ).
fof(fact_power__le__imp__le__exp,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ),
file('theBenchmark.p',fact_power__le__imp__le__exp) ).
fof(fact_power__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__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__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_finite__atLeastAtMost__int,axiom,
! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2))),
file('theBenchmark.p',fact_finite__atLeastAtMost__int) ).
fof(fact_finite__atLeastLessThan__int,axiom,
! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2))),
file('theBenchmark.p',fact_finite__atLeastLessThan__int) ).
fof(fact_finite__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_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_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_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_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_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__one,axiom,
! [V_n,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_power__one) ).
fof(fact_power__one__right,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ),
file('theBenchmark.p',fact_power__one__right) ).
fof(fact_power__mono,axiom,
! [V_n,V_b,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ),
file('theBenchmark.p',fact_power__mono) ).
fof(fact_zero__le__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
file('theBenchmark.p',fact_zero__le__power) ).
fof(fact_zero__less__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
file('theBenchmark.p',fact_zero__less__power) ).
fof(fact_power__eq__0__iff,axiom,
! [V_n_2,V_a_2,T_b] :
( ( class_Rings_Ozero__neq__one(T_b)
& class_Rings_Ono__zero__divisors(T_b)
& class_Rings_Omult__zero(T_b)
& class_Power_Opower(T_b) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_power__eq__0__iff) ).
fof(fact_one__le__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
file('theBenchmark.p',fact_one__le__power) ).
fof(fact_power__0__Suc,axiom,
! [V_n,T_a] :
( ( class_Rings_Osemiring__0(T_a)
& class_Power_Opower(T_a) )
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_OSuc,V_n)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_power__0__Suc) ).
fof(fact_power__inject__exp,axiom,
! [V_n_2,V_m_2,V_a_2,T_b] :
( class_Rings_Olinordered__semidom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)
<=> V_m_2 = V_n_2 ) ) ),
file('theBenchmark.p',fact_power__inject__exp) ).
fof(fact_power__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_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_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__zero__less__power__iff,axiom,
! [V_n_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)))
<=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) ) ),
file('theBenchmark.p',fact_nat__zero__less__power__iff) ).
fof(fact_nat__power__less__imp__less,axiom,
! [V_n,V_m,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ),
file('theBenchmark.p',fact_nat__power__less__imp__less) ).
fof(fact_power__less__imp__less__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_power__less__imp__less__base) ).
fof(fact_power__inject__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> V_a = V_b ) ) ) ),
file('theBenchmark.p',fact_power__inject__base) ).
fof(fact_power__le__imp__le__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_power__le__imp__le__base) ).
fof(fact_power__0__left,axiom,
! [V_n,T_a] :
( ( class_Rings_Osemiring__0(T_a)
& class_Power_Opower(T_a) )
=> ( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ) ),
file('theBenchmark.p',fact_power__0__left) ).
fof(fact_power__gt1,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)))) ) ),
file('theBenchmark.p',fact_power__gt1) ).
fof(fact_power__strict__increasing__iff,axiom,
! [V_y_2,V_x_2,V_b_2,T_b] :
( class_Rings_Olinordered__semidom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_power__strict__increasing__iff) ).
fof(fact_power__less__imp__less__exp,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ),
file('theBenchmark.p',fact_power__less__imp__less__exp) ).
fof(fact_power__strict__increasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ),
file('theBenchmark.p',fact_power__strict__increasing) ).
fof(fact_power__increasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ),
file('theBenchmark.p',fact_power__increasing) ).
fof(fact_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__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_simp__from__to,axiom,
! [V_i_2,V_j_2] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
=> c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),V_i_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
=> c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_simp__from__to) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_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_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_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
! [V_n,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_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_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_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_fun__left__comm_Ofold__fun__comm,axiom,
! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__fun__comm) ).
fof(fact_fun__left__comm_Ofold__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_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_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_I8_J,axiom,
! [V_t_2,V_A_2,V_D_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
=> ! [B_x] :
( ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
=> ! [B_xb] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
=> B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ),
file('theBenchmark.p',fact_aset_I8_J) ).
fof(fact_bset_I6_J,axiom,
! [V_t_2,V_B_2,V_D_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
=> ! [B_x] :
( ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
=> ! [B_xb] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
=> B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ),
file('theBenchmark.p',fact_bset_I6_J) ).
fof(fact_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_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_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_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_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_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_Pls__def) ).
fof(fact_rel__simps_I19_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
file('theBenchmark.p',fact_rel__simps_I19_J) ).
fof(fact_rel__simps_I2_J,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
file('theBenchmark.p',fact_rel__simps_I2_J) ).
fof(fact_add__Pls,axiom,
! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k,
file('theBenchmark.p',fact_add__Pls) ).
fof(fact_add__Pls__right,axiom,
! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k,
file('theBenchmark.p',fact_add__Pls__right) ).
fof(fact_diff__bin__simps_I1_J,axiom,
! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k,
file('theBenchmark.p',fact_diff__bin__simps_I1_J) ).
fof(fact_minus__Pls,axiom,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
file('theBenchmark.p',fact_minus__Pls) ).
fof(fact_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__right,axiom,
! [V_a,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = V_a ),
file('theBenchmark.p',fact_add__numeral__0__right) ).
fof(fact_add__numeral__0,axiom,
! [V_a,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)),V_a) = V_a ),
file('theBenchmark.p',fact_add__numeral__0) ).
fof(fact_bin__less__0__simps_I1_J,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('theBenchmark.p',fact_bin__less__0__simps_I1_J) ).
fof(fact_nat__number__of__Pls,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_nat__number__of__Pls) ).
fof(fact_semiring__norm_I113_J,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
file('theBenchmark.p',fact_semiring__norm_I113_J) ).
fof(fact_zero__is__num__zero,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
file('theBenchmark.p',fact_zero__is__num__zero) ).
fof(fact_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_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_number__of2,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
file('theBenchmark.p',fact_number__of2) ).
fof(fact_less__nat__number__of,axiom,
! [V_v_H_2,V_v_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) ) ),
file('theBenchmark.p',fact_less__nat__number__of) ).
fof(fact_le__nat__number__of,axiom,
! [V_v_H_2,V_v_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)))
<=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ),
file('theBenchmark.p',fact_le__nat__number__of) ).
fof(fact_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__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_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_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_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_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_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_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_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_succ__Pls,axiom,
c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
file('theBenchmark.p',fact_succ__Pls) ).
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_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_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_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_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_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_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_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_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_inj__int,axiom,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('theBenchmark.p',fact_inj__int) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
! [V_A_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) ).
fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
! [V_A_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) ),
file('theBenchmark.p',fact_transfer__nat__int__set__relations_I2_J) ).
fof(fact_transfer__int__nat__numerals_I4_J,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
file('theBenchmark.p',fact_transfer__int__nat__numerals_I4_J) ).
fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
! [V_B_2,V_A_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ),
file('theBenchmark.p',fact_transfer__nat__int__set__relations_I5_J) ).
fof(fact_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_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_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_transfer__int__nat__quantifiers_I1_J,axiom,
! [V_P_2] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
=> hBOOL(hAPP(V_P_2,B_x)) )
<=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ),
file('theBenchmark.p',fact_transfer__int__nat__quantifiers_I1_J) ).
fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
! [V_P_2] :
( ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
<=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ),
file('theBenchmark.p',fact_transfer__int__nat__quantifiers_I2_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
! [V_z] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
fof(fact_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_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_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,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_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_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_rel__simps_I22_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ),
file('theBenchmark.p',fact_rel__simps_I22_J) ).
fof(fact_rel__simps_I12_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ),
file('theBenchmark.p',fact_rel__simps_I12_J) ).
fof(fact_zero__le__imp__of__nat,axiom,
! [V_m,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m))) ),
file('theBenchmark.p',fact_zero__le__imp__of__nat) ).
fof(fact_of__nat__0__le__iff,axiom,
! [V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) ),
file('theBenchmark.p',fact_of__nat__0__le__iff) ).
fof(fact_negative__eq__positive,axiom,
! [V_m_2,V_n_2] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)
<=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_negative__eq__positive) ).
fof(fact_of__nat__less__0__iff,axiom,
! [V_m,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),c_Groups_Ozero__class_Ozero(T_a))) ),
file('theBenchmark.p',fact_of__nat__less__0__iff) ).
fof(fact_Bit1__def,axiom,
! [V_k] : c_Int_OBit1(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)),V_k),
file('theBenchmark.p',fact_Bit1__def) ).
fof(fact_not__int__zless__negative,axiom,
! [V_m,V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)))),
file('theBenchmark.p',fact_not__int__zless__negative) ).
fof(fact_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_succ__pred,axiom,
! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x,
file('theBenchmark.p',fact_succ__pred) ).
fof(fact_of__nat__1,axiom,
! [T_a] :
( class_Rings_Osemiring__1(T_a)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_of__nat__1) ).
fof(fact_minus__Bit1,axiom,
! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(V_k)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k))),
file('theBenchmark.p',fact_minus__Bit1) ).
fof(fact_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_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_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_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_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
! [V_y,V_x] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x),V_y)),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J) ).
fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
! [V_A_2] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) ),
file('theBenchmark.p',fact_transfer__nat__int__set__relations_I1_J) ).
fof(fact_inj__of__nat,axiom,
! [T_b] :
( class_Nat_Osemiring__char__0(T_b)
=> c_Fun_Oinj__on(tc_Nat_Onat,T_b,c_Nat_Osemiring__1__class_Oof__nat(T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_inj__of__nat) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J) ).
fof(fact_number__of__Bit1,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
file('theBenchmark.p',fact_number__of__Bit1) ).
fof(fact_int__le__0__conv,axiom,
! [V_n_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_int__le__0__conv) ).
fof(fact_numeral__1__eq__1,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_numeral__1__eq__1) ).
fof(fact_semiring__norm_I110_J,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ),
file('theBenchmark.p',fact_semiring__norm_I110_J) ).
fof(fact_int__Suc0__eq__1,axiom,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint),
file('theBenchmark.p',fact_int__Suc0__eq__1) ).
fof(fact_zless__iff__Suc__zadd,axiom,
! [V_z_2,V_w_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
<=> ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) ),
file('theBenchmark.p',fact_zless__iff__Suc__zadd) ).
fof(fact_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_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_int__zle__neg,axiom,
! [V_m_2,V_n_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))))
<=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_int__zle__neg) ).
fof(fact_int__Suc,axiom,
! [V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),
file('theBenchmark.p',fact_int__Suc) ).
fof(fact_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_eq__special_I2_J,axiom,
! [V_y_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
<=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ),
file('theBenchmark.p',fact_eq__special_I2_J) ).
fof(fact_eq__special_I4_J,axiom,
! [V_x_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
<=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) ) ),
file('theBenchmark.p',fact_eq__special_I4_J) ).
fof(fact_one__is__num__one,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
file('theBenchmark.p',fact_one__is__num__one) ).
fof(fact_zdiff__int,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) ),
file('theBenchmark.p',fact_zdiff__int) ).
fof(fact_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_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_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_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_iszero__Numeral0,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ),
file('theBenchmark.p',fact_iszero__Numeral0) ).
fof(fact_Nats__0,axiom,
! [T_b] :
( class_Rings_Osemiring__1(T_b)
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ),
file('theBenchmark.p',fact_Nats__0) ).
fof(fact_Nats__add,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Rings_Osemiring__1(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ),
file('theBenchmark.p',fact_Nats__add) ).
fof(fact_Nats__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_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_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_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_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_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_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_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_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_less__special_I4_J,axiom,
! [V_x_2,T_b] :
( ( class_Rings_Olinordered__idom(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ),
file('theBenchmark.p',fact_less__special_I4_J) ).
fof(fact_less__special_I2_J,axiom,
! [V_y_2,T_b] :
( ( class_Rings_Olinordered__idom(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ),
file('theBenchmark.p',fact_less__special_I2_J) ).
fof(fact_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_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_Suc__diff__eq__diff__pred,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),V_n))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)))) ),
file('theBenchmark.p',fact_Suc__diff__eq__diff__pred) ).
fof(fact_zdiff__int__split,axiom,
! [V_y_2,V_x_2,V_P_2] :
( hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2))))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
=> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))) ) ) ),
file('theBenchmark.p',fact_zdiff__int__split) ).
fof(fact_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_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_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_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_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_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_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_transfer__int__nat__relations_I1_J,axiom,
! [V_y_2,V_x_2] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)
<=> V_x_2 = V_y_2 ),
file('theBenchmark.p',fact_transfer__int__nat__relations_I1_J) ).
fof(fact_transfer__nat__int__set__relations_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_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_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_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_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_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_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_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_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_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_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_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_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_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_bin__less__0__simps_I3_J,axiom,
! [V_w_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('theBenchmark.p',fact_bin__less__0__simps_I3_J) ).
fof(fact_rel__simps_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_rel__simps_I10_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ),
file('theBenchmark.p',fact_rel__simps_I10_J) ).
fof(fact_rel__simps_I4_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ),
file('theBenchmark.p',fact_rel__simps_I4_J) ).
fof(fact_less__int__code_I15_J,axiom,
! [V_k2_2,V_k1_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ),
file('theBenchmark.p',fact_less__int__code_I15_J) ).
fof(fact_rel__simps_I16_J,axiom,
! [V_l_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
file('theBenchmark.p',fact_rel__simps_I16_J) ).
fof(fact_add__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_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_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_iszero__number__of__Bit0,axiom,
! [V_w_2,T_b] :
( ( class_Int_Oring__char__0(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
<=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ),
file('theBenchmark.p',fact_iszero__number__of__Bit0) ).
fof(fact_succ__Bit0,axiom,
! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k),
file('theBenchmark.p',fact_succ__Bit0) ).
fof(fact_succ__Bit1,axiom,
! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)),
file('theBenchmark.p',fact_succ__Bit1) ).
fof(fact_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_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_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_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_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_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_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_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__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_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_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_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_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_number__of1,axiom,
! [V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_n))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_n)))) ) ),
file('theBenchmark.p',fact_number__of1) ).
fof(fact_transfer__int__nat__numerals_I3_J,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('theBenchmark.p',fact_transfer__int__nat__numerals_I3_J) ).
fof(fact_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_one__add__one__is__two,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
file('theBenchmark.p',fact_one__add__one__is__two) ).
fof(fact_zero__eq__power2,axiom,
! [V_a_2,T_b] :
( class_Rings_Oring__1__no__zero__divisors(T_b)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_b)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_zero__eq__power2) ).
fof(fact_zero__power2,axiom,
! [T_a] :
( class_Rings_Osemiring__1(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_zero__power2) ).
fof(fact_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_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_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_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_zero__le__power2,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
file('theBenchmark.p',fact_zero__le__power2) ).
fof(fact_power2__le__imp__le,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ),
file('theBenchmark.p',fact_power2__le__imp__le) ).
fof(fact_power2__eq__imp__eq,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> V_x = V_y ) ) ) ),
file('theBenchmark.p',fact_power2__eq__imp__eq) ).
fof(fact_zero__less__power2,axiom,
! [V_a_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
<=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_zero__less__power2) ).
fof(fact_power2__less__0,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))) ),
file('theBenchmark.p',fact_power2__less__0) ).
fof(fact_sum__power2__eq__zero__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_b)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_sum__power2__eq__zero__iff) ).
fof(fact_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_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_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_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_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_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_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_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_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_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_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_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
! [V_y,V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).
fof(fact_zmult__int,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
file('theBenchmark.p',fact_zmult__int) ).
fof(fact_int__mult,axiom,
! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),
file('theBenchmark.p',fact_int__mult) ).
fof(fact_of__nat__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_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_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_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_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_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_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_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__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_mult__zero__right,axiom,
! [V_a,T_a] :
( class_Rings_Omult__zero(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mult__zero__right) ).
fof(fact_mult__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_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(fact_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__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_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(fact_crossproduct__noteq,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
=> ( ( V_c_2 != V_d_2
& V_a_2 != V_b_2 )
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)) ) ),
file('theBenchmark.p',fact_crossproduct__noteq) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [V_b,V_m,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_crossproduct__eq,axiom,
! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2))
<=> ( V_y_2 = V_z_2
| V_w_2 = V_x_2 ) ) ),
file('theBenchmark.p',fact_crossproduct__eq) ).
fof(fact_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_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_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_mult__cancel2,axiom,
! [V_n_2,V_k_2,V_m_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)
<=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = V_n_2 ) ),
file('theBenchmark.p',fact_mult__cancel2) ).
fof(fact_mult__cancel1,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
<=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = V_n_2 ) ),
file('theBenchmark.p',fact_mult__cancel1) ).
fof(fact_mult__is__0,axiom,
! [V_n_2,V_m_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_mult__is__0) ).
fof(fact_mult__0__right,axiom,
! [V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_mult__0__right) ).
fof(fact_mult__0,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_mult__0) ).
fof(fact_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__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__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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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,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_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_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_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_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_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_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_not__square__less__zero,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__ring(T_a)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ),
file('theBenchmark.p',fact_not__square__less__zero) ).
fof(fact_mult__less__cancel__right__disj,axiom,
! [V_b_2,V_c_2,V_a_2,T_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__right__disj) ).
fof(fact_mult__less__cancel__left__disj,axiom,
! [V_b_2,V_a_2,V_c_2,T_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__left__disj) ).
fof(fact_mult__less__cancel__left__pos,axiom,
! [V_b_2,V_a_2,V_c_2,T_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__left__pos) ).
fof(fact_mult__pos__pos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ),
file('theBenchmark.p',fact_mult__pos__pos) ).
fof(fact_mult__pos__neg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('theBenchmark.p',fact_mult__pos__neg) ).
fof(fact_mult__pos__neg2,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('theBenchmark.p',fact_mult__pos__neg2) ).
fof(fact_zero__less__mult__pos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ),
file('theBenchmark.p',fact_zero__less__mult__pos) ).
fof(fact_zero__less__mult__pos2,axiom,
! [V_a,V_b,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ),
file('theBenchmark.p',fact_zero__less__mult__pos2) ).
fof(fact_mult__less__cancel__left__neg,axiom,
! [V_b_2,V_a_2,V_c_2,T_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__left__neg) ).
fof(fact_mult__neg__pos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('theBenchmark.p',fact_mult__neg__pos) ).
fof(fact_mult__neg__neg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ),
file('theBenchmark.p',fact_mult__neg__neg) ).
fof(fact_mult__strict__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ),
file('theBenchmark.p',fact_mult__strict__right__mono) ).
fof(fact_mult__strict__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ),
file('theBenchmark.p',fact_mult__strict__left__mono) ).
fof(fact_comm__mult__strict__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__comm__semiring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ),
file('theBenchmark.p',fact_comm__mult__strict__left__mono) ).
fof(fact_mult__strict__right__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ),
file('theBenchmark.p',fact_mult__strict__right__mono__neg) ).
fof(fact_mult__strict__left__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ),
file('theBenchmark.p',fact_mult__strict__left__mono__neg) ).
fof(fact_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_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_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_eq__add__iff1,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
( class_Rings_Oring(T_b)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2) = V_d_2 ) ),
file('theBenchmark.p',fact_eq__add__iff1) ).
fof(fact_eq__add__iff2,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
( class_Rings_Oring(T_b)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
<=> V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ),
file('theBenchmark.p',fact_eq__add__iff2) ).
fof(fact_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_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_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_right__diff__distrib__number__of,axiom,
! [V_c,V_b,V_v,T_b] :
( ( class_Rings_Oring(T_b)
& class_Int_Onumber(T_b) )
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)) ),
file('theBenchmark.p',fact_right__diff__distrib__number__of) ).
fof(fact_left__diff__distrib__number__of,axiom,
! [V_v,V_b,V_a,T_b] :
( ( class_Rings_Oring(T_b)
& class_Int_Onumber(T_b) )
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ),
file('theBenchmark.p',fact_left__diff__distrib__number__of) ).
fof(fact_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_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_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_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_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__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__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_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_power__Suc2,axiom,
! [V_n,V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) ),
file('theBenchmark.p',fact_power__Suc2) ).
fof(fact_power__Suc,axiom,
! [V_n,V_a,T_a] :
( class_Power_Opower(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
file('theBenchmark.p',fact_power__Suc) ).
fof(fact_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_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_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_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_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_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_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_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_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_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_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_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_mult__left__le__imp__le,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__left__le__imp__le) ).
fof(fact_mult__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__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__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__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__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__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__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__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__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__le__cancel__left__neg,axiom,
! [V_b_2,V_a_2,V_c_2,T_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ),
file('theBenchmark.p',fact_mult__le__cancel__left__neg) ).
fof(fact_mult__le__cancel__left__pos,axiom,
! [V_b_2,V_a_2,V_c_2,T_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ),
file('theBenchmark.p',fact_mult__le__cancel__left__pos) ).
fof(fact_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_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_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_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_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_le__add__iff1,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
( class_Rings_Oordered__ring(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ),
file('theBenchmark.p',fact_le__add__iff1) ).
fof(fact_le__add__iff2,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
( class_Rings_Oordered__ring(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ),
file('theBenchmark.p',fact_le__add__iff2) ).
fof(fact_less__add__iff1,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
( class_Rings_Oordered__ring(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ),
file('theBenchmark.p',fact_less__add__iff1) ).
fof(fact_less__add__iff2,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
( class_Rings_Oordered__ring(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ),
file('theBenchmark.p',fact_less__add__iff2) ).
fof(fact_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_nat__mult__2__right,axiom,
! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_z),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z),
file('theBenchmark.p',fact_nat__mult__2__right) ).
fof(fact_nat__mult__2,axiom,
! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z),
file('theBenchmark.p',fact_nat__mult__2) ).
fof(fact_power__even__eq,axiom,
! [V_n,V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
file('theBenchmark.p',fact_power__even__eq) ).
fof(fact_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_power__minus__even,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Oring__1(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) ),
file('theBenchmark.p',fact_power__minus__even) ).
fof(fact_power2__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_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_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_nat__le__add__iff1,axiom,
! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ),
file('theBenchmark.p',fact_nat__le__add__iff1) ).
fof(fact_nat__diff__add__eq1,axiom,
! [V_n,V_m,V_u,V_i,V_j] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_u)),V_m)),V_n) ),
file('theBenchmark.p',fact_nat__diff__add__eq1) ).
fof(fact_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_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_left__add__mult__distrib,axiom,
! [V_k,V_j,V_u,V_i] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k),
file('theBenchmark.p',fact_left__add__mult__distrib) ).
fof(fact_nat__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_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_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_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__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__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_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_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_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_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_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_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_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_mod__diff__cong,axiom,
! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
( class_Divides_Oring__div(T_a)
=> ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
=> ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_H),V_b_H),V_c) ) ) ),
file('theBenchmark.p',fact_mod__diff__cong) ).
fof(fact_mod__diff__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Oring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ),
file('theBenchmark.p',fact_mod__diff__eq) ).
fof(fact_mod__diff__left__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Oring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ),
file('theBenchmark.p',fact_mod__diff__left__eq) ).
fof(fact_mod__diff__right__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Oring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ),
file('theBenchmark.p',fact_mod__diff__right__eq) ).
fof(fact_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_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__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__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__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__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_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__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_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_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_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_DIVISION__BY__ZERO,axiom,
! [V_a] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a
& hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('theBenchmark.p',fact_DIVISION__BY__ZERO) ).
fof(fact_zdiv__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_mod__mod__trivial,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ),
file('theBenchmark.p',fact_mod__mod__trivial) ).
fof(fact_mod__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__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__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_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_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_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_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_zmod__simps_I3_J,axiom,
! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c),
file('theBenchmark.p',fact_zmod__simps_I3_J) ).
fof(fact_zmod__zmult1__eq,axiom,
! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c),
file('theBenchmark.p',fact_zmod__zmult1__eq) ).
fof(fact_zdiff__zmod__left,axiom,
! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m),
file('theBenchmark.p',fact_zdiff__zmod__left) ).
fof(fact_zdiff__zmod__right,axiom,
! [V_m,V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m),
file('theBenchmark.p',fact_zdiff__zmod__right) ).
fof(fact_zminus__zmod,axiom,
! [V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_x),V_m),
file('theBenchmark.p',fact_zminus__zmod) ).
fof(fact_zmod__zminus__zminus,axiom,
! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),
file('theBenchmark.p',fact_zmod__zminus__zminus) ).
fof(fact_zmod__zminus2,axiom,
! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)),
file('theBenchmark.p',fact_zmod__zminus2) ).
fof(fact_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__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__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_zpower__zmod,axiom,
! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y),V_m),
file('theBenchmark.p',fact_zpower__zmod) ).
fof(fact_mod__mult__self1__is__0,axiom,
! [V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mod__mult__self1__is__0) ).
fof(fact_mod__mult__self2__is__0,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mod__mult__self2__is__0) ).
fof(fact_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_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_zdiv__zminus1__eq__if,axiom,
! [V_a,V_b] :
( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_zdiv__zminus1__eq__if) ).
fof(fact_zdiv__zminus2__eq__if,axiom,
! [V_a,V_b] :
( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_zdiv__zminus2__eq__if) ).
fof(fact_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_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_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_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_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_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_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_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_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__eq__0__iff,axiom,
! [V_d_2,V_m_2] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ),
file('theBenchmark.p',fact_zmod__eq__0__iff) ).
fof(fact_zmod__zminus1__not__zero,axiom,
! [V_l,V_k] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('theBenchmark.p',fact_zmod__zminus1__not__zero) ).
fof(fact_zmod__zminus2__not__zero,axiom,
! [V_l,V_k] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('theBenchmark.p',fact_zmod__zminus2__not__zero) ).
fof(fact_div__mult__mult1,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ),
file('theBenchmark.p',fact_div__mult__mult1) ).
fof(fact_div__mult__mult2,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ),
file('theBenchmark.p',fact_div__mult__mult2) ).
fof(fact_div__mult__self1__is__id,axiom,
! [V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),V_b) = V_a ) ),
file('theBenchmark.p',fact_div__mult__self1__is__id) ).
fof(fact_div__mult__self2__is__id,axiom,
! [V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_b) = V_a ) ),
file('theBenchmark.p',fact_div__mult__self2__is__id) ).
fof(fact_div__mult__mult1__if,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) )
& ( V_c = c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_div__mult__mult1__if) ).
fof(fact_div__self,axiom,
! [V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ),
file('theBenchmark.p',fact_div__self) ).
fof(fact_split__neg__lemma,axiom,
! [V_n_2,V_P_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
<=> ! [B_i,B_j] :
( ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
=> hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ),
file('theBenchmark.p',fact_split__neg__lemma) ).
fof(fact_split__pos__lemma,axiom,
! [V_n_2,V_P_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
=> ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
<=> ! [B_i,B_j] :
( ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
=> hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ),
file('theBenchmark.p',fact_split__pos__lemma) ).
fof(fact_zdiv__eq__0__iff,axiom,
! [V_k_2,V_i_2] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) )
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_zdiv__eq__0__iff) ).
fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
! [V_a_2,V_b_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ),
file('theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).
fof(fact_pos__imp__zdiv__pos__iff,axiom,
! [V_i_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ),
file('theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).
fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
! [V_b_2,V_a_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) ) ) ),
file('theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).
fof(fact_zdiv__mono2,axiom,
! [V_b,V_b_H,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H))) ) ) ),
file('theBenchmark.p',fact_zdiv__mono2) ).
fof(fact_div__nonneg__neg__le0,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('theBenchmark.p',fact_div__nonneg__neg__le0) ).
fof(fact_div__pos__pos__trivial,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_div__pos__pos__trivial) ).
fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
! [V_a_2,V_b_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).
fof(fact_div__nonpos__pos__le0,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('theBenchmark.p',fact_div__nonpos__pos__le0) ).
fof(fact_zdiv__mono2__neg,axiom,
! [V_b,V_b_H,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ),
file('theBenchmark.p',fact_zdiv__mono2__neg) ).
fof(fact_div__neg__neg__trivial,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_div__neg__neg__trivial) ).
fof(fact_zdiv__mono1,axiom,
! [V_b,V_a_H,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b))) ) ),
file('theBenchmark.p',fact_zdiv__mono1) ).
fof(fact_zdiv__mono1__neg,axiom,
! [V_b,V_a_H,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ),
file('theBenchmark.p',fact_zdiv__mono1__neg) ).
fof(fact_int__div__less__self,axiom,
! [V_k,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_k)),V_x)) ) ),
file('theBenchmark.p',fact_int__div__less__self) ).
fof(fact_zdiv__zmult2__eq,axiom,
! [V_b,V_a,V_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_c) ),
file('theBenchmark.p',fact_zdiv__zmult2__eq) ).
fof(fact_pos__mod__sign,axiom,
! [V_a,V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ),
file('theBenchmark.p',fact_pos__mod__sign) ).
fof(fact_pos__mod__conj,axiom,
! [V_a,V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ),
file('theBenchmark.p',fact_pos__mod__conj) ).
fof(fact_mod__pos__pos__trivial,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ),
file('theBenchmark.p',fact_mod__pos__pos__trivial) ).
fof(fact_neg__mod__sign,axiom,
! [V_a,V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('theBenchmark.p',fact_neg__mod__sign) ).
fof(fact_neg__mod__conj,axiom,
! [V_a,V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('theBenchmark.p',fact_neg__mod__conj) ).
fof(fact_mod__neg__neg__trivial,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ),
file('theBenchmark.p',fact_mod__neg__neg__trivial) ).
fof(fact_zmod__zminus2__eq__if,axiom,
! [V_b,V_a] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_zmod__zminus2__eq__if) ).
fof(fact_zmod__zminus1__eq__if,axiom,
! [V_b,V_a] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_zmod__zminus1__eq__if) ).
fof(fact_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__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__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_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_split__zdiv,axiom,
! [V_k_2,V_n_2,V_P_2] :
( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ! [B_i] :
( ? [B_j] :
( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
=> hBOOL(hAPP(V_P_2,B_i)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
=> ! [B_i] :
( ? [B_j] :
( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
=> hBOOL(hAPP(V_P_2,B_i)) ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
file('theBenchmark.p',fact_split__zdiv) ).
fof(fact_divmod__int__rel__div__eq,axiom,
! [V_r_1,V_y,V_b_1,V_a_1] :
( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1)
=> ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) ) ) )
=> ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ),
file('theBenchmark.p',fact_divmod__int__rel__div__eq) ).
fof(fact_split__zmod,axiom,
! [V_k_2,V_n_2,V_P_2] :
( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ! [B_i,B_j] :
( ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
=> hBOOL(hAPP(V_P_2,B_j)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
=> ! [B_i,B_j] :
( ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
=> hBOOL(hAPP(V_P_2,B_j)) ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(V_P_2,V_n_2)) ) ) ),
file('theBenchmark.p',fact_split__zmod) ).
fof(fact_zmult2__lemma__aux3,axiom,
! [V_q,V_b,V_r,V_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ),
file('theBenchmark.p',fact_zmult2__lemma__aux3) ).
fof(fact_zmult2__lemma__aux4,axiom,
! [V_q,V_b,V_r,V_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))) ) ) ),
file('theBenchmark.p',fact_zmult2__lemma__aux4) ).
fof(fact_zmult2__lemma__aux1,axiom,
! [V_q,V_r,V_b,V_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ),
file('theBenchmark.p',fact_zmult2__lemma__aux1) ).
fof(fact_zmult2__lemma__aux2,axiom,
! [V_q,V_r,V_b,V_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
file('theBenchmark.p',fact_zmult2__lemma__aux2) ).
fof(fact_divmod__int__rel__mod__eq,axiom,
! [V_y,V_q_1,V_b_1,V_a_1] :
( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_q_1)),V_y)
=> ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) ) ) )
=> ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ),
file('theBenchmark.p',fact_divmod__int__rel__mod__eq) ).
fof(fact_zmod__number__of__Bit0,axiom,
! [V_w,V_v] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))),
file('theBenchmark.p',fact_zmod__number__of__Bit0) ).
fof(fact_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_nat__int,axiom,
! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n,
file('theBenchmark.p',fact_nat__int) ).
fof(fact_rel__simps_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_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_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_nat__div__distrib,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) ),
file('theBenchmark.p',fact_nat__div__distrib) ).
fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ),
file('theBenchmark.p',fact_Divides_Otransfer__nat__int__functions_I1_J) ).
fof(fact_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_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_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_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__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__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_ex__nat,axiom,
! [V_P_2] :
( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
<=> ? [B_x] :
( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ),
file('theBenchmark.p',fact_ex__nat) ).
fof(fact_all__nat,axiom,
! [V_P_2] :
( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
=> hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ),
file('theBenchmark.p',fact_all__nat) ).
fof(fact_transfer__nat__int__relations_I1_J,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
=> ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_transfer__nat__int__relations_I1_J) ).
fof(fact_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_mod__eq__0__iff,axiom,
! [V_d_2,V_m_2] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ),
file('theBenchmark.p',fact_mod__eq__0__iff) ).
fof(fact_mod__geq,axiom,
! [V_n,V_m] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ),
file('theBenchmark.p',fact_mod__geq) ).
fof(fact_mod__if,axiom,
! [V_n,V_m] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ),
file('theBenchmark.p',fact_mod__if) ).
fof(fact_mod__mult__self3,axiom,
! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),
file('theBenchmark.p',fact_mod__mult__self3) ).
fof(fact_le__mod__geq,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ),
file('theBenchmark.p',fact_le__mod__geq) ).
fof(fact_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_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_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_bin__less__0__simps_I2_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('theBenchmark.p',fact_bin__less__0__simps_I2_J) ).
fof(fact_rel__simps_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_I3_J,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
file('theBenchmark.p',fact_rel__simps_I3_J) ).
fof(fact_rel__simps_I6_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
file('theBenchmark.p',fact_rel__simps_I6_J) ).
fof(fact_rel__simps_I13_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ),
file('theBenchmark.p',fact_rel__simps_I13_J) ).
fof(fact_rel__simps_I9_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ),
file('theBenchmark.p',fact_rel__simps_I9_J) ).
fof(fact_rel__simps_I28_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ),
file('theBenchmark.p',fact_rel__simps_I28_J) ).
fof(fact_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_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_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_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_Int_OMin__def,axiom,
c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('theBenchmark.p',fact_Int_OMin__def) ).
fof(fact_mult__Min,axiom,
! [V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),
file('theBenchmark.p',fact_mult__Min) ).
fof(fact_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_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_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_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_pred__Pls,axiom,
c_Int_Opred(c_Int_OPls) = c_Int_OMin,
file('theBenchmark.p',fact_pred__Pls) ).
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_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_pred__Min,axiom,
c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
file('theBenchmark.p',fact_pred__Min) ).
fof(fact_nonzero__number__of__Min,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ),
file('theBenchmark.p',fact_nonzero__number__of__Min) ).
fof(fact_succ__Min,axiom,
c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
file('theBenchmark.p',fact_succ__Min) ).
fof(fact_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_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_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_one__div__nat__number__of,axiom,
! [V_v_H] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))),
file('theBenchmark.p',fact_one__div__nat__number__of) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J) ).
fof(fact_div__le__mono2,axiom,
! [V_k,V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_n)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_m))) ) ),
file('theBenchmark.p',fact_div__le__mono2) ).
fof(fact_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__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_div__less__dividend,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ) ),
file('theBenchmark.p',fact_div__less__dividend) ).
fof(fact_nat__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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_zmod__minus1__right,axiom,
! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_zmod__minus1__right) ).
fof(fact_diff__bin__simps_I4_J,axiom,
! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)),
file('theBenchmark.p',fact_diff__bin__simps_I4_J) ).
fof(fact_minus__Min,axiom,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls),
file('theBenchmark.p',fact_minus__Min) ).
fof(fact_zmult__eq__1__iff,axiom,
! [V_n_2,V_m_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( ( V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
& V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
| ( V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
file('theBenchmark.p',fact_zmult__eq__1__iff) ).
fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
! [V_n,V_m] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
=> ( V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_pos__zmult__eq__1__iff__lemma) ).
fof(fact_diff__bin__simps_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_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_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_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_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_card__atLeastZeroLessThan__int,axiom,
! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) = hAPP(c_Int_Onat,V_u_2),
file('theBenchmark.p',fact_card__atLeastZeroLessThan__int) ).
fof(fact_div__if,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('theBenchmark.p',fact_div__if) ).
fof(fact_div__geq,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ),
file('theBenchmark.p',fact_div__geq) ).
fof(fact_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_split__div,axiom,
! [V_k_2,V_n_2,V_P_2] :
( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
<=> ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ! [B_i,B_j] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
=> ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
=> hBOOL(hAPP(V_P_2,B_i)) ) ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('theBenchmark.p',fact_split__div) ).
fof(fact_zero__less__nat__eq,axiom,
! [V_z_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,V_z_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ),
file('theBenchmark.p',fact_zero__less__nat__eq) ).
fof(fact_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_P_2] :
( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [B_n] :
( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
=> hBOOL(hAPP(V_P_2,B_n)) ) ) ),
file('theBenchmark.p',fact_split__nat) ).
fof(fact_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_split__mod,axiom,
! [V_k_2,V_n_2,V_P_2] :
( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
<=> ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ! [B_i,B_j] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
=> ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
=> hBOOL(hAPP(V_P_2,B_j)) ) ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(V_P_2,V_n_2)) ) ) ),
file('theBenchmark.p',fact_split__mod) ).
fof(fact_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_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J) ).
fof(fact_nat__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_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_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_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_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__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_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_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_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_H,axiom,
! [V_n_2,V_m_2,V_P_2] :
( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
<=> ( ? [B_q] :
( hBOOL(hAPP(V_P_2,B_q))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,B_q))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2)) )
| ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('theBenchmark.p',fact_split__div_H) ).
fof(fact_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_Suc__div__eq__add3__div__number__of,axiom,
! [V_v,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),
file('theBenchmark.p',fact_Suc__div__eq__add3__div__number__of) ).
fof(fact_Suc__div__eq__add3__div,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),V_n),
file('theBenchmark.p',fact_Suc__div__eq__add3__div) ).
fof(fact_div__Suc__eq__div__add3,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)),
file('theBenchmark.p',fact_div__Suc__eq__div__add3) ).
fof(fact_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_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_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_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_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_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_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_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_card__atLeastAtMost__int,axiom,
! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('theBenchmark.p',fact_card__atLeastAtMost__int) ).
fof(fact_nat__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_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_div__pos__neg__trivial,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ),
file('theBenchmark.p',fact_div__pos__neg__trivial) ).
fof(fact_zmod__minus1,axiom,
! [V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
file('theBenchmark.p',fact_zmod__minus1) ).
fof(fact_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_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_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_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_Suc__n__div__2__gt__zero,axiom,
! [V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
file('theBenchmark.p',fact_Suc__n__div__2__gt__zero) ).
fof(fact_power__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_nat__aux__def,axiom,
! [V_n,V_i] : c_Int_Onat__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_i)),V_n),
file('theBenchmark.p',fact_nat__aux__def) ).
fof(fact_transfer__morphism__nat__int,axiom,
c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('theBenchmark.p',fact_transfer__morphism__nat__int) ).
fof(fact_periodic__finite__ex,axiom,
! [V_P_2,V_d_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
=> ( ! [B_x,B_k] :
( hBOOL(hAPP(V_P_2,B_x))
<=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2)))) )
=> ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
<=> ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_d_2))) ) ) ) ),
file('theBenchmark.p',fact_periodic__finite__ex) ).
fof(fact_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_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
! [V_B_2,V_A_2] :
( c_Nat__Transfer_Onat__set(V_A_2)
=> ( c_Nat__Transfer_Onat__set(V_B_2)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
! [V_B_2,V_A_2] :
( c_Nat__Transfer_Onat__set(V_A_2)
=> ( c_Nat__Transfer_Onat__set(V_B_2)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J) ).
fof(fact_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_transfer__int__nat__set__relations_I4_J,axiom,
! [V_B_2,V_A_2] :
( c_Nat__Transfer_Onat__set(V_A_2)
=> ( c_Nat__Transfer_Onat__set(V_B_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ),
file('theBenchmark.p',fact_transfer__int__nat__set__relations_I4_J) ).
fof(fact_transfer__int__nat__set__relations_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_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_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_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_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_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__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_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_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
=> c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ),
file('theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__function__closures) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
! [V_x_2,V_A_2] :
( c_Nat__Transfer_Onat__set(V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J) ).
fof(fact_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_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_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_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_transfer__int__nat__set__relations_I2_J,axiom,
! [V_A_2,V_x_2] :
( c_Nat__Transfer_Ois__nat(V_x_2)
=> ( c_Nat__Transfer_Onat__set(V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ),
file('theBenchmark.p',fact_transfer__int__nat__set__relations_I2_J) ).
fof(fact_setsum__bounded,axiom,
! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
( ( class_Rings_Osemiring__1(T_c)
& class_Groups_Oordered__ab__semigroup__add(T_c) )
=> ( ! [B_i] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_K_2))) ) ),
file('theBenchmark.p',fact_setsum__bounded) ).
fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
! [V_n_2,V_m_2] :
( c_Nat__Transfer_Ois__nat(V_m_2)
=> ( c_Nat__Transfer_Ois__nat(V_n_2)
=> c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,V_m_2),hAPP(c_Int_Onat,V_n_2))) ) ),
file('theBenchmark.p',fact_SetInterval_Otransfer__int__nat__set__functions) ).
fof(fact_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_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_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
! [V_y,V_x] :
( c_Nat__Transfer_Ois__nat(V_x)
=> ( c_Nat__Transfer_Ois__nat(V_y)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
! [V_y,V_x] :
( c_Nat__Transfer_Ois__nat(V_x)
=> ( c_Nat__Transfer_Ois__nat(V_y)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J) ).
fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
! [V_y,V_x] :
( c_Nat__Transfer_Ois__nat(V_x)
=> ( c_Nat__Transfer_Ois__nat(V_y)
=> c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ),
file('theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I2_J) ).
fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
! [V_y,V_x] :
( c_Nat__Transfer_Ois__nat(V_x)
=> ( c_Nat__Transfer_Ois__nat(V_y)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ),
file('theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I1_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
! [V_n,V_x] :
( c_Nat__Transfer_Ois__nat(V_x)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
! [V_y,V_x] :
( c_Nat__Transfer_Ois__nat(V_x)
=> ( c_Nat__Transfer_Ois__nat(V_y)
=> c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J) ).
fof(fact_of__int__eq__0__iff,axiom,
! [V_z_2,T_b] :
( class_Int_Oring__char__0(T_b)
=> ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_of__int__eq__0__iff) ).
fof(fact_of__int__0__eq__iff,axiom,
! [V_z_2,T_b] :
( class_Int_Oring__char__0(T_b)
=> ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
<=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_of__int__0__eq__iff) ).
fof(fact_of__int__0,axiom,
! [T_a] :
( class_Rings_Oring__1(T_a)
=> hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_of__int__0) ).
fof(fact_of__int__le__iff,axiom,
! [V_z_2,V_w_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ),
file('theBenchmark.p',fact_of__int__le__iff) ).
fof(fact_of__int__less__iff,axiom,
! [V_z_2,V_w_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ),
file('theBenchmark.p',fact_of__int__less__iff) ).
fof(fact_of__int__add,axiom,
! [V_z,V_w,T_a] :
( class_Rings_Oring__1(T_a)
=> hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ),
file('theBenchmark.p',fact_of__int__add) ).
fof(fact_of__int__number__of__eq,axiom,
! [V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ),
file('theBenchmark.p',fact_of__int__number__of__eq) ).
fof(fact_of__int__mult,axiom,
! [V_z,V_w,T_a] :
( class_Rings_Oring__1(T_a)
=> hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ),
file('theBenchmark.p',fact_of__int__mult) ).
fof(fact_of__int__1,axiom,
! [T_a] :
( class_Rings_Oring__1(T_a)
=> hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_of__int__1) ).
fof(fact_of__int__diff,axiom,
! [V_z,V_w,T_a] :
( class_Rings_Oring__1(T_a)
=> hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ),
file('theBenchmark.p',fact_of__int__diff) ).
fof(fact_of__int__of__nat__eq,axiom,
! [V_n,T_a] :
( class_Rings_Oring__1(T_a)
=> hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ),
file('theBenchmark.p',fact_of__int__of__nat__eq) ).
fof(fact_of__int__minus,axiom,
! [V_z,T_a] :
( class_Rings_Oring__1(T_a)
=> hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ),
file('theBenchmark.p',fact_of__int__minus) ).
fof(fact_Ints__of__int,axiom,
! [V_z_2,T_b] :
( class_Rings_Oring__1(T_b)
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Int_Oring__1__class_OInts(T_b))) ),
file('theBenchmark.p',fact_Ints__of__int) ).
fof(fact_of__int__power,axiom,
! [V_n,V_z,T_a] :
( class_Rings_Oring__1(T_a)
=> hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)),V_n) ),
file('theBenchmark.p',fact_of__int__power) ).
fof(fact_is__nat__def,axiom,
! [V_x_2] :
( c_Nat__Transfer_Ois__nat(V_x_2)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ),
file('theBenchmark.p',fact_is__nat__def) ).
fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
! [V_y_2,V_x_2] :
( c_Nat__Transfer_Ois__nat(V_x_2)
=> c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ),
file('theBenchmark.p',fact_SetInterval_Otransfer__int__nat__set__function__closures) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
! [V_x_2,V_A_2] :
( c_Nat__Transfer_Onat__set(V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
=> c_Nat__Transfer_Ois__nat(V_x_2) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J) ).
fof(fact_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_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_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_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_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_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_decr__mult__lemma,axiom,
! [V_k_2,V_P_2,V_d_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
=> ( ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
=> ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ),
file('theBenchmark.p',fact_decr__mult__lemma) ).
fof(fact_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_incr__mult__lemma,axiom,
! [V_k_2,V_P_2,V_d_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
=> ( ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
=> ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ),
file('theBenchmark.p',fact_incr__mult__lemma) ).
fof(fact_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__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_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_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_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_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_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_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_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_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_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_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_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__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_power__abs,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n) ),
file('theBenchmark.p',fact_power__abs) ).
fof(fact_abs__minus__cancel,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) ),
file('theBenchmark.p',fact_abs__minus__cancel) ).
fof(fact_abs__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__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__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__add__abs,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ),
file('theBenchmark.p',fact_abs__add__abs) ).
fof(fact_abs__eq__0,axiom,
! [V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add__abs(T_b)
=> ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_abs__eq__0) ).
fof(fact_abs__zero,axiom,
! [T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_abs__zero) ).
fof(fact_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__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_empty__fold__graphE,axiom,
! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2))
=> V_x_2 = V_z_2 ),
file('theBenchmark.p',fact_empty__fold__graphE) ).
fof(fact_fold__graph_OemptyI,axiom,
! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)),
file('theBenchmark.p',fact_fold__graph_OemptyI) ).
fof(fact_fold__graph_Oequations_I1_J,axiom,
! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)),
file('theBenchmark.p',fact_fold__graph_Oequations_I1_J) ).
fof(fact_fold__graph__imp__finite,axiom,
! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
file('theBenchmark.p',fact_fold__graph__imp__finite) ).
fof(fact_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_abs__ge__zero,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ),
file('theBenchmark.p',fact_abs__ge__zero) ).
fof(fact_abs__le__zero__iff,axiom,
! [V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add__abs(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_abs__le__zero__iff) ).
fof(fact_abs__of__nonneg,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ),
file('theBenchmark.p',fact_abs__of__nonneg) ).
fof(fact_abs__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_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__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_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_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_abs__power__minus,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
file('theBenchmark.p',fact_abs__power__minus) ).
fof(fact_abs__zmult__eq__1,axiom,
! [V_n,V_m] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('theBenchmark.p',fact_abs__zmult__eq__1) ).
fof(fact_abs__sgn,axiom,
! [V_k,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ),
file('theBenchmark.p',fact_abs__sgn) ).
fof(fact_mult__sgn__abs,axiom,
! [V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)) = V_x ),
file('theBenchmark.p',fact_mult__sgn__abs) ).
fof(fact_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_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_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_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__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__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__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_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_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_abs__minus__one,axiom,
! [T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_abs__minus__one) ).
fof(fact_zabs__less__one__iff,axiom,
! [V_z_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('theBenchmark.p',fact_zabs__less__one__iff) ).
fof(fact_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_zabs__def,axiom,
! [V_i] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) ),
file('theBenchmark.p',fact_zabs__def) ).
fof(fact_nat__abs__mult__distrib,axiom,
! [V_z,V_w] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_w))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z))),
file('theBenchmark.p',fact_nat__abs__mult__distrib) ).
fof(fact_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_fold__graph__insert__swap,axiom,
! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
( class_Groups_Oab__semigroup__mult(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_y_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2),V_y_2))) ) ) ),
file('theBenchmark.p',fact_fold__graph__insert__swap) ).
fof(fact_Sup__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_abs__number__of,axiom,
! [V_x,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a)))
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a)))
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) ) ) ),
file('theBenchmark.p',fact_abs__number__of) ).
fof(fact_abs__power__minus__one,axiom,
! [V_n,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_n)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_abs__power__minus__one) ).
fof(fact_zero__less__zpower__abs__iff,axiom,
! [V_n_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2)),V_n_2)))
<=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_zero__less__zpower__abs__iff) ).
fof(fact_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_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_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_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_Diff1__fold__graph,axiom,
! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_y_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ),
file('theBenchmark.p',fact_Diff1__fold__graph) ).
fof(fact_fold1__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_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_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_fold1Set_Ointros,axiom,
! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_x_2)) ) ),
file('theBenchmark.p',fact_fold1Set_Ointros) ).
fof(fact_fun__left__comm_Ofold__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_c_2,T_b] :
( class_Rings_Odivision__ring(T_b)
=> ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
<=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) ) ),
file('theBenchmark.p',fact_nonzero__divide__eq__eq) ).
fof(fact_nonzero__eq__divide__eq,axiom,
! [V_b_2,V_a_2,V_c_2,T_b] :
( class_Rings_Odivision__ring(T_b)
=> ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
=> ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) ) ),
file('theBenchmark.p',fact_nonzero__eq__divide__eq) ).
fof(fact_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_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_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_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_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__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_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_divide__eq__eq__number__of,axiom,
! [V_w_2,V_c_2,V_b_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Ofield__inverse__zero(T_b) )
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
<=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
=> hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) ) ) ) ),
file('theBenchmark.p',fact_divide__eq__eq__number__of) ).
fof(fact_eq__divide__eq__number__of,axiom,
! [V_c_2,V_b_2,V_w_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Ofield__inverse__zero(T_b) )
=> ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
<=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
=> hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) = V_b_2 ) ) ) ),
file('theBenchmark.p',fact_eq__divide__eq__number__of) ).
fof(fact_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_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_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_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__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_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_c_2,V_b_2,V_w_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Olinordered__field__inverse__zero(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) ) ) ) ),
file('theBenchmark.p',fact_less__divide__eq__number__of) ).
fof(fact_divide__less__eq__number__of,axiom,
! [V_w_2,V_c_2,V_b_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Olinordered__field__inverse__zero(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) ) ) ) ),
file('theBenchmark.p',fact_divide__less__eq__number__of) ).
fof(fact_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_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_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_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_c_2,V_b_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Olinordered__field__inverse__zero(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) ) ) ) ),
file('theBenchmark.p',fact_divide__le__eq__number__of) ).
fof(fact_le__divide__eq__number__of,axiom,
! [V_c_2,V_b_2,V_w_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Olinordered__field__inverse__zero(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) ) ) ) ),
file('theBenchmark.p',fact_le__divide__eq__number__of) ).
fof(fact_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_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_le__divide__eq,axiom,
! [V_c_2,V_b_2,V_a_2,T_b] :
( class_Fields_Olinordered__field__inverse__zero(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ),
file('theBenchmark.p',fact_le__divide__eq) ).
fof(fact_divide__le__eq,axiom,
! [V_a_2,V_c_2,V_b_2,T_b] :
( class_Fields_Olinordered__field__inverse__zero(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ),
file('theBenchmark.p',fact_divide__le__eq) ).
fof(fact_pos__le__divide__eq,axiom,
! [V_b_2,V_a_2,V_c_2,T_b] :
( class_Fields_Olinordered__field(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ),
file('theBenchmark.p',fact_pos__le__divide__eq) ).
fof(fact_pos__divide__le__eq,axiom,
! [V_a_2,V_b_2,V_c_2,T_b] :
( class_Fields_Olinordered__field(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ),
file('theBenchmark.p',fact_pos__divide__le__eq) ).
fof(fact_times__divide__times__eq,axiom,
! [V_w,V_z,V_y,V_x,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_z),V_w)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_w)) ),
file('theBenchmark.p',fact_times__divide__times__eq) ).
fof(fact_minus__divide__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_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_zero__le__divide__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Fields_Olinordered__field__inverse__zero(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_zero__le__divide__iff) ).
fof(fact_divide__le__0__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Fields_Olinordered__field__inverse__zero(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_divide__le__0__iff) ).
fof(fact_divide__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ),
file('theBenchmark.p',fact_divide__right__mono) ).
fof(fact_divide__right__mono__neg,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c))) ) ) ),
file('theBenchmark.p',fact_divide__right__mono__neg) ).
fof(fact_divide__strict__right__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ),
file('theBenchmark.p',fact_divide__strict__right__mono__neg) ).
fof(fact_divide__strict__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ),
file('theBenchmark.p',fact_divide__strict__right__mono) ).
fof(fact_divide__neg__neg,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ),
file('theBenchmark.p',fact_divide__neg__neg) ).
fof(fact_divide__neg__pos,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('theBenchmark.p',fact_divide__neg__pos) ).
fof(fact_divide__pos__neg,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('theBenchmark.p',fact_divide__pos__neg) ).
fof(fact_divide__pos__pos,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ),
file('theBenchmark.p',fact_divide__pos__pos) ).
fof(fact_divide__less__0__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Fields_Olinordered__field__inverse__zero(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_divide__less__0__iff) ).
fof(fact_zero__less__divide__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Fields_Olinordered__field__inverse__zero(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_zero__less__divide__iff) ).
fof(fact_eq__divide__eq,axiom,
! [V_c_2,V_b_2,V_a_2,T_b] :
( class_Fields_Ofield__inverse__zero(T_b)
=> ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
<=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) ) ) ),
file('theBenchmark.p',fact_eq__divide__eq) ).
fof(fact_divide__eq__eq,axiom,
! [V_a_2,V_c_2,V_b_2,T_b] :
( class_Fields_Ofield__inverse__zero(T_b)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
<=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) ) ) ),
file('theBenchmark.p',fact_divide__eq__eq) ).
fof(fact_mult__divide__mult__cancel__right,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ),
file('theBenchmark.p',fact_mult__divide__mult__cancel__right) ).
fof(fact_mult__divide__mult__cancel__left,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ),
file('theBenchmark.p',fact_mult__divide__mult__cancel__left) ).
fof(fact_frac__eq__eq,axiom,
! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
( class_Fields_Ofield(T_b)
=> ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
=> ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_w_2),V_z_2)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2) ) ) ) ),
file('theBenchmark.p',fact_frac__eq__eq) ).
fof(fact_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_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_c_2,T_b] :
( class_Fields_Olinordered__field(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ),
file('theBenchmark.p',fact_neg__divide__less__eq) ).
fof(fact_neg__less__divide__eq,axiom,
! [V_b_2,V_a_2,V_c_2,T_b] :
( class_Fields_Olinordered__field(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ),
file('theBenchmark.p',fact_neg__less__divide__eq) ).
fof(fact_mult__imp__less__div__pos,axiom,
! [V_x,V_z,V_y,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ),
file('theBenchmark.p',fact_mult__imp__less__div__pos) ).
fof(fact_mult__imp__div__pos__less,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)) ) ) ),
file('theBenchmark.p',fact_mult__imp__div__pos__less) ).
fof(fact_pos__divide__less__eq,axiom,
! [V_a_2,V_b_2,V_c_2,T_b] :
( class_Fields_Olinordered__field(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ),
file('theBenchmark.p',fact_pos__divide__less__eq) ).
fof(fact_pos__less__divide__eq,axiom,
! [V_b_2,V_a_2,V_c_2,T_b] :
( class_Fields_Olinordered__field(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ),
file('theBenchmark.p',fact_pos__less__divide__eq) ).
fof(fact_divide__less__eq,axiom,
! [V_a_2,V_c_2,V_b_2,T_b] :
( class_Fields_Olinordered__field__inverse__zero(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ),
file('theBenchmark.p',fact_divide__less__eq) ).
fof(fact_less__divide__eq,axiom,
! [V_c_2,V_b_2,V_a_2,T_b] :
( class_Fields_Olinordered__field__inverse__zero(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ),
file('theBenchmark.p',fact_less__divide__eq) ).
fof(fact_add__num__frac,axiom,
! [V_x,V_z,V_y,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( V_y != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ),
file('theBenchmark.p',fact_add__num__frac) ).
fof(fact_add__divide__eq__iff,axiom,
! [V_y,V_x,V_z,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_z != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ),
file('theBenchmark.p',fact_add__divide__eq__iff) ).
fof(fact_add__frac__num,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( V_y != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ),
file('theBenchmark.p',fact_add__frac__num) ).
fof(fact_divide__add__eq__iff,axiom,
! [V_y,V_x,V_z,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_z != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ),
file('theBenchmark.p',fact_divide__add__eq__iff) ).
fof(fact_add__frac__eq,axiom,
! [V_w,V_x,V_z,V_y,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_y != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_z != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ),
file('theBenchmark.p',fact_add__frac__eq) ).
fof(fact_diff__divide__eq__iff,axiom,
! [V_y,V_x,V_z,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_z != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ),
file('theBenchmark.p',fact_diff__divide__eq__iff) ).
fof(fact_divide__diff__eq__iff,axiom,
! [V_y,V_x,V_z,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_z != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ),
file('theBenchmark.p',fact_divide__diff__eq__iff) ).
fof(fact_diff__frac__eq,axiom,
! [V_w,V_x,V_z,V_y,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_y != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_z != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ),
file('theBenchmark.p',fact_diff__frac__eq) ).
fof(fact_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_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_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_divide__left__mono__neg,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ),
file('theBenchmark.p',fact_divide__left__mono__neg) ).
fof(fact_divide__left__mono,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ),
file('theBenchmark.p',fact_divide__left__mono) ).
fof(fact_neg__divide__le__eq,axiom,
! [V_a_2,V_b_2,V_c_2,T_b] :
( class_Fields_Olinordered__field(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ),
file('theBenchmark.p',fact_neg__divide__le__eq) ).
fof(fact_neg__le__divide__eq,axiom,
! [V_b_2,V_a_2,V_c_2,T_b] :
( class_Fields_Olinordered__field(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ),
file('theBenchmark.p',fact_neg__le__divide__eq) ).
fof(fact_mult__imp__le__div__pos,axiom,
! [V_x,V_z,V_y,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ),
file('theBenchmark.p',fact_mult__imp__le__div__pos) ).
fof(fact_mult__imp__div__pos__le,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)) ) ) ),
file('theBenchmark.p',fact_mult__imp__div__pos__le) ).
fof(fact_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_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_nat0__intermed__int__val,axiom,
! [V_k_2,V_f_2,V_n_2] :
( ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
=> ? [B_i] :
( hAPP(V_f_2,B_i) = V_k_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) ) ) ) ),
file('theBenchmark.p',fact_nat0__intermed__int__val) ).
fof(fact_int__val__lemma,axiom,
! [V_k_2,V_f_2,V_n_2] :
( ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
=> ? [B_i] :
( hAPP(V_f_2,B_i) = V_k_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) ) ) ) ),
file('theBenchmark.p',fact_int__val__lemma) ).
fof(fact_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_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_setprod_Oinfinite,axiom,
! [V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ),
file('theBenchmark.p',fact_setprod_Oinfinite) ).
fof(fact_setprod__infinite,axiom,
! [V_f_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ),
file('theBenchmark.p',fact_setprod__infinite) ).
fof(fact_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_setprod__pos__nat__iff,axiom,
! [V_f_2,V_S_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) ) ),
file('theBenchmark.p',fact_setprod__pos__nat__iff) ).
fof(fact_setprod__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_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_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_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_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_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_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_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_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__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_setprod__pos__nat,axiom,
! [V_f_2,V_S_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2))) ) ),
file('theBenchmark.p',fact_setprod__pos__nat) ).
fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_v_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ~ ! [B_y] :
( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
=> ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE) ).
fof(fact_fun__left__comm__idem_Ofold__insert__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_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_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_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_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_mod__induct__0,axiom,
! [V_i_2,V_P_2,V_p_2] :
( ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
=> ( hBOOL(hAPP(V_P_2,B_i))
=> hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
=> ( hBOOL(hAPP(V_P_2,V_i_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
=> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('theBenchmark.p',fact_mod__induct__0) ).
fof(fact_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_c_2,V_b_2,V_A_2,T_b] :
( class_Lattices_Osemilattice__inf(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_c_2),V_A_2))) ) ) ),
file('theBenchmark.p',fact_inf__le__fold__inf) ).
fof(fact_fold__sup__le__sup,axiom,
! [V_c_2,V_b_2,V_A_2,T_b] :
( class_Lattices_Osemilattice__sup(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_c_2))) ) ) ),
file('theBenchmark.p',fact_fold__sup__le__sup) ).
fof(fact_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_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_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_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_setprod__pos,axiom,
! [V_f_2,V_A_2,T_b,T_c] :
( class_Rings_Olinordered__semidom(T_c)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ),
file('theBenchmark.p',fact_setprod__pos) ).
fof(fact_setprod__nonneg,axiom,
! [V_f_2,V_A_2,T_b,T_c] :
( class_Rings_Olinordered__semidom(T_c)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ),
file('theBenchmark.p',fact_setprod__nonneg) ).
fof(fact_finite__induct,axiom,
! [V_P_2,V_F_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
=> ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
=> ( ! [B_x,B_F] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F))
=> ( hBOOL(hAPP(V_P_2,B_F))
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F))) ) ) )
=> hBOOL(hAPP(V_P_2,V_F_2)) ) ) ),
file('theBenchmark.p',fact_finite__induct) ).
fof(fact_fold__graph_H_Ointros_I2_J,axiom,
! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_y_2)
=> c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_fold__graph_H_Ointros_I2_J) ).
fof(fact_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_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_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__of__mono,axiom,
! [V_n_2,V_m_2,V_f_2,T_b,T_c] :
( ( class_Orderings_Olinorder(T_b)
& class_Orderings_Olinorder(T_c) )
=> ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,V_n_2)) = hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_min__of__mono) ).
fof(fact_min__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__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__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_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__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_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__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__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__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_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__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_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_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_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_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__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__le__iff__disj,axiom,
! [V_z_2,V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ),
file('theBenchmark.p',fact_min__le__iff__disj) ).
fof(fact_min__max_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__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__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__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__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__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__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_Omono__inf,axiom,
! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
( ( class_Orderings_Olinorder(T_b)
& class_Lattices_Osemilattice__inf(T_c) )
=> ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2)))) ) ),
file('theBenchmark.p',fact_min__max_Omono__inf) ).
fof(fact_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_c_2,V_b_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
file('theBenchmark.p',fact_Int__atLeastAtMostR1) ).
fof(fact_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_min__ord__min,axiom,
! [T_b] :
( class_Orderings_Oord(T_b)
=> c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ),
file('theBenchmark.p',fact_min__ord__min) ).
fof(fact_Min_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_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_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_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_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_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_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_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_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_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__disjoint,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Ounion__disjoint) ).
fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Ounion__inter) ).
fof(fact_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__disjoint,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ) ),
file('theBenchmark.p',fact_Min_Ounion__disjoint) ).
fof(fact_Min_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_Min_Ounion__inter) ).
fof(fact_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_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_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_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_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_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_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_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_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_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__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_nat__gcd_Osimps,axiom,
! [V_x,V_y] :
( ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Nitpick_Onat__gcd(V_x,V_y) = c_Nitpick_Onat__gcd(V_y,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y)) )
& ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Nitpick_Onat__gcd(V_x,V_y) = V_x ) ),
file('theBenchmark.p',fact_nat__gcd_Osimps) ).
fof(fact_Nitpick_Oint__gcd__def,axiom,
! [V_y,V_x] : hAPP(hAPP(c_Nitpick_Oint__gcd,V_x),V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))),
file('theBenchmark.p',fact_Nitpick_Oint__gcd__def) ).
fof(fact_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__fold__inf,axiom,
! [V_c_2,V_b_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_c_2),V_A_2))) ) ) ),
file('theBenchmark.p',fact_min__max_Oinf__le__fold__inf) ).
fof(fact_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_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_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__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__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__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__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_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_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_max__of__mono,axiom,
! [V_n_2,V_m_2,V_f_2,T_b,T_c] :
( ( class_Orderings_Olinorder(T_b)
& class_Orderings_Olinorder(T_c) )
=> ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,V_n_2)) = hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_max__of__mono) ).
fof(fact_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_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_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_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_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_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_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_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__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_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__inf__le,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)))) ),
file('theBenchmark.p',fact_min__max_Odistrib__inf__le) ).
fof(fact_min__max_Odistrib__sup__le,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)))) ),
file('theBenchmark.p',fact_min__max_Odistrib__sup__le) ).
fof(fact_minus__max__eq__min,axiom,
! [V_y,V_x,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ),
file('theBenchmark.p',fact_minus__max__eq__min) ).
fof(fact_minus__min__eq__max,axiom,
! [V_y,V_x,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ),
file('theBenchmark.p',fact_minus__min__eq__max) ).
fof(fact_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_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_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_Omono__sup,axiom,
! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
( ( class_Orderings_Olinorder(T_b)
& class_Lattices_Osemilattice__sup(T_c) )
=> ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_A_2),V_B_2)))) ) ),
file('theBenchmark.p',fact_min__max_Omono__sup) ).
fof(fact_Int__atLeastAtMost,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
file('theBenchmark.p',fact_Int__atLeastAtMost) ).
fof(fact_Int__atLeastLessThan,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
file('theBenchmark.p',fact_Int__atLeastLessThan) ).
fof(fact_Int__greaterThanAtMost,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
file('theBenchmark.p',fact_Int__greaterThanAtMost) ).
fof(fact_Int__greaterThanLessThan,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
file('theBenchmark.p',fact_Int__greaterThanLessThan) ).
fof(fact_Int__atLeastAtMostL2,axiom,
! [V_c_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_b_2) ),
file('theBenchmark.p',fact_Int__atLeastAtMostL2) ).
fof(fact_Int__atLeastAtMostR2,axiom,
! [V_d_2,V_c_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_d_2) ),
file('theBenchmark.p',fact_Int__atLeastAtMostR2) ).
fof(fact_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__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_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_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__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_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__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_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_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_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_Max_Oclosed,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Max_Oclosed) ).
fof(fact_min__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_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_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_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_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_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_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_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_min__max_OSup__fin_Oclosed,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Oclosed) ).
fof(fact_min__max_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_Max_Ohom__commute,axiom,
! [V_N_2,V_h_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
file('theBenchmark.p',fact_Max_Ohom__commute) ).
fof(fact_min__max_Ofold__sup__le__sup,axiom,
! [V_c_2,V_b_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_c_2))) ) ) ),
file('theBenchmark.p',fact_min__max_Ofold__sup__le__sup) ).
fof(fact_Min__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_field__le__epsilon,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( ! [B_e] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),B_e))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ),
file('theBenchmark.p',fact_field__le__epsilon) ).
fof(fact_minus__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_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_pair__box_Osize_I1_J,axiom,
! [V_b_2,V_a_2,V_fb_2,V_fa_2,T_c,T_b] : c_Nitpick_Opair__box_Opair__box__size(T_b,T_c,V_fa_2,V_fb_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(V_fb_2,V_b_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_pair__box_Osize_I1_J) ).
fof(fact_arith__series__int,axiom,
! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))),
file('theBenchmark.p',fact_arith__series__int) ).
fof(fact_negDivAlg__eqn__1__number__of,axiom,
! [V_w] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))
=> c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))
=> c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ) ),
file('theBenchmark.p',fact_negDivAlg__eqn__1__number__of) ).
fof(fact_fold__image__reindex,axiom,
! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
( class_Groups_Oab__semigroup__mult(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),V_z_2),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_h_2)),V_z_2),V_A_2) ) ) ),
file('theBenchmark.p',fact_fold__image__reindex) ).
fof(fact_INF1__D,axiom,
! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_INF1__D) ).
fof(fact_INF1__E,axiom,
! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
=> ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_INF1__E) ).
fof(fact_INF2__D,axiom,
! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ),
file('theBenchmark.p',fact_INF2__D) ).
fof(fact_INF2__E,axiom,
! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
=> ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_INF2__E) ).
fof(fact_INT__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_SUP2__I,axiom,
! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ),
file('theBenchmark.p',fact_SUP2__I) ).
fof(fact_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_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_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_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_Union__image__eq,axiom,
! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
file('theBenchmark.p',fact_Union__image__eq) ).
fof(fact_UNION__eq__Union__image,axiom,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)),
file('theBenchmark.p',fact_UNION__eq__Union__image) ).
fof(fact_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_min__Suc1,axiom,
! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),V_m_2),
file('theBenchmark.p',fact_min__Suc1) ).
fof(fact_min__Suc2,axiom,
! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),V_n_2)),V_m_2),
file('theBenchmark.p',fact_min__Suc2) ).
fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
! [V_n_2,V_m_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_setsum__shift__bounds__Suc__ivl) ).
fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)),
file('theBenchmark.p',fact_transfer__nat__int__sum__prod2_I1_J) ).
fof(fact_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_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_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_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_transfer__nat__int__sum__prod_I2_J,axiom,
! [V_A_2,V_f_2,T_b] :
( ( class_Groups_Ocomm__monoid__mult(T_b)
& class_Groups_Ocomm__monoid__add(T_b) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ),
file('theBenchmark.p',fact_transfer__nat__int__sum__prod_I2_J) ).
fof(fact_setsum__shift__bounds__cl__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_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_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_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_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_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_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_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_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_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_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_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_image__constant__conv,axiom,
! [V_c_2,T_c,T_b,V_A_2] :
( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_image__constant__conv) ).
fof(fact_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_SUP__UN__eq,axiom,
! [V_x_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ),
file('theBenchmark.p',fact_SUP__UN__eq) ).
fof(fact_finite__range__imageI,axiom,
! [V_f_2,T_d,V_g_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Oimage(T_c,T_d,hAPP(hAPP(c_COMBB(T_b,T_d,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ),
file('theBenchmark.p',fact_finite__range__imageI) ).
fof(fact_UN__simps_I1_J,axiom,
! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_UN__simps_I1_J) ).
fof(fact_UN__singleton,axiom,
! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2,
file('theBenchmark.p',fact_UN__singleton) ).
fof(fact_UN__extend__simps_I1_J,axiom,
! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ),
file('theBenchmark.p',fact_UN__extend__simps_I1_J) ).
fof(fact_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_INF__INT__eq2,axiom,
! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ),
file('theBenchmark.p',fact_INF__INT__eq2) ).
fof(fact_SUP__UN__eq2,axiom,
! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ),
file('theBenchmark.p',fact_SUP__UN__eq2) ).
fof(fact_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_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_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_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_UN__simps_I6_J,axiom,
! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
file('theBenchmark.p',fact_UN__simps_I6_J) ).
fof(fact_UN__extend__simps_I7_J,axiom,
! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)),
file('theBenchmark.p',fact_UN__extend__simps_I7_J) ).
fof(fact_UN__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_INTER__UNIV__conv_I2_J,axiom,
! [V_B_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_INTER__UNIV__conv_I2_J) ).
fof(fact_INTER__UNIV__conv_I1_J,axiom,
! [V_B_2,V_A_2,T_c,T_b] :
( c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_INTER__UNIV__conv_I1_J) ).
fof(fact_INT__constant,axiom,
! [V_c_2,T_c,T_b,V_A_2] :
( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2 )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_INT__constant) ).
fof(fact_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_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_Compl__INT,axiom,
! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
file('theBenchmark.p',fact_Compl__INT) ).
fof(fact_Compl__UN,axiom,
! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
file('theBenchmark.p',fact_Compl__UN) ).
fof(fact_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_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_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_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_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_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_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_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2)
=> hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ),
file('theBenchmark.p',fact_o__eq__dest) ).
fof(fact_o__eq__elim,axiom,
! [V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2)
=> ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ),
file('theBenchmark.p',fact_o__eq__elim) ).
fof(fact_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_I8_J,axiom,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
file('theBenchmark.p',fact_INT__simps_I8_J) ).
fof(fact_INT__extend__simps_I8_J,axiom,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2),
file('theBenchmark.p',fact_INT__extend__simps_I8_J) ).
fof(fact_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__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_K__record__comp,axiom,
! [V_x_2,V_f_2,V_c_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_f_2),V_x_2) = V_c_2,
file('theBenchmark.p',fact_K__record__comp) ).
fof(fact_o__eq__dest__lhs,axiom,
! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_c_2
=> hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ),
file('theBenchmark.p',fact_o__eq__dest__lhs) ).
fof(fact_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_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_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_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_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_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_SUP__commute,axiom,
! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))) ),
file('theBenchmark.p',fact_SUP__commute) ).
fof(fact_INT__extend__simps_I5_J,axiom,
! [V_B_2,V_C_2,T_c,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)),
file('theBenchmark.p',fact_INT__extend__simps_I5_J) ).
fof(fact_INT__simps_I5_J,axiom,
! [V_B_2,V_a_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
file('theBenchmark.p',fact_INT__simps_I5_J) ).
fof(fact_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_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_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_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_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_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_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_UN__constant,axiom,
! [V_c_2,T_c,T_b,V_A_2] :
( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2 )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_UN__constant) ).
fof(fact_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_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_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_inj__on__id2,axiom,
! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2),
file('theBenchmark.p',fact_inj__on__id2) ).
fof(fact_INT__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__iff,axiom,
! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ),
file('theBenchmark.p',fact_INT__iff) ).
fof(fact_pred__equals__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_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__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_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_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_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_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_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_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_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_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_UN__atMost__UNIV,axiom,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
file('theBenchmark.p',fact_UN__atMost__UNIV) ).
fof(fact_fun__left__comm_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_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_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__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_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_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_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_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_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_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_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_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_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_setsum__addf,axiom,
! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ),
file('theBenchmark.p',fact_setsum__addf) ).
fof(fact_less__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_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_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_less__eq__Suc__le__raw,axiom,
! [V_n_2] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),
file('theBenchmark.p',fact_less__eq__Suc__le__raw) ).
fof(fact_UN__upper,axiom,
! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_UN__upper) ).
fof(fact_setsum_Odistrib,axiom,
! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Oplus__class_Oplus(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),V_A_2)) ) ),
file('theBenchmark.p',fact_setsum_Odistrib) ).
fof(fact_INF__leI,axiom,
! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2))) ) ),
file('theBenchmark.p',fact_INF__leI) ).
fof(fact_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_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_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_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__Int__distrib,axiom,
! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)),
file('theBenchmark.p',fact_INT__Int__distrib) ).
fof(fact_UN__simps_I5_J,axiom,
! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
file('theBenchmark.p',fact_UN__simps_I5_J) ).
fof(fact_UN__simps_I4_J,axiom,
! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
file('theBenchmark.p',fact_UN__simps_I4_J) ).
fof(fact_UN__extend__simps_I5_J,axiom,
! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)),
file('theBenchmark.p',fact_UN__extend__simps_I5_J) ).
fof(fact_Int__UN__distrib,axiom,
! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)),
file('theBenchmark.p',fact_Int__UN__distrib) ).
fof(fact_UN__extend__simps_I4_J,axiom,
! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)),
file('theBenchmark.p',fact_UN__extend__simps_I4_J) ).
fof(fact_Int__UN__distrib2,axiom,
! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))),
file('theBenchmark.p',fact_Int__UN__distrib2) ).
fof(fact_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_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_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_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__Int__eq,axiom,
! [V_x_2,V_S_2,V_R_2,T_b] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) ),
file('theBenchmark.p',fact_inf__Int__eq) ).
fof(fact_INT__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_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_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__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_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_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_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__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_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_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_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_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__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__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__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__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__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_of__nat__setprod,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( ( class_Rings_Osemiring__1(T_b)
& class_Groups_Ocomm__monoid__mult(T_b) )
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ),
file('theBenchmark.p',fact_of__nat__setprod) ).
fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)),
file('theBenchmark.p',fact_transfer__nat__int__sum__prod2_I2_J) ).
fof(fact_image__add__atLeastLessThan,axiom,
! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)),
file('theBenchmark.p',fact_image__add__atLeastLessThan) ).
fof(fact_image__add__atLeastAtMost,axiom,
! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)),
file('theBenchmark.p',fact_image__add__atLeastAtMost) ).
fof(fact_setsum__delta_H,axiom,
! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) ) ) ),
file('theBenchmark.p',fact_setsum__delta_H) ).
fof(fact_setsum__delta,axiom,
! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) ) ) ),
file('theBenchmark.p',fact_setsum__delta) ).
fof(fact_image__constant,axiom,
! [V_c_2,T_c,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_image__constant) ).
fof(fact_INT__greaterThan__UNIV,axiom,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
file('theBenchmark.p',fact_INT__greaterThan__UNIV) ).
fof(fact_setprod__delta_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_image__eq__UN,axiom,
! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Set_Oinsert(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
file('theBenchmark.p',fact_image__eq__UN) ).
fof(fact_INT__simps_I4_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_INT__simps_I4_J) ).
fof(fact_vimage__const,axiom,
! [T_c,V_A_2,V_c_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_vimage__const) ).
fof(fact_setsum__constant,axiom,
! [V_A_2,V_y_2,T_c,T_b] :
( class_Rings_Osemiring__1(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_y_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))),V_y_2) ),
file('theBenchmark.p',fact_setsum__constant) ).
fof(fact_power__number__of__even,axiom,
! [V_w_2,V_z_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ),
file('theBenchmark.p',fact_power__number__of__even) ).
fof(fact_fold__image__distrib,axiom,
! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)) ) ),
file('theBenchmark.p',fact_fold__image__distrib) ).
fof(fact_dual__max,axiom,
! [T_b] :
( class_Orderings_Olinorder(T_b)
=> c_Orderings_Oord_Omax(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omin(T_b) ),
file('theBenchmark.p',fact_dual__max) ).
fof(fact_dual__min,axiom,
! [T_b] :
( class_Orderings_Olinorder(T_b)
=> c_Orderings_Oord_Omin(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omax(T_b) ),
file('theBenchmark.p',fact_dual__min) ).
fof(fact_setprod__constant,axiom,
! [V_y_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_COMBK(T_c,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_y_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ),
file('theBenchmark.p',fact_setprod__constant) ).
fof(fact_sup__SUPR__fold__sup,axiom,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),V_B_2),V_A_2) ) ),
file('theBenchmark.p',fact_sup__SUPR__fold__sup) ).
fof(fact_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_inf__INFI__fold__inf,axiom,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),V_B_2),V_A_2) ) ),
file('theBenchmark.p',fact_inf__INFI__fold__inf) ).
fof(fact_zpower__number__of__even,axiom,
! [V_w_2,V_z_2] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))),
file('theBenchmark.p',fact_zpower__number__of__even) ).
fof(fact_comp__surj,axiom,
! [V_g_2,T_d,V_f_2,T_b,T_c] :
( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
=> ( hAPP(c_Set_Oimage(T_b,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(T_c,T_d,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_comp__surj) ).
fof(fact_setsum__lessThan__Suc,axiom,
! [V_n_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,V_n_2)) ),
file('theBenchmark.p',fact_setsum__lessThan__Suc) ).
fof(fact_UN__o,axiom,
! [V_f_2,V_g_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_d,tc_fun(T_b,tc_HOL_Obool),T_c,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_g_2),
file('theBenchmark.p',fact_UN__o) ).
fof(fact_inj__comp,axiom,
! [V_g_2,T_d,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
=> c_Fun_Oinj__on(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) ) ),
file('theBenchmark.p',fact_inj__comp) ).
fof(fact_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__atMost__Suc,axiom,
! [V_n_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) ),
file('theBenchmark.p',fact_setsum__atMost__Suc) ).
fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
! [V_A_2,V_f_2,T_b] :
( ( class_Groups_Ocomm__monoid__mult(T_b)
& class_Groups_Ocomm__monoid__add(T_b) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ),
file('theBenchmark.p',fact_transfer__nat__int__sum__prod_I1_J) ).
fof(fact_Un__Union__image,axiom,
! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))),
file('theBenchmark.p',fact_Un__Union__image) ).
fof(fact_image__add__int__atLeastLessThan,axiom,
! [V_u_2,V_l_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2),
file('theBenchmark.p',fact_image__add__int__atLeastLessThan) ).
fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
! [V_f_2,V_A_2,T_b] :
( ( class_Groups_Ocomm__monoid__mult(T_b)
& class_Groups_Ocomm__monoid__add(T_b) )
=> ( c_Nat__Transfer_Onat__set(V_A_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ),
file('theBenchmark.p',fact_transfer__int__nat__sum__prod_I2_J) ).
fof(fact_Powp__Pow__eq,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Predicate_OPowp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ),
file('theBenchmark.p',fact_Powp__Pow__eq) ).
fof(fact_setsum__restrict__set,axiom,
! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ),
file('theBenchmark.p',fact_setsum__restrict__set) ).
fof(fact_image__eq__fold__image,axiom,
! [V_f_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_c,tc_HOL_Obool),T_b,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Set_Oinsert(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_A_2) ),
file('theBenchmark.p',fact_image__eq__fold__image) ).
fof(fact_power__number__of__even__number__of,axiom,
! [V_w_2,V_v_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ),
file('theBenchmark.p',fact_power__number__of__even__number__of) ).
fof(fact_SUPR__fold__sup,axiom,
! [V_f_2,V_A_2,T_b,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(T_c)),V_A_2) ) ),
file('theBenchmark.p',fact_SUPR__fold__sup) ).
fof(fact_card__def,axiom,
! [V_A_2,T_b] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) ),
file('theBenchmark.p',fact_card__def) ).
fof(fact_card_Oeq__fold__g,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ),
file('theBenchmark.p',fact_card_Oeq__fold__g) ).
fof(fact_fun__left__comm__idem__remove,axiom,
! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),
file('theBenchmark.p',fact_fun__left__comm__idem__remove) ).
fof(fact_INFI__fold__inf,axiom,
! [V_f_2,V_A_2,T_b,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),c_Orderings_Otop__class_Otop(T_c)),V_A_2) ) ),
file('theBenchmark.p',fact_INFI__fold__inf) ).
fof(fact_vimage__if,axiom,
! [V_B_2,T_c,V_d_2,V_A_2,V_c_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
=> hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
=> hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2) ) ) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
=> hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = V_B_2 )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
=> hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ) ) ),
file('theBenchmark.p',fact_vimage__if) ).
fof(fact_diff__nat__eq__if,axiom,
! [V_z_2,V_z_H_2] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),V_z_H_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(c_Int_Onat,V_z_2) ) ),
file('theBenchmark.p',fact_diff__nat__eq__if) ).
fof(fact_negDivAlg__div__mod,axiom,
! [V_l,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
=> c_Divides_OnegDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ),
file('theBenchmark.p',fact_negDivAlg__div__mod) ).
fof(fact_negDivAlg__minus1,axiom,
! [V_b] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('theBenchmark.p',fact_negDivAlg__minus1) ).
fof(fact_UN__le__eq__Un0,axiom,
! [V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2)),V_M_2)),hAPP(V_M_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_UN__le__eq__Un0) ).
fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
! [V_f_2,V_A_2,T_b] :
( ( class_Groups_Ocomm__monoid__mult(T_b)
& class_Groups_Ocomm__monoid__add(T_b) )
=> ( c_Nat__Transfer_Onat__set(V_A_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ),
file('theBenchmark.p',fact_transfer__int__nat__sum__prod_I1_J) ).
fof(fact_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_adjust__eq,axiom,
! [V_r_2,V_q_2,V_b_2] : hAPP(c_Divides_Oadjust(V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_r_2),V_b_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),V_r_2))),
file('theBenchmark.p',fact_adjust__eq) ).
fof(fact_setsum__head,axiom,
! [V_P_2,V_n_2,V_m_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_P_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_P_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_P_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ),
file('theBenchmark.p',fact_setsum__head) ).
fof(fact_minus__fold__remove,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2),V_A_2) ),
file('theBenchmark.p',fact_minus__fold__remove) ).
fof(fact_setsum__reindex,axiom,
! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2) ) ),
file('theBenchmark.p',fact_setsum__reindex) ).
fof(fact_eq__number__of__Suc,axiom,
! [V_n_2,V_v_2] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
<=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ),
file('theBenchmark.p',fact_eq__number__of__Suc) ).
fof(fact_Suc__eq__number__of,axiom,
! [V_v_2,V_n_2] :
( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
<=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ),
file('theBenchmark.p',fact_Suc__eq__number__of) ).
fof(fact_setprod__reindex,axiom,
! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2) ) ),
file('theBenchmark.p',fact_setprod__reindex) ).
fof(fact_setprod__reindex__cong,axiom,
! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
=> ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ),
file('theBenchmark.p',fact_setprod__reindex__cong) ).
fof(fact_nat__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_nat__number__of__Bit1,axiom,
! [V_w_2] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__number__of__Bit1) ).
fof(fact_geometric__sum,axiom,
! [V_n_2,V_x_2,T_b] :
( class_Fields_Ofield(T_b)
=> ( V_x_2 != c_Groups_Oone__class_Oone(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_Power_Opower__class_Opower(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_x_2),c_Groups_Oone__class_Oone(T_b))) ) ),
file('theBenchmark.p',fact_geometric__sum) ).
fof(fact_gauss__sum,axiom,
! [V_n_2,T_b] :
( class_Rings_Ocomm__semiring__1(T_b)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Groups_Oone__class_Oone(T_b))) ),
file('theBenchmark.p',fact_gauss__sum) ).
fof(fact_setsum__natinterval__difff,axiom,
! [V_f_2,V_n_2,V_m_2,T_b] :
( class_Groups_Oab__group__add(T_b)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = c_Groups_Ozero__class_Ozero(T_b) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
file('theBenchmark.p',fact_setsum__natinterval__difff) ).
fof(fact_less__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_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_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_max__number__of__Suc,axiom,
! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),c_Int_Onat)))),
file('theBenchmark.p',fact_max__number__of__Suc) ).
fof(fact_max__Suc__number__of,axiom,
! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))),
file('theBenchmark.p',fact_max__Suc__number__of) ).
fof(fact_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_power__number__of__odd,axiom,
! [V_z_2,V_w_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2))),c_COMBI(T_b))) ) ) ),
file('theBenchmark.p',fact_power__number__of__odd) ).
fof(fact_setprod__gen__delta,axiom,
! [V_c_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ),
file('theBenchmark.p',fact_setprod__gen__delta) ).
fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
! [V_x_2,V_y_2,V_c_2] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_c_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_c_2)) ) ),
file('theBenchmark.p',fact_image__minus__const__atLeastLessThan__nat) ).
fof(fact_setsum_Oreindex,axiom,
! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ),
file('theBenchmark.p',fact_setsum_Oreindex) ).
fof(fact_zpower__number__of__odd,axiom,
! [V_z_2,V_w_2] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z_2))),c_COMBI(tc_Int_Oint))) ) ),
file('theBenchmark.p',fact_zpower__number__of__odd) ).
fof(fact_setprod_Oreindex,axiom,
! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ),
file('theBenchmark.p',fact_setprod_Oreindex) ).
fof(fact_arith__series__general,axiom,
! [V_n_2,V_d_2,V_a_2,T_b] :
( class_Rings_Ocomm__semiring__1(T_b)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_b)),c_Nat_Osemiring__1__class_Oof__nat(T_b))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ),
file('theBenchmark.p',fact_arith__series__general) ).
fof(fact_negDivAlg_Osimps,axiom,
! [V_b,V_a] :
( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) )
=> c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) )
=> c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)) ) ),
file('theBenchmark.p',fact_negDivAlg_Osimps) ).
fof(fact_min__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_arith__series__nat,axiom,
! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_d_2)))),
file('theBenchmark.p',fact_arith__series__nat) ).
fof(fact_the__inv__into__comp,axiom,
! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))
=> ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))))
=> hAPP(c_Fun_Othe__inv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Fun_Othe__inv__into(T_d,T_b,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ),
file('theBenchmark.p',fact_the__inv__into__comp) ).
fof(fact_power__number__of__odd__number__of,axiom,
! [V_v_2,V_w_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)))),c_COMBI(T_b))) ) ) ),
file('theBenchmark.p',fact_power__number__of__odd__number__of) ).
fof(fact_negDivAlg__eqn__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_diff__nat__number__of,axiom,
! [V_v_2,V_v_H_2] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_v_H_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) ) ),
file('theBenchmark.p',fact_diff__nat__number__of) ).
fof(fact_norm__frac_Osimps,axiom,
! [V_a_2,V_b_2] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( ( ~ ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
=> c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) )
& ( ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
=> c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) ) ),
file('theBenchmark.p',fact_norm__frac_Osimps) ).
fof(fact_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_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_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_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_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_INF1__iff,axiom,
! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ),
file('theBenchmark.p',fact_INF1__iff) ).
fof(fact_INF2__iff,axiom,
! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ),
file('theBenchmark.p',fact_INF2__iff) ).
fof(fact_SUP2__iff,axiom,
! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_SUP2__iff) ).
fof(fact_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_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_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_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_rev__predicate2D,axiom,
! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_P_2] :
( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Q_2))
=> hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_rev__predicate2D) ).
fof(fact_predicate2D,axiom,
! [V_y_2,V_x_2,V_Q_2,V_P_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Q_2))
=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_predicate2D) ).
fof(fact_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_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_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_pair__imageI,axiom,
! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_d),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),V_A_2))) ),
file('theBenchmark.p',fact_pair__imageI) ).
fof(fact_of__int__num,axiom,
! [V_k_2,T_b] :
( class_Rings_Oring__1(T_b)
=> ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),T_b),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),tc_Int_Oint),c_COMBB(tc_fun(T_b,T_b),T_b,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,T_b),T_b),tc_Int_Oint),c_HOL_OLet(T_b,T_b)),c_Int_Oring__1__class_Oof__int(T_b)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,T_b)),tc_Int_Oint),c_COMBS(T_b,T_b,T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),tc_Int_Oint),c_COMBB(T_b,tc_fun(T_b,T_b),T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Oplus__class_Oplus(T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b)))),c_Groups_Oone__class_Oone(T_b))))),c_Divides_Odivmod__int(V_k_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k_2))) ) ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_of__int__num) ).
fof(fact_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_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_mem__splitI,axiom,
! [T_d,T_c,V_b_2,V_a_2,V_c_2,V_z_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)))) ),
file('theBenchmark.p',fact_mem__splitI) ).
fof(fact_splitD_H,axiom,
! [V_c_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_c_2))
=> hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ),
file('theBenchmark.p',fact_splitD_H) ).
fof(fact_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_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_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_split__paired__All,axiom,
! [T_c,T_b,V_P_2] :
( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
<=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ),
file('theBenchmark.p',fact_split__paired__All) ).
fof(fact_split__weak__cong,axiom,
! [V_c_2,T_d,T_c,T_b,V_q_2,V_p_2] :
( V_p_2 = V_q_2
=> hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_q_2) ),
file('theBenchmark.p',fact_split__weak__cong) ).
fof(fact_divmod__int__mod__div,axiom,
! [V_q,V_p] : c_Divides_Odivmod__int(V_p,V_q) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_p),V_q)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_p,V_q)),
file('theBenchmark.p',fact_divmod__int__mod__div) ).
fof(fact_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_split__eta,axiom,
! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_d),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_d,T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c))) = V_f_2,
file('theBenchmark.p',fact_split__eta) ).
fof(fact_swap__inj__on,axiom,
! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(tc_prod(T_b,T_c),tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_c,T_b)),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))),V_A_2),
file('theBenchmark.p',fact_swap__inj__on) ).
fof(fact_split__twice,axiom,
! [V_p_2,V_g_2,T_f,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,tc_prod(T_c,T_d)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_c,T_d)),tc_fun(T_f,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_f),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2))),V_g_2)),V_p_2),
file('theBenchmark.p',fact_split__twice) ).
fof(fact_Nitpick_OFrac__def,axiom,
c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
file('theBenchmark.p',fact_Nitpick_OFrac__def) ).
fof(fact_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_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_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_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_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_divmod__int__pdivmod,axiom,
! [V_l_2,V_k_2] :
( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l_2)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))) )
& ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2) ) ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
file('theBenchmark.p',fact_divmod__int__pdivmod) ).
fof(fact_apsnd__conv,axiom,
! [V_y_2,V_x_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),hAPP(V_f_2,V_y_2)),
file('theBenchmark.p',fact_apsnd__conv) ).
fof(fact_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_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_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__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__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_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_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_divmod__nat__rel__mult1__eq,axiom,
! [V_a,V_r,V_q,V_c,V_b] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
=> hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r),V_c)))) ) ),
file('theBenchmark.p',fact_divmod__nat__rel__mult1__eq) ).
fof(fact_divmod__nat__rel__mult2__eq,axiom,
! [V_c,V_r,V_q,V_b,V_a] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
=> hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)))) ) ) ),
file('theBenchmark.p',fact_divmod__nat__rel__mult2__eq) ).
fof(fact_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_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__eq,axiom,
! [V_qr,V_n,V_m] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
=> c_Divides_Odivmod__nat(V_m,V_n) = V_qr ),
file('theBenchmark.p',fact_divmod__nat__eq) ).
fof(fact_divmod__nat__rel__divmod__nat,axiom,
! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))),
file('theBenchmark.p',fact_divmod__nat__rel__divmod__nat) ).
fof(fact_mod__eq,axiom,
! [V_r,V_q,V_n,V_m] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ),
file('theBenchmark.p',fact_mod__eq) ).
fof(fact_div__eq,axiom,
! [V_r,V_q,V_n,V_m] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ),
file('theBenchmark.p',fact_div__eq) ).
fof(fact_divmod__nat__rel,axiom,
! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)))),
file('theBenchmark.p',fact_divmod__nat__rel) ).
fof(fact_divmod__nat__rel__add1__eq,axiom,
! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_aq),V_ar)))
=> ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_bq),V_br)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
=> hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br),V_c)))) ) ) ),
file('theBenchmark.p',fact_divmod__nat__rel__add1__eq) ).
fof(fact_nat__rec__number__of,axiom,
! [V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),c_Int_Onat)))),
file('theBenchmark.p',fact_nat__rec__number__of) ).
fof(fact_pair__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_Osimps_I2_J,axiom,
! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__case(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
file('theBenchmark.p',fact_pair__box_Osimps_I2_J) ).
fof(fact_pair__box_Orecs,axiom,
! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__rec(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
file('theBenchmark.p',fact_pair__box_Orecs) ).
fof(fact_negDivAlg_Opsimps,axiom,
! [V_b_2,V_a_2] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
=> ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) )
=> c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OnegDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) )
=> c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2)) ) ) ),
file('theBenchmark.p',fact_negDivAlg_Opsimps) ).
fof(fact_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_coinduct3__mono__lemma,axiom,
! [V_B_2,V_X_2,V_f_2,T_c,T_b] :
( class_Orderings_Oorder(T_b)
=> ( c_Orderings_Oorder__class_Omono(T_b,tc_fun(T_c,tc_HOL_Obool),V_f_2)
=> c_Orderings_Oorder__class_Omono(T_b,tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_f_2)),V_X_2))),V_B_2)) ) ),
file('theBenchmark.p',fact_coinduct3__mono__lemma) ).
fof(fact_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__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_Opsimps,axiom,
! [V_b_2,V_a_2] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
=> ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) )
=> c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OposDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) )
=> c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2) ) ) ),
file('theBenchmark.p',fact_posDivAlg_Opsimps) ).
fof(fact_norm__frac_Opsimps,axiom,
! [V_b_2,V_a_2] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( ( ~ ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
=> c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) )
& ( ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
=> c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) ) ) ),
file('theBenchmark.p',fact_norm__frac_Opsimps) ).
fof(fact_negDivAlg_Opinduct,axiom,
! [V_P_2,V_a1_2,V_a0_2] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
=> ( ! [B_a,B_b] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
=> ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_a),B_b))) )
=> hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
=> hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
=> hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
file('theBenchmark.p',fact_negDivAlg_Opinduct) ).
fof(fact_posDivAlg_Opinduct,axiom,
! [V_P_2,V_a1_2,V_a0_2] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
=> ( ! [B_a,B_b] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
=> ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) )
=> hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
=> hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
=> hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
file('theBenchmark.p',fact_posDivAlg_Opinduct) ).
fof(fact_accp__subset,axiom,
! [V_R2_2,V_R1_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_R1_2),V_R2_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_b,V_R2_2)),c_Wellfounded_Oaccp(T_b,V_R1_2))) ),
file('theBenchmark.p',fact_accp__subset) ).
fof(fact_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_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_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__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_nat__gcd_Opsimps,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)))
=> ( ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Nitpick_Onat__gcd(V_x_2,V_y_2) = c_Nitpick_Onat__gcd(V_y_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x_2,V_y_2)) )
& ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) ) ),
file('theBenchmark.p',fact_nat__gcd_Opsimps) ).
fof(fact_nat_Osize_I2_J,axiom,
! [V_nat] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_nat_Osize_I2_J) ).
fof(fact_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__apsnd,axiom,
! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)),
file('theBenchmark.p',fact_snd__apsnd) ).
fof(fact_apsnd__eq__conv,axiom,
! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
( hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_g_2),V_x_2)
<=> hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) ),
file('theBenchmark.p',fact_apsnd__eq__conv) ).
fof(fact_snd__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_snd__conv,axiom,
! [V_b,V_a,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a),V_b)) = V_b,
file('theBenchmark.p',fact_snd__conv) ).
fof(fact_snd__eqD,axiom,
! [V_a,V_y,V_x,T_a,T_b] :
( hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x),V_y)) = V_a
=> V_y = V_a ),
file('theBenchmark.p',fact_snd__eqD) ).
fof(fact_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_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_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_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_Ocommute__left__comp,axiom,
! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),V_g_2)) ),
file('theBenchmark.p',fact_folding_Ocommute__left__comp) ).
fof(fact_folding_Ocommute__comp,axiom,
! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) ),
file('theBenchmark.p',fact_folding_Ocommute__comp) ).
fof(fact_folding_Ocommute__comps_I1_J,axiom,
! [V_h_2,V_g_2,T_g,V_f_2,T_d,T_e,T_f,V_F_2,V_fa_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2)
=> hAPP(c_Fun_Ocomp(T_f,T_e,T_d,V_f_2),hAPP(c_Fun_Ocomp(T_g,T_f,T_d,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_g,T_e,T_d,hAPP(c_Fun_Ocomp(T_f,T_e,T_g,V_f_2),V_g_2)),V_h_2) ),
file('theBenchmark.p',fact_folding_Ocommute__comps_I1_J) ).
fof(fact_mod__nat__def,axiom,
! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)),
file('theBenchmark.p',fact_mod__nat__def) ).
fof(fact_folding_Ocommute__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_Oeq__fold,axiom,
! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_s_2),V_A_2) ) ),
file('theBenchmark.p',fact_folding_Oeq__fold) ).
fof(fact_folding_Oinsert,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ),
file('theBenchmark.p',fact_folding_Oinsert) ).
fof(fact_folding_Ounion__inter,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ),
file('theBenchmark.p',fact_folding_Ounion__inter) ).
fof(fact_folding_Oinsert__remove,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ),
file('theBenchmark.p',fact_folding_Oinsert__remove) ).
fof(fact_folding_Ounion,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_folding_Ounion) ).
fof(fact_norm__frac_Opinduct,axiom,
! [V_P_2,V_a1_2,V_a0_2] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
=> ( ! [B_a,B_b] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b))) )
=> hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
=> hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
file('theBenchmark.p',fact_norm__frac_Opinduct) ).
fof(fact_div__pos__neg__1__number__of,axiom,
! [V_w] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) ),
file('theBenchmark.p',fact_div__pos__neg__1__number__of) ).
fof(fact_nat__def,axiom,
! [V_z_2] : hAPP(c_Int_Onat,V_z_2) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))),
file('theBenchmark.p',fact_nat__def) ).
fof(fact_Pair__fst__snd__eq,axiom,
! [T_c,T_b,V_t_2,V_s_2] :
( V_s_2 = V_t_2
<=> ( hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2)
& hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2) ) ),
file('theBenchmark.p',fact_Pair__fst__snd__eq) ).
fof(fact_prod__eqI,axiom,
! [V_q,V_p,T_b,T_a] :
( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
=> ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
=> V_p = V_q ) ),
file('theBenchmark.p',fact_prod__eqI) ).
fof(fact_fst__apsnd,axiom,
! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_b,T_d),V_x_2),
file('theBenchmark.p',fact_fst__apsnd) ).
fof(fact_fst__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_Rep__Integ__inject,axiom,
! [V_y_2,V_x_2] :
( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
<=> V_x_2 = V_y_2 ),
file('theBenchmark.p',fact_Rep__Integ__inject) ).
fof(fact_fst__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_surjective__pairing,axiom,
! [T_b,T_a,V_t] : V_t = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_t)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_t)),
file('theBenchmark.p',fact_surjective__pairing) ).
fof(fact_pair__collapse,axiom,
! [V_p,T_b,T_a] : hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p)) = V_p,
file('theBenchmark.p',fact_pair__collapse) ).
fof(fact_prod__case__beta,axiom,
! [V_p_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)),
file('theBenchmark.p',fact_prod__case__beta) ).
fof(fact_div__int__def,axiom,
! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)),
file('theBenchmark.p',fact_div__int__def) ).
fof(fact_split__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__beta,axiom,
! [V_z_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_P_2),V_z_2) = hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_z_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_z_2)),
file('theBenchmark.p',fact_split__beta) ).
fof(fact_split__def,axiom,
! [V_p_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_c_2),V_p_2) = hAPP(hAPP(V_c_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)),
file('theBenchmark.p',fact_split__def) ).
fof(fact_split__comp,axiom,
! [V_x_2,V_g_2,V_f_2,T_e,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),hAPP(c_Fun_Ocomp(T_e,tc_fun(T_d,T_b),T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)),
file('theBenchmark.p',fact_split__comp) ).
fof(fact_div__neg__pos,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b)) ) ),
file('theBenchmark.p',fact_div__neg__pos) ).
fof(fact_div__pos__pos,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b)) ) ),
file('theBenchmark.p',fact_div__pos__pos) ).
fof(fact_div__pos__pos__1__number__of,axiom,
! [V_w] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ),
file('theBenchmark.p',fact_div__pos__pos__1__number__of) ).
fof(fact_div__pos__neg,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ),
file('theBenchmark.p',fact_div__pos__neg) ).
fof(fact_div__neg__neg,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ),
file('theBenchmark.p',fact_div__neg__neg) ).
fof(fact_prod__size__simp,axiom,
! [V_p_2,V_g_2,V_f_2,T_c,T_b] : c_Product__Type_Oprod_Oprod__size(T_b,T_c,V_f_2,V_g_2,V_p_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_prod__size__simp) ).
fof(fact_exI__realizer,axiom,
! [T_b,T_c,V_x_2,V_y_2,V_P_2] :
( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2))
=> hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)))) ),
file('theBenchmark.p',fact_exI__realizer) ).
fof(fact_conjI__realizer,axiom,
! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_P_2] :
( hBOOL(hAPP(V_P_2,V_p_2))
=> ( hBOOL(hAPP(V_Q_2,V_q_2))
=> ( hBOOL(hAPP(V_Q_2,hAPP(c_Product__Type_Osnd(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2))))
& hBOOL(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2)))) ) ) ),
file('theBenchmark.p',fact_conjI__realizer) ).
fof(fact_div__nat__def,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)),
file('theBenchmark.p',fact_div__nat__def) ).
fof(fact_divmod__nat__rel__def,axiom,
! [V_qr_2,V_n_2,V_m_2] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
<=> ( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) ) ) ) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)) ) ),
file('theBenchmark.p',fact_divmod__nat__rel__def) ).
fof(fact_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_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_nat__gcd_Opinduct,axiom,
! [V_P_2,V_a1_2,V_a0_2] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a0_2),V_a1_2)))
=> ( ! [B_x,B_y] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y)))
=> ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
=> hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) )
=> hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
file('theBenchmark.p',fact_nat__gcd_Opinduct) ).
fof(fact_The__split__eq,axiom,
! [V_y_2,V_x_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2),
file('theBenchmark.p',fact_The__split__eq) ).
fof(fact_split__paired__The,axiom,
! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_P_2) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))),
file('theBenchmark.p',fact_split__paired__The) ).
fof(fact_the__inv__into__def,axiom,
! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2))),
file('theBenchmark.p',fact_the__inv__into__def) ).
fof(fact_fold__def,axiom,
! [V_A_2,V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold__graph(T_c,T_b,V_f_2,V_z_2,V_A_2)),
file('theBenchmark.p',fact_fold__def) ).
fof(fact_divmod__nat__def,axiom,
! [V_n_2,V_m_2] : c_Divides_Odivmod__nat(V_m_2,V_n_2) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(V_m_2,V_n_2)),
file('theBenchmark.p',fact_divmod__nat__def) ).
fof(fact_fold1__def,axiom,
! [V_A_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2)),
file('theBenchmark.p',fact_fold1__def) ).
fof(fact_The__split,axiom,
! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))),
file('theBenchmark.p',fact_The__split) ).
fof(fact_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_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_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_mlex__leq,axiom,
! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ) ),
file('theBenchmark.p',fact_mlex__leq) ).
fof(fact_mlex__less,axiom,
! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ),
file('theBenchmark.p',fact_mlex__less) ).
fof(fact_Least__mono,axiom,
! [V_S_2,V_f_2,T_b,T_c] :
( ( class_Orderings_Oorder(T_b)
& class_Orderings_Oorder(T_c) )
=> ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
=> ( ? [B_x] :
( ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_S_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) )
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
=> c_Orderings_Oord__class_OLeast(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2))) = hAPP(V_f_2,c_Orderings_Oord__class_OLeast(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))) ) ) ),
file('theBenchmark.p',fact_Least__mono) ).
fof(fact_folding__image_Oreindex,axiom,
! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
=> hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_c,T_b,T_c,V_g_2),V_h_2)),V_A_2) ) ) ),
file('theBenchmark.p',fact_folding__image_Oreindex) ).
fof(fact_nat_Osize_I4_J,axiom,
! [V_nat] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_nat_Osize_I4_J) ).
fof(fact_LeastI,axiom,
! [V_k_2,V_P_2,T_b] :
( class_Orderings_Owellorder(T_b)
=> ( hBOOL(hAPP(V_P_2,V_k_2))
=> hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))) ) ),
file('theBenchmark.p',fact_LeastI) ).
fof(fact_nat__size,axiom,
! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n,
file('theBenchmark.p',fact_nat__size) ).
fof(fact_LeastI__ex,axiom,
! [V_P_2,T_b] :
( class_Orderings_Owellorder(T_b)
=> ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
=> hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))) ) ),
file('theBenchmark.p',fact_LeastI__ex) ).
fof(fact_Least__le,axiom,
! [V_k_2,V_P_2,T_b] :
( class_Orderings_Owellorder(T_b)
=> ( hBOOL(hAPP(V_P_2,V_k_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Orderings_Oord__class_OLeast(T_b,V_P_2)),V_k_2)) ) ),
file('theBenchmark.p',fact_Least__le) ).
fof(fact_not__less__Least,axiom,
! [V_P_2,V_k_2,T_b] :
( class_Orderings_Owellorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),c_Orderings_Oord__class_OLeast(T_b,V_P_2)))
=> ~ hBOOL(hAPP(V_P_2,V_k_2)) ) ),
file('theBenchmark.p',fact_not__less__Least) ).
fof(fact_folding__image_Odistrib,axiom,
! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(V_f_2,hAPP(hAPP(V_F_2,V_g_2),V_A_2)),hAPP(hAPP(V_F_2,V_h_2),V_A_2)) ) ),
file('theBenchmark.p',fact_folding__image_Odistrib) ).
fof(fact_nat_Osize_I3_J,axiom,
hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_nat_Osize_I3_J) ).
fof(fact_Least__Suc,axiom,
! [V_n_2,V_P_2] :
( hBOOL(hAPP(V_P_2,V_n_2))
=> ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_P_2) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_OSuc))) ) ),
file('theBenchmark.p',fact_Least__Suc) ).
fof(fact_folding__image_Oeq__fold,axiom,
! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ),
file('theBenchmark.p',fact_folding__image_Oeq__fold) ).
fof(fact_prod_Orecs,axiom,
! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Product__Type_Oprod_Oprod__rec(T_c,T_d,T_b,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
file('theBenchmark.p',fact_prod_Orecs) ).
fof(fact_setsum__reindex__nonzero,axiom,
! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
=> ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
=> ( B_x != B_y
=> ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
=> hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_S_2) ) ) ),
file('theBenchmark.p',fact_setsum__reindex__nonzero) ).
fof(fact_UN__finite2__eq,axiom,
! [V_B_2,V_k_2,V_A_2,T_b] :
( ! [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2)
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2) ),
file('theBenchmark.p',fact_UN__finite2__eq) ).
fof(fact_UN__finite__subset,axiom,
! [V_C_2,V_A_2,T_b] :
( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),V_C_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),V_C_2)) ),
file('theBenchmark.p',fact_UN__finite__subset) ).
fof(fact_image__INT,axiom,
! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) )
=> ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
=> hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2)) ) ) ),
file('theBenchmark.p',fact_image__INT) ).
fof(fact_in__lex__prod,axiom,
! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_b,T_c,V_r_2,V_s_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_b_H_2)),V_s_2))
& V_a_2 = V_a_H_2 )
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_H_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_in__lex__prod) ).
fof(fact_same__fstI,axiom,
! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_P_2] :
( hBOOL(hAPP(V_P_2,V_x_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2))) ) ),
file('theBenchmark.p',fact_same__fstI) ).
fof(fact_in__finite__psubset,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_b)))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_in__finite__psubset) ).
fof(fact_folding__idem_Ounion__idem,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ),
file('theBenchmark.p',fact_folding__idem_Ounion__idem) ).
fof(fact_folding__idem_Oidem__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_folding__idem_Oinsert__idem,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ),
file('theBenchmark.p',fact_folding__idem_Oinsert__idem) ).
fof(fact_folding__idem_Osubset__comp__idem,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) = hAPP(V_F_2,V_A_2) ) ) ),
file('theBenchmark.p',fact_folding__idem_Osubset__comp__idem) ).
fof(fact_setsum__nonneg__leq__bound,axiom,
! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
=> ( ! [B_i] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ),
file('theBenchmark.p',fact_setsum__nonneg__leq__bound) ).
fof(fact_setsum__nonneg__0,axiom,
! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
=> ( ! [B_i] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = c_Groups_Ozero__class_Ozero(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
=> hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ),
file('theBenchmark.p',fact_setsum__nonneg__0) ).
fof(fact_sum__diff__distrib,axiom,
! [V_n_2,V_P_2,V_Q_2] :
( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Q_2,B_x)),hAPP(V_P_2,B_x)))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_P_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Q_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_P_2)),V_Q_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ),
file('theBenchmark.p',fact_sum__diff__distrib) ).
fof(fact_apsnd__apfst,axiom,
! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_e,T_d),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_e,T_d),V_x_2))),
file('theBenchmark.p',fact_apsnd__apfst) ).
fof(fact_apfst__apsnd,axiom,
! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2))),
file('theBenchmark.p',fact_apfst__apsnd) ).
fof(fact_pair__lessI2,axiom,
! [V_t_2,V_s_2,V_b_2,V_a_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ) ),
file('theBenchmark.p',fact_pair__lessI2) ).
fof(fact_apfst__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_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_apfst__eq__conv,axiom,
! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
( hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_g_2),V_x_2)
<=> hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) ),
file('theBenchmark.p',fact_apfst__eq__conv) ).
fof(fact_fst__apfst,axiom,
! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)),
file('theBenchmark.p',fact_fst__apfst) ).
fof(fact_apfst__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_apsnd__apfst__commute,axiom,
! [V_p_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,V_g_2),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_e,V_f_2),V_p_2)),
file('theBenchmark.p',fact_apsnd__apfst__commute) ).
fof(fact_pair__lessI1,axiom,
! [V_t_2,V_s_2,V_b_2,V_a_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ),
file('theBenchmark.p',fact_pair__lessI1) ).
fof(fact_pair__leqI2,axiom,
! [V_t_2,V_s_2,V_b_2,V_a_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ) ),
file('theBenchmark.p',fact_pair__leqI2) ).
fof(fact_smin__insertI,axiom,
! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__strict))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__strict)) ) ) ),
file('theBenchmark.p',fact_smin__insertI) ).
fof(fact_smax__insertI,axiom,
! [V_X_2,V_x_2,V_Y_2,V_y_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),V_Y_2)),c_FunDef_Omax__strict))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_X_2)),V_Y_2)),c_FunDef_Omax__strict)) ) ) ),
file('theBenchmark.p',fact_smax__insertI) ).
fof(fact_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_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_pair__leqI1,axiom,
! [V_t_2,V_s_2,V_b_2,V_a_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ),
file('theBenchmark.p',fact_pair__leqI1) ).
fof(fact_wmax__insertI,axiom,
! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omax__weak))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)),V_YS_2)),c_FunDef_Omax__weak)) ) ) ),
file('theBenchmark.p',fact_wmax__insertI) ).
fof(fact_wmin__insertI,axiom,
! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__weak))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__weak)) ) ) ),
file('theBenchmark.p',fact_wmin__insertI) ).
fof(fact_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_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_max__rpair__set,axiom,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)),
file('theBenchmark.p',fact_max__rpair__set) ).
fof(fact_max__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_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__extp__max__ext__eq,axiom,
! [V_xa_2,V_x_2,V_R_2,T_b] :
( c_Wellfounded_Omax__extp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_R_2),V_x_2,V_xa_2)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ),
file('theBenchmark.p',fact_max__extp__max__ext__eq) ).
fof(fact_less__than__iff,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Wellfounded_Oless__than))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ),
file('theBenchmark.p',fact_less__than__iff) ).
fof(fact_intrel__iff,axiom,
! [V_v_2,V_u_2,V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2))),c_Int_Ointrel))
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2) ),
file('theBenchmark.p',fact_intrel__iff) ).
fof(fact_pair__less__def,axiom,
c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
file('theBenchmark.p',fact_pair__less__def) ).
fof(fact_mlex__prod__def,axiom,
! [V_R_2,V_f_2,T_b] : c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_b),T_b),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_b,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(tc_Nat_Onat,T_b)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_prod(tc_Nat_Onat,T_b)),T_b),c_Product__Type_OPair(tc_Nat_Onat,T_b)),V_f_2)),c_COMBI(T_b))),
file('theBenchmark.p',fact_mlex__prod__def) ).
fof(fact_rp__inv__image__rp,axiom,
! [V_f_2,T_c,V_P_2,T_b] :
( c_FunDef_Oreduction__pair(T_b,V_P_2)
=> c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_P_2),V_f_2)) ),
file('theBenchmark.p',fact_rp__inv__image__rp) ).
fof(fact_strong__setprod__reindex__cong,axiom,
! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hAPP(V_g_2,B_x) = hAPP(hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2),B_x) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ),
file('theBenchmark.p',fact_strong__setprod__reindex__cong) ).
fof(fact_rp__inv__image__def,axiom,
! [T_c,T_b] : c_FunDef_Orp__inv__image(T_b,T_c) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBS(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(T_c,T_b)),c_Product__Type_OPair(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),c_Relation_Oinv__image(T_b,T_c))))),c_Relation_Oinv__image(T_b,T_c))),
file('theBenchmark.p',fact_rp__inv__image__def) ).
fof(fact_in__inv__image,axiom,
! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2)) ),
file('theBenchmark.p',fact_in__inv__image) ).
fof(fact_equiv__intrel__iff,axiom,
! [V_y_2,V_x_2] :
( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_Int_Ointrel)) ),
file('theBenchmark.p',fact_equiv__intrel__iff) ).
fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
( ( class_Groups_Ocomm__monoid__mult(T_b)
& class_Groups_Ocomm__monoid__add(T_b) )
=> ( V_A_2 = V_B_2
=> ( c_Nat__Transfer_Onat__set(V_B_2)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
=> hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_g_2),V_B_2) ) ) ) ),
file('theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I2_J) ).
fof(fact_Image__empty,axiom,
! [V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Image__empty) ).
fof(fact_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_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__mono,axiom,
! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ),
file('theBenchmark.p',fact_Image__mono) ).
fof(fact_Image__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__INT__subset,axiom,
! [V_B_2,V_A_2,T_d,V_r_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)))),
file('theBenchmark.p',fact_Image__INT__subset) ).
fof(fact_Image__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_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_measure__def,axiom,
! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than),
file('theBenchmark.p',fact_measure__def) ).
fof(fact_of__int,axiom,
! [V_j_2,V_i_2,T_b] :
( class_Rings_Oring__1(T_b)
=> hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_i_2),V_j_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_j_2)) ),
file('theBenchmark.p',fact_of__int) ).
fof(fact_One__int__def,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
file('theBenchmark.p',fact_One__int__def) ).
fof(fact_mult,axiom,
! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_v_2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_u_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
file('theBenchmark.p',fact_mult) ).
fof(fact_Rep__Integ__inverse,axiom,
! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2,
file('theBenchmark.p',fact_Rep__Integ__inverse) ).
fof(fact_minus,axiom,
! [V_y_2,V_x_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_y_2),V_x_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
file('theBenchmark.p',fact_minus) ).
fof(fact_Zero__int__def,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
file('theBenchmark.p',fact_Zero__int__def) ).
fof(fact_int__def,axiom,
! [V_m_2] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
file('theBenchmark.p',fact_int__def) ).
fof(fact_add,axiom,
! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y_2),V_v_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
file('theBenchmark.p',fact_add) ).
fof(fact_nat,axiom,
! [V_y_2,V_x_2] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2),
file('theBenchmark.p',fact_nat) ).
fof(fact_minus__int__def,axiom,
! [V_z_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_2) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))),
file('theBenchmark.p',fact_minus__int__def) ).
fof(fact_less,axiom,
! [V_v_2,V_u_2,V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ),
file('theBenchmark.p',fact_less) ).
fof(fact_le,axiom,
! [V_v_2,V_u_2,V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ),
file('theBenchmark.p',fact_le) ).
fof(fact_irrefl__def,axiom,
! [V_r_2,T_b] :
( c_Relation_Oirrefl(T_b,V_r_2)
<=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ),
file('theBenchmark.p',fact_irrefl__def) ).
fof(fact_eq__Abs__Integ,axiom,
! [V_z_2] :
~ ! [B_x,B_y] : V_z_2 != hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
file('theBenchmark.p',fact_eq__Abs__Integ) ).
fof(fact_Field__insert,axiom,
! [V_r_2,V_b_2,V_a_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_b),V_r_2)),
file('theBenchmark.p',fact_Field__insert) ).
fof(fact_Field__Union,axiom,
! [V_R_2,T_b] : hAPP(c_Relation_OField(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Relation_OField(T_b)),V_R_2)),
file('theBenchmark.p',fact_Field__Union) ).
fof(fact_Field__empty,axiom,
! [T_b] : hAPP(c_Relation_OField(T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Field__empty) ).
fof(fact_mono__Field,axiom,
! [V_s_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2))) ),
file('theBenchmark.p',fact_mono__Field) ).
fof(fact_Field__Un,axiom,
! [V_s_2,V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2)),
file('theBenchmark.p',fact_Field__Un) ).
fof(fact_finite__Field,axiom,
! [V_r_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ),
file('theBenchmark.p',fact_finite__Field) ).
fof(fact_Id__on__def,axiom,
! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),
file('theBenchmark.p',fact_Id__on__def) ).
fof(fact_quotient__def,axiom,
! [V_r_2,V_A_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),c_Relation_OImage(T_b,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)))),
file('theBenchmark.p',fact_quotient__def) ).
fof(fact_ImageE,axiom,
! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
=> ~ ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_ImageE) ).
fof(fact_quotient__empty,axiom,
! [V_r_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),
file('theBenchmark.p',fact_quotient__empty) ).
fof(fact_quotient__is__empty2,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)
<=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_quotient__is__empty2) ).
fof(fact_quotient__is__empty,axiom,
! [V_r_2,V_A_2,T_b] :
( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
<=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_quotient__is__empty) ).
fof(fact_Id__on__def_H,axiom,
! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),c_fequal))),V_A_2)),
file('theBenchmark.p',fact_Id__on__def_H) ).
fof(fact_Id__on__empty,axiom,
! [T_b] : c_Relation_OId__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),
file('theBenchmark.p',fact_Id__on__empty) ).
fof(fact_Image__Id__on,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
file('theBenchmark.p',fact_Image__Id__on) ).
fof(fact_quotient__diff1,axiom,
! [V_a_2,V_A_2,V_r_2,T_b] :
( c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2)) ) ),
file('theBenchmark.p',fact_quotient__diff1) ).
fof(fact_quotientI,axiom,
! [V_r_2,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ),
file('theBenchmark.p',fact_quotientI) ).
fof(fact_Id__on__eqI,axiom,
! [V_A_2,T_b,V_b_2,V_a_2] :
( V_a_2 = V_b_2
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId__on(T_b,V_A_2))) ) ),
file('theBenchmark.p',fact_Id__on__eqI) ).
fof(fact_Id__on__iff,axiom,
! [V_A_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Relation_OId__on(T_b,V_A_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
& V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_Id__on__iff) ).
fof(fact_singleton__quotient,axiom,
! [V_r_2,V_x_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))),
file('theBenchmark.p',fact_singleton__quotient) ).
fof(fact_card__quotient__disjoint,axiom,
! [V_r_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2)
=> hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ),
file('theBenchmark.p',fact_card__quotient__disjoint) ).
fof(fact_equiv__class__nondisjoint,axiom,
! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_equiv__class__nondisjoint) ).
fof(fact_subset__equiv__class,axiom,
! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ),
file('theBenchmark.p',fact_subset__equiv__class) ).
fof(fact_quotientE,axiom,
! [V_r_2,V_A_2,V_X_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
=> ~ ! [B_x] :
( V_X_2 = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_quotientE) ).
fof(fact_equiv__intrel,axiom,
c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel),
file('theBenchmark.p',fact_equiv__intrel) ).
fof(fact_Union__quotient,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = V_A_2 ),
file('theBenchmark.p',fact_Union__quotient) ).
fof(fact_equiv__class__self,axiom,
! [V_a_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
file('theBenchmark.p',fact_equiv__class__self) ).
fof(fact_quotient__disj,axiom,
! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| V_X_2 = V_Y_2 ) ) ) ),
file('theBenchmark.p',fact_quotient__disj) ).
fof(fact_equiv__class__eq,axiom,
! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
=> hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ),
file('theBenchmark.p',fact_equiv__class__eq) ).
fof(fact_quotient__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__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_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_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_identity__equivp,axiom,
! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal),
file('theBenchmark.p',fact_identity__equivp) ).
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_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__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__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_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_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_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_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_Id__onE,axiom,
! [V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_c_2),c_Relation_OId__on(T_b,V_A_2)))
=> ~ ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ),
file('theBenchmark.p',fact_Id__onE) ).
fof(fact_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_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_refl__onD,axiom,
! [V_a_2,V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_refl__onD) ).
fof(fact_refl__onD1,axiom,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
file('theBenchmark.p',fact_refl__onD1) ).
fof(fact_refl__onD2,axiom,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ),
file('theBenchmark.p',fact_refl__onD2) ).
fof(fact_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_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_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_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_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_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_type__definition_ORep__range,axiom,
! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
=> hAPP(c_Set_Oimage(T_b,T_c,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ),
file('theBenchmark.p',fact_type__definition_ORep__range) ).
fof(fact_type__definition_OAbs__image,axiom,
! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
=> hAPP(c_Set_Oimage(T_c,T_b,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_type__definition_OAbs__image) ).
fof(fact_type__definition_OAbs__inject,axiom,
! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
=> ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ) ),
file('theBenchmark.p',fact_type__definition_OAbs__inject) ).
fof(fact_type__definition_ORep__inject,axiom,
! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
=> ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_type__definition_ORep__inject) ).
fof(fact_type__definition_ORep__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,axiom,
! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ),
file('theBenchmark.p',fact_type__definition_ORep) ).
fof(fact_type__definition_OAbs__inverse,axiom,
! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
=> hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ),
file('theBenchmark.p',fact_type__definition_OAbs__inverse) ).
fof(fact_max__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_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_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_image__split__eq__Sigma,axiom,
! [V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Set_Oimage(T_d,tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_Oimage(T_d,T_c,V_g_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_b),c_Set_Ovimage(T_d,T_b,V_f_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_A_2))),
file('theBenchmark.p',fact_image__split__eq__Sigma) ).
fof(fact_Rep__Integ__induct,axiom,
! [V_P_2,V_y_2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
=> ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
=> hBOOL(hAPP(V_P_2,V_y_2)) ) ),
file('theBenchmark.p',fact_Rep__Integ__induct) ).
fof(fact_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__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__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__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__UNIV2,axiom,
! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
file('theBenchmark.p',fact_Compl__Times__UNIV2) ).
fof(fact_Compl__Times__UNIV1,axiom,
! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))),
file('theBenchmark.p',fact_Compl__Times__UNIV1) ).
fof(fact_setprod__cartesian__product,axiom,
! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
( class_Groups_Ocomm__monoid__mult(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) ),
file('theBenchmark.p',fact_setprod__cartesian__product) ).
fof(fact_Sigma__Un__distrib1,axiom,
! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)),
file('theBenchmark.p',fact_Sigma__Un__distrib1) ).
fof(fact_Times__Un__distrib1,axiom,
! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),
file('theBenchmark.p',fact_Times__Un__distrib1) ).
fof(fact_Sigma__Un__distrib2,axiom,
! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)),
file('theBenchmark.p',fact_Sigma__Un__distrib2) ).
fof(fact_swap__product,axiom,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_b,T_c)),hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2)),
file('theBenchmark.p',fact_swap__product) ).
fof(fact_finite__cartesian__product,axiom,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ) ),
file('theBenchmark.p',fact_finite__cartesian__product) ).
fof(fact_equiv__type,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ),
file('theBenchmark.p',fact_equiv__type) ).
fof(fact_Sigma__Int__distrib2,axiom,
! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)),
file('theBenchmark.p',fact_Sigma__Int__distrib2) ).
fof(fact_Times__Int__distrib1,axiom,
! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),
file('theBenchmark.p',fact_Times__Int__distrib1) ).
fof(fact_Sigma__Int__distrib1,axiom,
! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)),
file('theBenchmark.p',fact_Sigma__Int__distrib1) ).
fof(fact_Id__on__subset__Times,axiom,
! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId__on(T_b,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))),
file('theBenchmark.p',fact_Id__on__subset__Times) ).
fof(fact_UNIV__Times__UNIV,axiom,
! [T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
file('theBenchmark.p',fact_UNIV__Times__UNIV) ).
fof(fact_SigmaE2,axiom,
! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ),
file('theBenchmark.p',fact_SigmaE2) ).
fof(fact_SigmaD2,axiom,
! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ),
file('theBenchmark.p',fact_SigmaD2) ).
fof(fact_SigmaD1,axiom,
! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
file('theBenchmark.p',fact_SigmaD1) ).
fof(fact_mem__Sigma__iff,axiom,
! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
& hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_mem__Sigma__iff) ).
fof(fact_card__cartesian__product__singleton,axiom,
! [V_A_2,V_x_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2),
file('theBenchmark.p',fact_card__cartesian__product__singleton) ).
fof(fact_Times__subset__cancel2,axiom,
! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_Times__subset__cancel2) ).
fof(fact_Image__subset,axiom,
! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_C_2)),V_B_2)) ),
file('theBenchmark.p',fact_Image__subset) ).
fof(fact_finite__cartesian__productD1,axiom,
! [V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
file('theBenchmark.p',fact_finite__cartesian__productD1) ).
fof(fact_finite__cartesian__productD2,axiom,
! [V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ),
file('theBenchmark.p',fact_finite__cartesian__productD2) ).
fof(fact_fst__image__times,axiom,
! [V_A_2,T_c,T_b,V_B_2] :
( ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = V_A_2 )
& ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_fst__image__times) ).
fof(fact_snd__image__times,axiom,
! [V_B_2,T_c,T_b,V_A_2] :
( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = V_B_2 )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_snd__image__times) ).
fof(fact_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_insert__times__insert,axiom,
! [V_B_2,V_b_2,V_A_2,V_a_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))),
file('theBenchmark.p',fact_insert__times__insert) ).
fof(fact_finite__equiv__class,axiom,
! [V_X_2,V_r_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ),
file('theBenchmark.p',fact_finite__equiv__class) ).
fof(fact_vimage__Times,axiom,
! [V_B_2,V_A_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,tc_prod(T_c,T_d),V_f_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,T_b,c_Product__Type_Ofst(T_c,T_d)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_d,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_d,T_b,c_Product__Type_Osnd(T_c,T_d)),V_f_2)),V_B_2)),
file('theBenchmark.p',fact_vimage__Times) ).
fof(fact_UN__Times__distrib,axiom,
! [V_F_2,V_E_2,V_B_2,V_A_2,T_c,T_b,T_e,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_d,T_e),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_d),V_B_2))),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_d),c_Product__Type_OSigma(T_b,T_c)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_e),c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_F_2))),
file('theBenchmark.p',fact_UN__Times__distrib) ).
fof(fact_Sigma__def,axiom,
! [V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_c),c_Set_Oinsert(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))))),
file('theBenchmark.p',fact_Sigma__def) ).
fof(fact_finite__quotient,axiom,
! [V_r_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ) ),
file('theBenchmark.p',fact_finite__quotient) ).
fof(fact_Ex__inj__on__UNION__Sigma,axiom,
! [V_A_2,V_I_2,T_c,T_b] :
? [B_f] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,tc_prod(T_c,T_b),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_I_2),V_A_2)))
& c_Fun_Oinj__on(T_b,tc_prod(T_c,T_b),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) ),
file('theBenchmark.p',fact_Ex__inj__on__UNION__Sigma) ).
fof(fact_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_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_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_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_SigmaE,axiom,
! [V_B_2,V_A_2,V_c_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
=> ~ ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x)))
=> V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ),
file('theBenchmark.p',fact_SigmaE) ).
fof(fact_map__pair__surj,axiom,
! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
=> ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_map__pair__surj) ).
fof(fact_map__pair__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_map__pair__ident,axiom,
! [V_z_2,T_c,T_b] : hAPP(c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)),V_z_2) = V_z_2,
file('theBenchmark.p',fact_map__pair__ident) ).
fof(fact_snd__prod__fun,axiom,
! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Omap__pair(T_d,T_c,T_e,T_b,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2)),
file('theBenchmark.p',fact_snd__prod__fun) ).
fof(fact_map__pair_Ocomp,axiom,
! [V_i_2,V_h_2,V_g_2,V_f_2,T_c,T_b,T_e,T_d,T_g,T_f] : hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g_2),V_i_2)),
file('theBenchmark.p',fact_map__pair_Ocomp) ).
fof(fact_map__pair__compose,axiom,
! [V_g2_2,V_g1_2,T_g,V_f2_2,V_f1_2,T_f,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_f2_2,V_g2_2)),
file('theBenchmark.p',fact_map__pair__compose) ).
fof(fact_map__pair_Ocompositionality,axiom,
! [V_prod_2,V_i_2,V_h_2,T_g,T_f,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_f,T_b,T_g,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_f,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_e,T_c,T_g,V_g_2),V_i_2)),V_prod_2),
file('theBenchmark.p',fact_map__pair_Ocompositionality) ).
fof(fact_snd__comp__map__pair,axiom,
! [V_g_2,V_f_2,T_c,T_b,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_d),T_d,tc_prod(T_b,T_c),c_Product__Type_Osnd(T_e,T_d)),c_Product__Type_Omap__pair(T_b,T_e,T_c,T_d,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_d,tc_prod(T_b,T_c),V_g_2),c_Product__Type_Osnd(T_b,T_c)),
file('theBenchmark.p',fact_snd__comp__map__pair) ).
fof(fact_fst__comp__map__pair,axiom,
! [V_g_2,V_f_2,T_c,T_b,T_e,T_d] : hAPP(c_Fun_Ocomp(tc_prod(T_d,T_e),T_d,tc_prod(T_b,T_c),c_Product__Type_Ofst(T_d,T_e)),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,tc_prod(T_b,T_c),V_f_2),c_Product__Type_Ofst(T_b,T_c)),
file('theBenchmark.p',fact_fst__comp__map__pair) ).
fof(fact_map__pair__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_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_prod__fun__imageE,axiom,
! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_c_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(c_Set_Oimage(tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2)),V_R_2)))
=> ~ ! [B_x,B_y] :
( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),B_x),B_y)),V_R_2)) ) ),
file('theBenchmark.p',fact_prod__fun__imageE) ).
fof(fact_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_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_CollectI,axiom,
! [T_b,V_a_2,V_P_2] :
( hBOOL(hAPP(V_P_2,V_a_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ),
file('theBenchmark.p',fact_CollectI) ).
fof(fact_finite__Collect__conjI,axiom,
! [V_Q_2,V_P_2,T_b] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2)),V_Q_2)))) ),
file('theBenchmark.p',fact_finite__Collect__conjI) ).
fof(fact_finite__Collect__less__nat,axiom,
! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_k_2)))),
file('theBenchmark.p',fact_finite__Collect__less__nat) ).
fof(fact_finite__Collect__le__nat,axiom,
! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_k_2)))),
file('theBenchmark.p',fact_finite__Collect__le__nat) ).
fof(fact_SetCompr__Sigma__eq,axiom,
! [V_Q_2,V_P_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),V_Q_2)),
file('theBenchmark.p',fact_SetCompr__Sigma__eq) ).
fof(fact_Collect__split,axiom,
! [V_Q_2,V_P_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Q_2))),
file('theBenchmark.p',fact_Collect__split) ).
fof(fact_vimage__Collect__eq,axiom,
! [V_P_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_c),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_P_2),V_f_2)),
file('theBenchmark.p',fact_vimage__Collect__eq) ).
fof(fact_Collect__neg__eq,axiom,
! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),
file('theBenchmark.p',fact_Collect__neg__eq) ).
fof(fact_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_Collect__empty__eq,axiom,
! [V_P_2,T_b] :
( hAPP(c_Set_OCollect(T_b),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ),
file('theBenchmark.p',fact_Collect__empty__eq) ).
fof(fact_empty__Collect__eq,axiom,
! [V_P_2,T_b] :
( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_P_2)
<=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ),
file('theBenchmark.p',fact_empty__Collect__eq) ).
fof(fact_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_Collect__disj__eq,axiom,
! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)),
file('theBenchmark.p',fact_Collect__disj__eq) ).
fof(fact_Collect__def,axiom,
! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),V_P_2) = V_P_2,
file('theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__conj__eq,axiom,
! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)),
file('theBenchmark.p',fact_Collect__conj__eq) ).
fof(fact_finite__Collect__disjI,axiom,
! [V_Q_2,V_P_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2))))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) ) ),
file('theBenchmark.p',fact_finite__Collect__disjI) ).
fof(fact_insert__Collect,axiom,
! [V_P_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)))),V_P_2)),
file('theBenchmark.p',fact_insert__Collect) ).
fof(fact_CollectE,axiom,
! [V_P_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
=> hBOOL(hAPP(V_P_2,V_a_2)) ),
file('theBenchmark.p',fact_CollectE) ).
fof(fact_CollectD,axiom,
! [V_P_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
=> hBOOL(hAPP(V_P_2,V_a_2)) ),
file('theBenchmark.p',fact_CollectD) ).
fof(fact_mem__Collect__eq,axiom,
! [V_P_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
<=> hBOOL(hAPP(V_P_2,V_a_2)) ),
file('theBenchmark.p',fact_mem__Collect__eq) ).
fof(fact_Collect__mem__eq,axiom,
! [V_A_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)) = V_A_2,
file('theBenchmark.p',fact_Collect__mem__eq) ).
fof(fact_insert__compr__raw,axiom,
! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
file('theBenchmark.p',fact_insert__compr__raw) ).
fof(fact_insert__compr,axiom,
! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
file('theBenchmark.p',fact_insert__compr) ).
fof(fact_Un__def,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
file('theBenchmark.p',fact_Un__def) ).
fof(fact_Int__Collect,axiom,
! [V_P_2,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))))
<=> ( hBOOL(hAPP(V_P_2,V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
file('theBenchmark.p',fact_Int__Collect) ).
fof(fact_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_Collect__conv__if,axiom,
! [T_b,V_a_2,V_P_2] :
( ( ~ hBOOL(hAPP(V_P_2,V_a_2))
=> hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hBOOL(hAPP(V_P_2,V_a_2))
=> hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ),
file('theBenchmark.p',fact_Collect__conv__if) ).
fof(fact_Collect__conv__if2,axiom,
! [T_b,V_a_2,V_P_2] :
( ( ~ hBOOL(hAPP(V_P_2,V_a_2))
=> hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hBOOL(hAPP(V_P_2,V_a_2))
=> hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ),
file('theBenchmark.p',fact_Collect__conv__if2) ).
fof(fact_singleton__conv,axiom,
! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
file('theBenchmark.p',fact_singleton__conv) ).
fof(fact_singleton__conv2,axiom,
! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
file('theBenchmark.p',fact_singleton__conv2) ).
fof(fact_set__diff__eq,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))),
file('theBenchmark.p',fact_set__diff__eq) ).
fof(fact_finite__Collect__not,axiom,
! [V_P_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ),
file('theBenchmark.p',fact_finite__Collect__not) ).
fof(fact_insert__def,axiom,
! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2),
file('theBenchmark.p',fact_insert__def) ).
fof(fact_Compl__eq,axiom,
! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),
file('theBenchmark.p',fact_Compl__eq) ).
fof(fact_vimage__def,axiom,
! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(T_c)),V_f_2)),V_B_2)),
file('theBenchmark.p',fact_vimage__def) ).
fof(fact_Collect__ball__eq,axiom,
! [V_P_2,V_A_2,T_c,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),V_P_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_P_2))),
file('theBenchmark.p',fact_Collect__ball__eq) ).
fof(fact_Collect__imp__eq,axiom,
! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(c_Set_OCollect(T_b),V_Q_2)),
file('theBenchmark.p',fact_Collect__imp__eq) ).
fof(fact_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__M__bounded__by__nat,axiom,
! [V_i_2,V_P_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),V_P_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))),
file('theBenchmark.p',fact_finite__M__bounded__by__nat) ).
fof(fact_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_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_if__image__distrib,axiom,
! [V_S_2,V_g_2,V_f_2,V_P_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),V_P_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),V_P_2)))),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_P_2))))),
file('theBenchmark.p',fact_if__image__distrib) ).
fof(fact_nat__seg__image__imp__finite,axiom,
! [V_n_2,V_f_2,T_b,V_A_2] :
( V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,V_f_2),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_n_2)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
file('theBenchmark.p',fact_nat__seg__image__imp__finite) ).
fof(fact_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_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_Image__singleton,axiom,
! [V_a_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_b))),hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2))),V_r_2)),
file('theBenchmark.p',fact_Image__singleton) ).
fof(fact_setsum__cases,axiom,
! [V_g_2,V_f_2,V_P_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),V_P_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2))))) ) ),
file('theBenchmark.p',fact_setsum__cases) ).
fof(fact_card__less__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_setsum__multicount,axiom,
! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2))
=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = V_k_2 )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_c),V_T_2)) ) ) ),
file('theBenchmark.p',fact_setsum__multicount) ).
fof(fact_min__max_Osup__Inf1__distrib,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ),
file('theBenchmark.p',fact_min__max_Osup__Inf1__distrib) ).
fof(fact_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__image__set,axiom,
! [V_f_2,T_c,V_P_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_b)),c_fequal)),V_f_2)))),V_P_2))))) ),
file('theBenchmark.p',fact_finite__image__set) ).
fof(fact_finite__Collect__bounded__ex,axiom,
! [V_Q_2,T_c,V_P_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2)))))
<=> ! [B_y] :
( hBOOL(hAPP(V_P_2,B_y))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_y)))) ) ) ),
file('theBenchmark.p',fact_finite__Collect__bounded__ex) ).
fof(fact_inj__graph,axiom,
! [T_c,T_b] : c_Fun_Oinj__on(tc_fun(T_b,T_c),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Set_OCollect(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool)),hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))),
file('theBenchmark.p',fact_inj__graph) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
! [V_P_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J) ).
fof(fact_finite__psubset__def,axiom,
! [T_b] : c_Wellfounded_Ofinite__psubset(T_b) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_b)))),
file('theBenchmark.p',fact_finite__psubset__def) ).
fof(fact_inv__image__def,axiom,
! [V_f_2,V_r_2,T_b,T_c] : hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_c,T_c)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_c),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),T_b),c_COMBB(T_c,tc_prod(T_c,T_c),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_prod(T_c,T_c)),T_b),c_Product__Type_OPair(T_c,T_c)),V_f_2))),V_f_2)))),V_r_2))),
file('theBenchmark.p',fact_inv__image__def) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
! [V_P_2] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
! [V_P_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_P_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),V_P_2),c_Int_Onat)))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J) ).
fof(fact_add__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_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_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_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_inf__Sup1__distrib,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Odistrib__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ),
file('theBenchmark.p',fact_inf__Sup1__distrib) ).
fof(fact_inf__Sup2__distrib,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Odistrib__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ),
file('theBenchmark.p',fact_inf__Sup2__distrib) ).
fof(fact_min__max_Oinf__Sup2__distrib,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omin(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ),
file('theBenchmark.p',fact_min__max_Oinf__Sup2__distrib) ).
fof(fact_min__max_Osup__Inf2__distrib,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omax(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ),
file('theBenchmark.p',fact_min__max_Osup__Inf2__distrib) ).
fof(fact_Nitpick_Oprod__def,axiom,
! [V_B_2,V_A_2,T_c,T_b] : c_Nitpick_Oprod(T_b,T_c,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2)))),
file('theBenchmark.p',fact_Nitpick_Oprod__def) ).
fof(fact_int__ge__less__than__def,axiom,
! [V_d_2] : c_Int_Oint__ge__less__than(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
file('theBenchmark.p',fact_int__ge__less__than__def) ).
fof(fact_int__ge__less__than2__def,axiom,
! [V_d_2] : c_Int_Oint__ge__less__than2(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
file('theBenchmark.p',fact_int__ge__less__than2__def) ).
fof(fact_reflp__def,axiom,
! [V_r_2,T_b] :
( c_Predicate_Oreflp(T_b,V_r_2)
<=> c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ),
file('theBenchmark.p',fact_reflp__def) ).
fof(fact_setsum__mult__setsum__if__inj,axiom,
! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
( class_Rings_Osemiring__0(T_d)
=> ( c_Fun_Oinj__on(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_d),c_Fun_Oid(T_d)),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),T_d),c_COMBB(T_d,tc_HOL_Obool,T_c)),c_fequal))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))))))) ) ),
file('theBenchmark.p',fact_setsum__mult__setsum__if__inj) ).
fof(fact_setsum__multicount__gen,axiom,
! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2))
=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_s_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = hAPP(V_k_2,B_x) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_k_2),V_t_2) ) ) ),
file('theBenchmark.p',fact_setsum__multicount__gen) ).
fof(fact_inj__on__id,axiom,
! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2),
file('theBenchmark.p',fact_inj__on__id) ).
fof(fact_o__eq__id__dest,axiom,
! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_c_2)
=> hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ),
file('theBenchmark.p',fact_o__eq__id__dest) ).
fof(fact_o__id,axiom,
! [V_f_2,T_c,T_b] : hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_f_2),c_Fun_Oid(T_b)) = V_f_2,
file('theBenchmark.p',fact_o__id) ).
fof(fact_id__o,axiom,
! [V_g_2,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_g_2) = V_g_2,
file('theBenchmark.p',fact_id__o) ).
fof(fact_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_id__def,axiom,
! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1,
file('theBenchmark.p',fact_id__def) ).
fof(fact_apsnd__id,axiom,
! [T_b,T_c] : c_Product__Type_Oapsnd(T_c,T_c,T_b,c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
file('theBenchmark.p',fact_apsnd__id) ).
fof(fact_reflpE,axiom,
! [V_x_2,V_r_2,T_b] :
( c_Predicate_Oreflp(T_b,V_r_2)
=> hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ),
file('theBenchmark.p',fact_reflpE) ).
fof(fact_id__apply,axiom,
! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x,
file('theBenchmark.p',fact_id__apply) ).
fof(fact_vimage__id,axiom,
! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2,
file('theBenchmark.p',fact_vimage__id) ).
fof(fact_map__pair_Oid,axiom,
! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_Fun_Oid(T_b),c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
file('theBenchmark.p',fact_map__pair_Oid) ).
fof(fact_map__pair_Oidentity,axiom,
! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
file('theBenchmark.p',fact_map__pair_Oidentity) ).
fof(fact_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_image__id,axiom,
! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2,
file('theBenchmark.p',fact_image__id) ).
fof(fact_surj__id,axiom,
! [T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_surj__id) ).
fof(fact_folding_Oempty,axiom,
! [V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ),
file('theBenchmark.p',fact_folding_Oempty) ).
fof(fact_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_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_split__Pair,axiom,
! [T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
file('theBenchmark.p',fact_split__Pair) ).
fof(fact_setsum__reindex__id,axiom,
! [V_B_2,V_f_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ),
file('theBenchmark.p',fact_setsum__reindex__id) ).
fof(fact_setprod__reindex__id,axiom,
! [V_B_2,V_f_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ),
file('theBenchmark.p',fact_setprod__reindex__id) ).
fof(fact_finite__conv__nat__seg__image,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
<=> ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,B_f),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),B_n))) ),
file('theBenchmark.p',fact_finite__conv__nat__seg__image) ).
fof(fact_rel__comp__def,axiom,
! [V_s_2,V_r_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_d))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBC(T_d,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_d),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_b,T_d)))),c_Product__Type_OPair(T_b,T_d)))),V_r_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_d,T_c)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_d,T_c),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_d,T_c)))),hAPP(c_COMBC(T_d,T_c,tc_prod(T_d,T_c)),c_Product__Type_OPair(T_d,T_c))))),V_s_2))))),
file('theBenchmark.p',fact_rel__comp__def) ).
fof(fact_Range__Collect__split,axiom,
! [V_P_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_P_2))),
file('theBenchmark.p',fact_Range__Collect__split) ).
fof(fact_rel__compI,axiom,
! [V_s_2,V_c_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_b_2),V_c_2)),V_s_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_a_2),V_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ),
file('theBenchmark.p',fact_rel__compI) ).
fof(fact_RangeI,axiom,
! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ),
file('theBenchmark.p',fact_RangeI) ).
fof(fact_rel__comp__UNION__distrib2,axiom,
! [V_s_2,V_r_2,V_I_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_e),c_Relation_Orel__comp(T_b,T_d,T_c)),V_r_2)),V_s_2)),
file('theBenchmark.p',fact_rel__comp__UNION__distrib2) ).
fof(fact_rel__comp__UNION__distrib,axiom,
! [V_r_2,V_I_2,T_e,V_s_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e),hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2)),V_r_2)),
file('theBenchmark.p',fact_rel__comp__UNION__distrib) ).
fof(fact_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_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_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__distrib,axiom,
! [V_T_2,V_S_2,V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_T_2)),
file('theBenchmark.p',fact_rel__comp__distrib) ).
fof(fact_rel__comp__distrib2,axiom,
! [V_R_2,V_T_2,V_S_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_S_2),V_T_2)),V_R_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_T_2),V_R_2)),
file('theBenchmark.p',fact_rel__comp__distrib2) ).
fof(fact_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__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_union__comp__emptyR,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
=> ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
=> hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_union__comp__emptyR) ).
fof(fact_union__comp__emptyL,axiom,
! [V_B_2,V_C_2,V_A_2,T_b] :
( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
=> ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_B_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
=> hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_union__comp__emptyL) ).
fof(fact_Range__Union,axiom,
! [V_S_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_c,T_b)),
file('theBenchmark.p',fact_Range__Union) ).
fof(fact_Range__empty,axiom,
! [T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Range__empty) ).
fof(fact_Range__empty__iff,axiom,
! [V_r_2,T_b,T_c] :
( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ),
file('theBenchmark.p',fact_Range__empty__iff) ).
fof(fact_rel__comp__subset__Sigma,axiom,
! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_B_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_2))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_C_2)))) ) ),
file('theBenchmark.p',fact_rel__comp__subset__Sigma) ).
fof(fact_Range__Un__eq,axiom,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)),
file('theBenchmark.p',fact_Range__Un__eq) ).
fof(fact_finite__Range,axiom,
! [V_r_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ),
file('theBenchmark.p',fact_finite__Range) ).
fof(fact_snd__eq__Range,axiom,
! [V_R_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_b,c_Product__Type_Osnd(T_c,T_b)),V_R_2) = hAPP(c_Relation_ORange(T_c,T_b),V_R_2),
file('theBenchmark.p',fact_snd__eq__Range) ).
fof(fact_Range__iff,axiom,
! [V_r_2,T_c,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
<=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),V_a_2)),V_r_2)) ),
file('theBenchmark.p',fact_Range__iff) ).
fof(fact_Range__insert,axiom,
! [V_r_2,V_b_2,V_a_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)),
file('theBenchmark.p',fact_Range__insert) ).
fof(fact_Range__Int__subset,axiom,
! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)))),
file('theBenchmark.p',fact_Range__Int__subset) ).
fof(fact_Range__Diff__subset,axiom,
! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2))),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)))),
file('theBenchmark.p',fact_Range__Diff__subset) ).
fof(fact_max__ext__compat,axiom,
! [V_S_2,V_R_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_b,V_R_2))) ),
file('theBenchmark.p',fact_max__ext__compat) ).
fof(fact_min__ext__compat,axiom,
! [V_S_2,V_R_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_b,V_R_2))) ),
file('theBenchmark.p',fact_min__ext__compat) ).
fof(fact_RangeP__Range__eq,axiom,
! [V_x_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ),
file('theBenchmark.p',fact_RangeP__Range__eq) ).
fof(fact_RangeE,axiom,
! [V_r_2,T_c,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
=> ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) ),
file('theBenchmark.p',fact_RangeE) ).
fof(fact_pred__comp__rel__comp__eq,axiom,
! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))),V_s_2)),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ),
file('theBenchmark.p',fact_pred__comp__rel__comp__eq) ).
fof(fact_pred__comp_Ointros,axiom,
! [T_d,T_c,T_b,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] :
( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2))
=> hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a_2),V_c_2)) ) ),
file('theBenchmark.p',fact_pred__comp_Ointros) ).
fof(fact_RangeP_Ointros,axiom,
! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
=> hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ),
file('theBenchmark.p',fact_RangeP_Ointros) ).
fof(fact_pred__comp_Oequations,axiom,
! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a1_2),V_a3_2))
<=> ? [B_b] :
( hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2))
& hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) ) ),
file('theBenchmark.p',fact_pred__comp_Oequations) ).
fof(fact_RangeP_Oequations,axiom,
! [V_a2_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
<=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ),
file('theBenchmark.p',fact_RangeP_Oequations) ).
fof(fact_reduction__pairI,axiom,
! [V_S_2,V_R_2,T_b] :
( c_Wellfounded_Owf(T_b,V_R_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
=> c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ),
file('theBenchmark.p',fact_reduction__pairI) ).
fof(fact_Domain__Collect__split,axiom,
! [V_P_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),V_P_2)),
file('theBenchmark.p',fact_Domain__Collect__split) ).
fof(fact_the__eq__trivial,axiom,
! [V_a_2,T_b] : c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2,
file('theBenchmark.p',fact_the__eq__trivial) ).
fof(fact_wf__less__than,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
file('theBenchmark.p',fact_wf__less__than) ).
fof(fact_wf__empty,axiom,
! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),
file('theBenchmark.p',fact_wf__empty) ).
fof(fact_wf__inv__image,axiom,
! [V_f_2,T_c,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ),
file('theBenchmark.p',fact_wf__inv__image) ).
fof(fact_wf__lex__prod,axiom,
! [V_rb_2,T_c,V_ra_2,T_b] :
( c_Wellfounded_Owf(T_b,V_ra_2)
=> ( c_Wellfounded_Owf(T_c,V_rb_2)
=> c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ),
file('theBenchmark.p',fact_wf__lex__prod) ).
fof(fact_wf__measure,axiom,
! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)),
file('theBenchmark.p',fact_wf__measure) ).
fof(fact_DomainI,axiom,
! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ),
file('theBenchmark.p',fact_DomainI) ).
fof(fact_wf__comp__self,axiom,
! [V_R_2,T_b] :
( c_Wellfounded_Owf(T_b,V_R_2)
<=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ),
file('theBenchmark.p',fact_wf__comp__self) ).
fof(fact_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__irrefl,axiom,
! [V_a_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ),
file('theBenchmark.p',fact_wf__irrefl) ).
fof(fact_wf__asym,axiom,
! [V_x_2,V_a_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_wf__asym) ).
fof(fact_wf__not__sym,axiom,
! [V_x_2,V_a_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_wf__not__sym) ).
fof(fact_wf__not__refl,axiom,
! [V_a_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ),
file('theBenchmark.p',fact_wf__not__refl) ).
fof(fact_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__Int1,axiom,
! [V_r_H_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2)) ),
file('theBenchmark.p',fact_wf__Int1) ).
fof(fact_wf__Int2,axiom,
! [V_r_H_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2)) ),
file('theBenchmark.p',fact_wf__Int2) ).
fof(fact_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__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__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_wf__less,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))),
file('theBenchmark.p',fact_wf__less) ).
fof(fact_wf__int__ge__less__than2,axiom,
! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)),
file('theBenchmark.p',fact_wf__int__ge__less__than2) ).
fof(fact_wf__int__ge__less__than,axiom,
! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)),
file('theBenchmark.p',fact_wf__int__ge__less__than) ).
fof(fact_wf__Un,axiom,
! [V_s_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> ( c_Wellfounded_Owf(T_b,V_s_2)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_s_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ),
file('theBenchmark.p',fact_wf__Un) ).
fof(fact_wf__acc__iff,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
<=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ),
file('theBenchmark.p',fact_wf__acc__iff) ).
fof(fact_acc__wfD,axiom,
! [V_x_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ),
file('theBenchmark.p',fact_acc__wfD) ).
fof(fact_wf__no__loop,axiom,
! [V_R_2,T_b] :
( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
=> c_Wellfounded_Owf(T_b,V_R_2) ),
file('theBenchmark.p',fact_wf__no__loop) ).
fof(fact_wf__union__merge,axiom,
! [V_S_2,V_R_2,T_b] :
( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
<=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_S_2),V_R_2))),V_S_2)) ),
file('theBenchmark.p',fact_wf__union__merge) ).
fof(fact_Domain__empty,axiom,
! [T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Domain__empty) ).
fof(fact_Domain__empty__iff,axiom,
! [V_r_2,T_c,T_b] :
( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ),
file('theBenchmark.p',fact_Domain__empty__iff) ).
fof(fact_Domain__mono,axiom,
! [V_s_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_s_2))) ),
file('theBenchmark.p',fact_Domain__mono) ).
fof(fact_Domain__Un__eq,axiom,
! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)),
file('theBenchmark.p',fact_Domain__Un__eq) ).
fof(fact_finite__Domain,axiom,
! [V_r_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ),
file('theBenchmark.p',fact_finite__Domain) ).
fof(fact_fst__eq__Domain,axiom,
! [V_R_2,T_c,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),V_R_2) = hAPP(c_Relation_ODomain(T_b,T_c),V_R_2),
file('theBenchmark.p',fact_fst__eq__Domain) ).
fof(fact_wf__iff__no__infinite__down__chain,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
<=> ~ ? [B_f] :
! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2)) ),
file('theBenchmark.p',fact_wf__iff__no__infinite__down__chain) ).
fof(fact_wfE__pf,axiom,
! [V_A_2,V_R_2,T_b] :
( c_Wellfounded_Owf(T_b,V_R_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),V_A_2)))
=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_wfE__pf) ).
fof(fact_wf__union__compatible,axiom,
! [V_S_2,V_R_2,T_b] :
( c_Wellfounded_Owf(T_b,V_R_2)
=> ( c_Wellfounded_Owf(T_b,V_S_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ),
file('theBenchmark.p',fact_wf__union__compatible) ).
fof(fact_Domain__iff,axiom,
! [V_r_2,T_c,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
<=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) ),
file('theBenchmark.p',fact_Domain__iff) ).
fof(fact_wf,axiom,
! [T_b] :
( class_Orderings_Owellorder(T_b)
=> c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_b)))) ),
file('theBenchmark.p',fact_wf) ).
fof(fact_Domain__insert,axiom,
! [V_r_2,V_b_2,V_a_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)),
file('theBenchmark.p',fact_Domain__insert) ).
fof(fact_reduction__pair__def,axiom,
! [V_P_2,T_b] :
( c_FunDef_Oreduction__pair(T_b,V_P_2)
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
& c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)) ) ),
file('theBenchmark.p',fact_reduction__pair__def) ).
fof(fact_reduction__pair__lemma,axiom,
! [V_S_2,V_R_2,V_P_2,T_b] :
( c_FunDef_Oreduction__pair(T_b,V_P_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
=> ( c_Wellfounded_Owf(T_b,V_S_2)
=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ),
file('theBenchmark.p',fact_reduction__pair__lemma) ).
fof(fact_Domain__Int__subset,axiom,
! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)))),
file('theBenchmark.p',fact_Domain__Int__subset) ).
fof(fact_Domain__Diff__subset,axiom,
! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2))),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)))),
file('theBenchmark.p',fact_Domain__Diff__subset) ).
fof(fact_Field__def,axiom,
! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_r_2)),
file('theBenchmark.p',fact_Field__def) ).
fof(fact_wf__map__pair__image,axiom,
! [V_f_2,T_c,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> c_Wellfounded_Owf(T_c,hAPP(c_Set_Oimage(tc_prod(T_b,T_b),tc_prod(T_c,T_c),c_Product__Type_Omap__pair(T_b,T_c,T_b,T_c,V_f_2,V_f_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_wf__map__pair__image) ).
fof(fact_Domain__Union,axiom,
! [V_S_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_b,T_c)),
file('theBenchmark.p',fact_Domain__Union) ).
fof(fact_the__sym__eq__trivial,axiom,
! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2,
file('theBenchmark.p',fact_the__sym__eq__trivial) ).
fof(fact_DomainP__Domain__eq,axiom,
! [V_x_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ),
file('theBenchmark.p',fact_DomainP__Domain__eq) ).
fof(fact_wf__lenlex,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ),
file('theBenchmark.p',fact_wf__lenlex) ).
fof(fact_DomainE,axiom,
! [V_r_2,T_c,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
=> ~ ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) ),
file('theBenchmark.p',fact_DomainE) ).
fof(fact_DomainP_Ointros,axiom,
! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
=> hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ),
file('theBenchmark.p',fact_DomainP_Ointros) ).
fof(fact_DomainP_Oequations,axiom,
! [V_a1_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
<=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ),
file('theBenchmark.p',fact_DomainP_Oequations) ).
fof(fact_pred__nat__def,axiom,
c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))),
file('theBenchmark.p',fact_pred__nat__def) ).
fof(fact_wf__lex,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ),
file('theBenchmark.p',fact_wf__lex) ).
fof(fact_wf__lexn,axiom,
! [V_n_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ),
file('theBenchmark.p',fact_wf__lexn) ).
fof(fact_lex__def,axiom,
! [V_r_2,T_b] : c_List_Olex(T_b,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_b,V_r_2)),
file('theBenchmark.p',fact_lex__def) ).
fof(fact_lexn_Osimps_I1_J,axiom,
! [V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),
file('theBenchmark.p',fact_lexn_Osimps_I1_J) ).
fof(fact_wf__pred__nat,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
file('theBenchmark.p',fact_wf__pred__nat) ).
fof(fact_wf__same__fst,axiom,
! [T_b,V_R_2,T_c,V_P_2] :
( ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
=> c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) )
=> c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2)) ),
file('theBenchmark.p',fact_wf__same__fst) ).
fof(fact_wf__if__measure,axiom,
! [T_b,V_g_2,V_f_2,V_P_2] :
( ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,hAPP(V_g_2,B_x))),hAPP(V_f_2,B_x))) )
=> c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),V_g_2))))) ),
file('theBenchmark.p',fact_wf__if__measure) ).
fof(fact_wfP__def,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_OwfP(T_b,V_r_2)
<=> c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ),
file('theBenchmark.p',fact_wfP__def) ).
fof(fact_wfP__empty,axiom,
! [T_b] : c_Wellfounded_OwfP(T_b,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse))),
file('theBenchmark.p',fact_wfP__empty) ).
fof(fact_accp__wfPD,axiom,
! [V_x_2,V_r_2,T_b] :
( c_Wellfounded_OwfP(T_b,V_r_2)
=> hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ),
file('theBenchmark.p',fact_accp__wfPD) ).
fof(fact_wfP__accp__iff,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_OwfP(T_b,V_r_2)
<=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ),
file('theBenchmark.p',fact_wfP__accp__iff) ).
fof(fact_wfP__subset,axiom,
! [V_p_2,V_r_2,T_b] :
( c_Wellfounded_OwfP(T_b,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_p_2),V_r_2))
=> c_Wellfounded_OwfP(T_b,V_p_2) ) ),
file('theBenchmark.p',fact_wfP__subset) ).
fof(fact_wf__in__rel,axiom,
! [V_R_2,T_b] :
( c_Wellfounded_Owf(T_b,V_R_2)
=> c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ),
file('theBenchmark.p',fact_wf__in__rel) ).
fof(fact_wfP__wf__eq,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2))
<=> c_Wellfounded_Owf(T_b,V_r_2) ),
file('theBenchmark.p',fact_wfP__wf__eq) ).
fof(fact_wfP__acyclicP,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_OwfP(T_b,V_r_2)
=> c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ),
file('theBenchmark.p',fact_wfP__acyclicP) ).
fof(fact_pigeonhole__infinite,axiom,
! [V_f_2,T_c,V_A_2,T_b] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
=> ? [B_x] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),hAPP(V_f_2,B_x))))))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ),
file('theBenchmark.p',fact_pigeonhole__infinite) ).
fof(fact_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_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_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_Nitpick_Owf_H__def,axiom,
! [V_r_2,T_b] :
( c_Nitpick_Owf_H(T_b,V_r_2)
<=> ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) )
& c_Wellfounded_Oacyclic(T_b,V_r_2) ) ),
file('theBenchmark.p',fact_Nitpick_Owf_H__def) ).
fof(fact_Abs__Integ__induct,axiom,
! [V_x_2,V_P_2] :
( ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
=> hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) )
=> hBOOL(hAPP(V_P_2,V_x_2)) ),
file('theBenchmark.p',fact_Abs__Integ__induct) ).
fof(fact_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__splitE,axiom,
! [V_p_2,V_c_2,T_d,T_c,V_z_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),V_p_2)))
=> ~ ! [B_x,B_y] :
( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ),
file('theBenchmark.p',fact_mem__splitE) ).
fof(fact_mem__splitI2,axiom,
! [V_c_2,V_z_2,T_d,T_c,T_b,V_p_2] :
( ! [B_a,B_b] :
( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)
=> hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) )
=> hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_c_2),V_p_2))) ),
file('theBenchmark.p',fact_mem__splitI2) ).
fof(fact_Eps__split,axiom,
! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))),
file('theBenchmark.p',fact_Eps__split) ).
fof(fact_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_c_2,V_P_2] :
( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
=> ( V_c_2 = c_Hilbert__Choice_OEps(T_b,V_P_2)
=> hBOOL(hAPP(V_P_2,V_c_2)) ) ),
file('theBenchmark.p',fact_exE__some) ).
fof(fact_some__sym__eq__trivial,axiom,
! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2,
file('theBenchmark.p',fact_some__sym__eq__trivial) ).
fof(fact_some__eq__trivial,axiom,
! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2,
file('theBenchmark.p',fact_some__eq__trivial) ).
fof(fact_some__eq__ex,axiom,
! [T_b,V_P_2] :
( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
<=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ),
file('theBenchmark.p',fact_some__eq__ex) ).
fof(fact_someI__ex,axiom,
! [T_b,V_P_2] :
( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
=> hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ),
file('theBenchmark.p',fact_someI__ex) ).
fof(fact_tfl__some,axiom,
! [T_b,B_P] :
( ? [B_x] : hBOOL(hAPP(B_P,B_x))
=> hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ),
file('theBenchmark.p',fact_tfl__some) ).
fof(fact_someI,axiom,
! [T_b,V_x_2,V_P_2] :
( hBOOL(hAPP(V_P_2,V_x_2))
=> hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ),
file('theBenchmark.p',fact_someI) ).
fof(fact_split__paired__Eps,axiom,
! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_P_2) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))),
file('theBenchmark.p',fact_split__paired__Eps) ).
fof(fact_Eps__split__eq,axiom,
! [V_y_2,V_x_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2),
file('theBenchmark.p',fact_Eps__split__eq) ).
fof(fact_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_coinduct__set,axiom,
! [V_X_2,V_a_2,V_f_2,T_b] :
( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))) ) ) ),
file('theBenchmark.p',fact_coinduct__set) ).
fof(fact_def__coinduct__set,axiom,
! [V_X_2,V_a_2,V_f_2,T_b,V_A_2] :
( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)
=> ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_A_2))))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_def__coinduct__set) ).
fof(fact_def__gfp__unfold,axiom,
! [V_f_2,V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> V_A_2 = hAPP(V_f_2,V_A_2) ) ) ),
file('theBenchmark.p',fact_def__gfp__unfold) ).
fof(fact_gfp__unfold,axiom,
! [V_f_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2) = hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)) ) ),
file('theBenchmark.p',fact_gfp__unfold) ).
fof(fact_gfp__upperbound,axiom,
! [V_f_2,V_X_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,V_X_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))) ) ),
file('theBenchmark.p',fact_gfp__upperbound) ).
fof(fact_weak__coinduct,axiom,
! [V_f_2,V_X_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,V_X_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))) ) ),
file('theBenchmark.p',fact_weak__coinduct) ).
fof(fact_gfp__lemma2,axiom,
! [V_f_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))) ) ),
file('theBenchmark.p',fact_gfp__lemma2) ).
fof(fact_gfp__lemma3,axiom,
! [V_f_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))) ) ),
file('theBenchmark.p',fact_gfp__lemma3) ).
fof(fact_weak__coinduct__image,axiom,
! [V_f_2,V_g_2,T_c,V_X_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),V_X_2)),hAPP(V_f_2,hAPP(c_Set_Oimage(T_b,T_c,V_g_2),V_X_2))))
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_g_2,V_a_2)),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_c,tc_HOL_Obool),V_f_2))) ) ),
file('theBenchmark.p',fact_weak__coinduct__image) ).
fof(fact_gfp__fun__UnI2,axiom,
! [V_X_2,V_a_2,V_f_2,T_b] :
( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))))) ) ),
file('theBenchmark.p',fact_gfp__fun__UnI2) ).
fof(fact_coinduct,axiom,
! [V_X_2,V_f_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))) ) ) ),
file('theBenchmark.p',fact_coinduct) ).
fof(fact_coinduct__lemma,axiom,
! [V_f_2,V_X_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))))
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))))) ) ) ),
file('theBenchmark.p',fact_coinduct__lemma) ).
fof(fact_def__coinduct,axiom,
! [V_X_2,V_f_2,V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),V_A_2))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_def__coinduct) ).
fof(fact_def__coinduct3,axiom,
! [V_X_2,V_a_2,V_f_2,T_b,V_A_2] :
( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)
=> ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),V_A_2)))))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_def__coinduct3) ).
fof(fact_coinduct3,axiom,
! [V_X_2,V_a_2,V_f_2,T_b] :
( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))))))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))) ) ) ),
file('theBenchmark.p',fact_coinduct3) ).
fof(fact_def__Collect__coinduct,axiom,
! [V_X_2,V_a_2,V_P_2,T_b,V_A_2] :
( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_OCollect(T_b)),V_P_2))
=> ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_OCollect(T_b)),V_P_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
=> ( ! [B_z] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_z),V_X_2))
=> hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_A_2)),B_z)) )
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_def__Collect__coinduct) ).
fof(fact_lfp__lowerbound,axiom,
! [V_A_2,V_f_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_A_2)),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),V_A_2)) ) ),
file('theBenchmark.p',fact_lfp__lowerbound) ).
fof(fact_lfp__const,axiom,
! [V_t_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> c_Inductive_Ocomplete__lattice__class_Olfp(T_b,hAPP(c_COMBK(T_b,T_b),V_t_2)) = V_t_2 ),
file('theBenchmark.p',fact_lfp__const) ).
fof(fact_lfp__unfold,axiom,
! [V_f_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2) = hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)) ) ),
file('theBenchmark.p',fact_lfp__unfold) ).
fof(fact_def__lfp__unfold,axiom,
! [V_f_2,V_h_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( V_h_2 = c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> V_h_2 = hAPP(V_f_2,V_h_2) ) ) ),
file('theBenchmark.p',fact_def__lfp__unfold) ).
fof(fact_lfp__lemma2,axiom,
! [V_f_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2))),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2))) ) ),
file('theBenchmark.p',fact_lfp__lemma2) ).
fof(fact_lfp__lemma3,axiom,
! [V_f_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)))) ) ),
file('theBenchmark.p',fact_lfp__lemma3) ).
fof(fact_def__lfp__induct,axiom,
! [V_P_2,V_f_2,V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_A_2),V_P_2))),V_P_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_A_2),V_P_2)) ) ) ) ),
file('theBenchmark.p',fact_def__lfp__induct) ).
fof(fact_lfp__induct,axiom,
! [V_P_2,V_f_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),V_P_2))),V_P_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),V_P_2)) ) ) ),
file('theBenchmark.p',fact_lfp__induct) ).
fof(fact_coinduct3__lemma,axiom,
! [V_f_2,V_X_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))))))
=> ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))))) ) ),
file('theBenchmark.p',fact_coinduct3__lemma) ).
fof(fact_def__lfp__induct__set,axiom,
! [V_P_2,V_a_2,V_f_2,T_b,V_A_2] :
( V_A_2 = c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)
=> ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2)))))
=> hBOOL(hAPP(V_P_2,B_x)) )
=> hBOOL(hAPP(V_P_2,V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_def__lfp__induct__set) ).
fof(fact_lfp__induct__set,axiom,
! [V_P_2,V_f_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))
=> ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)),hAPP(c_Set_OCollect(T_b),V_P_2)))))
=> hBOOL(hAPP(V_P_2,B_x)) )
=> hBOOL(hAPP(V_P_2,V_a_2)) ) ) ),
file('theBenchmark.p',fact_lfp__induct__set) ).
fof(fact_lfp__induct2,axiom,
! [V_P_2,V_f_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_f_2)))
=> ( c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_f_2)
=> ( ! [B_a,B_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_f_2)),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2))))))
=> hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) )
=> hBOOL(hAPP(hAPP(V_P_2,V_a_2),V_b_2)) ) ) ),
file('theBenchmark.p',fact_lfp__induct2) ).
fof(fact_wf__no__infinite__down__chainE,axiom,
! [V_f_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> ~ ! [B_k] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_k))),hAPP(V_f_2,B_k))),V_r_2)) ),
file('theBenchmark.p',fact_wf__no__infinite__down__chainE) ).
fof(fact_iterate_Osimps,axiom,
! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_b,tc_prod(T_c,T_b)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_c,T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_f_2)) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2) ) ),
file('theBenchmark.p',fact_iterate_Osimps) ).
fof(fact_scomp__unfold,axiom,
! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_e),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_d,T_e),hAPP(V_f_2,V_x_2))),
file('theBenchmark.p',fact_scomp__unfold) ).
fof(fact_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__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__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__apply,axiom,
! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)),
file('theBenchmark.p',fact_scomp__apply) ).
fof(fact_scomp__def,axiom,
! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)),
file('theBenchmark.p',fact_scomp__def) ).
fof(fact_less__eq,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_less__eq) ).
fof(fact_wf__eq__minimal,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
<=> ! [B_Q] :
( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
=> ? [B_x] :
( ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) )
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) ) ) ),
file('theBenchmark.p',fact_wf__eq__minimal) ).
fof(fact_wf__trancl,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ),
file('theBenchmark.p',fact_wf__trancl) ).
fof(fact_less__than__def,axiom,
c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
file('theBenchmark.p',fact_less__than__def) ).
fof(fact_acyclic__def,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Oacyclic(T_b,V_r_2)
<=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
file('theBenchmark.p',fact_acyclic__def) ).
fof(fact_trancl_Or__into__trancl,axiom,
! [V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
file('theBenchmark.p',fact_trancl_Or__into__trancl) ).
fof(fact_trancl__subset__Field2,axiom,
! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_Relation_OField(T_b),V_r_2))))),
file('theBenchmark.p',fact_trancl__subset__Field2) ).
fof(fact_r__into__trancl_H,axiom,
! [V_r_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
file('theBenchmark.p',fact_r__into__trancl_H) ).
fof(fact_trancl__empty,axiom,
! [T_b] : c_Transitive__Closure_Otrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),
file('theBenchmark.p',fact_trancl__empty) ).
fof(fact_trancl__domain,axiom,
! [V_r_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_b),V_r_2),
file('theBenchmark.p',fact_trancl__domain) ).
fof(fact_trancl__range,axiom,
! [V_r_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ORange(T_b,T_b),V_r_2),
file('theBenchmark.p',fact_trancl__range) ).
fof(fact_finite__trancl,axiom,
! [V_r_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ),
file('theBenchmark.p',fact_finite__trancl) ).
fof(fact_trancl__trans,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_trancl__trans) ).
fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).
fof(fact_trancl__into__trancl2,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_trancl__into__trancl2) ).
fof(fact_r__r__into__trancl,axiom,
! [V_c_2,V_R_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_R_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_R_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ),
file('theBenchmark.p',fact_r__r__into__trancl) ).
fof(fact_trancl__mono,axiom,
! [V_s_2,V_r_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ),
file('theBenchmark.p',fact_trancl__mono) ).
fof(fact_trancl__unfold,axiom,
! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_r_2)),
file('theBenchmark.p',fact_trancl__unfold) ).
fof(fact_trancl__subset__Sigma,axiom,
! [V_A_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ),
file('theBenchmark.p',fact_trancl__subset__Sigma) ).
fof(fact_trancl__Int__subset,axiom,
! [V_s_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)) ) ),
file('theBenchmark.p',fact_trancl__Int__subset) ).
fof(fact_trancl__insert,axiom,
! [V_r_2,V_x_2,V_y_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBC(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),V_y_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))))),
file('theBenchmark.p',fact_trancl__insert) ).
fof(fact_reflcl__set__eq,axiom,
! [V_y_2,V_x_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),c_fequal),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))) ),
file('theBenchmark.p',fact_reflcl__set__eq) ).
fof(fact_r__into__rtrancl,axiom,
! [V_r_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
file('theBenchmark.p',fact_r__into__rtrancl) ).
fof(fact_rtrancl_Ortrancl__refl,axiom,
! [V_r_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))),
file('theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
fof(fact_IdI,axiom,
! [V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Relation_OId(T_b))),
file('theBenchmark.p',fact_IdI) ).
fof(fact_trancl__into__rtrancl,axiom,
! [V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
file('theBenchmark.p',fact_trancl__into__rtrancl) ).
fof(fact_trancl__unfold__left,axiom,
! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
file('theBenchmark.p',fact_trancl__unfold__left) ).
fof(fact_trancl__unfold__right,axiom,
! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2),
file('theBenchmark.p',fact_trancl__unfold__right) ).
fof(fact_trancl__reflcl,axiom,
! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
file('theBenchmark.p',fact_trancl__reflcl) ).
fof(fact_reflcl__trancl,axiom,
! [V_r_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
file('theBenchmark.p',fact_reflcl__trancl) ).
fof(fact_rtrancl__trancl__absorb,axiom,
! [V_R_2,T_b] : c_Transitive__Closure_Otrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
file('theBenchmark.p',fact_rtrancl__trancl__absorb) ).
fof(fact_trancl__rtrancl__absorb,axiom,
! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Otrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
file('theBenchmark.p',fact_trancl__rtrancl__absorb) ).
fof(fact_Domain__rtrancl,axiom,
! [V_R_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Domain__rtrancl) ).
fof(fact_Range__rtrancl,axiom,
! [V_R_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Range__rtrancl) ).
fof(fact_rtrancl__trans,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_rtrancl__trans) ).
fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).
fof(fact_converse__rtrancl__into__rtrancl,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).
fof(fact_rtrancl__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_refl__rtrancl,axiom,
! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
file('theBenchmark.p',fact_refl__rtrancl) ).
fof(fact_rtrancl__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_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__reflcl__absorb,axiom,
! [V_R_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
file('theBenchmark.p',fact_rtrancl__reflcl__absorb) ).
fof(fact_rtrancl__Un__rtrancl,axiom,
! [V_S_2,V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) = c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)),
file('theBenchmark.p',fact_rtrancl__Un__rtrancl) ).
fof(fact_rtrancl__reflcl,axiom,
! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
file('theBenchmark.p',fact_rtrancl__reflcl) ).
fof(fact_rtrancl__Un__subset,axiom,
! [V_S_2,V_R_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))),
file('theBenchmark.p',fact_rtrancl__Un__subset) ).
fof(fact_rtrancl__mono,axiom,
! [V_s_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ),
file('theBenchmark.p',fact_rtrancl__mono) ).
fof(fact_rtrancl__subset,axiom,
! [V_S_2,V_R_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
=> c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ),
file('theBenchmark.p',fact_rtrancl__subset) ).
fof(fact_rtrancl__subset__rtrancl,axiom,
! [V_s_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_s_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ),
file('theBenchmark.p',fact_rtrancl__subset__rtrancl) ).
fof(fact_in__rtrancl__UnI,axiom,
! [V_S_2,V_R_2,V_x_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))) ),
file('theBenchmark.p',fact_in__rtrancl__UnI) ).
fof(fact_rtrancl__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__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__empty,axiom,
! [T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Relation_OId(T_b),
file('theBenchmark.p',fact_rtrancl__empty) ).
fof(fact_R__O__Id,axiom,
! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_c),V_R_2),c_Relation_OId(T_c)) = V_R_2,
file('theBenchmark.p',fact_R__O__Id) ).
fof(fact_Id__O__R,axiom,
! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_c),c_Relation_OId(T_b)),V_R_2) = V_R_2,
file('theBenchmark.p',fact_Id__O__R) ).
fof(fact_Image__Id,axiom,
! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2,
file('theBenchmark.p',fact_Image__Id) ).
fof(fact_pair__in__Id__conv,axiom,
! [V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId(T_b)))
<=> V_a_2 = V_b_2 ),
file('theBenchmark.p',fact_pair__in__Id__conv) ).
fof(fact_rtrancl__trancl__trancl,axiom,
! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_rtrancl__trancl__trancl) ).
fof(fact_trancl__rtrancl__trancl,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_trancl__rtrancl__trancl) ).
fof(fact_rtrancl__into__trancl1,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_rtrancl__into__trancl1) ).
fof(fact_rtranclD,axiom,
! [V_R_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
& V_a_2 != V_b_2 )
| V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_rtranclD) ).
fof(fact_rtrancl__into__trancl2,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_rtrancl__into__trancl2) ).
fof(fact_rtrancl__eq__or__trancl,axiom,
! [V_R_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
& V_x_2 != V_y_2 )
| V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_rtrancl__eq__or__trancl) ).
fof(fact_Domain__Id,axiom,
! [T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Domain__Id) ).
fof(fact_Range__Id,axiom,
! [T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Range__Id) ).
fof(fact_refl__Id,axiom,
! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Relation_OId(T_b)),
file('theBenchmark.p',fact_refl__Id) ).
fof(fact_pair__leq__def,axiom,
c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))),
file('theBenchmark.p',fact_pair__leq__def) ).
fof(fact_Not__Domain__rtrancl,axiom,
! [V_y_2,V_R_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_Not__Domain__rtrancl) ).
fof(fact_acc__downwards,axiom,
! [V_b_2,V_r_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_acc__downwards) ).
fof(fact_acc__downwards__aux,axiom,
! [V_r_2,V_a_2,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_acc__downwards__aux) ).
fof(fact_wf__insert,axiom,
! [V_r_2,V_x_2,V_y_2,T_b] :
( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2))
<=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
& c_Wellfounded_Owf(T_b,V_r_2) ) ),
file('theBenchmark.p',fact_wf__insert) ).
fof(fact_acyclic__insert,axiom,
! [V_r_2,V_x_2,V_y_2,T_b] :
( c_Wellfounded_Oacyclic(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2))
<=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
& c_Wellfounded_Oacyclic(T_b,V_r_2) ) ),
file('theBenchmark.p',fact_acyclic__insert) ).
fof(fact_refl__reflcl,axiom,
! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))),
file('theBenchmark.p',fact_refl__reflcl) ).
fof(fact_Id__def,axiom,
! [T_b] : c_Relation_OId(T_b) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_b),tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),tc_prod(T_b,T_b)),c_COMBB(tc_prod(T_b,T_b),tc_HOL_Obool,T_b)),c_fequal)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))))),
file('theBenchmark.p',fact_Id__def) ).
fof(fact_irrefl__diff__Id,axiom,
! [V_r_2,T_b] : c_Relation_Oirrefl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))),
file('theBenchmark.p',fact_irrefl__diff__Id) ).
fof(fact_pred__nat__trancl__eq__le,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_pred__nat__trancl__eq__le) ).
fof(fact_trancl__subset__Sigma__aux,axiom,
! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| V_a_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_trancl__subset__Sigma__aux) ).
fof(fact_irrefl__tranclI,axiom,
! [V_x_2,V_r_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
file('theBenchmark.p',fact_irrefl__tranclI) ).
fof(fact_sequence__trans,axiom,
! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
( ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))),hAPP(V_f_2,V_i_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
file('theBenchmark.p',fact_sequence__trans) ).
fof(fact_rtrancl__converse,axiom,
! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
file('theBenchmark.p',fact_rtrancl__converse) ).
fof(fact_converse__Id,axiom,
! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b),
file('theBenchmark.p',fact_converse__Id) ).
fof(fact_acyclic__converse,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
<=> c_Wellfounded_Oacyclic(T_b,V_r_2) ),
file('theBenchmark.p',fact_acyclic__converse) ).
fof(fact_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__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_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_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__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_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_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__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_converse__iff,axiom,
! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ),
file('theBenchmark.p',fact_converse__iff) ).
fof(fact_converseI,axiom,
! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ),
file('theBenchmark.p',fact_converseI) ).
fof(fact_converseD,axiom,
! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ),
file('theBenchmark.p',fact_converseD) ).
fof(fact_converse__Un,axiom,
! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)),
file('theBenchmark.p',fact_converse__Un) ).
fof(fact_converse__rel__comp,axiom,
! [V_s_2,V_r_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_b),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(c_Relation_Oconverse(T_d,T_b),V_s_2)),hAPP(c_Relation_Oconverse(T_c,T_d),V_r_2)),
file('theBenchmark.p',fact_converse__rel__comp) ).
fof(fact_converse__UNION,axiom,
! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)),
file('theBenchmark.p',fact_converse__UNION) ).
fof(fact_trancl__converse,axiom,
! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)),
file('theBenchmark.p',fact_trancl__converse) ).
fof(fact_wf__converse__trancl,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
=> c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
file('theBenchmark.p',fact_wf__converse__trancl) ).
fof(fact_equiv__comp__eq,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2 ),
file('theBenchmark.p',fact_equiv__comp__eq) ).
fof(fact_Range__def,axiom,
! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),
file('theBenchmark.p',fact_Range__def) ).
fof(fact_Domain__converse,axiom,
! [V_r_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) = hAPP(c_Relation_ORange(T_c,T_b),V_r_2),
file('theBenchmark.p',fact_Domain__converse) ).
fof(fact_Range__converse,axiom,
! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_c),V_r_2),
file('theBenchmark.p',fact_Range__converse) ).
fof(fact_rtrancl__converseI,axiom,
! [V_r_2,V_x_2,V_y_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ),
file('theBenchmark.p',fact_rtrancl__converseI) ).
fof(fact_rtrancl__converseD,axiom,
! [V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
file('theBenchmark.p',fact_rtrancl__converseD) ).
fof(fact_trancl__converseI,axiom,
! [V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ),
file('theBenchmark.p',fact_trancl__converseI) ).
fof(fact_trancl__converseD,axiom,
! [V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))) ),
file('theBenchmark.p',fact_trancl__converseD) ).
fof(fact_Image__subset__eq,axiom,
! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)),V_B_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))))) ),
file('theBenchmark.p',fact_Image__subset__eq) ).
fof(fact_refl__on__comp__subset,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2))) ),
file('theBenchmark.p',fact_refl__on__comp__subset) ).
fof(fact_comp__equivI,axiom,
! [V_A_2,V_r_2,T_b] :
( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2
=> ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2
=> c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ),
file('theBenchmark.p',fact_comp__equivI) ).
fof(fact_finite__acyclic__wf__converse,axiom,
! [V_r_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
=> c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ),
file('theBenchmark.p',fact_finite__acyclic__wf__converse) ).
fof(fact_converse__def,axiom,
! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_b)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_c,T_b)))),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))))),V_r_2))),
file('theBenchmark.p',fact_converse__def) ).
fof(fact_Image__INT__eq,axiom,
! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
=> hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)) ) ),
file('theBenchmark.p',fact_Image__INT__eq) ).
fof(fact_total__on__diff__Id,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Relation_Ototal__on(T_b,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))
<=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ),
file('theBenchmark.p',fact_total__on__diff__Id) ).
fof(fact_single__valued__Id,axiom,
! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)),
file('theBenchmark.p',fact_single__valued__Id) ).
fof(fact_single__valued__subset,axiom,
! [V_s_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2))
=> ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
=> c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ),
file('theBenchmark.p',fact_single__valued__subset) ).
fof(fact_single__valued__rel__comp,axiom,
! [V_s_2,T_d,V_r_2,T_c,T_b] :
( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
=> ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
=> c_Relation_Osingle__valued(T_b,T_d,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)) ) ),
file('theBenchmark.p',fact_single__valued__rel__comp) ).
fof(fact_single__valued__Id__on,axiom,
! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)),
file('theBenchmark.p',fact_single__valued__Id__on) ).
fof(fact_total__on__empty,axiom,
! [V_r_2,T_b] : c_Relation_Ototal__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_r_2),
file('theBenchmark.p',fact_total__on__empty) ).
fof(fact_total__on__converse,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
<=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ),
file('theBenchmark.p',fact_total__on__converse) ).
fof(fact_single__valuedD,axiom,
! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_z_2)),V_r_2))
=> V_y_2 = V_z_2 ) ) ),
file('theBenchmark.p',fact_single__valuedD) ).
fof(fact_single__valued__def,axiom,
! [V_r_2,T_c,T_b] :
( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
<=> ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)),V_r_2))
=> ! [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)),V_r_2))
=> B_y = B_z ) ) ),
file('theBenchmark.p',fact_single__valued__def) ).
fof(fact_total__on__def,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
=> ( B_x != B_xa
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_xa),B_x)),V_r_2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_r_2)) ) ) ) ) ),
file('theBenchmark.p',fact_total__on__def) ).
fof(fact_single__valued__confluent,axiom,
! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
( c_Relation_Osingle__valued(T_b,T_b,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ) ),
file('theBenchmark.p',fact_single__valued__confluent) ).
fof(fact_Image__Int__eq,axiom,
! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2))
=> hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)) ),
file('theBenchmark.p',fact_Image__Int__eq) ).
fof(fact_rtrancl__imp__UN__rel__pow,axiom,
! [V_R_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)))) ),
file('theBenchmark.p',fact_rtrancl__imp__UN__rel__pow) ).
fof(fact_acyclicI,axiom,
! [V_r_2,T_b] :
( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> c_Wellfounded_Oacyclic(T_b,V_r_2) ),
file('theBenchmark.p',fact_acyclicI) ).
fof(fact_single__valued__rel__pow,axiom,
! [V_n_2,V_R_2,T_b] :
( c_Relation_Osingle__valued(T_b,T_b,V_R_2)
=> c_Relation_Osingle__valued(T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) ),
file('theBenchmark.p',fact_single__valued__rel__pow) ).
fof(fact_comp__funpow,axiom,
! [V_f_2,V_n_2,T_c,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),V_n_2),c_Fun_Ocomp(T_c,T_c,T_b,V_f_2)) = c_Fun_Ocomp(T_c,T_c,T_b,hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_n_2),V_f_2)),
file('theBenchmark.p',fact_comp__funpow) ).
fof(fact_funpow__swap1,axiom,
! [V_x_2,V_n_2,T_b,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),hAPP(V_f_2,V_x_2)),
file('theBenchmark.p',fact_funpow__swap1) ).
fof(fact_funpow__mult,axiom,
! [V_f_2,V_m_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2),
file('theBenchmark.p',fact_funpow__mult) ).
fof(fact_wf__exp,axiom,
! [V_R_2,V_n_2,T_b] :
( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))
=> c_Wellfounded_Owf(T_b,V_R_2) ),
file('theBenchmark.p',fact_wf__exp) ).
fof(fact_rel__pow__commute,axiom,
! [V_n_2,V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2),
file('theBenchmark.p',fact_rel__pow__commute) ).
fof(fact_rel__pow__1,axiom,
! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_R_2) = V_R_2,
file('theBenchmark.p',fact_rel__pow__1) ).
fof(fact_rtrancl__power,axiom,
! [V_R_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
<=> ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) ),
file('theBenchmark.p',fact_rtrancl__power) ).
fof(fact_rel__pow__imp__rtrancl,axiom,
! [V_R_2,V_n_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ),
file('theBenchmark.p',fact_rel__pow__imp__rtrancl) ).
fof(fact_relpow_Osimps_I2_J,axiom,
! [V_R_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2),
file('theBenchmark.p',fact_relpow_Osimps_I2_J) ).
fof(fact_rel__pow__add,axiom,
! [V_R_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),
file('theBenchmark.p',fact_rel__pow__add) ).
fof(fact_relpow_Osimps_I1_J,axiom,
! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_b),
file('theBenchmark.p',fact_relpow_Osimps_I1_J) ).
fof(fact_rel__pow__0__E,axiom,
! [V_R_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2)))
=> V_x_2 = V_y_2 ),
file('theBenchmark.p',fact_rel__pow__0__E) ).
fof(fact_rel__pow__0__I,axiom,
! [V_R_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))),
file('theBenchmark.p',fact_rel__pow__0__I) ).
fof(fact_rel__pow__Suc__I2,axiom,
! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ),
file('theBenchmark.p',fact_rel__pow__Suc__I2) ).
fof(fact_rel__pow__Suc__I,axiom,
! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_R_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ),
file('theBenchmark.p',fact_rel__pow__Suc__I) ).
fof(fact_funpow_Osimps_I2_J,axiom,
! [V_f_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)),
file('theBenchmark.p',fact_funpow_Osimps_I2_J) ).
fof(fact_funpow__add,axiom,
! [V_f_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)),
file('theBenchmark.p',fact_funpow__add) ).
fof(fact_funpow_Osimps_I1_J,axiom,
! [V_f_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_b),
file('theBenchmark.p',fact_funpow_Osimps_I1_J) ).
fof(fact_trancl__power,axiom,
! [V_R_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
<=> ? [B_n] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) ) ),
file('theBenchmark.p',fact_trancl__power) ).
fof(fact_rtrancl__is__UN__rel__pow,axiom,
! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)),
file('theBenchmark.p',fact_rtrancl__is__UN__rel__pow) ).
fof(fact_funpow__code__def,axiom,
! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b),
file('theBenchmark.p',fact_funpow__code__def) ).
fof(fact_rel__pow__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_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2),V_Q_2))))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2)))
=> ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_Q_2))
=> B_y = B_x ) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2))) ) ),
file('theBenchmark.p',fact_rtrancl__Un__separator__converseE) ).
fof(fact_rtrancl__Un__separatorE,axiom,
! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2),V_Q_2))))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_b,V_P_2)))
=> ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_Q_2))
=> B_x = B_y ) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2))) ) ),
file('theBenchmark.p',fact_rtrancl__Un__separatorE) ).
fof(fact_rel__pow__Suc__E,axiom,
! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
=> ~ ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ),
file('theBenchmark.p',fact_rel__pow__Suc__E) ).
fof(fact_rel__pow__Suc__D2,axiom,
! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
=> ? [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2)) ) ),
file('theBenchmark.p',fact_rel__pow__Suc__D2) ).
fof(fact_rel__pow__Suc__E2,axiom,
! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
=> ~ ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ) ),
file('theBenchmark.p',fact_rel__pow__Suc__E2) ).
fof(fact_tranclD2,axiom,
! [V_R_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
=> ? [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),V_R_2))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ),
file('theBenchmark.p',fact_tranclD2) ).
fof(fact_tranclD,axiom,
! [V_R_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
=> ? [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),V_R_2)) ) ),
file('theBenchmark.p',fact_tranclD) ).
fof(fact_IdE,axiom,
! [V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b)))
=> ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ),
file('theBenchmark.p',fact_IdE) ).
fof(fact_transfer__nat__int__set__cong,axiom,
! [V_P_H_2,V_P_2] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
=> ( hBOOL(hAPP(V_P_2,B_x))
<=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
=> hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2)) ),
file('theBenchmark.p',fact_transfer__nat__int__set__cong) ).
fof(fact_Int__Collect__mono,axiom,
! [V_Q_2,V_P_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> ( hBOOL(hAPP(V_P_2,B_x))
=> hBOOL(hAPP(V_Q_2,B_x)) ) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_b),V_Q_2)))) ) ),
file('theBenchmark.p',fact_Int__Collect__mono) ).
fof(fact_converseE,axiom,
! [V_r_2,V_yx_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_yx_2),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
=> ~ ! [B_x,B_y] :
( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),B_y)),V_r_2)) ) ),
file('theBenchmark.p',fact_converseE) ).
fof(fact_rel__compE,axiom,
! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2)))
=> ~ ! [B_x,B_y,B_z] :
( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),B_x),B_y)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_y),B_z)),V_s_2)) ) ) ),
file('theBenchmark.p',fact_rel__compE) ).
fof(fact_Nitpick_Oplus__frac__def,axiom,
! [V_r_2,V_q_2,T_b] : c_Nitpick_Oplus__frac(T_b,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_b),V_q_2),hAPP(c_Nitpick_Odenom(T_b),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_b),tc_Int_Oint),c_Nitpick_Ofrac(T_b)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_q_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_q_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_r_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_r_2)))))),c_COMBI(tc_Int_Oint))),
file('theBenchmark.p',fact_Nitpick_Oplus__frac__def) ).
fof(fact_Nitpick_Otimes__frac__def,axiom,
! [V_r,V_q,T_a] : c_Nitpick_Otimes__frac(T_a,V_q,V_r) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Odenom(T_a),V_r))),
file('theBenchmark.p',fact_Nitpick_Otimes__frac__def) ).
fof(fact_Nitpick_Oof__frac__def,axiom,
! [V_q,T_a,T_b] :
( ( class_Rings_Oring__1(T_b)
& class_Rings_Oinverse(T_b) )
=> c_Nitpick_Oof__frac(T_a,T_b,V_q) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Odenom(T_a),V_q))) ),
file('theBenchmark.p',fact_Nitpick_Oof__frac__def) ).
fof(fact_Nitpick_Oinverse__frac__def,axiom,
! [V_q,T_a] : c_Nitpick_Oinverse__frac(T_a,V_q) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_q)),
file('theBenchmark.p',fact_Nitpick_Oinverse__frac__def) ).
fof(fact_Nitpick_Ouminus__frac__def,axiom,
! [V_q,T_a] : c_Nitpick_Ouminus__frac(T_a,V_q) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Nitpick_Odenom(T_a),V_q))),
file('theBenchmark.p',fact_Nitpick_Ouminus__frac__def) ).
fof(fact_Nitpick_Oless__frac__def,axiom,
! [V_r_2,V_q_2,T_b] :
( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('theBenchmark.p',fact_Nitpick_Oless__frac__def) ).
fof(fact_Nitpick_Oless__eq__frac__def,axiom,
! [V_r_2,V_q_2,T_b] :
( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('theBenchmark.p',fact_Nitpick_Oless__eq__frac__def) ).
fof(fact_Nitpick_Odenom__def,axiom,
! [T_b] : c_Nitpick_Odenom(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)),
file('theBenchmark.p',fact_Nitpick_Odenom__def) ).
fof(fact_Nitpick_Onum__def,axiom,
! [T_b] : c_Nitpick_Onum(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)),
file('theBenchmark.p',fact_Nitpick_Onum__def) ).
fof(fact_internal__split__def,axiom,
! [T_d,T_c,T_b] : c_Product__Type_Ointernal__split(T_b,T_c,T_d) = c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),
file('theBenchmark.p',fact_internal__split__def) ).
fof(fact_bool_Osize_I1_J,axiom,
c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_bool_Osize_I1_J) ).
fof(fact_internal__split__conv,axiom,
! [V_b_2,V_a_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_c_2,V_a_2),V_b_2),
file('theBenchmark.p',fact_internal__split__conv) ).
fof(fact_bool_Osize_I2_J,axiom,
c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_bool_Osize_I2_J) ).
fof(fact_finite__less__ub,axiom,
! [V_u_2,V_f_2] :
( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_f_2)),V_u_2)))) ),
file('theBenchmark.p',fact_finite__less__ub) ).
fof(fact_lenlex__def,axiom,
! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_b),c_Wellfounded_Oless__than,c_List_Olex(T_b,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_b))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_COMBI(tc_List_Olist(T_b)))),
file('theBenchmark.p',fact_lenlex__def) ).
fof(fact_lexn__length,axiom,
! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2 ) ),
file('theBenchmark.p',fact_lexn__length) ).
fof(fact_neq__if__length__neq,axiom,
! [V_ys,V_xs,T_a] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)
=> V_xs != V_ys ),
file('theBenchmark.p',fact_neq__if__length__neq) ).
fof(fact_lenlex__conv,axiom,
! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_List_Olex(T_b,V_r_2)))))),
file('theBenchmark.p',fact_lenlex__conv) ).
fof(fact_length__sublist,axiom,
! [V_I_2,V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2)))),
file('theBenchmark.p',fact_length__sublist) ).
fof(fact_lexn_Osimps_I2_J,axiom,
! [V_n_2,V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_b,tc_List_Olist(T_b)),tc_prod(T_b,tc_List_Olist(T_b))),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_Product__Type_Omap__pair(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),c_Wellfounded_Olex__prod(T_b,tc_List_Olist(T_b),V_r_2,hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2)))))),
file('theBenchmark.p',fact_lexn_Osimps_I2_J) ).
fof(fact_impossible__Cons,axiom,
! [V_x,V_ys,V_xs,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)))
=> V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ),
file('theBenchmark.p',fact_impossible__Cons) ).
fof(fact_list_Oinject,axiom,
! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
( hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_H_2),V_list_H_2)
<=> ( V_list_2 = V_list_H_2
& V_a_2 = V_a_H_2 ) ),
file('theBenchmark.p',fact_list_Oinject) ).
fof(fact_not__Cons__self2,axiom,
! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs,
file('theBenchmark.p',fact_not__Cons__self2) ).
fof(fact_not__Cons__self,axiom,
! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),
file('theBenchmark.p',fact_not__Cons__self) ).
fof(fact_list_Osize_I4_J,axiom,
! [V_list,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),V_list)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_list)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_list_Osize_I4_J) ).
fof(fact_Cons__in__lex,axiom,
! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olex(T_b,V_r_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olex(T_b,V_r_2)))
& V_x_2 = V_y_2 )
| ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ),
file('theBenchmark.p',fact_Cons__in__lex) ).
fof(fact_set__Cons__def,axiom,
! [V_XS_2,V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBS(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_HOL_Obool,tc_List_Olist(T_b))),c_fequal))),c_List_Olist_OCons(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),V_XS_2)))))),
file('theBenchmark.p',fact_set__Cons__def) ).
fof(fact_pick_Osimps,axiom,
! [V_xs,V_x,T_a,V_i] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x)))
=> hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Random_Opick(T_a,V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x)))
=> hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a),V_x) ) ),
file('theBenchmark.p',fact_pick_Osimps) ).
fof(fact_select__weight__cons__zero,axiom,
! [V_xs_2,V_x_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2),
file('theBenchmark.p',fact_select__weight__cons__zero) ).
fof(fact_lexord__cons__cons,axiom,
! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2))),c_List_Olexord(T_b,V_r_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
& V_a_2 = V_b_2 )
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_lexord__cons__cons) ).
fof(fact_lexord__lex,axiom,
! [V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olex(T_b,V_r_2)))
<=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_lexord__lex) ).
fof(fact_rtrancl__listrel1__ConsI2,axiom,
! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ),
file('theBenchmark.p',fact_rtrancl__listrel1__ConsI2) ).
fof(fact_list_Osize_I2_J,axiom,
! [V_list_2,V_a_2,V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),c_List_Olist_Olist__size(T_b,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_list_Osize_I2_J) ).
fof(fact_Cons__acc__listrel1I,axiom,
! [V_xs_2,V_r_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ),
file('theBenchmark.p',fact_Cons__acc__listrel1I) ).
fof(fact_listrel1__mono,axiom,
! [V_s_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel1(T_b,V_s_2))) ),
file('theBenchmark.p',fact_listrel1__mono) ).
fof(fact_listrel1__converse,axiom,
! [V_r_2,T_b] : c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)),
file('theBenchmark.p',fact_listrel1__converse) ).
fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))),
file('theBenchmark.p',fact_listrel1__rtrancl__subset__rtrancl__listrel1) ).
fof(fact_rtrancl__listrel1__ConsI1,axiom,
! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ),
file('theBenchmark.p',fact_rtrancl__listrel1__ConsI1) ).
fof(fact_listrel1I2,axiom,
! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2))) ),
file('theBenchmark.p',fact_listrel1I2) ).
fof(fact_rtrancl__listrel1__eq__len,axiom,
! [V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2) ),
file('theBenchmark.p',fact_rtrancl__listrel1__eq__len) ).
fof(fact_listrel1__eq__len,axiom,
! [V_r_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ),
file('theBenchmark.p',fact_listrel1__eq__len) ).
fof(fact_in__listrel1__converse,axiom,
! [V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)))) ),
file('theBenchmark.p',fact_in__listrel1__converse) ).
fof(fact_listrel1I1,axiom,
! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_xs_2))),c_List_Olistrel1(T_b,V_r_2))) ),
file('theBenchmark.p',fact_listrel1I1) ).
fof(fact_Cons__listrel1__Cons,axiom,
! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
& V_x_2 = V_y_2 )
| ( V_xs_2 = V_ys_2
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ),
file('theBenchmark.p',fact_Cons__listrel1__Cons) ).
fof(fact_listrel__Cons,axiom,
! [V_xs_2,V_x_2,V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = c_List_Oset__Cons(T_b,hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))))),
file('theBenchmark.p',fact_listrel__Cons) ).
fof(fact_lexord__irreflexive,axiom,
! [V_y_2,V_r_2,T_b] :
( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ),
file('theBenchmark.p',fact_lexord__irreflexive) ).
fof(fact_listrel__rtrancl__refl,axiom,
! [V_r_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_xs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))),
file('theBenchmark.p',fact_listrel__rtrancl__refl) ).
fof(fact_listrel__mono,axiom,
! [V_s_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_List_Olistrel(T_b,V_s_2))) ),
file('theBenchmark.p',fact_listrel__mono) ).
fof(fact_listrel__subset__rtrancl__listrel1,axiom,
! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))),
file('theBenchmark.p',fact_listrel__subset__rtrancl__listrel1) ).
fof(fact_listrel__eq__len,axiom,
! [V_r_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ),
file('theBenchmark.p',fact_listrel__eq__len) ).
fof(fact_listrel__rtrancl__trans,axiom,
! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ),
file('theBenchmark.p',fact_listrel__rtrancl__trans) ).
fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
! [V_r_2,T_b] : c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)),
file('theBenchmark.p',fact_listrel__rtrancl__eq__rtrancl__listrel1) ).
fof(fact_listrel__reflcl__if__listrel1,axiom,
! [V_r_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ),
file('theBenchmark.p',fact_listrel__reflcl__if__listrel1) ).
fof(fact_listrel1__subset__listrel,axiom,
! [V_r_H_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2))
=> ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel(T_b,V_r_H_2))) ) ),
file('theBenchmark.p',fact_listrel1__subset__listrel) ).
fof(fact_rtrancl__listrel1__if__listrel,axiom,
! [V_r_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ),
file('theBenchmark.p',fact_rtrancl__listrel1__if__listrel) ).
fof(fact_listrel_OCons,axiom,
! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_listrel_OCons) ).
fof(fact_listrelp__listrel__eq,axiom,
! [V_xa_2,V_x_2,V_r_2,T_b] :
( c_List_Olistrelp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2),V_x_2,V_xa_2)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_xa_2)),c_List_Olistrel(T_b,V_r_2))) ),
file('theBenchmark.p',fact_listrelp__listrel__eq) ).
fof(fact_listrel__Cons2,axiom,
! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2)))
=> ~ ! [B_x,B_xs] :
( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_y_2)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),B_xs),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) ) ) ),
file('theBenchmark.p',fact_listrel__Cons2) ).
fof(fact_listrelp_Oequations_I2_J,axiom,
! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
( c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a4_2))
<=> ( c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2)
& hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ),
file('theBenchmark.p',fact_listrelp_Oequations_I2_J) ).
fof(fact_listrelp_OCons,axiom,
! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
=> ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
=> c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) ),
file('theBenchmark.p',fact_listrelp_OCons) ).
fof(fact_listrel__Cons1,axiom,
! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_b,V_r_2)))
=> ~ ! [B_y,B_ys] :
( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),B_y)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),B_ys)),c_List_Olistrel(T_b,V_r_2))) ) ) ),
file('theBenchmark.p',fact_listrel__Cons1) ).
fof(fact_listrel__subset,axiom,
! [V_A_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2))))) ),
file('theBenchmark.p',fact_listrel__subset) ).
fof(fact_lists__UNIV,axiom,
! [T_b] : c_List_Olists(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),
file('theBenchmark.p',fact_lists__UNIV) ).
fof(fact_lists__mono,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olists(T_b,V_A_2)),c_List_Olists(T_b,V_B_2))) ),
file('theBenchmark.p',fact_lists__mono) ).
fof(fact_equiv__listrel,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> c_Equiv__Relations_Oequiv(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ),
file('theBenchmark.p',fact_equiv__listrel) ).
fof(fact_listrel__refl__on,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> c_Relation_Orefl__on(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ),
file('theBenchmark.p',fact_listrel__refl__on) ).
fof(fact_Cons__in__lists__iff,axiom,
! [V_A_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_List_Olists(T_b,V_A_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
file('theBenchmark.p',fact_Cons__in__lists__iff) ).
fof(fact_lists__accI,axiom,
! [V_r_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2)))) ),
file('theBenchmark.p',fact_lists__accI) ).
fof(fact_lists__accD,axiom,
! [V_r_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ),
file('theBenchmark.p',fact_lists__accD) ).
fof(fact_listrel__iff__nth,axiom,
! [V_r_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
<=> ( ! [B_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_n))),V_r_2)) )
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ),
file('theBenchmark.p',fact_listrel__iff__nth) ).
fof(fact_lexord__linear,axiom,
! [V_y_2,V_x_2,V_r_2,T_b] :
( ! [B_a,B_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_b),B_a)),V_r_2))
| B_a = B_b
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_b)),V_r_2)) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_x_2)),c_List_Olexord(T_b,V_r_2)))
| V_x_2 = V_y_2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_lexord__linear) ).
fof(fact_infinite__UNIV__listI,axiom,
! [T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))),
file('theBenchmark.p',fact_infinite__UNIV__listI) ).
fof(fact_list__eq__iff__nth__eq,axiom,
! [T_b,V_ys_2,V_xs_2] :
( V_xs_2 = V_ys_2
<=> ( ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) )
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ),
file('theBenchmark.p',fact_list__eq__iff__nth__eq) ).
fof(fact_nth__Cons__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__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_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__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__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__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_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_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_length__take,axiom,
! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n),
file('theBenchmark.p',fact_length__take) ).
fof(fact_take__take,axiom,
! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),V_m)),V_xs),
file('theBenchmark.p',fact_take__take) ).
fof(fact_List_Oset_Osimps_I2_J,axiom,
! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)),
file('theBenchmark.p',fact_List_Oset_Osimps_I2_J) ).
fof(fact_sublist__upt__eq__take,axiom,
! [V_n_2,V_l_2,T_b] : c_List_Osublist(T_b,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_l_2),
file('theBenchmark.p',fact_sublist__upt__eq__take) ).
fof(fact_card__length,axiom,
! [V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
file('theBenchmark.p',fact_card__length) ).
fof(fact_all__set__conv__all__nth,axiom,
! [V_P_2,V_xs_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_P_2,B_x)) )
<=> ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ),
file('theBenchmark.p',fact_all__set__conv__all__nth) ).
fof(fact_list__size__estimation,axiom,
! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ),
file('theBenchmark.p',fact_list__size__estimation) ).
fof(fact_list__size__estimation_H,axiom,
! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ),
file('theBenchmark.p',fact_list__size__estimation_H) ).
fof(fact_in__lists__conv__set,axiom,
! [V_A_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_in__lists__conv__set) ).
fof(fact_length__pos__if__in__set,axiom,
! [V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ),
file('theBenchmark.p',fact_length__pos__if__in__set) ).
fof(fact_nth__mem,axiom,
! [V_xs_2,T_b,V_n_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ),
file('theBenchmark.p',fact_nth__mem) ).
fof(fact_in__set__conv__nth,axiom,
! [V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
<=> ? [B_i] :
( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ),
file('theBenchmark.p',fact_in__set__conv__nth) ).
fof(fact_lists__eq__set,axiom,
! [V_A_2,T_b] : c_List_Olists(T_b,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2)),
file('theBenchmark.p',fact_lists__eq__set) ).
fof(fact_set__conv__nth,axiom,
! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))),
file('theBenchmark.p',fact_set__conv__nth) ).
fof(fact_finite__lists__length__eq,axiom,
! [V_n_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ),
file('theBenchmark.p',fact_finite__lists__length__eq) ).
fof(fact_finite__lists__length__le,axiom,
! [V_n_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ),
file('theBenchmark.p',fact_finite__lists__length__le) ).
fof(fact_listrel__iff__zip,axiom,
! [V_r_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),B_x)) )
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ),
file('theBenchmark.p',fact_listrel__iff__zip) ).
fof(fact_set__zip,axiom,
! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_c)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(T_b,T_c)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),tc_Nat_Onat),c_Product__Type_OPair(T_b,T_c)),hAPP(c_List_Onth(T_b),V_xs_2))),hAPP(c_List_Onth(T_c),V_ys_2)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))))),
file('theBenchmark.p',fact_set__zip) ).
fof(fact_take__zip,axiom,
! [V_ys,V_xs,V_n,T_b,T_a] : hAPP(hAPP(c_List_Otake(tc_prod(T_a,T_b)),V_n),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_b),V_n),V_ys)),
file('theBenchmark.p',fact_take__zip) ).
fof(fact_length__zip,axiom,
! [V_ys,V_xs,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(T_a,T_b))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),
file('theBenchmark.p',fact_length__zip) ).
fof(fact_zip__Cons__Cons,axiom,
! [V_ys,V_y,V_xs,V_x,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),
file('theBenchmark.p',fact_zip__Cons__Cons) ).
fof(fact_list__eq__iff__zip__eq,axiom,
! [T_b,V_ys_2,V_xs_2] :
( V_xs_2 = V_ys_2
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) )
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ),
file('theBenchmark.p',fact_list__eq__iff__zip__eq) ).
fof(fact_zip__same,axiom,
! [V_xs_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2))))
<=> ( V_a_2 = V_b_2
& hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
file('theBenchmark.p',fact_zip__same) ).
fof(fact_set__zip__leftD,axiom,
! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
file('theBenchmark.p',fact_set__zip__leftD) ).
fof(fact_set__zip__rightD,axiom,
! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ),
file('theBenchmark.p',fact_set__zip__rightD) ).
fof(fact_in__set__zipE,axiom,
! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
=> ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ),
file('theBenchmark.p',fact_in__set__zipE) ).
fof(fact_nth__zip,axiom,
! [V_ys,T_b,V_xs,T_a,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)))
=> hAPP(hAPP(c_List_Onth(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_b),V_ys),V_i)) ) ),
file('theBenchmark.p',fact_nth__zip) ).
fof(fact_greaterThanLessThan__upto,axiom,
! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
file('theBenchmark.p',fact_greaterThanLessThan__upto) ).
fof(fact_listsum__setsum__nth,axiom,
! [V_xs_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ),
file('theBenchmark.p',fact_listsum__setsum__nth) ).
fof(fact_set__upto,axiom,
! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2),
file('theBenchmark.p',fact_set__upto) ).
fof(fact_atLeastAtMost__upto,axiom,
! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)),
file('theBenchmark.p',fact_atLeastAtMost__upto) ).
fof(fact_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_elem__le__listsum__nat,axiom,
! [V_ns,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns))) ),
file('theBenchmark.p',fact_elem__le__listsum__nat) ).
fof(fact_listsum__simps_I2_J,axiom,
! [V_xs,V_x,T_a] :
( class_Groups_Omonoid__add(T_a)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)) ),
file('theBenchmark.p',fact_listsum__simps_I2_J) ).
fof(fact_atLeastLessThan__upto,axiom,
! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
file('theBenchmark.p',fact_atLeastLessThan__upto) ).
fof(fact_greaterThanAtMost__upto,axiom,
! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)),
file('theBenchmark.p',fact_greaterThanAtMost__upto) ).
fof(fact_nat__list__def,axiom,
! [V_l_2] :
( c_List_Onat__list(V_l_2)
<=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ),
file('theBenchmark.p',fact_nat__list__def) ).
fof(fact_list__size__pointwise,axiom,
! [V_g_2,V_f_2,V_xs_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_b,V_g_2,V_xs_2))) ),
file('theBenchmark.p',fact_list__size__pointwise) ).
fof(fact_listsum__update__nat,axiom,
! [V_n,V_ns,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns)))
=> hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,V_ns),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns)),V_n)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)) ),
file('theBenchmark.p',fact_listsum__update__nat) ).
fof(fact_butlast__take,axiom,
! [V_xs,T_a,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> c_List_Obutlast(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ),
file('theBenchmark.p',fact_butlast__take) ).
fof(fact_list__update__beyond,axiom,
! [V_x,V_i,V_xs,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i))
=> hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ),
file('theBenchmark.p',fact_list__update__beyond) ).
fof(fact_list__update__id,axiom,
! [V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)) = V_xs,
file('theBenchmark.p',fact_list__update__id) ).
fof(fact_nth__list__update__neq,axiom,
! [V_x,V_xs,T_a,V_j,V_i] :
( V_i != V_j
=> hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) ),
file('theBenchmark.p',fact_nth__list__update__neq) ).
fof(fact_length__list__update,axiom,
! [V_x,V_i,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs),
file('theBenchmark.p',fact_length__list__update) ).
fof(fact_butlast__list__update,axiom,
! [V_x,V_xs,T_a,V_k] :
( ( V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
=> c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = hAPP(hAPP(c_List_Olist__update(T_a,c_List_Obutlast(T_a,V_xs)),V_k),V_x) )
& ( V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
=> c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Obutlast(T_a,V_xs) ) ),
file('theBenchmark.p',fact_butlast__list__update) ).
fof(fact_zip__update,axiom,
! [V_y,V_ys,V_x,V_i,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),V_y)) = hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),
file('theBenchmark.p',fact_zip__update) ).
fof(fact_update__zip,axiom,
! [V_xy,V_i,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),V_xy) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(c_Product__Type_Ofst(T_a,T_b),V_xy))),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),hAPP(c_Product__Type_Osnd(T_a,T_b),V_xy))),
file('theBenchmark.p',fact_update__zip) ).
fof(fact_list__update__swap,axiom,
! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
( V_i != V_i_H
=> hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i_H),V_x_H) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i_H),V_x_H)),V_i),V_x) ),
file('theBenchmark.p',fact_list__update__swap) ).
fof(fact_list__update__overwrite,axiom,
! [V_y,V_x,V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i),V_y) = hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y),
file('theBenchmark.p',fact_list__update__overwrite) ).
fof(fact_list__update_Osimps_I2_J,axiom,
! [V_v_2,V_i_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,tc_List_Olist(T_b)),c_List_Olist__update(T_b,V_xs_2)),V_v_2)),V_i_2),
file('theBenchmark.p',fact_list__update_Osimps_I2_J) ).
fof(fact_list__update__code_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__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_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_card__distinct,axiom,
! [V_xs_2,T_b] :
( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
file('theBenchmark.p',fact_card__distinct) ).
fof(fact_distinct__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_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__Nil1,axiom,
! [V_r_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel(T_b,V_r_2)))
=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_listrel__Nil1) ).
fof(fact_listrel__Nil2,axiom,
! [V_r_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2)))
=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_listrel__Nil2) ).
fof(fact_distinct__butlast,axiom,
! [T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ),
file('theBenchmark.p',fact_distinct__butlast) ).
fof(fact_distinct_Osimps_I1_J,axiom,
! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))),
file('theBenchmark.p',fact_distinct_Osimps_I1_J) ).
fof(fact_distinct__remove1,axiom,
! [V_x,V_xs,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ),
file('theBenchmark.p',fact_distinct__remove1) ).
fof(fact_butlast_Osimps_I1_J,axiom,
! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_butlast_Osimps_I1_J) ).
fof(fact_butlast_Osimps_I2_J,axiom,
! [V_x,T_a,V_xs] :
( ( V_xs != c_List_Olist_ONil(T_a)
=> c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Obutlast(T_a,V_xs)) )
& ( V_xs = c_List_Olist_ONil(T_a)
=> c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) ),
file('theBenchmark.p',fact_butlast_Osimps_I2_J) ).
fof(fact_remove1_Osimps_I2_J,axiom,
! [V_xs,T_a,V_y,V_x] :
( ( V_x != V_y
=> c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Oremove1(T_a,V_x,V_xs)) )
& ( V_x = V_y
=> c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) ),
file('theBenchmark.p',fact_remove1_Osimps_I2_J) ).
fof(fact_list_Osimps_I3_J,axiom,
! [V_list_H,V_a_H,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H) != c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_list_Osimps_I3_J) ).
fof(fact_list_Osimps_I2_J,axiom,
! [V_list_H,V_a_H,T_a] : c_List_Olist_ONil(T_a) != hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H),
file('theBenchmark.p',fact_list_Osimps_I2_J) ).
fof(fact_upto__empty,axiom,
! [V_i,V_j] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
=> c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ),
file('theBenchmark.p',fact_upto__empty) ).
fof(fact_take__eq__Nil,axiom,
! [V_xs_2,V_n_2,T_b] :
( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
<=> ( V_xs_2 = c_List_Olist_ONil(T_b)
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_take__eq__Nil) ).
fof(fact_take__0,axiom,
! [V_xs,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_take__0) ).
fof(fact_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_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_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__update__nonempty,axiom,
! [V_x_2,V_k_2,V_xs_2,T_b] :
( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_list__update__nonempty) ).
fof(fact_list__update_Osimps_I1_J,axiom,
! [V_v,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_v) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_list__update_Osimps_I1_J) ).
fof(fact_list__update__code_I1_J,axiom,
! [V_y,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_y) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_list__update__code_I1_J) ).
fof(fact_in__set__remove1,axiom,
! [V_xs_2,T_b,V_b_2,V_a_2] :
( V_a_2 != V_b_2
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_b_2,V_xs_2))))
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
file('theBenchmark.p',fact_in__set__remove1) ).
fof(fact_notin__set__remove1,axiom,
! [V_y_2,V_xs_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_y_2,V_xs_2)))) ),
file('theBenchmark.p',fact_notin__set__remove1) ).
fof(fact_remove1__idem,axiom,
! [V_xs_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ),
file('theBenchmark.p',fact_remove1__idem) ).
fof(fact_sublist__empty,axiom,
! [V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_b),
file('theBenchmark.p',fact_sublist__empty) ).
fof(fact_set__remove1__subset,axiom,
! [V_xs_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
file('theBenchmark.p',fact_set__remove1__subset) ).
fof(fact_length__greater__0__conv,axiom,
! [V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
<=> V_xs_2 != c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_length__greater__0__conv) ).
fof(fact_take__1__Cons,axiom,
! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)),
file('theBenchmark.p',fact_take__1__Cons) ).
fof(fact_not__Nil__listrel1,axiom,
! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel1(T_b,V_r_2))),
file('theBenchmark.p',fact_not__Nil__listrel1) ).
fof(fact_not__listrel1__Nil,axiom,
! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel1(T_b,V_r_2))),
file('theBenchmark.p',fact_not__listrel1__Nil) ).
fof(fact_listrel_ONil,axiom,
! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2))),
file('theBenchmark.p',fact_listrel_ONil) ).
fof(fact_lexord__Nil__right,axiom,
! [V_r_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olexord(T_b,V_r_2))),
file('theBenchmark.p',fact_lexord__Nil__right) ).
fof(fact_Nil__notin__lex,axiom,
! [V_r_2,V_ys_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_ys_2)),c_List_Olex(T_b,V_r_2))),
file('theBenchmark.p',fact_Nil__notin__lex) ).
fof(fact_Nil2__notin__lex,axiom,
! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olex(T_b,V_r_2))),
file('theBenchmark.p',fact_Nil2__notin__lex) ).
fof(fact_take__Cons,axiom,
! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otake(T_b)),V_xs_2)),V_n_2),
file('theBenchmark.p',fact_take__Cons) ).
fof(fact_upto_Osimps,axiom,
! [V_j,V_i] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
=> c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
=> c_List_Oupto(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j)) ) ),
file('theBenchmark.p',fact_upto_Osimps) ).
fof(fact_sublist__singleton,axiom,
! [V_x_2,T_b,V_A_2] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
=> c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = c_List_Olist_ONil(T_b) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
=> c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ),
file('theBenchmark.p',fact_sublist__singleton) ).
fof(fact_lists__empty,axiom,
! [T_b] : c_List_Olists(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),
file('theBenchmark.p',fact_lists__empty) ).
fof(fact_take__Cons_H,axiom,
! [V_xs,V_x,T_a,V_n] :
( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)) )
& ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) ),
file('theBenchmark.p',fact_take__Cons_H) ).
fof(fact_upto__rec__number__of,axiom,
! [V_n,V_m] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
=> c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = c_List_Olist_ONil(tc_Int_Oint) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
=> c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) ) ),
file('theBenchmark.p',fact_upto__rec__number__of) ).
fof(fact_listrel__Nil,axiom,
! [V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),
file('theBenchmark.p',fact_listrel__Nil) ).
fof(fact_set__Cons__sing__Nil,axiom,
! [V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_b,tc_List_Olist(T_b),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))),V_A_2),
file('theBenchmark.p',fact_set__Cons__sing__Nil) ).
fof(fact_length__remove1,axiom,
! [V_xs_2,V_x_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
file('theBenchmark.p',fact_length__remove1) ).
fof(fact_upto_Opsimps,axiom,
! [V_j_2,V_i_2] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_i_2),V_j_2)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
=> c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
=> c_List_Oupto(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i_2),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ) ) ),
file('theBenchmark.p',fact_upto_Opsimps) ).
fof(fact_select,axiom,
! [V_s_2,T_b,V_xs_2] :
( V_xs_2 != c_List_Olist_ONil(T_b)
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ),
file('theBenchmark.p',fact_select) ).
fof(fact_listset_Osimps_I1_J,axiom,
! [T_b] : c_List_Olistset(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),
file('theBenchmark.p',fact_listset_Osimps_I1_J) ).
fof(fact_zip__Cons1,axiom,
! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_c,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),T_c),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_c),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)))),hAPP(c_List_Ozip(T_b,T_c),V_xs_2))),V_ys_2),
file('theBenchmark.p',fact_zip__Cons1) ).
fof(fact_list_Osimps_I5_J,axiom,
! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_2),V_list_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_list_2),
file('theBenchmark.p',fact_list_Osimps_I5_J) ).
fof(fact_list_Osimps_I4_J,axiom,
! [V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),c_List_Olist_ONil(T_c)) = V_f1_2,
file('theBenchmark.p',fact_list_Osimps_I4_J) ).
fof(fact_listset_Osimps_I2_J,axiom,
! [V_As_2,V_A_2,T_b] : c_List_Olistset(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_b,V_A_2,c_List_Olistset(T_b,V_As_2)),
file('theBenchmark.p',fact_listset_Osimps_I2_J) ).
fof(fact_zip__Cons,axiom,
! [V_ys_2,V_y_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_b,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),T_b),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_b),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),c_List_Ozip(T_b,T_c)),V_ys_2))),V_xs_2),
file('theBenchmark.p',fact_zip__Cons) ).
fof(fact_sorted__list__of__set__remove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = c_List_Oremove1(T_b,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) ) ),
file('theBenchmark.p',fact_sorted__list__of__set__remove) ).
fof(fact_upto_Opinduct,axiom,
! [V_P_2,V_a1_2,V_a0_2] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
=> ( ! [B_i,B_j] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_i),B_j)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
=> hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j)) )
=> hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) )
=> hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
file('theBenchmark.p',fact_upto_Opinduct) ).
fof(fact_sorted__list__of__set__empty,axiom,
! [T_b] :
( class_Orderings_Olinorder(T_b)
=> c_List_Olinorder__class_Osorted__list__of__set(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_sorted__list__of__set__empty) ).
fof(fact_anamorph_Osimps,axiom,
! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(tc_List_Olist(T_b),T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),c_COMBB(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),T_b),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),T_c))),c_List_Olist_OCons(T_b))))),hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))),hAPP(V_f_2,V_x_2)) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2) ) ),
file('theBenchmark.p',fact_anamorph_Osimps) ).
fof(fact_sublist__Cons,axiom,
! [V_A_2,V_l_2,V_x_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_b)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olist_ONil(T_b))),c_List_Osublist(T_b,V_l_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_A_2)))),
file('theBenchmark.p',fact_sublist__Cons) ).
fof(fact_append1__eq__conv,axiom,
! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b)))
<=> ( V_x_2 = V_y_2
& V_xs_2 = V_ys_2 ) ),
file('theBenchmark.p',fact_append1__eq__conv) ).
fof(fact_Cons__eq__append__conv,axiom,
! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2)
<=> ( ? [B_ys_H] :
( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2)
& hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2 )
| ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2
& V_ys_2 = c_List_Olist_ONil(T_b) ) ) ),
file('theBenchmark.p',fact_Cons__eq__append__conv) ).
fof(fact_append__eq__Cons__conv,axiom,
! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
<=> ( ? [B_ys_H] :
( hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2
& V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) )
| ( V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
& V_ys_2 = c_List_Olist_ONil(T_b) ) ) ),
file('theBenchmark.p',fact_append__eq__Cons__conv) ).
fof(fact_Cons__eq__appendI,axiom,
! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
=> ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
=> hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ),
file('theBenchmark.p',fact_Cons__eq__appendI) ).
fof(fact_append__Cons,axiom,
! [V_ys,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_ys) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),
file('theBenchmark.p',fact_append__Cons) ).
fof(fact_append__in__lists__conv,axiom,
! [V_A_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)),c_List_Olists(T_b,V_A_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2)))
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ),
file('theBenchmark.p',fact_append__in__lists__conv) ).
fof(fact_append__assoc,axiom,
! [V_zs,V_ys,V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs)),
file('theBenchmark.p',fact_append__assoc) ).
fof(fact_append__eq__append__conv2,axiom,
! [V_tsa_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_tsa_2)
<=> ? [B_us] :
( ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_tsa_2)
& hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2 )
| ( hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_tsa_2
& V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us) ) ) ),
file('theBenchmark.p',fact_append__eq__append__conv2) ).
fof(fact_same__append__eq,axiom,
! [V_zs_2,V_ys_2,V_xs_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2)
<=> V_ys_2 = V_zs_2 ),
file('theBenchmark.p',fact_same__append__eq) ).
fof(fact_append__same__eq,axiom,
! [V_zs_2,V_xs_2,V_ys_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_xs_2)
<=> V_ys_2 = V_zs_2 ),
file('theBenchmark.p',fact_append__same__eq) ).
fof(fact_append__eq__appendI,axiom,
! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
=> ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
=> hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ),
file('theBenchmark.p',fact_append__eq__appendI) ).
fof(fact_listsum__append,axiom,
! [V_ys,V_xs,T_a] :
( class_Groups_Omonoid__add(T_a)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_ys)) ),
file('theBenchmark.p',fact_listsum__append) ).
fof(fact_length__append,axiom,
! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)),
file('theBenchmark.p',fact_length__append) ).
fof(fact_zip__append,axiom,
! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_us)
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_vs)
=> hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_List_Oappend(T_b),V_us),V_vs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_us)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),V_vs)) ) ),
file('theBenchmark.p',fact_zip__append) ).
fof(fact_set__append,axiom,
! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)),
file('theBenchmark.p',fact_set__append) ).
fof(fact_eq__Nil__appendI,axiom,
! [T_a,V_ys,V_xs] :
( V_xs = V_ys
=> V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ),
file('theBenchmark.p',fact_eq__Nil__appendI) ).
fof(fact_append__self__conv2,axiom,
! [V_ys_2,V_xs_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_append__self__conv2) ).
fof(fact_append__self__conv,axiom,
! [V_ys_2,V_xs_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
<=> V_ys_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_append__self__conv) ).
fof(fact_append__is__Nil__conv,axiom,
! [V_ys_2,V_xs_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
<=> ( V_ys_2 = c_List_Olist_ONil(T_b)
& V_xs_2 = c_List_Olist_ONil(T_b) ) ),
file('theBenchmark.p',fact_append__is__Nil__conv) ).
fof(fact_self__append__conv2,axiom,
! [V_xs_2,T_b,V_ys_2] :
( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_self__append__conv2) ).
fof(fact_self__append__conv,axiom,
! [V_ys_2,T_b,V_xs_2] :
( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
<=> V_ys_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_self__append__conv) ).
fof(fact_append__Nil2,axiom,
! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs,
file('theBenchmark.p',fact_append__Nil2) ).
fof(fact_Nil__is__append__conv,axiom,
! [V_ys_2,V_xs_2,T_b] :
( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
<=> ( V_ys_2 = c_List_Olist_ONil(T_b)
& V_xs_2 = c_List_Olist_ONil(T_b) ) ),
file('theBenchmark.p',fact_Nil__is__append__conv) ).
fof(fact_append__Nil,axiom,
! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys,
file('theBenchmark.p',fact_append__Nil) ).
fof(fact_butlast__append,axiom,
! [V_xs,T_a,V_ys] :
( ( V_ys != c_List_Olist_ONil(T_a)
=> c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Obutlast(T_a,V_ys)) )
& ( V_ys = c_List_Olist_ONil(T_a)
=> c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) ),
file('theBenchmark.p',fact_butlast__append) ).
fof(fact_nth__append__length,axiom,
! [V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = V_x,
file('theBenchmark.p',fact_nth__append__length) ).
fof(fact_nth__append__length__plus,axiom,
! [V_n,V_ys,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_ys),V_n),
file('theBenchmark.p',fact_nth__append__length__plus) ).
fof(fact_take__append,axiom,
! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)),
file('theBenchmark.p',fact_take__append) ).
fof(fact_list__update__append1,axiom,
! [V_x,V_ys,V_xs,T_a,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_i),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_ys) ),
file('theBenchmark.p',fact_list__update__append1) ).
fof(fact_list__update__length,axiom,
! [V_y,V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_y) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)),
file('theBenchmark.p',fact_list__update__length) ).
fof(fact_remove1__append,axiom,
! [V_ys_2,V_xs_2,V_x_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oremove1(T_b,V_x_2,V_ys_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)),V_ys_2) ) ),
file('theBenchmark.p',fact_remove1__append) ).
fof(fact_in__set__butlast__appendI,axiom,
! [V_ys_2,V_xs_2,V_x_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2))))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) )
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))))) ),
file('theBenchmark.p',fact_in__set__butlast__appendI) ).
fof(fact_butlast__snoc,axiom,
! [V_x,V_xs,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_xs,
file('theBenchmark.p',fact_butlast__snoc) ).
fof(fact_append__listrel1I,axiom,
! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_us_2),V_vs_2)),c_List_Olistrel1(T_b,V_r_2)))
& V_xs_2 = V_ys_2 )
| ( V_us_2 = V_vs_2
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2))),c_List_Olistrel1(T_b,V_r_2))) ),
file('theBenchmark.p',fact_append__listrel1I) ).
fof(fact_lexord__append__leftI,axiom,
! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2))) ),
file('theBenchmark.p',fact_lexord__append__leftI) ).
fof(fact_distinct__append,axiom,
! [V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
<=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
& hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
& hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ),
file('theBenchmark.p',fact_distinct__append) ).
fof(fact_nth__append,axiom,
! [V_ys,V_xs,T_a,V_n] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ) ),
file('theBenchmark.p',fact_nth__append) ).
fof(fact_list__update__append,axiom,
! [V_x,V_ys,V_xs,T_a,V_n] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist__update(T_a,V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_x)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_n),V_x)),V_ys) ) ),
file('theBenchmark.p',fact_list__update__append) ).
fof(fact_sublist__append,axiom,
! [V_A_2,V_l_H_2,V_l_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Osublist(T_b,V_l_2,V_A_2)),c_List_Osublist(T_b,V_l_H_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_l_2)))),V_A_2)))),
file('theBenchmark.p',fact_sublist__append) ).
fof(fact_listrel1I,axiom,
! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
=> ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_vs_2))
=> ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_vs_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ),
file('theBenchmark.p',fact_listrel1I) ).
fof(fact_lexord__append__left__rightI,axiom,
! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2)))),c_List_Olexord(T_b,V_r_2))) ),
file('theBenchmark.p',fact_lexord__append__left__rightI) ).
fof(fact_take__Suc__conv__app__nth,axiom,
! [V_xs,T_a,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),c_List_Olist_ONil(T_a))) ),
file('theBenchmark.p',fact_take__Suc__conv__app__nth) ).
fof(fact_snoc__listrel1__snoc__iff,axiom,
! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)))),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))))),c_List_Olistrel1(T_b,V_r_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
& V_xs_2 = V_ys_2 )
| ( V_x_2 = V_y_2
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ),
file('theBenchmark.p',fact_snoc__listrel1__snoc__iff) ).
fof(fact_listrel1E,axiom,
! [V_r_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
=> ~ ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
=> ! [B_us,B_vs] :
( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
=> V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ),
file('theBenchmark.p',fact_listrel1E) ).
fof(fact_lexord__append__leftD,axiom,
! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2)))
=> ( ! [B_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_a)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_lexord__append__leftD) ).
fof(fact_rotate1__def,axiom,
! [V_xs_2,T_b] : hAPP(c_List_Orotate1(T_b),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)))),V_xs_2),
file('theBenchmark.p',fact_rotate1__def) ).
fof(fact_upd__conv__take__nth__drop,axiom,
! [V_a,V_xs,T_a,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_a) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))) ),
file('theBenchmark.p',fact_upd__conv__take__nth__drop) ).
fof(fact_append__take__drop__id,axiom,
! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = V_xs,
file('theBenchmark.p',fact_append__take__drop__id) ).
fof(fact_drop__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_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_nth__via__drop,axiom,
! [V_ys,V_y,V_xs,V_n,T_a] :
( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
=> hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ),
file('theBenchmark.p',fact_nth__via__drop) ).
fof(fact_distinct1__rotate,axiom,
! [V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
<=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
file('theBenchmark.p',fact_distinct1__rotate) ).
fof(fact_distinct__drop,axiom,
! [V_i,V_xs,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ),
file('theBenchmark.p',fact_distinct__drop) ).
fof(fact_drop__butlast,axiom,
! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),
file('theBenchmark.p',fact_drop__butlast) ).
fof(fact_butlast__drop,axiom,
! [V_xs,V_n,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)),
file('theBenchmark.p',fact_butlast__drop) ).
fof(fact_take__drop,axiom,
! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_m),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs)),
file('theBenchmark.p',fact_take__drop) ).
fof(fact_drop__take,axiom,
! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),
file('theBenchmark.p',fact_drop__take) ).
fof(fact_drop__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__drop,axiom,
! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n),
file('theBenchmark.p',fact_length__drop) ).
fof(fact_length__rotate1,axiom,
! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate1(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs),
file('theBenchmark.p',fact_length__rotate1) ).
fof(fact_set__rotate1,axiom,
! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
file('theBenchmark.p',fact_set__rotate1) ).
fof(fact_in__set__dropD,axiom,
! [V_xs_2,V_n_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
file('theBenchmark.p',fact_in__set__dropD) ).
fof(fact_set__drop__subset,axiom,
! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
file('theBenchmark.p',fact_set__drop__subset) ).
fof(fact_rotate1__is__Nil__conv,axiom,
! [V_xs_2,T_b] :
( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_rotate1__is__Nil__conv) ).
fof(fact_drop__Nil,axiom,
! [V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_drop__Nil) ).
fof(fact_set__drop__subset__set__drop,axiom,
! [V_xs_2,T_b,V_m_2,V_n_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)))) ),
file('theBenchmark.p',fact_set__drop__subset__set__drop) ).
fof(fact_drop__all,axiom,
! [V_n,V_xs,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n))
=> hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ),
file('theBenchmark.p',fact_drop__all) ).
fof(fact_drop__eq__Nil,axiom,
! [V_xs_2,V_n_2,T_b] :
( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_n_2)) ),
file('theBenchmark.p',fact_drop__eq__Nil) ).
fof(fact_drop__append,axiom,
! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)),
file('theBenchmark.p',fact_drop__append) ).
fof(fact_append__eq__conv__conj,axiom,
! [V_zs_2,V_ys_2,V_xs_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
<=> ( V_ys_2 = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2)
& V_xs_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2) ) ),
file('theBenchmark.p',fact_append__eq__conv__conj) ).
fof(fact_drop__Cons,axiom,
! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Odrop(T_b)),V_xs_2),V_n_2),
file('theBenchmark.p',fact_drop__Cons) ).
fof(fact_drop__Cons_H,axiom,
! [V_xs,V_x,T_a,V_n] :
( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) )
& ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ) ),
file('theBenchmark.p',fact_drop__Cons_H) ).
fof(fact_nth__drop,axiom,
! [V_xs,T_a,V_i,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)) ),
file('theBenchmark.p',fact_nth__drop) ).
fof(fact_append__eq__append__conv__if,axiom,
! [V_ys_092_060_094isub_0622_2,V_ys_092_060_094isub_0621_2,V_xs_092_060_094isub_0622_2,V_xs_092_060_094isub_0621_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2)
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)))
=> ( hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2)),V_xs_092_060_094isub_0622_2) = V_ys_092_060_094isub_0622_2
& hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) = V_ys_092_060_094isub_0621_2 ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)))
=> ( V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2)
& V_xs_092_060_094isub_0621_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2) ) ) ) ),
file('theBenchmark.p',fact_append__eq__append__conv__if) ).
fof(fact_nth__drop_H,axiom,
! [V_xs,T_a,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs) ),
file('theBenchmark.p',fact_nth__drop_H) ).
fof(fact_rotate__simps,axiom,
! [V_xs,V_x,T_b,T_a] :
( hAPP(c_List_Orotate1(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),c_List_Olist_ONil(T_b)))
& hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ),
file('theBenchmark.p',fact_rotate__simps) ).
fof(fact_drop__Cons__number__of,axiom,
! [V_xs,V_x,T_a,V_v] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ) ),
file('theBenchmark.p',fact_drop__Cons__number__of) ).
fof(fact_take__add,axiom,
! [V_xs,T_a,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_j),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ),
file('theBenchmark.p',fact_take__add) ).
fof(fact_rotate1__length01,axiom,
! [V_xs,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
=> hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ),
file('theBenchmark.p',fact_rotate1__length01) ).
fof(fact_zip__append2,axiom,
! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Oappend(T_b),V_ys),V_zs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_ys)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_zs)),
file('theBenchmark.p',fact_zip__append2) ).
fof(fact_zip__append1,axiom,
! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))),
file('theBenchmark.p',fact_zip__append1) ).
fof(fact_id__take__nth__drop,axiom,
! [V_xs,T_a,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> V_xs = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))) ),
file('theBenchmark.p',fact_id__take__nth__drop) ).
fof(fact_take__hd__drop,axiom,
! [V_xs,T_a,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) ),
file('theBenchmark.p',fact_take__hd__drop) ).
fof(fact_hd__drop__conv__nth,axiom,
! [V_n,T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ) ),
file('theBenchmark.p',fact_hd__drop__conv__nth) ).
fof(fact_hd_Osimps,axiom,
! [V_xs,V_x,T_a] : hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x,
file('theBenchmark.p',fact_hd_Osimps) ).
fof(fact_hd__append,axiom,
! [V_ys,T_a,V_xs] :
( ( V_xs != c_List_Olist_ONil(T_a)
=> hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs) )
& ( V_xs = c_List_Olist_ONil(T_a)
=> hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_ys) ) ),
file('theBenchmark.p',fact_hd__append) ).
fof(fact_hd__append2,axiom,
! [V_ys,T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs) ),
file('theBenchmark.p',fact_hd__append2) ).
fof(fact_hd__in__set,axiom,
! [T_b,V_xs_2] :
( V_xs_2 != c_List_Olist_ONil(T_b)
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ),
file('theBenchmark.p',fact_hd__in__set) ).
fof(fact_hd__conv__nth,axiom,
! [T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> hAPP(c_List_Ohd(T_a),V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('theBenchmark.p',fact_hd__conv__nth) ).
fof(fact_rotate1__hd__tl,axiom,
! [T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> hAPP(c_List_Orotate1(T_a),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),c_List_Olist_ONil(T_a))) ),
file('theBenchmark.p',fact_rotate1__hd__tl) ).
fof(fact_hd__rotate__conv__nth,axiom,
! [V_n,T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> hAPP(c_List_Ohd(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
file('theBenchmark.p',fact_hd__rotate__conv__nth) ).
fof(fact_tl__drop,axiom,
! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)),
file('theBenchmark.p',fact_tl__drop) ).
fof(fact_drop__tl,axiom,
! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),
file('theBenchmark.p',fact_drop__tl) ).
fof(fact_tl_Osimps_I2_J,axiom,
! [V_xs,V_x,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs,
file('theBenchmark.p',fact_tl_Osimps_I2_J) ).
fof(fact_distinct__rotate,axiom,
! [V_xs_2,V_n_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
<=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
file('theBenchmark.p',fact_distinct__rotate) ).
fof(fact_distinct__tl,axiom,
! [V_xs,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ),
file('theBenchmark.p',fact_distinct__tl) ).
fof(fact_rotate0,axiom,
! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)),
file('theBenchmark.p',fact_rotate0) ).
fof(fact_rotate__rotate,axiom,
! [V_xs,V_n,V_m,T_a] : hAPP(c_List_Orotate(T_a,V_m),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_xs),
file('theBenchmark.p',fact_rotate__rotate) ).
fof(fact_rotate__add,axiom,
! [V_n_2,V_m_2,T_b] : c_List_Orotate(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orotate(T_b,V_m_2)),c_List_Orotate(T_b,V_n_2)),
file('theBenchmark.p',fact_rotate__add) ).
fof(fact_length__rotate,axiom,
! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs),
file('theBenchmark.p',fact_length__rotate) ).
fof(fact_set__rotate,axiom,
! [V_xs_2,V_n_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
file('theBenchmark.p',fact_set__rotate) ).
fof(fact_rotate__is__Nil__conv,axiom,
! [V_xs_2,V_n_2,T_b] :
( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_rotate__is__Nil__conv) ).
fof(fact_tl_Osimps_I1_J,axiom,
! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_tl_Osimps_I1_J) ).
fof(fact_rotate1__rotate__swap,axiom,
! [V_xs,V_n,T_a] : hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orotate1(T_a),V_xs)),
file('theBenchmark.p',fact_rotate1__rotate__swap) ).
fof(fact_rotate__def,axiom,
! [V_n_2,T_b] : c_List_Orotate(T_b,V_n_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_n_2),c_List_Orotate1(T_b)),
file('theBenchmark.p',fact_rotate__def) ).
fof(fact_tl__append2,axiom,
! [V_ys,T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),V_ys) ),
file('theBenchmark.p',fact_tl__append2) ).
fof(fact_take__tl,axiom,
! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs)),
file('theBenchmark.p',fact_take__tl) ).
fof(fact_rotate__conv__mod,axiom,
! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(c_List_Orotate(T_a,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs),
file('theBenchmark.p',fact_rotate__conv__mod) ).
fof(fact_drop__Suc,axiom,
! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)),
file('theBenchmark.p',fact_drop__Suc) ).
fof(fact_rotate__Suc,axiom,
! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)),
file('theBenchmark.p',fact_rotate__Suc) ).
fof(fact_tl__append,axiom,
! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,hAPP(c_List_Otl(T_b),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b)),V_ys_2))),V_xs_2),
file('theBenchmark.p',fact_tl__append) ).
fof(fact_rotate__id,axiom,
! [V_xs,T_a,V_n] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ),
file('theBenchmark.p',fact_rotate__id) ).
fof(fact_rotate__length01,axiom,
! [V_n,V_xs,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
=> hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ),
file('theBenchmark.p',fact_rotate__length01) ).
fof(fact_length__tl,axiom,
! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('theBenchmark.p',fact_length__tl) ).
fof(fact_tl__take,axiom,
! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(T_a),V_xs)),
file('theBenchmark.p',fact_tl__take) ).
fof(fact_take__Suc,axiom,
! [V_n,T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs))) ),
file('theBenchmark.p',fact_take__Suc) ).
fof(fact_rotate__drop__take,axiom,
! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)),hAPP(hAPP(c_List_Otake(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)),
file('theBenchmark.p',fact_rotate__drop__take) ).
fof(fact_fold1__set,axiom,
! [V_xs_2,T_b] :
( class_Lattices_Oab__semigroup__idem__mult(T_b)
=> ( V_xs_2 != c_List_Olist_ONil(T_b)
=> hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Otl(T_b),V_xs_2)) ) ),
file('theBenchmark.p',fact_fold1__set) ).
fof(fact_lexord__append__rightI,axiom,
! [V_r_2,V_x_2,T_b,V_y_2] :
( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_y_2))),c_List_Olexord(T_b,V_r_2))) ),
file('theBenchmark.p',fact_lexord__append__rightI) ).
fof(fact_foldl__Nil,axiom,
! [V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),c_List_Olist_ONil(T_c)) = V_a_2,
file('theBenchmark.p',fact_foldl__Nil) ).
fof(fact_start__le__sum,axiom,
! [V_ns_2,V_n_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_ns_2))) ),
file('theBenchmark.p',fact_start__le__sum) ).
fof(fact_foldl__assoc,axiom,
! [V_zs_2,V_y_2,V_x_2,T_b] :
( class_Groups_Osemigroup__add(T_b)
=> hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_y_2),V_zs_2)) ),
file('theBenchmark.p',fact_foldl__assoc) ).
fof(fact_foldl__absorb0,axiom,
! [V_zs_2,V_x_2,T_b] :
( class_Groups_Omonoid__add(T_b)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_zs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_zs_2) ),
file('theBenchmark.p',fact_foldl__absorb0) ).
fof(fact_foldl__Cons,axiom,
! [V_xs_2,V_x_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_x_2)),V_xs_2),
file('theBenchmark.p',fact_foldl__Cons) ).
fof(fact_foldl__append,axiom,
! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2)),V_ys_2),
file('theBenchmark.p',fact_foldl__append) ).
fof(fact_listsum__foldl,axiom,
! [T_b] :
( class_Groups_Omonoid__add(T_b)
=> c_List_Omonoid__add__class_Olistsum(T_b) = c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)) ),
file('theBenchmark.p',fact_listsum__foldl) ).
fof(fact_sum__eq__0__conv,axiom,
! [V_ns_2,V_m_2] :
( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
=> B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_sum__eq__0__conv) ).
fof(fact_fun__left__comm__idem_Ofold__set,axiom,
! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
=> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),V_xs_2) ),
file('theBenchmark.p',fact_fun__left__comm__idem_Ofold__set) ).
fof(fact_Sup__set__fold,axiom,
! [V_xs_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Orderings_Obot__class_Obot(T_b)),V_xs_2) ),
file('theBenchmark.p',fact_Sup__set__fold) ).
fof(fact_Inf__set__fold,axiom,
! [V_xs_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Orderings_Otop__class_Otop(T_b)),V_xs_2) ),
file('theBenchmark.p',fact_Inf__set__fold) ).
fof(fact_Sup__fin__set__fold,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Lattices_Olattice(T_b)
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_xs_2) ),
file('theBenchmark.p',fact_Sup__fin__set__fold) ).
fof(fact_Inf__fin__set__fold,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Lattices_Olattice(T_b)
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_xs_2) ),
file('theBenchmark.p',fact_Inf__fin__set__fold) ).
fof(fact_Min__fin__set__fold,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2) ),
file('theBenchmark.p',fact_Min__fin__set__fold) ).
fof(fact_Max__fin__set__fold,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2) ),
file('theBenchmark.p',fact_Max__fin__set__fold) ).
fof(fact_min__max_OInf__fin__set__fold,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2) ),
file('theBenchmark.p',fact_min__max_OInf__fin__set__fold) ).
fof(fact_min__max_OSup__fin__set__fold,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2) ),
file('theBenchmark.p',fact_min__max_OSup__fin__set__fold) ).
fof(fact_SUPR__set__fold,axiom,
! [V_f_2,V_xs_2,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(T_b)),V_xs_2) ),
file('theBenchmark.p',fact_SUPR__set__fold) ).
fof(fact_INFI__set__fold,axiom,
! [V_f_2,V_xs_2,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),c_Orderings_Otop__class_Otop(T_b)),V_xs_2) ),
file('theBenchmark.p',fact_INFI__set__fold) ).
fof(fact_elem__le__sum,axiom,
! [V_ns_2,V_n_2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_ns_2))) ),
file('theBenchmark.p',fact_elem__le__sum) ).
fof(fact_sorted__list__of__set__insert,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
file('theBenchmark.p',fact_sorted__list__of__set__insert) ).
fof(fact_lexord__Nil__left,axiom,
! [V_r_2,V_y_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_y_2)),c_List_Olexord(T_b,V_r_2)))
<=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ),
file('theBenchmark.p',fact_lexord__Nil__left) ).
fof(fact_insort__key_Osimps_I1_J,axiom,
! [V_x_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ),
file('theBenchmark.p',fact_insort__key_Osimps_I1_J) ).
fof(fact_insort__key_Osimps_I2_J,axiom,
! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_ys_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) ) ) ),
file('theBenchmark.p',fact_insort__key_Osimps_I2_J) ).
fof(fact_insort__left__comm,axiom,
! [V_xs_2,V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) ),
file('theBenchmark.p',fact_insort__left__comm) ).
fof(fact_fun__left__comm__insort,axiom,
! [T_b] :
( class_Orderings_Olinorder(T_b)
=> c_Finite__Set_Ofun__left__comm(T_b,tc_List_Olist(T_b),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))) ),
file('theBenchmark.p',fact_fun__left__comm__insort) ).
fof(fact_insort__key__left__comm,axiom,
! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),V_xs_2)) ) ),
file('theBenchmark.p',fact_insort__key__left__comm) ).
fof(fact_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_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_remove1__insort,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) = V_xs_2 ),
file('theBenchmark.p',fact_remove1__insort) ).
fof(fact_insort__not__Nil,axiom,
! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_insort__not__Nil) ).
fof(fact_distinct__insort,axiom,
! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)))
<=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ),
file('theBenchmark.p',fact_distinct__insort) ).
fof(fact_insort__insert__insort__key,axiom,
! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
=> c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2) ) ),
file('theBenchmark.p',fact_insort__insert__insort__key) ).
fof(fact_insort__insert__insort,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2) ) ),
file('theBenchmark.p',fact_insort__insert__insort) ).
fof(fact_distinct__insort__insert,axiom,
! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_c,V_f_2,V_x_2,V_xs_2))) ) ),
file('theBenchmark.p',fact_distinct__insort__insert) ).
fof(fact_insort__insert__triv,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ),
file('theBenchmark.p',fact_insort__insert__triv) ).
fof(fact_set__insort__insert,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ),
file('theBenchmark.p',fact_set__insort__insert) ).
fof(fact_insort__insert__key__triv,axiom,
! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
=> c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ),
file('theBenchmark.p',fact_insort__insert__key__triv) ).
fof(fact_last__list__update,axiom,
! [V_x,V_k,T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> ( ( V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Olast(T_a,V_xs) )
& ( V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) ) ),
file('theBenchmark.p',fact_last__list__update) ).
fof(fact_last__conv__nth,axiom,
! [T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
file('theBenchmark.p',fact_last__conv__nth) ).
fof(fact_last__ConsL,axiom,
! [V_x,T_a,V_xs] :
( V_xs = c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ),
file('theBenchmark.p',fact_last__ConsL) ).
fof(fact_last__ConsR,axiom,
! [V_x,T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ),
file('theBenchmark.p',fact_last__ConsR) ).
fof(fact_last_Osimps,axiom,
! [V_x,T_a,V_xs] :
( ( V_xs != c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) )
& ( V_xs = c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ),
file('theBenchmark.p',fact_last_Osimps) ).
fof(fact_last__appendL,axiom,
! [V_xs,T_a,V_ys] :
( V_ys = c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ),
file('theBenchmark.p',fact_last__appendL) ).
fof(fact_last__appendR,axiom,
! [V_xs,T_a,V_ys] :
( V_ys != c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ),
file('theBenchmark.p',fact_last__appendR) ).
fof(fact_last__append,axiom,
! [V_xs,T_a,V_ys] :
( ( V_ys != c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) )
& ( V_ys = c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ),
file('theBenchmark.p',fact_last__append) ).
fof(fact_last__in__set,axiom,
! [T_b,V_as_2] :
( V_as_2 != c_List_Olist_ONil(T_b)
=> hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ),
file('theBenchmark.p',fact_last__in__set) ).
fof(fact_last__snoc,axiom,
! [V_x,V_xs,T_a] : c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_x,
file('theBenchmark.p',fact_last__snoc) ).
fof(fact_last__drop,axiom,
! [V_xs,T_a,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ),
file('theBenchmark.p',fact_last__drop) ).
fof(fact_snoc__eq__iff__butlast,axiom,
! [V_ys_2,V_x_2,V_xs_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = V_ys_2
<=> ( c_List_Olast(T_b,V_ys_2) = V_x_2
& c_List_Obutlast(T_b,V_ys_2) = V_xs_2
& V_ys_2 != c_List_Olist_ONil(T_b) ) ),
file('theBenchmark.p',fact_snoc__eq__iff__butlast) ).
fof(fact_append__butlast__last__id,axiom,
! [T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> hAPP(hAPP(c_List_Oappend(T_a),c_List_Obutlast(T_a,V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),c_List_Olast(T_a,V_xs)),c_List_Olist_ONil(T_a))) = V_xs ),
file('theBenchmark.p',fact_append__butlast__last__id) ).
fof(fact_lists_Osimps,axiom,
! [V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
<=> ( ? [B_a,B_l] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
& V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l) )
| V_a_2 = c_List_Olist_ONil(T_b) ) ),
file('theBenchmark.p',fact_lists_Osimps) ).
fof(fact_select__weigth__select,axiom,
! [T_b,V_xs_2] :
( V_xs_2 != c_List_Olist_ONil(T_b)
=> c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_b,V_xs_2) ),
file('theBenchmark.p',fact_select__weigth__select) ).
fof(fact_inj__mapI,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ),
file('theBenchmark.p',fact_inj__mapI) ).
fof(fact_last__map,axiom,
! [V_f_2,T_c,T_b,V_xs_2] :
( V_xs_2 != c_List_Olist_ONil(T_b)
=> c_List_Olast(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_b,V_xs_2)) ),
file('theBenchmark.p',fact_last__map) ).
fof(fact_foldl__map,axiom,
! [V_xs_2,V_f_2,T_d,V_a_2,V_g_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,T_b)),T_b),c_COMBB(T_c,T_b,T_d)),V_g_2)),V_f_2),V_a_2),V_xs_2),
file('theBenchmark.p',fact_foldl__map) ).
fof(fact_map__tl,axiom,
! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Otl(T_c),V_xs_2)) = hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
file('theBenchmark.p',fact_map__tl) ).
fof(fact_rotate__map,axiom,
! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(c_List_Orotate(T_b,V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orotate(T_c,V_n_2),V_xs_2)),
file('theBenchmark.p',fact_rotate__map) ).
fof(fact_zip__same__conv__map,axiom,
! [V_xs_2,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))),V_xs_2),
file('theBenchmark.p',fact_zip__same__conv__map) ).
fof(fact_zip__map__map,axiom,
! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_e),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),T_d),c_COMBB(T_c,tc_prod(T_b,T_c),T_e)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_d,T_e),V_xs_2),V_ys_2)),
file('theBenchmark.p',fact_zip__map__map) ).
fof(fact_zip__map1,axiom,
! [V_ys_2,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2)),
file('theBenchmark.p',fact_zip__map1) ).
fof(fact_map__zip__map,axiom,
! [V_ys_2,V_xs_2,V_g_2,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_e,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_d,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_d),V_f_2)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_e),c_Product__Type_OPair(T_c,T_d)),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_e,T_d),V_xs_2),V_ys_2)),
file('theBenchmark.p',fact_map__zip__map) ).
fof(fact_map__zip__map2,axiom,
! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),hAPP(hAPP(c_List_Omap(T_e,T_d),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_e),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_e,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_c,T_d)),tc_fun(T_e,T_b),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_e),V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),T_c),c_COMBB(T_d,tc_prod(T_c,T_d),T_e)),c_Product__Type_OPair(T_c,T_d))),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_c,T_e),V_xs_2),V_ys_2)),
file('theBenchmark.p',fact_map__zip__map2) ).
fof(fact_zip__map2,axiom,
! [V_ys_2,V_f_2,T_d,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),T_b),c_COMBB(T_c,tc_prod(T_b,T_c),T_d)),c_Product__Type_OPair(T_b,T_c))),V_f_2))),hAPP(hAPP(c_List_Ozip(T_b,T_d),V_xs_2),V_ys_2)),
file('theBenchmark.p',fact_zip__map2) ).
fof(fact_Nil__is__map__conv,axiom,
! [V_xs_2,V_f_2,T_c,T_b] :
( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
<=> V_xs_2 = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_Nil__is__map__conv) ).
fof(fact_map_Osimps_I1_J,axiom,
! [V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b),
file('theBenchmark.p',fact_map_Osimps_I1_J) ).
fof(fact_map__is__Nil__conv,axiom,
! [V_xs_2,V_f_2,T_b,T_c] :
( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
<=> V_xs_2 = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_map__is__Nil__conv) ).
fof(fact_map__update,axiom,
! [V_y_2,V_k_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)),
file('theBenchmark.p',fact_map__update) ).
fof(fact_map__eq__conv,axiom,
! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
=> hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ),
file('theBenchmark.p',fact_map__eq__conv) ).
fof(fact_map__eq__imp__length__eq,axiom,
! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2)
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_ys_2) ),
file('theBenchmark.p',fact_map__eq__imp__length__eq) ).
fof(fact_length__map,axiom,
! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2),
file('theBenchmark.p',fact_length__map) ).
fof(fact_listsum__subtractf,axiom,
! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
( class_Groups_Oab__group__add(T_b)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ),
file('theBenchmark.p',fact_listsum__subtractf) ).
fof(fact_listsum__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_listsum__mult__const,axiom,
! [V_xs_2,V_c_2,V_f_2,T_c,T_b] :
( class_Rings_Osemiring__0(T_b)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_c_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),V_c_2) ),
file('theBenchmark.p',fact_listsum__mult__const) ).
fof(fact_listsum__const__mult,axiom,
! [V_xs_2,V_f_2,V_c_2,T_c,T_b] :
( class_Rings_Osemiring__0(T_b)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) ),
file('theBenchmark.p',fact_listsum__const__mult) ).
fof(fact_listsum__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_inj__map__eq__map,axiom,
! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)
<=> V_xs_2 = V_ys_2 ) ),
file('theBenchmark.p',fact_inj__map__eq__map) ).
fof(fact_map__injective,axiom,
! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)
=> ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> V_xs_2 = V_ys_2 ) ),
file('theBenchmark.p',fact_map__injective) ).
fof(fact_map__ident,axiom,
! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2,
file('theBenchmark.p',fact_map__ident) ).
fof(fact_take__map,axiom,
! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2)),
file('theBenchmark.p',fact_take__map) ).
fof(fact_map__butlast,axiom,
! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Obutlast(T_c,V_xs_2)) = c_List_Obutlast(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
file('theBenchmark.p',fact_map__butlast) ).
fof(fact_set__map,axiom,
! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)),
file('theBenchmark.p',fact_set__map) ).
fof(fact_map_Osimps_I2_J,axiom,
! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
file('theBenchmark.p',fact_map_Osimps_I2_J) ).
fof(fact_map__append,axiom,
! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)),
file('theBenchmark.p',fact_map__append) ).
fof(fact_hd__map,axiom,
! [V_f_2,T_c,T_b,V_xs_2] :
( V_xs_2 != c_List_Olist_ONil(T_b)
=> hAPP(c_List_Ohd(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_b),V_xs_2)) ),
file('theBenchmark.p',fact_hd__map) ).
fof(fact_drop__map,axiom,
! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_xs_2)),
file('theBenchmark.p',fact_drop__map) ).
fof(fact_List_Omap_Oidentity,axiom,
! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)),
file('theBenchmark.p',fact_List_Omap_Oidentity) ).
fof(fact_List_Omap_Oid,axiom,
! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)),
file('theBenchmark.p',fact_List_Omap_Oid) ).
fof(fact_map__map,axiom,
! [V_xs_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_xs_2),
file('theBenchmark.p',fact_map__map) ).
fof(fact_List_Omap_Ocompositionality,axiom,
! [V_list_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_list_2),
file('theBenchmark.p',fact_List_Omap_Ocompositionality) ).
fof(fact_map__comp__map,axiom,
! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)),
file('theBenchmark.p',fact_map__comp__map) ).
fof(fact_List_Omap_Ocomp,axiom,
! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)),
file('theBenchmark.p',fact_List_Omap_Ocomp) ).
fof(fact_list__size__map,axiom,
! [V_xs_2,V_g_2,T_c,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_c,hAPP(c_Fun_Ocomp(T_b,tc_Nat_Onat,T_c,V_f_2),V_g_2),V_xs_2),
file('theBenchmark.p',fact_list__size__map) ).
fof(fact_map__inj__on,axiom,
! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)
=> ( c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(c_List_Oset(T_c),V_ys_2)))
=> V_xs_2 = V_ys_2 ) ),
file('theBenchmark.p',fact_map__inj__on) ).
fof(fact_inj__on__map__eq__map,axiom,
! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)))
=> ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)
<=> V_xs_2 = V_ys_2 ) ),
file('theBenchmark.p',fact_inj__on__map__eq__map) ).
fof(fact_nth__map,axiom,
! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)) ),
file('theBenchmark.p',fact_nth__map) ).
fof(fact_map__fun__upd,axiom,
! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hAPP(hAPP(c_List_Omap(T_b,T_c),c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_y_2,V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) ),
file('theBenchmark.p',fact_map__fun__upd) ).
fof(fact_distinct__map,axiom,
! [V_xs_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
<=> ( c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2))
& hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) ) ),
file('theBenchmark.p',fact_distinct__map) ).
fof(fact_listsum__abs,axiom,
! [V_xs_2,T_b] :
( class_Groups_Oordered__ab__group__add__abs(T_b)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_b,T_b),c_Groups_Oabs__class_Oabs(T_b)),V_xs_2)))) ),
file('theBenchmark.p',fact_listsum__abs) ).
fof(fact_uminus__listsum__map,axiom,
! [V_xs_2,V_f_2,T_c,T_b] :
( class_Groups_Oab__group__add(T_b)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_xs_2)) ),
file('theBenchmark.p',fact_uminus__listsum__map) ).
fof(fact_inj__on__mapI,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),V_A_2)))
=> c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),V_A_2) ),
file('theBenchmark.p',fact_inj__on__mapI) ).
fof(fact_inj__mapD,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))
=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_inj__mapD) ).
fof(fact_inj__map,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))
<=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_inj__map) ).
fof(fact_listsum__distinct__conv__setsum__set,axiom,
! [V_f_2,V_xs_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ),
file('theBenchmark.p',fact_listsum__distinct__conv__setsum__set) ).
fof(fact_listsum__triv,axiom,
! [V_xs_2,V_r_2,T_c,T_b] :
( class_Rings_Osemiring__1(T_b)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))),V_r_2) ),
file('theBenchmark.p',fact_listsum__triv) ).
fof(fact_listsum__map__remove1,axiom,
! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)))) ) ),
file('theBenchmark.p',fact_listsum__map__remove1) ).
fof(fact_Nitpick_Osetsum_H__def,axiom,
! [V_f_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b))))) ) ) ),
file('theBenchmark.p',fact_Nitpick_Osetsum_H__def) ).
fof(fact_pick__same,axiom,
! [V_xs_2,T_b,V_l_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_l_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hAPP(c_Random_Opick(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)),hAPP(c_Code__Numeral_Oof__nat,V_l_2)) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_l_2) ),
file('theBenchmark.p',fact_pick__same) ).
fof(fact_zero__code__numeral__def,axiom,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('theBenchmark.p',fact_zero__code__numeral__def) ).
fof(fact_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__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_Code__Numeral_Oof__nat__code,axiom,
c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',fact_Code__Numeral_Oof__nat__code) ).
fof(fact_one__code__numeral__def,axiom,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('theBenchmark.p',fact_one__code__numeral__def) ).
fof(fact_less__code__numeral__code,axiom,
! [V_m_2,V_n_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ),
file('theBenchmark.p',fact_less__code__numeral__code) ).
fof(fact_code__numeral_Oof__nat__inject,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
=> ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_code__numeral_Oof__nat__inject) ).
fof(fact_map__fst__zip,axiom,
! [V_ys_2,T_c,V_xs_2,T_b] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
=> hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_xs_2 ),
file('theBenchmark.p',fact_map__fst__zip) ).
fof(fact_map__snd__zip,axiom,
! [V_ys_2,T_c,V_xs_2,T_b] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
=> hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_ys_2 ),
file('theBenchmark.p',fact_map__snd__zip) ).
fof(fact_number__of__code__numeral__def,axiom,
c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat),
file('theBenchmark.p',fact_number__of__code__numeral__def) ).
fof(fact_zip__map__fst__snd,axiom,
! [V_zs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2)) = V_zs_2,
file('theBenchmark.p',fact_zip__map__fst__snd) ).
fof(fact_plus__code__numeral__code,axiom,
! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),
file('theBenchmark.p',fact_plus__code__numeral__code) ).
fof(fact_less__eq__code__numeral__code,axiom,
! [V_m_2,V_n_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ),
file('theBenchmark.p',fact_less__eq__code__numeral__code) ).
fof(fact_subtract__code__numeral__code,axiom,
! [V_m,V_n] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)),
file('theBenchmark.p',fact_subtract__code__numeral__code) ).
fof(fact_pick__member,axiom,
! [V_xs_2,T_b,V_i_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i_2),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Random_Opick(T_b,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ),
file('theBenchmark.p',fact_pick__member) ).
fof(fact_zip__eq__conv,axiom,
! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
=> ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
<=> ( hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2) = V_ys_2
& hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2) = V_xs_2 ) ) ),
file('theBenchmark.p',fact_zip__eq__conv) ).
fof(fact_list__size__conv__listsum,axiom,
! [V_xs_2,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(T_b,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),
file('theBenchmark.p',fact_list__size__conv__listsum) ).
fof(fact_code__numeral__not__eq__zero,axiom,
! [V_i_2] :
( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_i_2)) ),
file('theBenchmark.p',fact_code__numeral__not__eq__zero) ).
fof(fact_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_nat__of__of__nat,axiom,
! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n,
file('theBenchmark.p',fact_nat__of__of__nat) ).
fof(fact_of__nat__nat__of,axiom,
! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k,
file('theBenchmark.p',fact_of__nat__nat__of) ).
fof(fact_nat__of__inverse,axiom,
! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x,
file('theBenchmark.p',fact_nat__of__inverse) ).
fof(fact_times__code__numeral__def,axiom,
! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))),
file('theBenchmark.p',fact_times__code__numeral__def) ).
fof(fact_code__numeral_Onat__of__inject,axiom,
! [V_y_2,V_x_2] :
( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
<=> V_x_2 = V_y_2 ),
file('theBenchmark.p',fact_code__numeral_Onat__of__inject) ).
fof(fact_Code__Numeral_Onat__of__inject,axiom,
! [V_l_2,V_k_2] :
( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
<=> V_k_2 = V_l_2 ),
file('theBenchmark.p',fact_Code__Numeral_Onat__of__inject) ).
fof(fact_type__definition__code__numeral,axiom,
c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('theBenchmark.p',fact_type__definition__code__numeral) ).
fof(fact_less__code__numeral__def,axiom,
! [V_m_2,V_n_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) ),
file('theBenchmark.p',fact_less__code__numeral__def) ).
fof(fact_nat__of,axiom,
! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_x_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
file('theBenchmark.p',fact_nat__of) ).
fof(fact_nat__of__number,axiom,
! [V_k] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),V_k)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_k),
file('theBenchmark.p',fact_nat__of__number) ).
fof(fact_int__of__def,axiom,
c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of),
file('theBenchmark.p',fact_int__of__def) ).
fof(fact_less__eq__code__numeral__def,axiom,
! [V_m_2,V_n_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) ),
file('theBenchmark.p',fact_less__eq__code__numeral__def) ).
fof(fact_nat__of__code,axiom,
! [V_i] : hAPP(c_Code__Numeral_Onat__of,V_i) = c_Code__Numeral_Onat__of__aux(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('theBenchmark.p',fact_nat__of__code) ).
fof(fact_nat__of__aux__def,axiom,
! [V_n,V_i] : c_Code__Numeral_Onat__of__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_i)),V_n),
file('theBenchmark.p',fact_nat__of__aux__def) ).
fof(fact_Suc__code__numeral__def,axiom,
! [V_k] : c_Code__Numeral_OSuc__code__numeral(V_k) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,V_k))),
file('theBenchmark.p',fact_Suc__code__numeral__def) ).
fof(fact_minus__code__numeral__def,axiom,
! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))),
file('theBenchmark.p',fact_minus__code__numeral__def) ).
fof(fact_of__nat__inverse,axiom,
! [V_y_2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
=> hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ),
file('theBenchmark.p',fact_of__nat__inverse) ).
fof(fact_plus__code__numeral__def,axiom,
! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))),
file('theBenchmark.p',fact_plus__code__numeral__def) ).
fof(fact_div__code__numeral__def,axiom,
! [V_m,V_n] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))),
file('theBenchmark.p',fact_div__code__numeral__def) ).
fof(fact_mod__code__numeral__def,axiom,
! [V_m,V_n] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,V_n),hAPP(c_Code__Numeral_Onat__of,V_m))),
file('theBenchmark.p',fact_mod__code__numeral__def) ).
fof(fact_code__numeral__decr,axiom,
! [V_k] :
( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_k)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,V_k))) ),
file('theBenchmark.p',fact_code__numeral__decr) ).
fof(fact_New__DSequence_Opos__not__seq__def,axiom,
! [V_i_2,V_xq_2] : hAPP(c_New__DSequence_Opos__not__seq(V_xq_2),V_i_2) = c_Lazy__Sequence_Ohb__not__seq(hAPP(V_xq_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_i_2))),
file('theBenchmark.p',fact_New__DSequence_Opos__not__seq__def) ).
fof(fact_partition__set,axiom,
! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
( c_List_Opartition(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_yes_2)),hAPP(c_List_Oset(T_b),V_no_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ),
file('theBenchmark.p',fact_partition__set) ).
fof(fact_partition__P,axiom,
! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
( c_List_Opartition(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2)))
=> ~ hBOOL(hAPP(V_P_2,B_x)) )
& ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2)))
=> hBOOL(hAPP(V_P_2,B_x)) ) ) ),
file('theBenchmark.p',fact_partition__P) ).
fof(fact_partition_Osimps_I1_J,axiom,
! [V_P_2,T_b] : c_List_Opartition(T_b,V_P_2,c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b)),
file('theBenchmark.p',fact_partition_Osimps_I1_J) ).
fof(fact_partition_Osimps_I2_J,axiom,
! [V_xs_2,V_x_2,V_P_2,T_b] : c_List_Opartition(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),hAPP(c_If(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(V_P_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_List_Olist_OCons(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_List_Olist(T_b))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_List_Opartition(T_b,V_P_2,V_xs_2)),
file('theBenchmark.p',fact_partition_Osimps_I2_J) ).
fof(fact_lists__Int__eq,axiom,
! [V_B_2,V_A_2,T_b] : c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),c_List_Olists(T_b,V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),c_List_Olists(T_b,V_B_2))),
file('theBenchmark.p',fact_lists__Int__eq) ).
fof(fact_lists__IntI,axiom,
! [V_B_2,V_A_2,V_l_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_A_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_B_2)))
=> hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_l_2)) ) ),
file('theBenchmark.p',fact_lists__IntI) ).
fof(fact_listsp_ONil,axiom,
! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))),
file('theBenchmark.p',fact_listsp_ONil) ).
fof(fact_listsp_Oequations_I1_J,axiom,
! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))),
file('theBenchmark.p',fact_listsp_Oequations_I1_J) ).
fof(fact_in__listsp__conv__set,axiom,
! [V_xs_2,V_A_2,T_b] :
( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_A_2,B_x)) ) ),
file('theBenchmark.p',fact_in__listsp__conv__set) ).
fof(fact_listsp__conj__eq,axiom,
! [V_x_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_A_2)),V_B_2)),V_x_2))
<=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2))
& hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2)) ) ),
file('theBenchmark.p',fact_listsp__conj__eq) ).
fof(fact_listsp__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__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_Oequations_I2_J,axiom,
! [V_a2_2,V_a1_2,V_A_2,T_b] :
( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2)))
<=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2))
& hBOOL(hAPP(V_A_2,V_a1_2)) ) ),
file('theBenchmark.p',fact_listsp_Oequations_I2_J) ).
fof(fact_append__in__listsp__conv,axiom,
! [V_ys_2,V_xs_2,V_A_2,T_b] :
( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
<=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2))
& hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2)) ) ),
file('theBenchmark.p',fact_append__in__listsp__conv) ).
fof(fact_listsp__mono,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2))) ),
file('theBenchmark.p',fact_listsp__mono) ).
fof(fact_listsp__lists__eq,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2))) ),
file('theBenchmark.p',fact_listsp__lists__eq) ).
fof(fact_product_Osimps_I2_J,axiom,
! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : c_Enum_Oproduct(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Omap(T_c,tc_prod(T_b,T_c)),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)),V_ys_2)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)),
file('theBenchmark.p',fact_product_Osimps_I2_J) ).
fof(fact_list__all2__def,axiom,
! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2),B_x)) )
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ) ),
file('theBenchmark.p',fact_list__all2__def) ).
fof(fact_list__all2__map1,axiom,
! [V_bs_2,V_as_2,V_f_2,T_d,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_as_2),V_bs_2)
<=> c_List_Olist__all2(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),V_P_2),V_f_2),V_as_2,V_bs_2) ),
file('theBenchmark.p',fact_list__all2__map1) ).
fof(fact_list__all2__map2,axiom,
! [V_bs_2,V_f_2,T_d,V_as_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,V_as_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_bs_2))
<=> c_List_Olist__all2(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_d)),V_P_2)),V_f_2),V_as_2,V_bs_2) ),
file('theBenchmark.p',fact_list__all2__map2) ).
fof(fact_list__all2__dropI,axiom,
! [V_n_2,V_bs_2,V_as_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,V_as_2,V_bs_2)
=> c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_bs_2)) ),
file('theBenchmark.p',fact_list__all2__dropI) ).
fof(fact_list__all2__appendI,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2)
=> ( c_List_Olist__all2(T_b,T_c,V_P_2,V_c_2,V_d_2)
=> c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_a_2),V_c_2),hAPP(hAPP(c_List_Oappend(T_c),V_b_2),V_d_2)) ) ),
file('theBenchmark.p',fact_list__all2__appendI) ).
fof(fact_list__all2__append,axiom,
! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_c,V_xs_2,T_b] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
=> ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_vs_2))
<=> ( c_List_Olist__all2(T_b,T_c,V_P_2,V_us_2,V_vs_2)
& c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ) ) ),
file('theBenchmark.p',fact_list__all2__append) ).
fof(fact_list__all2__Cons,axiom,
! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2))
<=> ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
& hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_list__all2__Cons) ).
fof(fact_list__all2__takeI,axiom,
! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
=> c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_ys_2)) ),
file('theBenchmark.p',fact_list__all2__takeI) ).
fof(fact_list__all2__eq,axiom,
! [T_b,V_ys_2,V_xs_2] :
( V_xs_2 = V_ys_2
<=> c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2) ),
file('theBenchmark.p',fact_list__all2__eq) ).
fof(fact_list__all2__lengthD,axiom,
! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ),
file('theBenchmark.p',fact_list__all2__lengthD) ).
fof(fact_list__all2__Nil2,axiom,
! [V_xs_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,c_List_Olist_ONil(T_c))
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_list__all2__Nil2) ).
fof(fact_list__all2__Nil,axiom,
! [V_ys_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,c_List_Olist_ONil(T_b),V_ys_2)
<=> V_ys_2 = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_list__all2__Nil) ).
fof(fact_product_Osimps_I1_J,axiom,
! [V_uu,T_b,T_a] : c_Enum_Oproduct(T_a,T_b,c_List_Olist_ONil(T_a),V_uu) = c_List_Olist_ONil(tc_prod(T_a,T_b)),
file('theBenchmark.p',fact_product_Osimps_I1_J) ).
fof(fact_list__all2__nthD2,axiom,
! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
=> hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ),
file('theBenchmark.p',fact_list__all2__nthD2) ).
fof(fact_list__all2__nthD,axiom,
! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ),
file('theBenchmark.p',fact_list__all2__nthD) ).
fof(fact_list__all2__conv__all__nth,axiom,
! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
<=> ( ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),B_i))) )
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ) ),
file('theBenchmark.p',fact_list__all2__conv__all__nth) ).
fof(fact_list__all2__update__cong2,axiom,
! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
=> c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_list__all2__update__cong2) ).
fof(fact_list__all2__update__cong,axiom,
! [V_y_2,V_x_2,V_ys_2,V_P_2,T_c,V_xs_2,T_b,V_i_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
=> c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_list__all2__update__cong) ).
fof(fact_distinct__product,axiom,
! [V_ys,T_b,V_xs,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
=> hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ),
file('theBenchmark.p',fact_distinct__product) ).
fof(fact_product__list__set,axiom,
! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_List_Oset(T_c),V_ys_2))),
file('theBenchmark.p',fact_product__list__set) ).
fof(fact_sublists__powset,axiom,
! [V_xs_2,T_b] : hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_Osublists(T_b,V_xs_2))) = hAPP(c_Set_OPow(T_b),hAPP(c_List_Oset(T_b),V_xs_2)),
file('theBenchmark.p',fact_sublists__powset) ).
fof(fact_length__sublists,axiom,
! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),
file('theBenchmark.p',fact_length__sublists) ).
fof(fact_sublists_Osimps_I1_J,axiom,
! [T_a] : c_Enum_Osublists(T_a,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))),
file('theBenchmark.p',fact_sublists_Osimps_I1_J) ).
fof(fact_sublists_Osimps_I2_J,axiom,
! [V_xs_2,V_x_2,T_b] : c_Enum_Osublists(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_Enum_Osublists(T_b,V_xs_2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(T_b)),tc_fun(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(tc_List_Olist(T_b))),c_List_Oappend(tc_List_Olist(T_b))),hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_COMBI(tc_List_Olist(tc_List_Olist(T_b))))),
file('theBenchmark.p',fact_sublists_Osimps_I2_J) ).
fof(fact_distinct__set__sublists,axiom,
! [V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> hBOOL(hAPP(c_List_Odistinct(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),c_List_Oset(T_b)),c_Enum_Osublists(T_b,V_xs_2)))) ),
file('theBenchmark.p',fact_distinct__set__sublists) ).
fof(fact_set__n__lists,axiom,
! [V_xs_2,V_n_2,T_b] : hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2)) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),hAPP(c_List_Oset(T_b),V_xs_2)))),
file('theBenchmark.p',fact_set__n__lists) ).
fof(fact_enum__the__def,axiom,
! [V_P_2,T_b] : c_Enum_Oenum__the(T_b,V_P_2) = c_HOL_OThe(T_b,V_P_2),
file('theBenchmark.p',fact_enum__the__def) ).
fof(fact_distinct__n__lists,axiom,
! [V_n,V_xs,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ),
file('theBenchmark.p',fact_distinct__n__lists) ).
fof(fact_n__lists_Osimps_I1_J,axiom,
! [V_xs,T_a] : c_Enum_On__lists(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xs) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))),
file('theBenchmark.p',fact_n__lists_Osimps_I1_J) ).
fof(fact_n__lists__Nil,axiom,
! [T_a,V_n] :
( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) )
& ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ) ),
file('theBenchmark.p',fact_n__lists__Nil) ).
fof(fact_length__n__lists,axiom,
! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_On__lists(T_a,V_n,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n),
file('theBenchmark.p',fact_length__n__lists) ).
fof(fact_length__n__lists__elem,axiom,
! [V_xs_2,V_n_2,V_ys_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2))))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ),
file('theBenchmark.p',fact_length__n__lists__elem) ).
fof(fact_list__all2I,axiom,
! [V_P_2,V_b_2,V_a_2,T_c,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_a_2),V_b_2))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2),B_x)) )
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_b_2)
=> c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2) ) ),
file('theBenchmark.p',fact_list__all2I) ).
fof(fact_all__nth__imp__all__set,axiom,
! [V_x_2,V_P_2,V_xs_2,T_b] :
( ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_P_2,V_x_2)) ) ),
file('theBenchmark.p',fact_all__nth__imp__all__set) ).
fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),c_List_Oremdups(T_b,V_xs_2)) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__set__remdups) ).
fof(fact_map__removeAll__inj__on,axiom,
! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ),
file('theBenchmark.p',fact_map__removeAll__inj__on) ).
fof(fact_distinct__remdups,axiom,
! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))),
file('theBenchmark.p',fact_distinct__remdups) ).
fof(fact_length__remdups__leq,axiom,
! [V_xs,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),
file('theBenchmark.p',fact_length__remdups__leq) ).
fof(fact_remdups__id__iff__distinct,axiom,
! [V_xs_2,T_b] :
( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
<=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
file('theBenchmark.p',fact_remdups__id__iff__distinct) ).
fof(fact_distinct__removeAll,axiom,
! [V_x,V_xs,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ),
file('theBenchmark.p',fact_distinct__removeAll) ).
fof(fact_distinct__remdups__id,axiom,
! [V_xs,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> c_List_Oremdups(T_a,V_xs) = V_xs ),
file('theBenchmark.p',fact_distinct__remdups__id) ).
fof(fact_set__remdups,axiom,
! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
file('theBenchmark.p',fact_set__remdups) ).
fof(fact_length__remdups__eq,axiom,
! [V_xs_2,T_b] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
<=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ),
file('theBenchmark.p',fact_length__remdups__eq) ).
fof(fact_remdups__remdups,axiom,
! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs),
file('theBenchmark.p',fact_remdups__remdups) ).
fof(fact_remdups_Osimps_I1_J,axiom,
! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_remdups_Osimps_I1_J) ).
fof(fact_remdups__eq__nil__right__iff,axiom,
! [V_x_2,T_b] :
( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2)
<=> V_x_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_remdups__eq__nil__right__iff) ).
fof(fact_removeAll_Osimps_I1_J,axiom,
! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_removeAll_Osimps_I1_J) ).
fof(fact_remdups__eq__nil__iff,axiom,
! [V_x_2,T_b] :
( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b)
<=> V_x_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_remdups__eq__nil__iff) ).
fof(fact_removeAll_Osimps_I2_J,axiom,
! [V_xs,T_a,V_y,V_x] :
( ( V_x != V_y
=> hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)) )
& ( V_x = V_y
=> hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ),
file('theBenchmark.p',fact_removeAll_Osimps_I2_J) ).
fof(fact_removeAll__append,axiom,
! [V_ys,V_xs,V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)),hAPP(c_List_OremoveAll(T_a,V_x),V_ys)),
file('theBenchmark.p',fact_removeAll__append) ).
fof(fact_remdups__map__remdups,axiom,
! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremdups(T_c,V_xs_2))) = c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
file('theBenchmark.p',fact_remdups__map__remdups) ).
fof(fact_remove1__remdups,axiom,
! [V_x,V_xs,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> c_List_Oremove1(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oremove1(T_a,V_x,V_xs)) ),
file('theBenchmark.p',fact_remove1__remdups) ).
fof(fact_removeAll__id,axiom,
! [V_xs_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2) = V_xs_2 ),
file('theBenchmark.p',fact_removeAll__id) ).
fof(fact_distinct__remove1__removeAll,axiom,
! [V_x,V_xs,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ),
file('theBenchmark.p',fact_distinct__remove1__removeAll) ).
fof(fact_remdups_Osimps_I2_J,axiom,
! [V_xs_2,V_x_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oremdups(T_b,V_xs_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Oremdups(T_b,V_xs_2) ) ),
file('theBenchmark.p',fact_remdups_Osimps_I2_J) ).
fof(fact_length__remdups__card__conv,axiom,
! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)),
file('theBenchmark.p',fact_length__remdups__card__conv) ).
fof(fact_map__removeAll__inj,axiom,
! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ),
file('theBenchmark.p',fact_map__removeAll__inj) ).
fof(fact_set__removeAll,axiom,
! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
file('theBenchmark.p',fact_set__removeAll) ).
fof(fact_length__remdups__concat,axiom,
! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,c_List_Oconcat(T_b,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)),c_List_Oset(T_b))),
file('theBenchmark.p',fact_length__remdups__concat) ).
fof(fact_sorted__list__of__set__sort__remdups,axiom,
! [V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),c_List_Oremdups(T_b,V_xs_2)) ),
file('theBenchmark.p',fact_sorted__list__of__set__sort__remdups) ).
fof(fact_sort__key__simps_I1_J,axiom,
! [V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_sort__key__simps_I1_J) ).
fof(fact_foldl__conv__concat,axiom,
! [V_xss_2,V_xs_2,T_b] : hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oconcat(T_b,V_xss_2)),
file('theBenchmark.p',fact_foldl__conv__concat) ).
fof(fact_concat__conv__foldl,axiom,
! [V_xss_2,T_b] : c_List_Oconcat(T_b,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),c_List_Olist_ONil(T_b)),V_xss_2),
file('theBenchmark.p',fact_concat__conv__foldl) ).
fof(fact_length__sort,axiom,
! [V_xs_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ),
file('theBenchmark.p',fact_length__sort) ).
fof(fact_set__sort,axiom,
! [V_xs_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ),
file('theBenchmark.p',fact_set__sort) ).
fof(fact_distinct__sort,axiom,
! [V_xs_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)))
<=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ),
file('theBenchmark.p',fact_distinct__sort) ).
fof(fact_concat_Osimps_I1_J,axiom,
! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_concat_Osimps_I1_J) ).
fof(fact_concat_Osimps_I2_J,axiom,
! [V_xs,V_x,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),V_x),c_List_Oconcat(T_a,V_xs)),
file('theBenchmark.p',fact_concat_Osimps_I2_J) ).
fof(fact_Nil__eq__concat__conv,axiom,
! [V_xss_2,T_b] :
( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
=> B_x = c_List_Olist_ONil(T_b) ) ),
file('theBenchmark.p',fact_Nil__eq__concat__conv) ).
fof(fact_concat__eq__Nil__conv,axiom,
! [V_xss_2,T_b] :
( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
=> B_x = c_List_Olist_ONil(T_b) ) ),
file('theBenchmark.p',fact_concat__eq__Nil__conv) ).
fof(fact_map__concat,axiom,
! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oconcat(T_c,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)),
file('theBenchmark.p',fact_map__concat) ).
fof(fact_length__concat,axiom,
! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oconcat(T_b,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xss_2)),
file('theBenchmark.p',fact_length__concat) ).
fof(fact_set__concat,axiom,
! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oconcat(T_b,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)),c_List_Oset(T_b)),
file('theBenchmark.p',fact_set__concat) ).
fof(fact_sort__key__simps_I2_J,axiom,
! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) ),
file('theBenchmark.p',fact_sort__key__simps_I2_J) ).
fof(fact_concat__append,axiom,
! [V_ys,V_xs,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Oappend(tc_List_Olist(T_a)),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oconcat(T_a,V_xs)),c_List_Oconcat(T_a,V_ys)),
file('theBenchmark.p',fact_concat__append) ).
fof(fact_sort__foldl__insort,axiom,
! [V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))),c_List_Olist_ONil(T_b)),V_xs_2) ),
file('theBenchmark.p',fact_sort__foldl__insort) ).
fof(fact_concat__eq__concat__iff,axiom,
! [V_ys_2,V_xs_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) )
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
=> ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
<=> V_xs_2 = V_ys_2 ) ) ),
file('theBenchmark.p',fact_concat__eq__concat__iff) ).
fof(fact_concat__injective,axiom,
! [V_ys_2,V_xs_2,T_b] :
( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) )
=> V_xs_2 = V_ys_2 ) ) ),
file('theBenchmark.p',fact_concat__injective) ).
fof(fact_concat__map__singleton,axiom,
! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_c),c_List_Olist_OCons(T_b)),V_f_2)),c_List_Olist_ONil(T_b))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2),
file('theBenchmark.p',fact_concat__map__singleton) ).
fof(fact_n__lists_Osimps_I2_J,axiom,
! [V_xs_2,V_n_2,T_b] : c_Enum_On__lists(T_b,hAPP(c_Nat_OSuc,V_n_2),V_xs_2) = c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_List_Omap(T_b,tc_List_Olist(T_b))),hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),V_xs_2)),c_Enum_On__lists(T_b,V_n_2,V_xs_2))),
file('theBenchmark.p',fact_n__lists_Osimps_I2_J) ).
fof(fact_transpose_Osimps_I3_J,axiom,
! [V_xss_2,V_xs_2,V_x_2,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))),
file('theBenchmark.p',fact_transpose_Osimps_I3_J) ).
fof(fact_transpose__aux__filter__head,axiom,
! [V_xss_2,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),c_List_Ohd(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)),
file('theBenchmark.p',fact_transpose__aux__filter__head) ).
fof(fact_filter__concat,axiom,
! [V_xs_2,V_p_2,T_b] : hAPP(c_List_Ofilter(T_b,V_p_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Ofilter(T_b,V_p_2)),V_xs_2)),
file('theBenchmark.p',fact_filter__concat) ).
fof(fact_filter__sort,axiom,
! [V_xs_2,V_f_2,V_P_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) ),
file('theBenchmark.p',fact_filter__sort) ).
fof(fact_distinct__filter,axiom,
! [V_P_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) ),
file('theBenchmark.p',fact_distinct__filter) ).
fof(fact_filter__is__subset,axiom,
! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
file('theBenchmark.p',fact_filter__is__subset) ).
fof(fact_filter__id__conv,axiom,
! [V_xs_2,V_P_2,T_b] :
( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = V_xs_2
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_P_2,B_x)) ) ),
file('theBenchmark.p',fact_filter__id__conv) ).
fof(fact_length__filter__le,axiom,
! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
file('theBenchmark.p',fact_length__filter__le) ).
fof(fact_sum__length__filter__compl,axiom,
! [V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2),
file('theBenchmark.p',fact_sum__length__filter__compl) ).
fof(fact_filter__filter,axiom,
! [V_xs_2,V_Q_2,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Q_2)),V_P_2)),V_xs_2),
file('theBenchmark.p',fact_filter__filter) ).
fof(fact_remove1__filter__not,axiom,
! [V_xs_2,T_b,V_x_2,V_P_2] :
( ~ hBOOL(hAPP(V_P_2,V_x_2))
=> c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ),
file('theBenchmark.p',fact_remove1__filter__not) ).
fof(fact_filter__remove1,axiom,
! [V_xs_2,V_x_2,V_Q_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Q_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)),
file('theBenchmark.p',fact_filter__remove1) ).
fof(fact_filter__insort__triv,axiom,
! [V_xs_2,V_f_2,T_b,V_x_2,V_P_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( ~ hBOOL(hAPP(V_P_2,V_x_2))
=> hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ),
file('theBenchmark.p',fact_filter__insort__triv) ).
fof(fact_partition__filter1,axiom,
! [V_xs_2,V_P_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2),
file('theBenchmark.p',fact_partition__filter1) ).
fof(fact_partition__filter2,axiom,
! [V_xs_2,V_P_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_P_2)),V_xs_2),
file('theBenchmark.p',fact_partition__filter2) ).
fof(fact_partition__filter__conv,axiom,
! [V_xs_2,V_f_2,T_b] : c_List_Opartition(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_f_2)),V_xs_2)),
file('theBenchmark.p',fact_partition__filter__conv) ).
fof(fact_filter__map,axiom,
! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2)),V_xs_2)),
file('theBenchmark.p',fact_filter__map) ).
fof(fact_transpose_Osimps_I1_J,axiom,
! [T_a] : c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)),
file('theBenchmark.p',fact_transpose_Osimps_I1_J) ).
fof(fact_filter_Osimps_I1_J,axiom,
! [V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
file('theBenchmark.p',fact_filter_Osimps_I1_J) ).
fof(fact_filter_Osimps_I2_J,axiom,
! [V_xs_2,T_b,V_x_2,V_P_2] :
( ( ~ hBOOL(hAPP(V_P_2,V_x_2))
=> hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) )
& ( hBOOL(hAPP(V_P_2,V_x_2))
=> hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) ) ),
file('theBenchmark.p',fact_filter_Osimps_I2_J) ).
fof(fact_filter__append,axiom,
! [V_ys_2,V_xs_2,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2)),
file('theBenchmark.p',fact_filter__append) ).
fof(fact_filter__empty__conv,axiom,
! [V_xs_2,V_P_2,T_b] :
( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = c_List_Olist_ONil(T_b)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ~ hBOOL(hAPP(V_P_2,B_x)) ) ),
file('theBenchmark.p',fact_filter__empty__conv) ).
fof(fact_length__filter__map,axiom,
! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2)),V_xs_2)),
file('theBenchmark.p',fact_length__filter__map) ).
fof(fact_removeAll__filter__not,axiom,
! [V_xs_2,T_b,V_x_2,V_P_2] :
( ~ hBOOL(hAPP(V_P_2,V_x_2))
=> hAPP(c_List_OremoveAll(T_b,V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ),
file('theBenchmark.p',fact_removeAll__filter__not) ).
fof(fact_remdups__filter,axiom,
! [V_xs_2,V_P_2,T_b] : c_List_Oremdups(T_b,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Oremdups(T_b,V_xs_2)),
file('theBenchmark.p',fact_remdups__filter) ).
fof(fact_removeAll__filter__not__eq,axiom,
! [V_x_2,T_b] : c_List_OremoveAll(T_b,V_x_2) = c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(c_fequal,V_x_2))),
file('theBenchmark.p',fact_removeAll__filter__not__eq) ).
fof(fact_transpose_Osimps_I2_J,axiom,
! [V_xss,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss)) = c_List_Otranspose(T_a,V_xss),
file('theBenchmark.p',fact_transpose_Osimps_I2_J) ).
fof(fact_nth__transpose,axiom,
! [V_xs_2,T_b,V_i_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
=> hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2)) ),
file('theBenchmark.p',fact_nth__transpose) ).
fof(fact_transpose__map__map,axiom,
! [V_xs_2,V_f_2,T_c,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),c_List_Otranspose(T_c,V_xs_2)),
file('theBenchmark.p',fact_transpose__map__map) ).
fof(fact_set__filter,axiom,
! [V_xs_2,V_P_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)))),V_P_2)),
file('theBenchmark.p',fact_set__filter) ).
fof(fact_length__filter__less,axiom,
! [V_P_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ( ~ hBOOL(hAPP(V_P_2,V_x_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ),
file('theBenchmark.p',fact_length__filter__less) ).
fof(fact_set__minus__filter__out,axiom,
! [V_y_2,V_xs_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)),
file('theBenchmark.p',fact_set__minus__filter__out) ).
fof(fact_filter__in__sublist,axiom,
! [V_s_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_b,V_xs_2,V_s_2) ),
file('theBenchmark.p',fact_filter__in__sublist) ).
fof(fact_transpose__empty,axiom,
! [V_xs_2,T_b] :
( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
=> B_x = c_List_Olist_ONil(T_b) ) ),
file('theBenchmark.p',fact_transpose__empty) ).
fof(fact_length__filter__conv__card,axiom,
! [V_xs_2,V_p_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_p_2),V_xs_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_b),V_xs_2))))),
file('theBenchmark.p',fact_length__filter__conv__card) ).
fof(fact_transpose__aux__filter__tail,axiom,
! [V_xss_2,T_b] : c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otl(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)),
file('theBenchmark.p',fact_transpose__aux__filter__tail) ).
fof(fact_transpose_Opsimps_I3_J,axiom,
! [V_xss_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)))
=> c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))) ),
file('theBenchmark.p',fact_transpose_Opsimps_I3_J) ).
fof(fact_transpose_Opsimps_I2_J,axiom,
! [V_xss_2,T_b] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)))
=> c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)) = c_List_Otranspose(T_b,V_xss_2) ),
file('theBenchmark.p',fact_transpose_Opsimps_I2_J) ).
fof(fact_sublist__shift__lemma__Suc,axiom,
! [V_is_2,V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_P_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_b,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_b,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_P_2),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))),
file('theBenchmark.p',fact_sublist__shift__lemma__Suc) ).
fof(fact_select__weigth__drop__zero,axiom,
! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2),
file('theBenchmark.p',fact_select__weigth__drop__zero) ).
fof(fact_pick__drop__zero,axiom,
! [V_xs_2,T_b] : c_Random_Opick(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Opick(T_b,V_xs_2),
file('theBenchmark.p',fact_pick__drop__zero) ).
fof(fact_transpose_Opsimps_I1_J,axiom,
! [T_b] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),c_List_Olist_ONil(tc_List_Olist(T_b))))
=> c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ),
file('theBenchmark.p',fact_transpose_Opsimps_I1_J) ).
fof(fact_transpose__max__length,axiom,
! [V_xs_2,T_b] : c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xs_2)),
file('theBenchmark.p',fact_transpose__max__length) ).
fof(fact_transpose__aux__max,axiom,
! [V_xss_2,T_c,V_xs_2,T_b] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),V_xss_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_c)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_c)))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
file('theBenchmark.p',fact_transpose__aux__max) ).
fof(fact_foldr_Osimps_I1_J,axiom,
! [V_a_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c),V_a_2) = V_a_2,
file('theBenchmark.p',fact_foldr_Osimps_I1_J) ).
fof(fact_foldr_Osimps_I2_J,axiom,
! [V_a_2,V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2)),
file('theBenchmark.p',fact_foldr_Osimps_I2_J) ).
fof(fact_foldr__append,axiom,
! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,c_List_Ofoldr(T_c,T_b,V_f_2,V_ys_2,V_a_2)),
file('theBenchmark.p',fact_foldr__append) ).
fof(fact_foldr__conv__foldl,axiom,
! [V_a_2,V_xs_2,T_b] :
( class_Groups_Oab__semigroup__add(T_b)
=> c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) ),
file('theBenchmark.p',fact_foldr__conv__foldl) ).
fof(fact_foldr__map,axiom,
! [V_a_2,V_xs_2,V_f_2,T_d,V_g_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_g_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_d,T_b,hAPP(c_Fun_Ocomp(T_c,tc_fun(T_b,T_b),T_d,V_g_2),V_f_2),V_xs_2,V_a_2),
file('theBenchmark.p',fact_foldr__map) ).
fof(fact_foldl__foldr1__lemma,axiom,
! [V_xs_2,V_a_2,T_b] :
( class_Groups_Omonoid__add(T_b)
=> hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b))) ),
file('theBenchmark.p',fact_foldl__foldr1__lemma) ).
fof(fact_foldl__foldr1,axiom,
! [V_xs_2,T_b] :
( class_Groups_Omonoid__add(T_b)
=> hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_xs_2) = c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b)) ),
file('theBenchmark.p',fact_foldl__foldr1) ).
fof(fact_length__transpose,axiom,
! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('theBenchmark.p',fact_length__transpose) ).
fof(fact_sublist__def,axiom,
! [V_A_2,V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))),
file('theBenchmark.p',fact_sublist__def) ).
fof(fact_sublist__shift__lemma,axiom,
! [V_i_2,V_xs_2,V_A_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(V_i_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(T_b,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))),
file('theBenchmark.p',fact_sublist__shift__lemma) ).
fof(fact_set__upt,axiom,
! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2),
file('theBenchmark.p',fact_set__upt) ).
fof(fact_atLeastLessThan__upt,axiom,
! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)),
file('theBenchmark.p',fact_atLeastLessThan__upt) ).
fof(fact_upt__Suc,axiom,
! [V_j,V_i] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
=> c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
=> c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) ) ),
file('theBenchmark.p',fact_upt__Suc) ).
fof(fact_upt__Suc__append,axiom,
! [V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
=> c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) ),
file('theBenchmark.p',fact_upt__Suc__append) ).
fof(fact_upt__add__eq__append,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
=> c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),c_List_Oupt(V_j,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ),
file('theBenchmark.p',fact_upt__add__eq__append) ).
fof(fact_upt__rec,axiom,
! [V_j,V_i] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
=> c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
=> c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) ) ),
file('theBenchmark.p',fact_upt__rec) ).
fof(fact_upt__conv__Cons,axiom,
! [V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
=> c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) ),
file('theBenchmark.p',fact_upt__conv__Cons) ).
fof(fact_upt__conv__Nil,axiom,
! [V_i,V_j] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
=> c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ),
file('theBenchmark.p',fact_upt__conv__Nil) ).
fof(fact_upt__eq__Nil__conv,axiom,
! [V_j_2,V_i_2] :
( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
| V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_upt__eq__Nil__conv) ).
fof(fact_upt__0,axiom,
! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
file('theBenchmark.p',fact_upt__0) ).
fof(fact_take__upt,axiom,
! [V_n,V_m,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)),V_n))
=> hAPP(hAPP(c_List_Otake(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_n)) = c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)) ),
file('theBenchmark.p',fact_take__upt) ).
fof(fact_sorted__list__of__set__range,axiom,
! [V_n_2,V_m_2] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = c_List_Oupt(V_m_2,V_n_2),
file('theBenchmark.p',fact_sorted__list__of__set__range) ).
fof(fact_hd__upt,axiom,
! [V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
=> hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ),
file('theBenchmark.p',fact_hd__upt) ).
fof(fact_drop__upt,axiom,
! [V_j,V_i,V_m] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_j)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m),V_j),
file('theBenchmark.p',fact_drop__upt) ).
fof(fact_distinct__upt,axiom,
! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))),
file('theBenchmark.p',fact_distinct__upt) ).
fof(fact_length__upt,axiom,
! [V_j,V_i] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i),
file('theBenchmark.p',fact_length__upt) ).
fof(fact_upt__rec__number__of,axiom,
! [V_n,V_m] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)))
=> c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = c_List_Olist_ONil(tc_Nat_Onat) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)))
=> c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) ) ),
file('theBenchmark.p',fact_upt__rec__number__of) ).
fof(fact_upt__eq__Cons__conv,axiom,
! [V_xs_2,V_x_2,V_j_2,V_i_2] :
( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
<=> ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_j_2) = V_xs_2
& V_i_2 = V_x_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) ) ),
file('theBenchmark.p',fact_upt__eq__Cons__conv) ).
fof(fact_last__upt,axiom,
! [V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
=> c_List_Olast(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('theBenchmark.p',fact_last__upt) ).
fof(fact_map__Suc__upt,axiom,
! [V_n_2,V_m_2] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(V_m_2,V_n_2)) = c_List_Oupt(hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2)),
file('theBenchmark.p',fact_map__Suc__upt) ).
fof(fact_atLeastAtMost__upt,axiom,
! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_n_2,hAPP(c_Nat_OSuc,V_m_2))),
file('theBenchmark.p',fact_atLeastAtMost__upt) ).
fof(fact_atLeast__upt,axiom,
! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)),
file('theBenchmark.p',fact_atLeast__upt) ).
fof(fact_nth__upt,axiom,
! [V_j,V_k,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j))
=> hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k) ),
file('theBenchmark.p',fact_nth__upt) ).
fof(fact_greaterThanAtMost__upt,axiom,
! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),hAPP(c_Nat_OSuc,V_m_2))),
file('theBenchmark.p',fact_greaterThanAtMost__upt) ).
fof(fact_greaterThanLessThan__upt,axiom,
! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),V_m_2)),
file('theBenchmark.p',fact_greaterThanLessThan__upt) ).
fof(fact_atMost__upto,axiom,
! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))),
file('theBenchmark.p',fact_atMost__upto) ).
fof(fact_map__nth,axiom,
! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) = V_xs_2,
file('theBenchmark.p',fact_map__nth) ).
fof(fact_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__drop,axiom,
! [V_n,V_xs,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_List_Olinorder__class_Osorted(T_a,V_xs)
=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ),
file('theBenchmark.p',fact_sorted__drop) ).
fof(fact_sorted__upto,axiom,
! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)),
file('theBenchmark.p',fact_sorted__upto) ).
fof(fact_sorted__take,axiom,
! [V_n,V_xs,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_List_Olinorder__class_Osorted(T_a,V_xs)
=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ),
file('theBenchmark.p',fact_sorted__take) ).
fof(fact_sorted__remove1,axiom,
! [V_a,V_xs,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_List_Olinorder__class_Osorted(T_a,V_xs)
=> c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ),
file('theBenchmark.p',fact_sorted__remove1) ).
fof(fact_sorted__tl,axiom,
! [V_xs,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_List_Olinorder__class_Osorted(T_a,V_xs)
=> c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ),
file('theBenchmark.p',fact_sorted__tl) ).
fof(fact_sorted__insort,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2))
<=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ),
file('theBenchmark.p',fact_sorted__insort) ).
fof(fact_sorted__butlast,axiom,
! [V_xs,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( V_xs != c_List_Olist_ONil(T_a)
=> ( c_List_Olinorder__class_Osorted(T_a,V_xs)
=> c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ),
file('theBenchmark.p',fact_sorted__butlast) ).
fof(fact_sorted_Oequations_I1_J,axiom,
! [T_a] :
( class_Orderings_Olinorder(T_a)
=> c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ),
file('theBenchmark.p',fact_sorted_Oequations_I1_J) ).
fof(fact_sorted__many,axiom,
! [V_zs,V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))) ) ) ),
file('theBenchmark.p',fact_sorted__many) ).
fof(fact_sorted__many__eq,axiom,
! [V_zs_2,V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)))
<=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_sorted__many__eq) ).
fof(fact_sorted__remdups,axiom,
! [V_l,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_List_Olinorder__class_Osorted(T_a,V_l)
=> c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ),
file('theBenchmark.p',fact_sorted__remdups) ).
fof(fact_sorted__distinct__set__unique,axiom,
! [V_ys_2,V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> ( c_List_Olinorder__class_Osorted(T_b,V_ys_2)
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
=> ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
=> V_xs_2 = V_ys_2 ) ) ) ) ) ),
file('theBenchmark.p',fact_sorted__distinct__set__unique) ).
fof(fact_sorted__sort__key,axiom,
! [V_xs_2,V_f_2,T_c,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Osort__key(T_c,T_b,V_f_2,V_xs_2))) ),
file('theBenchmark.p',fact_sorted__sort__key) ).
fof(fact_sorted__insort__insert__key,axiom,
! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2))) ) ),
file('theBenchmark.p',fact_sorted__insort__insert__key) ).
fof(fact_sorted__map__remove1,axiom,
! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremove1(T_c,V_x_2,V_xs_2))) ) ),
file('theBenchmark.p',fact_sorted__map__remove1) ).
fof(fact_sorted__insort__key,axiom,
! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)))
<=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ),
file('theBenchmark.p',fact_sorted__insort__key) ).
fof(fact_sorted__filter,axiom,
! [V_P_2,V_xs_2,V_f_2,T_c,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2))) ) ),
file('theBenchmark.p',fact_sorted__filter) ).
fof(fact_sorted__map__same,axiom,
! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_c),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2))) ),
file('theBenchmark.p',fact_sorted__map__same) ).
fof(fact_sorted__same,axiom,
! [V_xs_2,V_g_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2)) ),
file('theBenchmark.p',fact_sorted__same) ).
fof(fact_sorted__Cons,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) )
& c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ),
file('theBenchmark.p',fact_sorted__Cons) ).
fof(fact_sorted__append,axiom,
! [V_ys_2,V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) )
& c_List_Olinorder__class_Osorted(T_b,V_ys_2)
& c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ),
file('theBenchmark.p',fact_sorted__append) ).
fof(fact_filter__insort,axiom,
! [V_x_2,V_P_2,V_xs_2,V_f_2,T_c,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
=> ( hBOOL(hAPP(V_P_2,V_x_2))
=> hAPP(c_List_Ofilter(T_c,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2)) ) ) ),
file('theBenchmark.p',fact_filter__insort) ).
fof(fact_sorted_Oequations_I2_J,axiom,
! [V_a1_2,V_a2_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
<=> ( c_List_Olinorder__class_Osorted(T_b,V_a1_2)
& ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) ) ) ) ),
file('theBenchmark.p',fact_sorted_Oequations_I2_J) ).
fof(fact_sorted__list__of__set,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)))
& c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
& hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2 ) ) ),
file('theBenchmark.p',fact_sorted__list__of__set) ).
fof(fact_insort__remove1,axiom,
! [V_xs_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ),
file('theBenchmark.p',fact_insort__remove1) ).
fof(fact_sorted__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_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_map__sorted__distinct__set__unique,axiom,
! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)))
=> ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
=> ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
=> ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
=> ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
=> ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
=> V_xs_2 = V_ys_2 ) ) ) ) ) ) ),
file('theBenchmark.p',fact_map__sorted__distinct__set__unique) ).
fof(fact_transpose__column,axiom,
! [V_i_2,V_xs_2,T_b] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
=> hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2) ) ),
file('theBenchmark.p',fact_transpose__column) ).
fof(fact_nth__nth__transpose__sorted,axiom,
! [V_j_2,V_i_2,V_xs_2,T_b] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2))))
=> hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_j_2)),V_i_2) ) ) ),
file('theBenchmark.p',fact_nth__nth__transpose__sorted) ).
fof(fact_inj__on__rev,axiom,
! [V_A_2,T_b] : c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orev(T_b),V_A_2),
file('theBenchmark.p',fact_inj__on__rev) ).
fof(fact_distinct__rev,axiom,
! [V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
<=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
file('theBenchmark.p',fact_distinct__rev) ).
fof(fact_rev_Osimps_I1_J,axiom,
! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_rev_Osimps_I1_J) ).
fof(fact_Nil__is__rev__conv,axiom,
! [V_xs_2,T_b] :
( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_Nil__is__rev__conv) ).
fof(fact_rev__is__Nil__conv,axiom,
! [V_xs_2,T_b] :
( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_rev__is__Nil__conv) ).
fof(fact_rev__singleton__conv,axiom,
! [V_x_2,V_xs_2,T_b] :
( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))
<=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ),
file('theBenchmark.p',fact_rev__singleton__conv) ).
fof(fact_singleton__rev__conv,axiom,
! [V_xs_2,V_x_2,T_b] :
( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(c_List_Orev(T_b),V_xs_2)
<=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ),
file('theBenchmark.p',fact_singleton__rev__conv) ).
fof(fact_rev__append,axiom,
! [V_ys,V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys)),hAPP(c_List_Orev(T_a),V_xs)),
file('theBenchmark.p',fact_rev__append) ).
fof(fact_rev__concat,axiom,
! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Orev(T_b)),hAPP(c_List_Orev(tc_List_Olist(T_b)),V_xs_2))),
file('theBenchmark.p',fact_rev__concat) ).
fof(fact_rev__map,axiom,
! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2)),
file('theBenchmark.p',fact_rev__map) ).
fof(fact_rev__filter,axiom,
! [V_xs_2,V_P_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(c_List_Orev(T_b),V_xs_2)),
file('theBenchmark.p',fact_rev__filter) ).
fof(fact_zip__rev,axiom,
! [V_ys,T_b,V_xs,T_a] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)
=> hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(c_List_Orev(T_a),V_xs)),hAPP(c_List_Orev(T_b),V_ys)) = hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) ),
file('theBenchmark.p',fact_zip__rev) ).
fof(fact_set__rev,axiom,
! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
file('theBenchmark.p',fact_set__rev) ).
fof(fact_list__all2__rev1,axiom,
! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2)
<=> c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) ),
file('theBenchmark.p',fact_list__all2__rev1) ).
fof(fact_list__all2__rev,axiom,
! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2),hAPP(c_List_Orev(T_c),V_ys_2))
<=> c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ),
file('theBenchmark.p',fact_list__all2__rev) ).
fof(fact_rev__is__rev__conv,axiom,
! [V_ys_2,V_xs_2,T_b] :
( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
<=> V_xs_2 = V_ys_2 ),
file('theBenchmark.p',fact_rev__is__rev__conv) ).
fof(fact_rev__swap,axiom,
! [V_ys_2,V_xs_2,T_b] :
( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
<=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ),
file('theBenchmark.p',fact_rev__swap) ).
fof(fact_rev__rev__ident,axiom,
! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs,
file('theBenchmark.p',fact_rev__rev__ident) ).
fof(fact_listsum__rev,axiom,
! [V_xs,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs) ),
file('theBenchmark.p',fact_listsum__rev) ).
fof(fact_length__rev,axiom,
! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs),
file('theBenchmark.p',fact_length__rev) ).
fof(fact_foldr__foldl,axiom,
! [V_a_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),V_f_2),V_a_2),hAPP(c_List_Orev(T_c),V_xs_2)),
file('theBenchmark.p',fact_foldr__foldl) ).
fof(fact_foldl__foldr,axiom,
! [V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2),V_a_2),
file('theBenchmark.p',fact_foldl__foldr) ).
fof(fact_rev_Osimps_I2_J,axiom,
! [V_xs,V_x,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))),
file('theBenchmark.p',fact_rev_Osimps_I2_J) ).
fof(fact_rev__eq__Cons__iff,axiom,
! [V_ys_2,V_y_2,V_xs_2,T_b] :
( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
<=> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Orev(T_b),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))) ),
file('theBenchmark.p',fact_rev__eq__Cons__iff) ).
fof(fact_last__rev,axiom,
! [T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ),
file('theBenchmark.p',fact_last__rev) ).
fof(fact_hd__rev,axiom,
! [T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ),
file('theBenchmark.p',fact_hd__rev) ).
fof(fact_sorted__transpose,axiom,
! [V_xs_2,T_b] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)))),
file('theBenchmark.p',fact_sorted__transpose) ).
fof(fact_rev__foldl__cons,axiom,
! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)),V_xs_2),
file('theBenchmark.p',fact_rev__foldl__cons) ).
fof(fact_rev__drop,axiom,
! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)),
file('theBenchmark.p',fact_rev__drop) ).
fof(fact_rev__take,axiom,
! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)),
file('theBenchmark.p',fact_rev__take) ).
fof(fact_rotate__rev,axiom,
! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Orev(T_a),hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))),V_xs)),
file('theBenchmark.p',fact_rotate__rev) ).
fof(fact_rev__nth,axiom,
! [V_xs,T_a,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hAPP(hAPP(c_List_Onth(T_a),hAPP(c_List_Orev(T_a),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_OSuc,V_n))) ),
file('theBenchmark.p',fact_rev__nth) ).
fof(fact_rev__update,axiom,
! [V_y,V_xs,T_a,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_y)) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_k)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_y) ),
file('theBenchmark.p',fact_rev__update) ).
fof(fact_sorted__rev__nth__mono,axiom,
! [V_j,V_i,V_xs,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i))) ) ) ) ),
file('theBenchmark.p',fact_sorted__rev__nth__mono) ).
fof(fact_foldr__max__sorted,axiom,
! [V_y_2,V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
=> ( ( V_xs_2 != c_List_Olist_ONil(T_b)
=> c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2) )
& ( V_xs_2 = c_List_Olist_ONil(T_b)
=> c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 ) ) ) ),
file('theBenchmark.p',fact_foldr__max__sorted) ).
fof(fact_length__transpose__sorted,axiom,
! [V_xs_2,T_b] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
=> ( ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('theBenchmark.p',fact_length__transpose__sorted) ).
fof(fact_transpose__column__length,axiom,
! [V_i_2,V_xs_2,T_b] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2)) ) ),
file('theBenchmark.p',fact_transpose__column__length) ).
fof(fact_transpose__transpose,axiom,
! [V_xs_2,T_b] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
=> c_List_Otranspose(T_b,c_List_Otranspose(T_b,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b))),V_xs_2) ),
file('theBenchmark.p',fact_transpose__transpose) ).
fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)),
file('theBenchmark.p',fact_transfer__nat__int__list__functions_I2_J) ).
fof(fact_sorted__takeWhile,axiom,
! [V_P_2,V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
=> c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_P_2,V_xs_2)) ) ),
file('theBenchmark.p',fact_sorted__takeWhile) ).
fof(fact_length__takeWhile__le,axiom,
! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
file('theBenchmark.p',fact_length__takeWhile__le) ).
fof(fact_takeWhile__eq__all__conv,axiom,
! [V_xs_2,V_P_2,T_b] :
( c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = V_xs_2
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_P_2,B_x)) ) ),
file('theBenchmark.p',fact_takeWhile__eq__all__conv) ).
fof(fact_set__takeWhileD,axiom,
! [V_xs_2,V_P_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))
=> ( hBOOL(hAPP(V_P_2,V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
file('theBenchmark.p',fact_set__takeWhileD) ).
fof(fact_zip__takeWhile__snd,axiom,
! [V_ys_2,V_P_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),c_List_OtakeWhile(T_c,V_P_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_b,T_c),V_P_2),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),
file('theBenchmark.p',fact_zip__takeWhile__snd) ).
fof(fact_zip__takeWhile__fst,axiom,
! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_b,T_c),V_P_2),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),
file('theBenchmark.p',fact_zip__takeWhile__fst) ).
fof(fact_takeWhile__map,axiom,
! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OtakeWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2),V_xs_2)),
file('theBenchmark.p',fact_takeWhile__map) ).
fof(fact_takeWhile__tail,axiom,
! [V_l_2,V_xs_2,T_b,V_x_2,V_P_2] :
( ~ hBOOL(hAPP(V_P_2,V_x_2))
=> c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2))) = c_List_OtakeWhile(T_b,V_P_2,V_xs_2) ),
file('theBenchmark.p',fact_takeWhile__tail) ).
fof(fact_takeWhile_Osimps_I2_J,axiom,
! [V_xs_2,T_b,V_x_2,V_P_2] :
( ( ~ hBOOL(hAPP(V_P_2,V_x_2))
=> c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b) )
& ( hBOOL(hAPP(V_P_2,V_x_2))
=> c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)) ) ),
file('theBenchmark.p',fact_takeWhile_Osimps_I2_J) ).
fof(fact_takeWhile_Osimps_I1_J,axiom,
! [V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
file('theBenchmark.p',fact_takeWhile_Osimps_I1_J) ).
fof(fact_takeWhile__eq__take,axiom,
! [V_xs_2,V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),V_xs_2),
file('theBenchmark.p',fact_takeWhile__eq__take) ).
fof(fact_distinct__takeWhile,axiom,
! [V_P_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))) ),
file('theBenchmark.p',fact_distinct__takeWhile) ).
fof(fact_return__list__def,axiom,
! [V_l_2] : c_List_Oreturn__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),V_l_2),
file('theBenchmark.p',fact_return__list__def) ).
fof(fact_takeWhile__append1,axiom,
! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ( ~ hBOOL(hAPP(V_P_2,V_x_2))
=> c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_P_2,V_xs_2) ) ),
file('theBenchmark.p',fact_takeWhile__append1) ).
fof(fact_nth__length__takeWhile,axiom,
! [V_xs_2,V_P_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))) ),
file('theBenchmark.p',fact_nth__length__takeWhile) ).
fof(fact_takeWhile__nth,axiom,
! [V_xs_2,V_P_2,T_b,V_j_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))
=> hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) ),
file('theBenchmark.p',fact_takeWhile__nth) ).
fof(fact_takeWhile__not__last,axiom,
! [T_b,V_xs_2] :
( V_xs_2 != c_List_Olist_ONil(T_b)
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),c_List_Olast(T_b,V_xs_2))),V_xs_2) = c_List_Obutlast(T_b,V_xs_2) ) ),
file('theBenchmark.p',fact_takeWhile__not__last) ).
fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
=> hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2),V_xs_2) ) ),
file('theBenchmark.p',fact_filter__equals__takeWhile__sorted__rev) ).
fof(fact_transfer__nat__int__list__return__embed,axiom,
! [V_l] :
( c_List_Onat__list(V_l)
=> c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ),
file('theBenchmark.p',fact_transfer__nat__int__list__return__embed) ).
fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
! [V_m,V_l] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),V_l),V_m) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(V_l)),c_List_Oembed__list(V_m))),
file('theBenchmark.p',fact_transfer__nat__int__list__functions_I1_J) ).
fof(fact_embed__list__def,axiom,
! [V_l_2] : c_List_Oembed__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_l_2),
file('theBenchmark.p',fact_embed__list__def) ).
fof(fact_takeWhile__neq__rev,axiom,
! [V_x_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Orev(T_b),hAPP(c_List_Otl(T_b),c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ),
file('theBenchmark.p',fact_takeWhile__neq__rev) ).
fof(fact_dropWhile__neq__rev,axiom,
! [V_x_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Orev(T_b),c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ),
file('theBenchmark.p',fact_dropWhile__neq__rev) ).
fof(fact_takeWhile__dropWhile__id,axiom,
! [V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),c_List_OdropWhile(T_b,V_P_2,V_xs_2)) = V_xs_2,
file('theBenchmark.p',fact_takeWhile__dropWhile__id) ).
fof(fact_sorted__dropWhile,axiom,
! [V_P_2,V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
=> c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_P_2,V_xs_2)) ) ),
file('theBenchmark.p',fact_sorted__dropWhile) ).
fof(fact_length__dropWhile__le,axiom,
! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
file('theBenchmark.p',fact_length__dropWhile__le) ).
fof(fact_dropWhile__eq__Nil__conv,axiom,
! [V_xs_2,V_P_2,T_b] :
( c_List_OdropWhile(T_b,V_P_2,V_xs_2) = c_List_Olist_ONil(T_b)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_P_2,B_x)) ) ),
file('theBenchmark.p',fact_dropWhile__eq__Nil__conv) ).
fof(fact_dropWhile_Osimps_I2_J,axiom,
! [V_xs_2,T_b,V_x_2,V_P_2] :
( ( ~ hBOOL(hAPP(V_P_2,V_x_2))
=> c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
& ( hBOOL(hAPP(V_P_2,V_x_2))
=> c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_OdropWhile(T_b,V_P_2,V_xs_2) ) ),
file('theBenchmark.p',fact_dropWhile_Osimps_I2_J) ).
fof(fact_dropWhile_Osimps_I1_J,axiom,
! [V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
file('theBenchmark.p',fact_dropWhile_Osimps_I1_J) ).
fof(fact_distinct__dropWhile,axiom,
! [V_P_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2))) ),
file('theBenchmark.p',fact_distinct__dropWhile) ).
fof(fact_hd__dropWhile,axiom,
! [V_xs_2,V_P_2,T_b] :
( c_List_OdropWhile(T_b,V_P_2,V_xs_2) != c_List_Olist_ONil(T_b)
=> ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)))) ),
file('theBenchmark.p',fact_hd__dropWhile) ).
fof(fact_dropWhile__map,axiom,
! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OdropWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2),V_xs_2)),
file('theBenchmark.p',fact_dropWhile__map) ).
fof(fact_dropWhile__append1,axiom,
! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ( ~ hBOOL(hAPP(V_P_2,V_x_2))
=> c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)),V_ys_2) ) ),
file('theBenchmark.p',fact_dropWhile__append1) ).
fof(fact_dropWhile__eq__Cons__conv,axiom,
! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_b] :
( c_List_OdropWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
<=> ( ~ hBOOL(hAPP(V_P_2,V_y_2))
& V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) ),
file('theBenchmark.p',fact_dropWhile__eq__Cons__conv) ).
fof(fact_dropWhile__eq__drop,axiom,
! [V_xs_2,V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),V_xs_2),
file('theBenchmark.p',fact_dropWhile__eq__drop) ).
fof(fact_dropWhile__nth,axiom,
! [V_xs_2,V_P_2,T_b,V_j_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_P_2,V_xs_2))))
=> hAPP(hAPP(c_List_Onth(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)))) ),
file('theBenchmark.p',fact_dropWhile__nth) ).
fof(fact_listsum__map__filter,axiom,
! [V_f_2,V_P_2,V_xs_2,T_b,T_c] :
( class_Groups_Omonoid__add(T_c)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ( ~ hBOOL(hAPP(V_P_2,B_x))
=> hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) )
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ),
file('theBenchmark.p',fact_listsum__map__filter) ).
fof(fact_sorted__nth__monoI,axiom,
! [V_xs,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ! [B_i,B_j] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_j))) ) )
=> c_List_Olinorder__class_Osorted(T_a,V_xs) ) ),
file('theBenchmark.p',fact_sorted__nth__monoI) ).
fof(fact_takeWhile__eq__filter,axiom,
! [V_xs_2,V_P_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2))))
=> ~ hBOOL(hAPP(V_P_2,B_x)) )
=> c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ),
file('theBenchmark.p',fact_takeWhile__eq__filter) ).
fof(fact_takeWhile__eq__take__P__nth,axiom,
! [V_P_2,V_xs_2,T_b,V_n_2] :
( ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) )
=> c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) ) ),
file('theBenchmark.p',fact_takeWhile__eq__take__P__nth) ).
fof(fact_length__takeWhile__less__P__nth,axiom,
! [V_xs_2,T_b,V_P_2,V_j_2] :
( ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2))
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)))) ) ),
file('theBenchmark.p',fact_length__takeWhile__less__P__nth) ).
fof(fact_sorted_Osimps,axiom,
! [V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,V_a_2)
<=> ( ? [B_xs,B_x] :
( c_List_Olinorder__class_Osorted(T_b,B_xs)
& ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) )
& V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs) )
| V_a_2 = c_List_Olist_ONil(T_b) ) ) ),
file('theBenchmark.p',fact_sorted_Osimps) ).
fof(fact_not__in__set__insert,axiom,
! [V_xs_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ),
file('theBenchmark.p',fact_not__in__set__insert) ).
fof(fact_List_Oinsert__def,axiom,
! [V_xs_2,V_x_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) ),
file('theBenchmark.p',fact_List_Oinsert__def) ).
fof(fact_insert__remdups,axiom,
! [V_xs,V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oinsert(T_a,V_x,V_xs)),
file('theBenchmark.p',fact_insert__remdups) ).
fof(fact_distinct__insert,axiom,
! [V_x,V_xs,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ),
file('theBenchmark.p',fact_distinct__insert) ).
fof(fact_in__set__insert,axiom,
! [V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ),
file('theBenchmark.p',fact_in__set__insert) ).
fof(fact_List_Oset__insert,axiom,
! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oinsert(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)),
file('theBenchmark.p',fact_List_Oset__insert) ).
fof(fact_insert__Nil,axiom,
! [V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)),
file('theBenchmark.p',fact_insert__Nil) ).
fof(fact_concat__map__maps,axiom,
! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2)) = c_List_Omaps(T_c,T_b,V_f_2,V_xs_2),
file('theBenchmark.p',fact_concat__map__maps) ).
fof(fact_maps__def,axiom,
! [V_xs_2,V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,V_xs_2) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2)),
file('theBenchmark.p',fact_maps__def) ).
fof(fact_maps__simps_I2_J,axiom,
! [V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b),
file('theBenchmark.p',fact_maps__simps_I2_J) ).
fof(fact_maps__simps_I1_J,axiom,
! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_c,T_b,V_f_2,V_xs_2)),
file('theBenchmark.p',fact_maps__simps_I1_J) ).
fof(fact_distinct__concat,axiom,
! [V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_b)),V_xs_2))
=> ( ! [B_ys] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
=> hBOOL(hAPP(c_List_Odistinct(T_b),B_ys)) )
=> ( ! [B_ys] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
=> ! [B_zs] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
=> ( B_ys != B_zs
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),B_ys)),hAPP(c_List_Oset(T_b),B_zs)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
=> hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Oconcat(T_b,V_xs_2))) ) ) ),
file('theBenchmark.p',fact_distinct__concat) ).
fof(fact_measures__lesseq,axiom,
! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ),
file('theBenchmark.p',fact_measures__lesseq) ).
fof(fact_wf__measures,axiom,
! [V_fs_2,T_b] : c_Wellfounded_Owf(T_b,c_List_Omeasures(T_b,V_fs_2)),
file('theBenchmark.p',fact_wf__measures) ).
fof(fact_in__measures_I1_J,axiom,
! [V_y_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_Nat_Onat))))),
file('theBenchmark.p',fact_in__measures_I1_J) ).
fof(fact_measures__def,axiom,
! [V_fs_2,T_b] : c_List_Omeasures(T_b,V_fs_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),T_b),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),T_b),c_List_Omap(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(T_b,tc_Nat_Onat),T_b,tc_Nat_Onat),c_COMBI(tc_fun(T_b,tc_Nat_Onat))))),V_fs_2)),
file('theBenchmark.p',fact_measures__def) ).
fof(fact_measures__less,axiom,
! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ),
file('theBenchmark.p',fact_measures__less) ).
fof(fact_in__measures_I2_J,axiom,
! [V_fs_2,V_f_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2))))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2)))
& hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ),
file('theBenchmark.p',fact_in__measures_I2_J) ).
fof(fact_foldl__apply,axiom,
! [V_s_2,V_g_2,V_h_2,V_f_2,T_c,T_d,V_xs_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hAPP(c_Fun_Ocomp(T_d,T_d,T_c,hAPP(V_f_2,B_x)),V_h_2) = hAPP(c_Fun_Ocomp(T_c,T_d,T_c,V_h_2),hAPP(V_g_2,B_x)) )
=> hAPP(c_List_Ofoldl(T_d,T_b,hAPP(c_COMBC(T_b,T_d,T_d),V_f_2),hAPP(V_h_2,V_s_2)),V_xs_2) = hAPP(V_h_2,hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_g_2),V_s_2),V_xs_2)) ),
file('theBenchmark.p',fact_foldl__apply) ).
fof(fact_order__fun_I2_J,axiom,
! [V_g_2,V_f_2,T_b,T_c] :
( ( class_Enum_Oenum(T_b)
& class_Orderings_Oorder(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
<=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_g_2))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) ) ),
file('theBenchmark.p',fact_order__fun_I2_J) ).
fof(fact_enum__ex__prod__def,axiom,
! [V_P_2,T_b,T_c] :
( ( class_Enum_Oenum(T_b)
& class_Enum_Oenum(T_c) )
=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_P_2))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__ex(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c))))) ) ),
file('theBenchmark.p',fact_enum__ex__prod__def) ).
fof(fact_exists__code,axiom,
! [V_P_2,T_b] :
( class_Enum_Oenum(T_b)
=> ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_P_2)) ) ),
file('theBenchmark.p',fact_exists__code) ).
fof(fact_enum__ex,axiom,
! [V_P_2,T_b] :
( class_Enum_Oenum(T_b)
=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_P_2))
<=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ),
file('theBenchmark.p',fact_enum__ex) ).
fof(fact_zip__obtain__same__length,axiom,
! [V_P_2,V_ys_2,T_c,V_xs_2,T_b] :
( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Otake(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_ys_2))
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)),hAPP(hAPP(c_List_Otake(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_ys_2)))) )
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) ),
file('theBenchmark.p',fact_zip__obtain__same__length) ).
fof(fact_pos__not__random__dseq__def,axiom,
! [V_seed_2,V_size_2,V_nrandom_2,V_R_2] : c_New__Random__Sequence_Opos__not__random__dseq(V_R_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2)),
file('theBenchmark.p',fact_pos__not__random__dseq__def) ).
fof(fact_dropWhile__append2,axiom,
! [V_ys_2,V_P_2,V_xs_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_P_2,B_x)) )
=> c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_b,V_P_2,V_ys_2) ),
file('theBenchmark.p',fact_dropWhile__append2) ).
fof(fact_list__all2__all__nthI,axiom,
! [V_P_2,V_b_2,T_c,V_a_2,T_b] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_b_2)
=> ( ! [B_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2)))
=> hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_c),V_b_2),B_n))) )
=> c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2) ) ),
file('theBenchmark.p',fact_list__all2__all__nthI) ).
fof(fact_finite__sorted__distinct__unique,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ? [B_x] :
( ! [B_y] :
( ( hBOOL(hAPP(c_List_Odistinct(T_b),B_y))
& c_List_Olinorder__class_Osorted(T_b,B_y)
& hAPP(c_List_Oset(T_b),B_y) = V_A_2 )
=> B_y = B_x )
& hBOOL(hAPP(c_List_Odistinct(T_b),B_x))
& c_List_Olinorder__class_Osorted(T_b,B_x)
& hAPP(c_List_Oset(T_b),B_x) = V_A_2 ) ) ),
file('theBenchmark.p',fact_finite__sorted__distinct__unique) ).
fof(fact_takeWhile__append2,axiom,
! [V_ys_2,V_P_2,V_xs_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_P_2,B_x)) )
=> c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_OtakeWhile(T_b,V_P_2,V_ys_2)) ),
file('theBenchmark.p',fact_takeWhile__append2) ).
fof(fact_insort__is__Cons,axiom,
! [V_a_2,V_f_2,V_xs_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_xs_2) ) ),
file('theBenchmark.p',fact_insort__is__Cons) ).
fof(fact_filter__eq__Cons__iff,axiom,
! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_b] :
( hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
<=> ? [B_us,B_vs] :
( V_xs_2 = hAPP(c_List_Ofilter(T_b,V_P_2),B_vs)
& hBOOL(hAPP(V_P_2,V_x_2))
& ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
=> ~ hBOOL(hAPP(V_P_2,B_x)) )
& V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs)) ) ),
file('theBenchmark.p',fact_filter__eq__Cons__iff) ).
fof(fact_Cons__eq__filter__iff,axiom,
! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2)
<=> ? [B_us,B_vs] :
( V_xs_2 = hAPP(c_List_Ofilter(T_b,V_P_2),B_vs)
& hBOOL(hAPP(V_P_2,V_x_2))
& ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
=> ~ hBOOL(hAPP(V_P_2,B_x)) )
& V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs)) ) ),
file('theBenchmark.p',fact_Cons__eq__filter__iff) ).
fof(fact_order__fun_I1_J,axiom,
! [V_g_2,V_f_2,T_b,T_c] :
( ( class_Enum_Oenum(T_b)
& class_Orderings_Oorder(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Oord__class_Oless__eq(T_c)),V_f_2)),V_g_2))) ) ),
file('theBenchmark.p',fact_order__fun_I1_J) ).
fof(fact_enum__all,axiom,
! [V_P_2,T_b] :
( class_Enum_Oenum(T_b)
=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_P_2))
<=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ),
file('theBenchmark.p',fact_enum__all) ).
fof(fact_all__code,axiom,
! [V_P_2,T_b] :
( class_Enum_Oenum(T_b)
=> ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_P_2)) ) ),
file('theBenchmark.p',fact_all__code) ).
fof(fact_enum__all__prod__def,axiom,
! [V_P_2,T_b,T_c] :
( ( class_Enum_Oenum(T_b)
& class_Enum_Oenum(T_c) )
=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_P_2))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__all(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c))))) ) ),
file('theBenchmark.p',fact_enum__all__prod__def) ).
fof(fact_list__ball__nth,axiom,
! [V_P_2,V_xs_2,T_b,V_n_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_P_2,B_x)) )
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) ) ),
file('theBenchmark.p',fact_list__ball__nth) ).
fof(fact_sorted_OCons,axiom,
! [V_x_2,V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) )
=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ) ),
file('theBenchmark.p',fact_sorted_OCons) ).
fof(fact_list__ex__length,axiom,
! [V_xs_2,V_P_2,T_b] :
( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
<=> ? [B_n] :
( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ),
file('theBenchmark.p',fact_list__ex__length) ).
fof(fact_in__set__conv__decomp__first,axiom,
! [V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
<=> ? [B_ys] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys)))
& ? [B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) ) ),
file('theBenchmark.p',fact_in__set__conv__decomp__first) ).
fof(fact_list__ex__simps_I2_J,axiom,
! [V_P_2,T_b] : ~ c_List_Olist__ex(T_b,V_P_2,c_List_Olist_ONil(T_b)),
file('theBenchmark.p',fact_list__ex__simps_I2_J) ).
fof(fact_list__ex__append,axiom,
! [V_ys_2,V_xs_2,V_P_2,T_b] :
( c_List_Olist__ex(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
<=> ( c_List_Olist__ex(T_b,V_P_2,V_ys_2)
| c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ),
file('theBenchmark.p',fact_list__ex__append) ).
fof(fact_list__ex__iff,axiom,
! [V_xs_2,V_P_2,T_b] :
( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
<=> ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
file('theBenchmark.p',fact_list__ex__iff) ).
fof(fact_list__ex__rev,axiom,
! [V_xs_2,V_P_2,T_b] :
( c_List_Olist__ex(T_b,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2))
<=> c_List_Olist__ex(T_b,V_P_2,V_xs_2) ),
file('theBenchmark.p',fact_list__ex__rev) ).
fof(fact_list__ex__simps_I1_J,axiom,
! [V_xs_2,V_x_2,V_P_2,T_b] :
( c_List_Olist__ex(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
<=> ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
| hBOOL(hAPP(V_P_2,V_x_2)) ) ),
file('theBenchmark.p',fact_list__ex__simps_I1_J) ).
fof(fact_list__ex__iff__not__all__inverval__nat,axiom,
! [V_j_2,V_i_2,V_P_2] :
( c_List_Olist__ex(tc_Nat_Onat,V_P_2,c_List_Oupt(V_i_2,V_j_2))
<=> ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),V_P_2),V_i_2,V_j_2) ),
file('theBenchmark.p',fact_list__ex__iff__not__all__inverval__nat) ).
fof(fact_in__set__conv__decomp,axiom,
! [V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
<=> ? [B_ys,B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) ),
file('theBenchmark.p',fact_in__set__conv__decomp) ).
fof(fact_in__set__conv__decomp__last,axiom,
! [V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
<=> ? [B_ys,B_zs] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs)))
& V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) ) ),
file('theBenchmark.p',fact_in__set__conv__decomp__last) ).
fof(fact_list__all__length,axiom,
! [V_xs_2,V_P_2,T_b] :
( c_List_Olist__all(T_b,V_P_2,V_xs_2)
<=> ! [B_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ),
file('theBenchmark.p',fact_list__all__length) ).
fof(fact_measure__function__int,axiom,
c_FunDef_Ois__measure(tc_Int_Oint,hAPP(c_Fun_Ocomp(tc_Int_Oint,tc_Nat_Onat,tc_Int_Oint,c_Int_Onat),c_Groups_Oabs__class_Oabs(tc_Int_Oint))),
file('theBenchmark.p',fact_measure__function__int) ).
fof(fact_list__all__simps_I2_J,axiom,
! [V_P_2,T_b] : c_List_Olist__all(T_b,V_P_2,c_List_Olist_ONil(T_b)),
file('theBenchmark.p',fact_list__all__simps_I2_J) ).
fof(fact_list__all__append,axiom,
! [V_ys_2,V_xs_2,V_P_2,T_b] :
( c_List_Olist__all(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
<=> ( c_List_Olist__all(T_b,V_P_2,V_ys_2)
& c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ),
file('theBenchmark.p',fact_list__all__append) ).
fof(fact_measure__size,axiom,
! [T_b] :
( class_Nat_Osize(T_b)
=> c_FunDef_Ois__measure(T_b,c_Nat_Osize__class_Osize(T_b)) ),
file('theBenchmark.p',fact_measure__size) ).
fof(fact_is__measure_Ointros,axiom,
! [V_f_2,T_b] : c_FunDef_Ois__measure(T_b,V_f_2),
file('theBenchmark.p',fact_is__measure_Ointros) ).
fof(fact_is__measure_Oequations,axiom,
! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2),
file('theBenchmark.p',fact_is__measure_Oequations) ).
fof(fact_is__measure_Osimps,axiom,
! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2),
file('theBenchmark.p',fact_is__measure_Osimps) ).
fof(fact_list__all__iff,axiom,
! [V_xs_2,V_P_2,T_b] :
( c_List_Olist__all(T_b,V_P_2,V_xs_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_P_2,B_x)) ) ),
file('theBenchmark.p',fact_list__all__iff) ).
fof(fact_measure__fst,axiom,
! [T_c,V_f_2,T_b] :
( c_FunDef_Ois__measure(T_b,V_f_2)
=> c_FunDef_Ois__measure(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_b,T_c)),V_f_2),c_Product__Type_Ofst(T_b,T_c))) ),
file('theBenchmark.p',fact_measure__fst) ).
fof(fact_measure__snd,axiom,
! [T_c,V_f_2,T_b] :
( c_FunDef_Ois__measure(T_b,V_f_2)
=> c_FunDef_Ois__measure(tc_prod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_c,T_b)),V_f_2),c_Product__Type_Osnd(T_c,T_b))) ),
file('theBenchmark.p',fact_measure__snd) ).
fof(fact_list__all__rev,axiom,
! [V_xs_2,V_P_2,T_b] :
( c_List_Olist__all(T_b,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2))
<=> c_List_Olist__all(T_b,V_P_2,V_xs_2) ),
file('theBenchmark.p',fact_list__all__rev) ).
fof(fact_list__all__simps_I1_J,axiom,
! [V_xs_2,V_x_2,V_P_2,T_b] :
( c_List_Olist__all(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
<=> ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
& hBOOL(hAPP(V_P_2,V_x_2)) ) ),
file('theBenchmark.p',fact_list__all__simps_I1_J) ).
fof(fact_Ball__set__list__all,axiom,
! [V_P_2,V_xs_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_P_2,B_x)) )
<=> c_List_Olist__all(T_b,V_P_2,V_xs_2) ),
file('theBenchmark.p',fact_Ball__set__list__all) ).
fof(fact_list__all__iff__raw,axiom,
! [V_xs_2,V_P_2,T_b] :
( c_List_Olist__all(T_b,V_P_2,V_xs_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_P_2,B_x)) ) ),
file('theBenchmark.p',fact_list__all__iff__raw) ).
fof(fact_list__all__iff__all__interval__nat,axiom,
! [V_j_2,V_i_2,V_P_2] :
( c_List_Olist__all(tc_Nat_Onat,V_P_2,c_List_Oupt(V_i_2,V_j_2))
<=> c_List_Oall__interval__nat(V_P_2,V_i_2,V_j_2) ),
file('theBenchmark.p',fact_list__all__iff__all__interval__nat) ).
fof(fact_list__ex1__simps_I2_J,axiom,
! [V_xs_2,V_x_2,V_P_2,T_b] :
( c_List_Olist__ex1(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
<=> ( ( ~ hBOOL(hAPP(V_P_2,V_x_2))
=> c_List_Olist__ex1(T_b,V_P_2,V_xs_2) )
& ( hBOOL(hAPP(V_P_2,V_x_2))
=> c_List_Olist__all(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))),hAPP(c_fequal,V_x_2)),V_xs_2) ) ) ),
file('theBenchmark.p',fact_list__ex1__simps_I2_J) ).
fof(fact_transfer__morphism__int__nat,axiom,
c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)),
file('theBenchmark.p',fact_transfer__morphism__int__nat) ).
fof(fact_list__ex1__simps_I1_J,axiom,
! [V_P_2,T_b] : ~ c_List_Olist__ex1(T_b,V_P_2,c_List_Olist_ONil(T_b)),
file('theBenchmark.p',fact_list__ex1__simps_I1_J) ).
fof(fact_bool_Osize_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_P_2,T_b] :
( c_List_Olist__ex1(T_b,V_P_2,V_xs_2)
<=> ? [B_x] :
( ! [B_y] :
( ( hBOOL(hAPP(V_P_2,B_y))
& hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) )
=> B_y = B_x )
& hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
file('theBenchmark.p',fact_list__ex1__iff) ).
fof(fact_New__DSequence_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_Oneg__decr__bind__def,axiom,
! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Oneg__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
file('theBenchmark.p',fact_New__Random__Sequence_Oneg__decr__bind__def) ).
fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Opos__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
file('theBenchmark.p',fact_New__Random__Sequence_Opos__decr__bind__def) ).
fof(fact_New__DSequence_Oneg__bind__def,axiom,
! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Oneg__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)),
file('theBenchmark.p',fact_New__DSequence_Oneg__bind__def) ).
fof(fact_New__DSequence_Opos__empty__def,axiom,
! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a),
file('theBenchmark.p',fact_New__DSequence_Opos__empty__def) ).
fof(fact_pos__empty__def,axiom,
! [V_seed_2,V_size_2,V_nrandom_2,T_b] : c_New__Random__Sequence_Opos__empty(T_b,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_b),
file('theBenchmark.p',fact_pos__empty__def) ).
fof(fact_neg__bind__def,axiom,
! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
file('theBenchmark.p',fact_neg__bind__def) ).
fof(fact_New__DSequence_Opos__bind__def,axiom,
! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Opos__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,V_i_2)),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)),
file('theBenchmark.p',fact_New__DSequence_Opos__bind__def) ).
fof(fact_neg__map__def,axiom,
! [V_P_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_P_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),T_c,c_New__Random__Sequence_Oneg__single(T_b)),V_f_2)),
file('theBenchmark.p',fact_neg__map__def) ).
fof(fact_neg__single__def,axiom,
! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_b,V_x_2),
file('theBenchmark.p',fact_neg__single__def) ).
fof(fact_pos__bind__def,axiom,
! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
file('theBenchmark.p',fact_pos__bind__def) ).
fof(fact_New__DSequence_Oneg__single__def,axiom,
! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Oneg__single(T_a,V_x),V_i_1) = c_Lazy__Sequence_Ohb__single(T_a,V_x),
file('theBenchmark.p',fact_New__DSequence_Oneg__single__def) ).
fof(fact_pos__map__def,axiom,
! [V_P_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_P_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),T_c,c_New__Random__Sequence_Opos__single(T_b)),V_f_2)),
file('theBenchmark.p',fact_pos__map__def) ).
fof(fact_pos__single__def,axiom,
! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_b,V_x_2),
file('theBenchmark.p',fact_pos__single__def) ).
fof(fact_length__splice,axiom,
! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osplice(T_a,V_xs,V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)),
file('theBenchmark.p',fact_length__splice) ).
fof(fact_splice_Osimps_I3_J,axiom,
! [V_ys,V_y,V_xs,V_x,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Osplice(T_a,V_xs,V_ys))),
file('theBenchmark.p',fact_splice_Osimps_I3_J) ).
fof(fact_splice__Nil2,axiom,
! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs,
file('theBenchmark.p',fact_splice__Nil2) ).
fof(fact_splice_Osimps_I1_J,axiom,
! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys,
file('theBenchmark.p',fact_splice_Osimps_I1_J) ).
fof(fact_splice_Osimps_I2_J,axiom,
! [V_va,V_v,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),
file('theBenchmark.p',fact_splice_Osimps_I2_J) ).
fof(fact_New__DSequence_Opos__single__def,axiom,
! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Opos__single(T_a,V_x),V_i_1) = hAPP(c_Lazy__Sequence_Osingle(T_a),V_x),
file('theBenchmark.p',fact_New__DSequence_Opos__single__def) ).
fof(fact_acyclicP__converse,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Predicate_Oconversep(T_b,T_b,V_r_2))))
<=> c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ),
file('theBenchmark.p',fact_acyclicP__converse) ).
fof(fact_converse__meet,axiom,
! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)),
file('theBenchmark.p',fact_converse__meet) ).
fof(fact_conversep__noteq,axiom,
! [V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot)),c_fequal)),V_x_2),V_y_2))
<=> V_x_2 != V_y_2 ),
file('theBenchmark.p',fact_conversep__noteq) ).
fof(fact_conversep__eq,axiom,
! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal,
file('theBenchmark.p',fact_conversep__eq) ).
fof(fact_conversep__conversep,axiom,
! [V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Oconversep(T_b,T_c,V_r_2)) = V_r_2,
file('theBenchmark.p',fact_conversep__conversep) ).
fof(fact_conversep__iff,axiom,
! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
<=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ),
file('theBenchmark.p',fact_conversep__iff) ).
fof(fact_conversep_Oequations,axiom,
! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2))
<=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ),
file('theBenchmark.p',fact_conversep_Oequations) ).
fof(fact_conversep_Ointros,axiom,
! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
=> hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2)) ),
file('theBenchmark.p',fact_conversep_Ointros) ).
fof(fact_conversepD,axiom,
! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ),
file('theBenchmark.p',fact_conversepD) ).
fof(fact_converse__pred__comp,axiom,
! [V_s_2,V_r_2,T_d,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Opred__comp(T_c,T_d,T_b,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_b,T_d,T_c,c_Predicate_Oconversep(T_d,T_b,V_s_2),c_Predicate_Oconversep(T_c,T_d,V_r_2)),
file('theBenchmark.p',fact_converse__pred__comp) ).
fof(fact_converse__join,axiom,
! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)),
file('theBenchmark.p',fact_converse__join) ).
fof(fact_conversep__converse__eq,axiom,
! [V_y_2,V_x_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ),
file('theBenchmark.p',fact_conversep__converse__eq) ).
fof(fact_,axiom,
! [V_s2_2,V_s1_2,T_c,T_b] : c_Lazy__Sequence_Oproduct(T_b,T_c,V_s1_2,V_s2_2) = hAPP(c_Lazy__Sequence_Obind(T_b,tc_prod(T_b,T_c),V_s1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_b),c_Lazy__Sequence_Obind(T_c,tc_prod(T_b,T_c),V_s2_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_c),c_Lazy__Sequence_Osingle(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),
file('theBenchmark.p',fact_) ).
fof(fact_tl__replicate,axiom,
! [V_x,T_a,V_n] :
( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_List_Otl(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_x) ),
file('theBenchmark.p',fact_tl__replicate) ).
fof(fact_replicate__length__filter,axiom,
! [V_xs_2,V_x_2,T_b] : c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2)),V_x_2) = hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2),
file('theBenchmark.p',fact_replicate__length__filter) ).
fof(fact_length__replicate,axiom,
! [V_x,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oreplicate(T_a,V_n,V_x)) = V_n,
file('theBenchmark.p',fact_length__replicate) ).
fof(fact_map__replicate__const,axiom,
! [V_lst_2,V_k_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_k_2)),V_lst_2) = c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_lst_2),V_k_2),
file('theBenchmark.p',fact_map__replicate__const) ).
fof(fact_replicate__app__Cons__same,axiom,
! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_xs)),
file('theBenchmark.p',fact_replicate__app__Cons__same) ).
fof(fact_replicate__Suc,axiom,
! [V_x,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(c_Nat_OSuc,V_n),V_x) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_n,V_x)),
file('theBenchmark.p',fact_replicate__Suc) ).
fof(fact_rev__replicate,axiom,
! [V_x,V_n,T_a] : hAPP(c_List_Orev(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,V_n,V_x),
file('theBenchmark.p',fact_rev__replicate) ).
fof(fact_take__replicate,axiom,
! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_k),V_x),
file('theBenchmark.p',fact_take__replicate) ).
fof(fact_drop__replicate,axiom,
! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_k),V_i),V_x),
file('theBenchmark.p',fact_drop__replicate) ).
fof(fact_hd__replicate,axiom,
! [V_x,T_a,V_n] :
( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ),
file('theBenchmark.p',fact_hd__replicate) ).
fof(fact_last__replicate,axiom,
! [V_x,T_a,V_n] :
( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ),
file('theBenchmark.p',fact_last__replicate) ).
fof(fact_zip__replicate,axiom,
! [V_y,V_j,V_x,V_i,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Oreplicate(T_a,V_i,V_x)),c_List_Oreplicate(T_b,V_j,V_y)) = c_List_Oreplicate(tc_prod(T_a,T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_j),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),
file('theBenchmark.p',fact_zip__replicate) ).
fof(fact_Bex__set__replicate,axiom,
! [V_P_2,V_a_2,V_n_2,T_b] :
( ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_a_2)))) )
<=> ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(V_P_2,V_a_2)) ) ),
file('theBenchmark.p',fact_Bex__set__replicate) ).
fof(fact_Ball__set__replicate,axiom,
! [V_P_2,V_a_2,V_n_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_a_2))))
=> hBOOL(hAPP(V_P_2,B_x)) )
<=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(V_P_2,V_a_2)) ) ),
file('theBenchmark.p',fact_Ball__set__replicate) ).
fof(fact_replicate__eq__replicate,axiom,
! [V_y_2,V_n_2,V_x_2,V_m_2,T_b] :
( c_List_Oreplicate(T_b,V_m_2,V_x_2) = c_List_Oreplicate(T_b,V_n_2,V_y_2)
<=> ( ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> V_x_2 = V_y_2 )
& V_m_2 = V_n_2 ) ),
file('theBenchmark.p',fact_replicate__eq__replicate) ).
fof(fact_nth__replicate,axiom,
! [V_x,T_a,V_n,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
=> hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ),
file('theBenchmark.p',fact_nth__replicate) ).
fof(fact_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_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_filter__replicate,axiom,
! [V_n_2,T_b,V_x_2,V_P_2] :
( ( ~ hBOOL(hAPP(V_P_2,V_x_2))
=> hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Olist_ONil(T_b) )
& ( hBOOL(hAPP(V_P_2,V_x_2))
=> hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,V_x_2) ) ),
file('theBenchmark.p',fact_filter__replicate) ).
fof(fact_concat__replicate__trivial,axiom,
! [V_i,T_a] : c_List_Oconcat(T_a,c_List_Oreplicate(tc_List_Olist(T_a),V_i,c_List_Olist_ONil(T_a))) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_concat__replicate__trivial) ).
fof(fact_replicate__0,axiom,
! [V_x,T_a] : c_List_Oreplicate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_replicate__0) ).
fof(fact_empty__replicate,axiom,
! [V_x_2,V_n_2,T_b] :
( c_List_Olist_ONil(T_b) = c_List_Oreplicate(T_b,V_n_2,V_x_2)
<=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_empty__replicate) ).
fof(fact_replicate__empty,axiom,
! [V_x_2,V_n_2,T_b] :
( c_List_Oreplicate(T_b,V_n_2,V_x_2) = c_List_Olist_ONil(T_b)
<=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_replicate__empty) ).
fof(fact_map__replicate,axiom,
! [V_x_2,V_n_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oreplicate(T_c,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,hAPP(V_f_2,V_x_2)),
file('theBenchmark.p',fact_map__replicate) ).
fof(fact_in__set__replicate,axiom,
! [V_y_2,V_n_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_y_2))))
<=> ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_in__set__replicate) ).
fof(fact_replicate__append__same,axiom,
! [V_x,V_i,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_i,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_i,V_x)),
file('theBenchmark.p',fact_replicate__append__same) ).
fof(fact_map__replicate__trivial,axiom,
! [V_i_2,V_x_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_COMBK(T_b,tc_Nat_Onat),V_x_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2)) = c_List_Oreplicate(T_b,V_i_2,V_x_2),
file('theBenchmark.p',fact_map__replicate__trivial) ).
fof(fact_set__replicate__conv__if,axiom,
! [V_x_2,T_b,V_n_2] :
( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_set__replicate__conv__if) ).
fof(fact_set__replicate,axiom,
! [V_x_2,T_b,V_n_2] :
( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_set__replicate) ).
fof(fact_set__replicate__Suc,axiom,
! [V_x_2,V_n_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,hAPP(c_Nat_OSuc,V_n_2),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
file('theBenchmark.p',fact_set__replicate__Suc) ).
fof(fact_small__lazy__list_Osimps,axiom,
! [V_d_2,T_b] :
( class_Lazy__Sequence_Osmall__lazy(T_b)
=> c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_b),V_d_2) = c_Lazy__Sequence_Oappend(tc_List_Olist(T_b),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)),hAPP(c_Lazy__Sequence_Obind(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),c_Lazy__Sequence_Oproduct(T_b,tc_List_Olist(T_b),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)))),c_List_Olist_OCons(T_b))))),c_Lazy__Sequence_Oempty(tc_List_Olist(T_b)))) ),
file('theBenchmark.p',fact_small__lazy__list_Osimps) ).
fof(fact_eq__comp__r,axiom,
! [V_R_2,T_b] : c_Predicate_Opred__comp(T_b,T_b,T_b,c_fequal,c_Predicate_Opred__comp(T_b,T_b,T_b,V_R_2,c_fequal)) = V_R_2,
file('theBenchmark.p',fact_eq__comp__r) ).
fof(fact_small__lazy__prod__def,axiom,
! [V_d,T_b,T_a] :
( ( class_Lazy__Sequence_Osmall__lazy(T_b)
& class_Lazy__Sequence_Osmall__lazy(T_a) )
=> c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(T_a,T_b),V_d) = c_Lazy__Sequence_Oproduct(T_a,T_b,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_a,V_d),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,V_d)) ),
file('theBenchmark.p',fact_small__lazy__prod__def) ).
fof(fact_New__DSequence_Opos__union__def,axiom,
! [V_i_2,V_yq_2,V_xq_2,T_b] : hAPP(c_New__DSequence_Opos__union(T_b,V_xq_2,V_yq_2),V_i_2) = c_Lazy__Sequence_Oappend(T_b,hAPP(V_xq_2,V_i_2),hAPP(V_yq_2,V_i_2)),
file('theBenchmark.p',fact_New__DSequence_Opos__union__def) ).
fof(fact_lazy__sequence_Osize_I4_J,axiom,
! [V_lazy__sequence,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a,V_lazy__sequence)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),V_lazy__sequence)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_lazy__sequence_Osize_I4_J) ).
fof(fact__01,axiom,
! [V_yq,V_xq,V_x,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq),V_yq) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,c_Lazy__Sequence_Oappend(T_a,V_xq,V_yq)),
file('theBenchmark.p',fact__01) ).
fof(fact_lazy__sequence_Oinject,axiom,
! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_b] :
( c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_H_2,V_lazy__sequence_H_2)
<=> ( V_lazy__sequence_2 = V_lazy__sequence_H_2
& V_a_2 = V_a_H_2 ) ),
file('theBenchmark.p',fact_lazy__sequence_Oinject) ).
fof(fact_pos__union__def,axiom,
! [V_seed_2,V_size_2,V_nrandom_2,V_R2_2,V_R1_2,T_b] : c_New__Random__Sequence_Opos__union(T_b,V_R1_2,V_R2_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__union(T_b,hAPP(hAPP(hAPP(V_R1_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(hAPP(V_R2_2,V_nrandom_2),V_size_2),V_seed_2)),
file('theBenchmark.p',fact_pos__union__def) ).
fof(fact_lazy__sequence_Osize_I2_J,axiom,
! [V_lazy__sequence_2,V_a_2,V_fa_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),V_lazy__sequence_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_lazy__sequence_Osize_I2_J) ).
fof(fact_small__lazy_H_Osimps,axiom,
! [V_i,V_d] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
=> c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i),c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
=> c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_small__lazy_H_Osimps) ).
fof(fact_small__lazy_H_Opsimps,axiom,
! [V_i_2,V_d_2] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
=> c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i_2),c_Lazy__Sequence_Osmall__lazy_H(V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
=> c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) ) ),
file('theBenchmark.p',fact_small__lazy_H_Opsimps) ).
fof(fact_small__lazy__int__def,axiom,
! [V_d] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,V_d) = c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d)),
file('theBenchmark.p',fact_small__lazy__int__def) ).
fof(fact_small__lazy_H_Opinduct,axiom,
! [V_P_2,V_a1_2,V_a0_2] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
=> ( ! [B_d,B_i] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
=> hBOOL(hAPP(hAPP(V_P_2,B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
=> hBOOL(hAPP(hAPP(V_P_2,B_d),B_i)) ) )
=> hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
file('theBenchmark.p',fact_small__lazy_H_Opinduct) ).
fof(fact_size__code,axiom,
! [V_xq_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),T_b),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)),
file('theBenchmark.p',fact_size__code) ).
fof(fact_lazy__sequence__size__code,axiom,
! [V_xq_2,V_s_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(hAPP(c_COMBC(T_b,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),T_b),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),T_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_s_2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)),
file('theBenchmark.p',fact_lazy__sequence__size__code) ).
fof(fact_seq__case,axiom,
! [V_xq_2,V_g_2,V_f_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f_2,V_g_2,V_xq_2) = c_Option_Ooption_Ooption__case(T_b,tc_prod(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c)),V_f_2,hAPP(c_Product__Type_Oprod_Oprod__case(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c),T_b),V_g_2),hAPP(c_Lazy__Sequence_Oyield(T_c),V_xq_2)),
file('theBenchmark.p',fact_seq__case) ).
fof(fact_yieldn__def,axiom,
! [T_b] : c_Lazy__Sequence_Oyieldn(T_b) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(T_b),T_b,c_Lazy__Sequence_Oyield(T_b)),
file('theBenchmark.p',fact_yieldn__def) ).
fof(fact_lazy__sequence_Osimps_I5_J,axiom,
! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2),
file('theBenchmark.p',fact_lazy__sequence_Osimps_I5_J) ).
fof(fact_refl__on__INTER,axiom,
! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
=> c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
=> c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) ),
file('theBenchmark.p',fact_refl__on__INTER) ).
fof(fact_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_P_2,T_b] :
( c_List_Olist__ex1(T_b,V_P_2,V_xs_2)
<=> ? [B_x] :
( ! [B_y] :
( ( hBOOL(hAPP(V_P_2,B_y))
& hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) )
=> B_y = B_x )
& hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
file('theBenchmark.p',fact_list__ex1__iff__raw) ).
fof(fact_setsum__UNION__zero,axiom,
! [V_f_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_S_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_S_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
=> ( ! [B_T1] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T1),V_S_2))
=> ! [B_T2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T2),V_S_2))
=> ( B_T1 != B_T2
=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T1))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T2))
=> hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2)),V_S_2) ) ) ) ),
file('theBenchmark.p',fact_setsum__UNION__zero) ).
fof(fact_THE__default__def,axiom,
! [V_d_2,T_b,V_P_2] :
( ( ~ ? [B_x] :
( ! [B_y] :
( hBOOL(hAPP(V_P_2,B_y))
=> B_y = B_x )
& hBOOL(hAPP(V_P_2,B_x)) )
=> c_FunDef_OTHE__default(T_b,V_d_2,V_P_2) = V_d_2 )
& ( ? [B_x] :
( ! [B_y] :
( hBOOL(hAPP(V_P_2,B_y))
=> B_y = B_x )
& hBOOL(hAPP(V_P_2,B_x)) )
=> c_FunDef_OTHE__default(T_b,V_d_2,V_P_2) = c_HOL_OThe(T_b,V_P_2) ) ),
file('theBenchmark.p',fact_THE__default__def) ).
fof(fact_SUP2__E,axiom,
! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
=> ~ ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ),
file('theBenchmark.p',fact_SUP2__E) ).
fof(fact_INF2__I,axiom,
! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) )
=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ),
file('theBenchmark.p',fact_INF2__I) ).
fof(fact_finite__maxlen,axiom,
! [V_M_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),V_M_2))
=> ? [B_n] :
! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),V_M_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),B_x)),B_n)) ) ),
file('theBenchmark.p',fact_finite__maxlen) ).
fof(fact_lazy__sequence_Osize_I3_J,axiom,
! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_lazy__sequence_Osize_I3_J) ).
fof(fact_lazy__sequence_Osize_I1_J,axiom,
! [V_fa_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_lazy__sequence_Osize_I1_J) ).
fof(fact__02,axiom,
! [V_yq,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),V_yq) = V_yq,
file('theBenchmark.p',fact__02) ).
fof(fact_lazy__sequence_Osimps_I3_J,axiom,
! [V_lazy__sequence_H,V_a_H,T_a] : c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H,V_lazy__sequence_H) != c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),
file('theBenchmark.p',fact_lazy__sequence_Osimps_I3_J) ).
fof(fact_lazy__sequence_Osimps_I2_J,axiom,
! [V_lazy__sequence_H,V_a_H,T_a] : c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) != c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H,V_lazy__sequence_H),
file('theBenchmark.p',fact_lazy__sequence_Osimps_I2_J) ).
fof(fact_lazy__sequence_Osimps_I4_J,axiom,
! [V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2,
file('theBenchmark.p',fact_lazy__sequence_Osimps_I4_J) ).
fof(fact_list__all__iff__all__interval__int,axiom,
! [V_j_2,V_i_2,V_P_2] :
( c_List_Olist__all(tc_Int_Oint,V_P_2,c_List_Oupto(V_i_2,V_j_2))
<=> c_List_Oall__interval__int(V_P_2,V_i_2,V_j_2) ),
file('theBenchmark.p',fact_list__all__iff__all__interval__int) ).
fof(fact_list__ex__iff__not__all__inverval__int,axiom,
! [V_j_2,V_i_2,V_P_2] :
( c_List_Olist__ex(tc_Int_Oint,V_P_2,c_List_Oupto(V_i_2,V_j_2))
<=> ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),V_P_2),V_i_2,V_j_2) ),
file('theBenchmark.p',fact_list__ex__iff__not__all__inverval__int) ).
fof(fact_all__interval__int__def,axiom,
! [V_j_2,V_i_2,V_P_2] :
( c_List_Oall__interval__int(V_P_2,V_i_2,V_j_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2)))
=> hBOOL(hAPP(V_P_2,B_x)) ) ),
file('theBenchmark.p',fact_all__interval__int__def) ).
fof(fact_code__numeral_Orecs_I2_J,axiom,
! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(hAPP(V_f2_2,V_code__numeral_2),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,V_code__numeral_2)),
file('theBenchmark.p',fact_code__numeral_Orecs_I2_J) ).
fof(fact_Random_Osimps,axiom,
! [V_size_2,V_g_2,T_b,V_nrandom_2] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
=> c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(V_g_2,V_size_2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(T_b,V_g_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_size_2))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(T_b)),c_Product__Type_Ofst(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
=> c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)) ) ),
file('theBenchmark.p',fact_Random_Osimps) ).
fof(fact_code__numeral_Orecs_I1_J,axiom,
! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2,
file('theBenchmark.p',fact_code__numeral_Orecs_I1_J) ).
fof(fact_Random__Sequence_Oempty__def,axiom,
! [V_size_2,V_nrandom_2,T_b] : c_Random__Sequence_Oempty(T_b,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)),
file('theBenchmark.p',fact_Random__Sequence_Oempty__def) ).
fof(fact_Random__Sequence_Osingle__def,axiom,
! [V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(T_b),V_x_2),V_nrandom_2),V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(T_b),V_x_2)),
file('theBenchmark.p',fact_Random__Sequence_Osingle__def) ).
fof(fact_Random__Sequence_Omap__def,axiom,
! [V_P_2,V_f_2,T_b,T_c] : c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_P_2) = c_Random__Sequence_Obind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_c,c_Random__Sequence_Osingle(T_b)),V_f_2)),
file('theBenchmark.p',fact_Random__Sequence_Omap__def) ).
fof(fact_exE__realizer,axiom,
! [T_d,V_f_2,V_Q_2,V_p_2,T_b,T_c,V_P_2] :
( hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2)),hAPP(c_Product__Type_Ofst(T_c,T_b),V_p_2)))
=> ( ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(V_P_2,B_y),B_x))
=> hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y))) )
=> hBOOL(hAPP(V_Q_2,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_d),V_f_2),V_p_2))) ) ),
file('theBenchmark.p',fact_exE__realizer) ).
fof(fact_Image__Collect__split,axiom,
! [V_A_2,V_P_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_P_2))),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_P_2)))),
file('theBenchmark.p',fact_Image__Collect__split) ).
fof(fact_lexord__trans,axiom,
! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_z_2)),c_List_Olexord(T_b,V_r_2)))
=> ( c_Relation_Otrans(T_b,V_r_2)
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_z_2)),c_List_Olexord(T_b,V_r_2))) ) ) ),
file('theBenchmark.p',fact_lexord__trans) ).
fof(fact_trans__less__than,axiom,
c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than),
file('theBenchmark.p',fact_trans__less__than) ).
fof(fact_trans__lex__prod,axiom,
! [V_R2_2,T_c,V_R1_2,T_b] :
( c_Relation_Otrans(T_b,V_R1_2)
=> ( c_Relation_Otrans(T_c,V_R2_2)
=> c_Relation_Otrans(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_R1_2,V_R2_2)) ) ),
file('theBenchmark.p',fact_trans__lex__prod) ).
fof(fact_transD,axiom,
! [V_c_2,V_b_2,V_a_2,V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),V_r_2)) ) ) ),
file('theBenchmark.p',fact_transD) ).
fof(fact_trans__def,axiom,
! [V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
<=> ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
=> ! [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_z)),V_r_2)) ) ) ),
file('theBenchmark.p',fact_trans__def) ).
fof(fact_trans__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__rtrancl,axiom,
! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
file('theBenchmark.p',fact_trans__rtrancl) ).
fof(fact_trans__Id,axiom,
! [T_b] : c_Relation_Otrans(T_b,c_Relation_OId(T_b)),
file('theBenchmark.p',fact_trans__Id) ).
fof(fact_trans__trancl,axiom,
! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)),
file('theBenchmark.p',fact_trans__trancl) ).
fof(fact_trancl__id,axiom,
! [V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> c_Transitive__Closure_Otrancl(T_b,V_r_2) = V_r_2 ),
file('theBenchmark.p',fact_trancl__id) ).
fof(fact_trans__Id__on,axiom,
! [V_A_2,T_b] : c_Relation_Otrans(T_b,c_Relation_OId__on(T_b,V_A_2)),
file('theBenchmark.p',fact_trans__Id__on) ).
fof(fact_trans__finite__psubset,axiom,
! [T_b] : c_Relation_Otrans(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)),
file('theBenchmark.p',fact_trans__finite__psubset) ).
fof(fact_lexord__transI,axiom,
! [V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olexord(T_b,V_r_2)) ),
file('theBenchmark.p',fact_lexord__transI) ).
fof(fact_listrel__trans,axiom,
! [V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ),
file('theBenchmark.p',fact_listrel__trans) ).
fof(fact_bex__empty,axiom,
! [V_P_2,T_b] :
~ ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ),
file('theBenchmark.p',fact_bex__empty) ).
fof(fact_trans__converse,axiom,
! [V_r_2,T_b] :
( c_Relation_Otrans(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
<=> c_Relation_Otrans(T_b,V_r_2) ),
file('theBenchmark.p',fact_trans__converse) ).
fof(fact_finite__Collect__bex,axiom,
! [V_Q_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),V_Q_2)))))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_x)))) ) ) ),
file('theBenchmark.p',fact_finite__Collect__bex) ).
fof(fact_bex__UNIV,axiom,
! [V_P_2,T_b] :
( ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
<=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ),
file('theBenchmark.p',fact_bex__UNIV) ).
fof(fact_trans__Int,axiom,
! [V_s_2,V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> ( c_Relation_Otrans(T_b,V_s_2)
=> c_Relation_Otrans(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ),
file('theBenchmark.p',fact_trans__Int) ).
fof(fact_SUPR__bool__eq,axiom,
! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_HOL_Obool) = c_Set_OBex(T_b),
file('theBenchmark.p',fact_SUPR__bool__eq) ).
fof(fact_trans__O__subset,axiom,
! [V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),V_r_2)),V_r_2)) ),
file('theBenchmark.p',fact_trans__O__subset) ).
fof(fact_trans__inv__image,axiom,
! [V_f_2,T_c,V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> c_Relation_Otrans(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ),
file('theBenchmark.p',fact_trans__inv__image) ).
fof(fact_Union__eq,axiom,
! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))),
file('theBenchmark.p',fact_Union__eq) ).
fof(fact_list__ex__iff__raw,axiom,
! [V_xs_2,V_P_2,T_b] :
( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
<=> ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
file('theBenchmark.p',fact_list__ex__iff__raw) ).
fof(fact_Bex__set__list__ex,axiom,
! [V_P_2,V_xs_2,T_b] :
( ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
<=> c_List_Olist__ex(T_b,V_P_2,V_xs_2) ),
file('theBenchmark.p',fact_Bex__set__list__ex) ).
fof(fact_UN__eq,axiom,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2))))),
file('theBenchmark.p',fact_UN__eq) ).
fof(fact_INT__eq,axiom,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2))))),
file('theBenchmark.p',fact_INT__eq) ).
fof(fact_Sup__fun__def,axiom,
! [V_x_2,V_A_2,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ),
file('theBenchmark.p',fact_Sup__fun__def) ).
fof(fact_Sup__apply,axiom,
! [V_x_2,V_A_2,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ),
file('theBenchmark.p',fact_Sup__apply) ).
fof(fact_Inf__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_transp__def,axiom,
! [V_r_2,T_b] :
( c_Predicate_Otransp(T_b,V_r_2)
<=> c_Relation_Otrans(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ),
file('theBenchmark.p',fact_transp__def) ).
fof(fact_transpE,axiom,
! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
( c_Predicate_Otransp(T_b,V_r_2)
=> ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
=> ( hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_z_2))
=> hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_z_2)) ) ) ),
file('theBenchmark.p',fact_transpE) ).
fof(fact_equivp__reflp__symp__transp,axiom,
! [V_R_2,T_b] :
( c_Equiv__Relations_Oequivp(T_b,V_R_2)
<=> ( c_Predicate_Otransp(T_b,V_R_2)
& c_Predicate_Osymp(T_b,V_R_2)
& c_Predicate_Oreflp(T_b,V_R_2) ) ),
file('theBenchmark.p',fact_equivp__reflp__symp__transp) ).
fof(fact_equivpI,axiom,
! [V_R_2,T_b] :
( c_Predicate_Oreflp(T_b,V_R_2)
=> ( c_Predicate_Osymp(T_b,V_R_2)
=> ( c_Predicate_Otransp(T_b,V_R_2)
=> c_Equiv__Relations_Oequivp(T_b,V_R_2) ) ) ),
file('theBenchmark.p',fact_equivpI) ).
fof(fact_sympE,axiom,
! [V_y_2,V_x_2,V_r_2,T_b] :
( c_Predicate_Osymp(T_b,V_r_2)
=> ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_sympE) ).
fof(fact_equivpE,axiom,
! [V_R_2,T_b] :
( c_Equiv__Relations_Oequivp(T_b,V_R_2)
=> ~ ( c_Predicate_Oreflp(T_b,V_R_2)
=> ( c_Predicate_Osymp(T_b,V_R_2)
=> ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ),
file('theBenchmark.p',fact_equivpE) ).
fof(fact_max__extp_Osimps,axiom,
! [V_a2_2,V_a1_2,V_R_2,T_b] :
( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
=> ? [B_xa] :
( hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) ) )
& V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) ) ),
file('theBenchmark.p',fact_max__extp_Osimps) ).
fof(fact_trans__diff__Id,axiom,
! [V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> ( c_Relation_Oantisym(T_b,V_r_2)
=> c_Relation_Otrans(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ) ),
file('theBenchmark.p',fact_trans__diff__Id) ).
fof(fact_antisym__Id__on,axiom,
! [V_A_2,T_b] : c_Relation_Oantisym(T_b,c_Relation_OId__on(T_b,V_A_2)),
file('theBenchmark.p',fact_antisym__Id__on) ).
fof(fact_antisym__converse,axiom,
! [V_r_2,T_b] :
( c_Relation_Oantisym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
<=> c_Relation_Oantisym(T_b,V_r_2) ),
file('theBenchmark.p',fact_antisym__converse) ).
fof(fact_antisym__empty,axiom,
! [T_b] : c_Relation_Oantisym(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),
file('theBenchmark.p',fact_antisym__empty) ).
fof(fact_antisym__Id,axiom,
! [T_b] : c_Relation_Oantisym(T_b,c_Relation_OId(T_b)),
file('theBenchmark.p',fact_antisym__Id) ).
fof(fact_antisym__subset,axiom,
! [V_s_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
=> ( c_Relation_Oantisym(T_b,V_s_2)
=> c_Relation_Oantisym(T_b,V_r_2) ) ),
file('theBenchmark.p',fact_antisym__subset) ).
fof(fact_antisym__def,axiom,
! [V_r_2,T_b] :
( c_Relation_Oantisym(T_b,V_r_2)
<=> ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2))
=> B_x = B_y ) ) ),
file('theBenchmark.p',fact_antisym__def) ).
fof(fact_antisymD,axiom,
! [V_b_2,V_a_2,V_r_2,T_b] :
( c_Relation_Oantisym(T_b,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),V_r_2))
=> V_a_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_antisymD) ).
fof(fact_antisym__reflcl,axiom,
! [V_r_2,T_b] :
( c_Relation_Oantisym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))
<=> c_Relation_Oantisym(T_b,V_r_2) ),
file('theBenchmark.p',fact_antisym__reflcl) ).
fof(fact_acyclic__impl__antisym__rtrancl,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Oacyclic(T_b,V_r_2)
=> c_Relation_Oantisym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ),
file('theBenchmark.p',fact_acyclic__impl__antisym__rtrancl) ).
fof(fact_fun__lub__def,axiom,
! [V_x_2,V_A_2,V_L_2,T_d,T_b,T_c] : c_Partial__Function_Ofun__lub(T_c,T_b,T_d,V_L_2,V_A_2,V_x_2) = hAPP(V_L_2,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(tc_fun(T_d,T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),T_c),hAPP(c_COMBS(tc_fun(T_d,T_c),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_d,T_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_d,T_c))),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,tc_fun(T_d,T_c))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),T_d,T_c),c_COMBI(tc_fun(T_d,T_c))),V_x_2)))))),
file('theBenchmark.p',fact_fun__lub__def) ).
fof(fact_sym__trans__comp__subset,axiom,
! [V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
=> ( c_Relation_Otrans(T_b,V_r_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_sym__trans__comp__subset) ).
fof(fact_symD,axiom,
! [V_b_2,V_a_2,V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_symD) ).
fof(fact_sym__def,axiom,
! [V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
<=> ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2)) ) ),
file('theBenchmark.p',fact_sym__def) ).
fof(fact_sym__rtrancl,axiom,
! [V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
=> c_Relation_Osym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ),
file('theBenchmark.p',fact_sym__rtrancl) ).
fof(fact_sym__Id,axiom,
! [T_b] : c_Relation_Osym(T_b,c_Relation_OId(T_b)),
file('theBenchmark.p',fact_sym__Id) ).
fof(fact_sym__Un,axiom,
! [V_s_2,V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
=> ( c_Relation_Osym(T_b,V_s_2)
=> c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ),
file('theBenchmark.p',fact_sym__Un) ).
fof(fact_sym__trancl,axiom,
! [V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
=> c_Relation_Osym(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ),
file('theBenchmark.p',fact_sym__trancl) ).
fof(fact_sym__Id__on,axiom,
! [V_A_2,T_b] : c_Relation_Osym(T_b,c_Relation_OId__on(T_b,V_A_2)),
file('theBenchmark.p',fact_sym__Id__on) ).
fof(fact_listrel__sym,axiom,
! [V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
=> c_Relation_Osym(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ),
file('theBenchmark.p',fact_listrel__sym) ).
fof(fact_sym__converse,axiom,
! [V_r_2,T_b] :
( c_Relation_Osym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
<=> c_Relation_Osym(T_b,V_r_2) ),
file('theBenchmark.p',fact_sym__converse) ).
fof(fact_sym__conv__converse__eq,axiom,
! [V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
<=> hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2) = V_r_2 ),
file('theBenchmark.p',fact_sym__conv__converse__eq) ).
fof(fact_sym__Int,axiom,
! [V_s_2,V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
=> ( c_Relation_Osym(T_b,V_s_2)
=> c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ),
file('theBenchmark.p',fact_sym__Int) ).
fof(fact_sym__Un__converse,axiom,
! [V_r_2,T_b] : c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))),
file('theBenchmark.p',fact_sym__Un__converse) ).
fof(fact_sym__inv__image,axiom,
! [V_f_2,T_c,V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
=> c_Relation_Osym(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ),
file('theBenchmark.p',fact_sym__inv__image) ).
fof(fact_sym__Int__converse,axiom,
! [V_r_2,T_b] : c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))),
file('theBenchmark.p',fact_sym__Int__converse) ).
fof(fact_equivE,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ~ ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> ( c_Relation_Osym(T_b,V_r_2)
=> ~ c_Relation_Otrans(T_b,V_r_2) ) ) ),
file('theBenchmark.p',fact_equivE) ).
fof(fact_equivI,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> ( c_Relation_Osym(T_b,V_r_2)
=> ( c_Relation_Otrans(T_b,V_r_2)
=> c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ),
file('theBenchmark.p',fact_equivI) ).
fof(fact_equiv__def,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
<=> ( c_Relation_Otrans(T_b,V_r_2)
& c_Relation_Osym(T_b,V_r_2)
& c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ),
file('theBenchmark.p',fact_equiv__def) ).
fof(fact_symp__def,axiom,
! [V_r_2,T_b] :
( c_Predicate_Osymp(T_b,V_r_2)
<=> c_Relation_Osym(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ),
file('theBenchmark.p',fact_symp__def) ).
fof(fact_part__equivp__refl__symp__transp,axiom,
! [V_R_2,T_b] :
( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
<=> ( c_Predicate_Otransp(T_b,V_R_2)
& c_Predicate_Osymp(T_b,V_R_2)
& ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) ) ),
file('theBenchmark.p',fact_part__equivp__refl__symp__transp) ).
fof(fact_part__equivpI,axiom,
! [T_b,V_R_2] :
( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
=> ( c_Predicate_Osymp(T_b,V_R_2)
=> ( c_Predicate_Otransp(T_b,V_R_2)
=> c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ) ),
file('theBenchmark.p',fact_part__equivpI) ).
fof(fact_equivp__implies__part__equivp,axiom,
! [V_R_2,T_b] :
( c_Equiv__Relations_Oequivp(T_b,V_R_2)
=> c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ),
file('theBenchmark.p',fact_equivp__implies__part__equivp) ).
fof(fact_part__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_part__equivpE,axiom,
! [V_R_2,T_b] :
( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
=> ~ ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
=> ( c_Predicate_Osymp(T_b,V_R_2)
=> ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ),
file('theBenchmark.p',fact_part__equivpE) ).
fof(fact_part__equivp__typedef,axiom,
! [V_R_2,T_b] :
( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
=> ? [B_d] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBS(T_b,T_b,tc_HOL_Obool),V_R_2),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b)),c_fequal)),V_R_2))))) ),
file('theBenchmark.p',fact_part__equivp__typedef) ).
fof(fact_inj__iff,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
<=> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b) ),
file('theBenchmark.p',fact_inj__iff) ).
fof(fact_inv__o__cancel,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b) ),
file('theBenchmark.p',fact_inv__o__cancel) ).
fof(fact_inv__id,axiom,
! [T_b] : c_Hilbert__Choice_Oinv__into(T_b,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Fun_Oid(T_b)) = c_Fun_Oid(T_b),
file('theBenchmark.p',fact_inv__id) ).
fof(fact_inv__f__eq,axiom,
! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( hAPP(V_f_2,V_x_2) = V_y_2
=> hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2) = V_x_2 ) ),
file('theBenchmark.p',fact_inv__f__eq) ).
fof(fact_inv__f__f,axiom,
! [V_x_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ),
file('theBenchmark.p',fact_inv__f__f) ).
fof(fact_inv__into__f__f,axiom,
! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ),
file('theBenchmark.p',fact_inv__into__f__f) ).
fof(fact_inv__into__f__eq,axiom,
! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( hAPP(V_f_2,V_x_2) = V_y_2
=> hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ),
file('theBenchmark.p',fact_inv__into__f__eq) ).
fof(fact_f__inv__into__f,axiom,
! [V_A_2,V_f_2,T_c,V_y_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
=> hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_y_2)) = V_y_2 ),
file('theBenchmark.p',fact_f__inv__into__f) ).
fof(fact_inv__into__into,axiom,
! [V_A_2,V_f_2,T_c,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_x_2)),V_A_2)) ),
file('theBenchmark.p',fact_inv__into__into) ).
fof(fact_inv__into__injective,axiom,
! [V_y_2,V_x_2,V_f_2,V_A_2,T_c,T_b] :
( hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_inv__into__injective) ).
fof(fact_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__into__def,axiom,
! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2))),
file('theBenchmark.p',fact_inv__into__def) ).
fof(fact_inv__def,axiom,
! [V_y_2,V_f_2,T_c,T_b] : hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2) = c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_y_2)),
file('theBenchmark.p',fact_inv__def) ).
fof(fact_o__inv__o__cancel,axiom,
! [V_g_2,T_d,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> hAPP(c_Fun_Ocomp(T_c,T_d,T_b,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))),V_f_2) = V_g_2 ),
file('theBenchmark.p',fact_o__inv__o__cancel) ).
fof(fact_surj__imp__inj__inv,axiom,
! [V_f_2,T_b,T_c] :
( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
=> c_Fun_Oinj__on(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_surj__imp__inj__inv) ).
fof(fact_inv__image__comp,axiom,
! [V_X_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_X_2)) = V_X_2 ),
file('theBenchmark.p',fact_inv__image__comp) ).
fof(fact_image__inv__f__f,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ),
file('theBenchmark.p',fact_image__inv__f__f) ).
fof(fact_inj__imp__surj__inv,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_inj__imp__surj__inv) ).
fof(fact_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_P_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
=> hBOOL(hAPP(V_P_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),B_y))) )
=> hBOOL(hAPP(V_P_2,V_x_2)) ) ),
file('theBenchmark.p',fact_inj__transfer) ).
fof(fact_fold__image__UN__disjoint,axiom,
! [V_g_2,V_A_2,T_c,V_I_2,T_b,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_I_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_I_2))
=> ( B_x != B_xa
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,B_x)),hAPP(V_A_2,B_xa)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) )
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),T_d,T_b),hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),c_Groups_Oone__class_Oone(T_d))),V_A_2)),c_Groups_Oone__class_Oone(T_d)),V_I_2) ) ) ) ),
file('theBenchmark.p',fact_fold__image__UN__disjoint) ).
fof(fact_nat__of__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_nat__of__induct,axiom,
! [V_P_2,V_y_2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
=> ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Code__Numeral_Onat__of,B_x)))
=> hBOOL(hAPP(V_P_2,V_y_2)) ) ),
file('theBenchmark.p',fact_nat__of__induct) ).
fof(fact_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_of__nat__induct,axiom,
! [V_x_2,V_P_2] :
( ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
=> hBOOL(hAPP(V_P_2,hAPP(c_Code__Numeral_Oof__nat,B_y))) )
=> hBOOL(hAPP(V_P_2,V_x_2)) ),
file('theBenchmark.p',fact_of__nat__induct) ).
fof(fact_lazy__sequence_Orecs_I1_J,axiom,
! [V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2,
file('theBenchmark.p',fact_lazy__sequence_Orecs_I1_J) ).
fof(fact_Least__Suc2,axiom,
! [V_m_2,V_Q_2,V_n_2,V_P_2] :
( hBOOL(hAPP(V_P_2,V_n_2))
=> ( hBOOL(hAPP(V_Q_2,V_m_2))
=> ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( ! [B_k] :
( hBOOL(hAPP(V_P_2,hAPP(c_Nat_OSuc,B_k)))
<=> hBOOL(hAPP(V_Q_2,B_k)) )
=> c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_P_2) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_Q_2)) ) ) ) ),
file('theBenchmark.p',fact_Least__Suc2) ).
fof(fact_lazy__sequence_Orecs_I2_J,axiom,
! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,V_lazy__sequence_2)),
file('theBenchmark.p',fact_lazy__sequence_Orecs_I2_J) ).
fof(fact_beyond__def,axiom,
! [V_l,V_k] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
=> c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
=> c_Quickcheck_Obeyond(V_k,V_l) = V_l ) ),
file('theBenchmark.p',fact_beyond__def) ).
fof(fact_bij__image__Collect__eq,axiom,
! [V_P_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),V_P_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))) ),
file('theBenchmark.p',fact_bij__image__Collect__eq) ).
fof(fact_bij__betw__id,axiom,
! [V_A_2,T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_A_2),
file('theBenchmark.p',fact_bij__betw__id) ).
fof(fact_bij__betw__inv__into,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
=> c_Fun_Obij__betw(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_B_2,V_A_2) ),
file('theBenchmark.p',fact_bij__betw__inv__into) ).
fof(fact_inv__into__inv__into__eq,axiom,
! [V_a_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_H_2,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2)),V_a_2) = hAPP(V_f_2,V_a_2) ) ),
file('theBenchmark.p',fact_inv__into__inv__into__eq) ).
fof(fact_bij__imp__bij__inv,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> c_Fun_Obij__betw(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_bij__imp__bij__inv) ).
fof(fact_inv__inv__eq,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)) = V_f_2 ),
file('theBenchmark.p',fact_inv__inv__eq) ).
fof(fact_o__inv__distrib,axiom,
! [V_g_2,T_d,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> ( c_Fun_Obij__betw(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> c_Hilbert__Choice_Oinv__into(T_d,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Hilbert__Choice_Oinv__into(T_d,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),V_g_2)),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)) ) ),
file('theBenchmark.p',fact_o__inv__distrib) ).
fof(fact_bij__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__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__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__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_finite__vimage__iff,axiom,
! [V_F_2,V_h_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ),
file('theBenchmark.p',fact_finite__vimage__iff) ).
fof(fact_bij__image__Compl__eq,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ),
file('theBenchmark.p',fact_bij__image__Compl__eq) ).
fof(fact_bij__def,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
<=> ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
& c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ),
file('theBenchmark.p',fact_bij__def) ).
fof(fact_bijI,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
=> c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ) ),
file('theBenchmark.p',fact_bijI) ).
fof(fact_bij__betw__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__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_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_inj__on__imp__bij__betw,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ),
file('theBenchmark.p',fact_inj__on__imp__bij__betw) ).
fof(fact_bij__betw__def,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
<=> ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = V_B_2
& c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
file('theBenchmark.p',fact_bij__betw__def) ).
fof(fact_bij__betw__imp__inj__on,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
=> c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
file('theBenchmark.p',fact_bij__betw__imp__inj__on) ).
fof(fact_bij__is__inj,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_bij__is__inj) ).
fof(fact_bij__betw__same__card,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ),
file('theBenchmark.p',fact_bij__betw__same__card) ).
fof(fact_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_beyond__zero,axiom,
! [V_k] : c_Quickcheck_Obeyond(V_k,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',fact_beyond__zero) ).
fof(fact_bij__betw__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__betw__finite,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ),
file('theBenchmark.p',fact_bij__betw__finite) ).
fof(fact_BIJ,axiom,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( ? [B_f] : c_Fun_Obij__betw(T_b,T_c,B_f,V_A_2,V_B_2)
<=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ),
file('theBenchmark.p',fact_BIJ) ).
fof(fact_bij__betw__id__iff,axiom,
! [V_B_2,V_A_2,T_b] :
( c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_B_2)
<=> V_A_2 = V_B_2 ),
file('theBenchmark.p',fact_bij__betw__id__iff) ).
fof(fact_bij__id,axiom,
! [T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),
file('theBenchmark.p',fact_bij__id) ).
fof(fact_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__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_curry__def,axiom,
! [V_y_2,V_x_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_c_2),V_x_2),V_y_2) = hAPP(V_c_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),
file('theBenchmark.p',fact_curry__def) ).
fof(fact_refl__on__UNION,axiom,
! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
=> c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
=> c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) ),
file('theBenchmark.p',fact_refl__on__UNION) ).
fof(fact_curryI,axiom,
! [V_b_2,V_a_2,T_c,T_b,V_f_2] :
( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
=> hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ),
file('theBenchmark.p',fact_curryI) ).
fof(fact_split__curry,axiom,
! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),c_Product__Type_Ocurry(T_b,T_c,T_d,V_f_2)) = V_f_2,
file('theBenchmark.p',fact_split__curry) ).
fof(fact_curry__split,axiom,
! [V_f_2,T_d,T_c,T_b] : c_Product__Type_Ocurry(T_b,T_c,T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)) = V_f_2,
file('theBenchmark.p',fact_curry__split) ).
fof(fact_curryD,axiom,
! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
=> hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ),
file('theBenchmark.p',fact_curryD) ).
fof(fact_curryE,axiom,
! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
=> hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ),
file('theBenchmark.p',fact_curryE) ).
fof(fact_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_bex__reg__eqv,axiom,
! [V_P_2,V_R_2,T_b] :
( c_Equiv__Relations_Oequivp(T_b,V_R_2)
=> ( ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2))) )
<=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ),
file('theBenchmark.p',fact_bex__reg__eqv) ).
fof(fact_wf__weak__decr__stable,axiom,
! [V_r_2,V_f_2,T_b] :
( ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2))
=> ? [B_i] :
! [B_k] : hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),B_k)) = hAPP(V_f_2,B_i) ) ),
file('theBenchmark.p',fact_wf__weak__decr__stable) ).
fof(fact_Respects__def,axiom,
! [V_x_2,V_R_2,T_b] :
( hBOOL(hAPP(c_Quotient_ORespects(T_b,V_R_2),V_x_2))
<=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ),
file('theBenchmark.p',fact_Respects__def) ).
fof(fact_in__respects,axiom,
! [V_R_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Quotient_ORespects(T_b,V_R_2)))
<=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ),
file('theBenchmark.p',fact_in__respects) ).
fof(fact_bex__reg__right,axiom,
! [V_P_2,V_Q_2,V_R_2,T_b] :
( c_Equiv__Relations_Oequivp(T_b,V_R_2)
=> ( ! [B_x] :
( hBOOL(hAPP(V_Q_2,B_x))
=> hBOOL(hAPP(V_P_2,B_x)) )
=> ( ? [B_x1] : hBOOL(hAPP(V_Q_2,B_x1))
=> ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2))) ) ) ) ),
file('theBenchmark.p',fact_bex__reg__right) ).
fof(fact_babs__reg__eqv,axiom,
! [V_P_2,T_c,V_R_2,T_b] :
( c_Equiv__Relations_Oequivp(T_b,V_R_2)
=> c_Quotient_OBabs(T_b,T_c,c_Quotient_ORespects(T_b,V_R_2),V_P_2) = V_P_2 ),
file('theBenchmark.p',fact_babs__reg__eqv) ).
fof(fact_Babs__def,axiom,
! [V_m_2,T_c,V_p_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_p_2))
=> hAPP(c_Quotient_OBabs(T_b,T_c,V_p_2,V_m_2),V_x_2) = hAPP(V_m_2,V_x_2) ),
file('theBenchmark.p',fact_Babs__def) ).
fof(fact_INT__anti__mono,axiom,
! [V_g_2,V_f_2,T_c,V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_g_2))) ) ),
file('theBenchmark.p',fact_INT__anti__mono) ).
fof(fact_INT__greatest,axiom,
! [V_B_2,V_C_2,T_c,V_A_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(V_B_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_INT__greatest) ).
fof(fact_converse__rtranclE2,axiom,
! [V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
=> ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2) != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2)
=> ~ ! [B_a,B_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) ) ) ),
file('theBenchmark.p',fact_converse__rtranclE2) ).
fof(fact_converse__rtrancl__induct2,axiom,
! [V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
=> ( hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2))
=> ( ! [B_a,B_b,B_aa,B_ba] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba))),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
=> ( hBOOL(hAPP(hAPP(V_P_2,B_aa),B_ba))
=> hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) )
=> hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2)) ) ) ),
file('theBenchmark.p',fact_converse__rtrancl__induct2) ).
fof(fact_rtrancl__induct2,axiom,
! [V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
=> ( hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2))
=> ( ! [B_a,B_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
=> ! [B_aa,B_ba] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba))),V_r_2))
=> ( hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
=> hBOOL(hAPP(hAPP(V_P_2,B_aa),B_ba)) ) ) )
=> hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2)) ) ) ),
file('theBenchmark.p',fact_rtrancl__induct2) ).
fof(fact_congruentI,axiom,
! [T_c,V_f_2,V_r_2,T_b] :
( ! [B_y,B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2))
=> hAPP(V_f_2,B_y) = hAPP(V_f_2,B_z) )
=> c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) ),
file('theBenchmark.p',fact_congruentI) ).
fof(fact_congruent2I_H,axiom,
! [T_d,V_f_2,V_r2_2,T_c,V_r1_2,T_b] :
( ! [B_y1,B_z1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y1),B_z1)),V_r1_2))
=> ! [B_y2,B_z2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y2),B_z2)),V_r2_2))
=> hAPP(hAPP(V_f_2,B_y1),B_y2) = hAPP(hAPP(V_f_2,B_z1),B_z2) ) )
=> c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) ),
file('theBenchmark.p',fact_congruent2I_H) ).
fof(fact__03,axiom,
! [V_xqq,V_xq,T_a] : c_Lazy__Sequence_Oflat(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(T_a),V_xq,V_xqq)) = c_Lazy__Sequence_Oappend(T_a,V_xq,c_Lazy__Sequence_Oflat(T_a,V_xqq)),
file('theBenchmark.p',fact__03) ).
fof(fact__04,axiom,
! [T_a] : c_Lazy__Sequence_Oflat(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(T_a))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),
file('theBenchmark.p',fact__04) ).
fof(fact__05,axiom,
! [V_f_2,V_xq_2,T_b,T_c] : hAPP(c_Lazy__Sequence_Obind(T_c,T_b,V_xq_2),V_f_2) = c_Lazy__Sequence_Oflat(T_b,c_Lazy__Sequence_Omap(T_c,tc_Lazy__Sequence_Olazy__sequence(T_b),V_f_2,V_xq_2)),
file('theBenchmark.p',fact__05) ).
fof(fact_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__mult__cancel,axiom,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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)))
=> ( 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_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ) ),
file('theBenchmark.p',fact_dvd__mult__cancel) ).
fof(fact_nat__mult__dvd__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_Rings_Odvd__class_Odvd(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_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_nat__mult__dvd__cancel1) ).
fof(fact_setprod__dvd__setprod__subset,axiom,
! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
( ( class_Rings_Odvd(T_c)
& class_Groups_Ocomm__monoid__mult(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))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))) ) ) ),
file('theBenchmark.p',fact_setprod__dvd__setprod__subset) ).
fof(fact_inf__period_I4_J,axiom,
! [V_t_2,V_D_2,V_d_2,T_b] :
( ( class_Rings_Odvd(T_b)
& class_Rings_Ocomm__ring(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
=> ! [B_x,B_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) ) ) ),
file('theBenchmark.p',fact_inf__period_I4_J) ).
fof(fact_inf__period_I3_J,axiom,
! [V_t_2,V_D_2,V_d_2,T_b] :
( ( class_Rings_Odvd(T_b)
& class_Rings_Ocomm__ring(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
=> ! [B_x,B_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) ) ) ),
file('theBenchmark.p',fact_inf__period_I3_J) ).
fof(fact_dvd__div__div__eq__mult,axiom,
! [V_d_2,V_b_2,V_c_2,V_a_2,T_b] :
( class_Divides_Osemiring__div(T_b)
=> ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
=> ( V_c_2 != c_Groups_Ozero__class_Ozero(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_c_2),V_d_2))
=> ( 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_d_2),V_c_2)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2) ) ) ) ) ) ),
file('theBenchmark.p',fact_dvd__div__div__eq__mult) ).
fof(fact_dvd__div__eq__mult,axiom,
! [V_c_2,V_b_2,V_a_2,T_b] :
( class_Divides_Osemiring__div(T_b)
=> ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
=> ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = V_c_2
<=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2) ) ) ) ),
file('theBenchmark.p',fact_dvd__div__eq__mult) ).
fof(fact_dvd__triv__left,axiom,
! [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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ),
file('theBenchmark.p',fact_dvd__triv__left) ).
fof(fact_dvd__triv__right,axiom,
! [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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) ),
file('theBenchmark.p',fact_dvd__triv__right) ).
fof(fact_dvd__mult2,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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ),
file('theBenchmark.p',fact_dvd__mult2) ).
fof(fact_dvd__mult,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(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_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ),
file('theBenchmark.p',fact_dvd__mult) ).
fof(fact_mult__dvd__mono,axiom,
! [V_d,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_c),V_d))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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__dvd__mono) ).
fof(fact_dvdI,axiom,
! [V_k,V_b,V_a,T_a] :
( class_Rings_Odvd(T_a)
=> ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)) ) ),
file('theBenchmark.p',fact_dvdI) ).
fof(fact_dvd__mult__left,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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ),
file('theBenchmark.p',fact_dvd__mult__left) ).
fof(fact_dvd__mult__right,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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) ) ),
file('theBenchmark.p',fact_dvd__mult__right) ).
fof(fact_dvd__mult__cancel__left,axiom,
! [V_b_2,V_a_2,V_c_2,T_b] :
( class_Rings_Oidom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
| V_c_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_dvd__mult__cancel__left) ).
fof(fact_dvd__mult__cancel__right,axiom,
! [V_b_2,V_c_2,V_a_2,T_b] :
( class_Rings_Oidom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
| V_c_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_dvd__mult__cancel__right) ).
fof(fact_div__mult__div__if__dvd,axiom,
! [V_w,V_z,V_x,V_y,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_w),V_z)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ),
file('theBenchmark.p',fact_div__mult__div__if__dvd) ).
fof(fact_dvd__div__mult,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_c) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_a) ) ),
file('theBenchmark.p',fact_dvd__div__mult) ).
fof(fact_dvd__div__mult__self,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_a) = V_b ) ),
file('theBenchmark.p',fact_dvd__div__mult__self) ).
fof(fact_div__mult__swap,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))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ) ),
file('theBenchmark.p',fact_div__mult__swap) ).
fof(fact_dvd__mult__div__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)) = V_b ) ),
file('theBenchmark.p',fact_dvd__mult__div__cancel) ).
fof(fact_nat__mult__dvd__cancel__disj,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2))
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).
fof(fact_unity__coeff__ex,axiom,
! [V_l_2,V_P_2,T_b] :
( ( class_Rings_Osemiring__0(T_b)
& class_Rings_Odvd(T_b) )
=> ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))
<=> ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),c_Groups_Ozero__class_Ozero(T_b)))) ) ) ),
file('theBenchmark.p',fact_unity__coeff__ex) ).
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_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__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__iff,axiom,
! [V_c_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_c_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
<=> ( V_b_2 = V_c_2
& V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_dvd_OatLeastAtMost__singleton__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_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__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_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_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__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__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_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_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,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_div__add,axiom,
! [V_y,V_x,V_z,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_z)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_y),V_z)) ) ) ),
file('theBenchmark.p',fact_div__add) ).
fof(fact_dvd__imp__mod__0,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
=> c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_dvd__imp__mod__0) ).
fof(fact_dvd__eq__mod__eq__0,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Divides_Osemiring__div(T_b)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
<=> c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_dvd__eq__mod__eq__0) ).
fof(fact_dvd__abs__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),V_m_2),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ),
file('theBenchmark.p',fact_dvd__abs__iff) ).
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(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_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_div__dvd__div,axiom,
! [V_c_2,V_b_2,V_a_2,T_b] :
( class_Divides_Osemiring__div(T_b)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_c_2),V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_c_2)) ) ) ) ),
file('theBenchmark.p',fact_div__dvd__div) ).
fof(fact_dvd__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_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__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_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(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice) ).
fof(arity_fun__Lattices_Obounded__lattice,axiom,
! [T_2,T_1] :
( class_Lattices_Obounded__lattice(T_1)
=> class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Lattices_Obounded__lattice) ).
fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
! [T_2,T_1] :
( class_Complete__Lattice_Ocomplete__lattice(T_1)
=> class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
! [T_2,T_1] :
( class_Lattices_Obounded__lattice(T_1)
=> class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Lattices_Obounded__lattice__top) ).
fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
! [T_2,T_1] :
( class_Lattices_Obounded__lattice(T_1)
=> class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Lattices_Obounded__lattice__bot) ).
fof(arity_fun__Lattices_Osemilattice__sup,axiom,
! [T_2,T_1] :
( class_Lattices_Olattice(T_1)
=> class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Lattices_Osemilattice__sup) ).
fof(arity_fun__Lattices_Osemilattice__inf,axiom,
! [T_2,T_1] :
( class_Lattices_Olattice(T_1)
=> class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Lattices_Osemilattice__inf) ).
fof(arity_fun__Lattices_Odistrib__lattice,axiom,
! [T_2,T_1] :
( class_Lattices_Odistrib__lattice(T_1)
=> class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Lattices_Odistrib__lattice) ).
fof(arity_fun__Lattices_Oboolean__algebra,axiom,
! [T_2,T_1] :
( class_Lattices_Oboolean__algebra(T_1)
=> class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [T_2,T_1] :
( class_Orderings_Opreorder(T_1)
=> class_Orderings_Opreorder(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(arity_fun__Finite__Set_Ofinite,axiom,
! [T_1,T_2] :
( ( class_Finite__Set_Ofinite(T_1)
& class_Finite__Set_Ofinite(T_2) )
=> class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).
fof(arity_fun__Lattices_Olattice,axiom,
! [T_2,T_1] :
( class_Lattices_Olattice(T_1)
=> class_Lattices_Olattice(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Lattices_Olattice) ).
fof(arity_fun__Orderings_Oorder,axiom,
! [T_2,T_1] :
( class_Orderings_Oorder(T_1)
=> class_Orderings_Oorder(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(arity_fun__Orderings_Otop,axiom,
! [T_2,T_1] :
( class_Orderings_Otop(T_1)
=> class_Orderings_Otop(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Orderings_Otop) ).
fof(arity_fun__Orderings_Oord,axiom,
! [T_2,T_1] :
( class_Orderings_Oord(T_1)
=> class_Orderings_Oord(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Orderings_Obot,axiom,
! [T_2,T_1] :
( class_Orderings_Obot(T_1)
=> class_Orderings_Obot(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Orderings_Obot) ).
fof(arity_fun__Groups_Ouminus,axiom,
! [T_2,T_1] :
( class_Groups_Ouminus(T_1)
=> class_Groups_Ouminus(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Groups_Ouminus) ).
fof(arity_fun__Groups_Ominus,axiom,
! [T_2,T_1] :
( class_Groups_Ominus(T_1)
=> class_Groups_Ominus(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Groups_Ominus) ).
fof(arity_fun__Enum_Oenum,axiom,
! [T_1,T_2] :
( ( class_Enum_Oenum(T_1)
& class_Enum_Oenum(T_2) )
=> class_Enum_Oenum(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Enum_Oenum) ).
fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__semigroup__add) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).
fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom,
class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Lazy__Sequence_Osmall__lazy) ).
fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
class_Lattices_Osemilattice__sup(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Lattices_Osemilattice__sup) ).
fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
class_Lattices_Osemilattice__inf(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Lattices_Osemilattice__inf) ).
fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Lattices_Odistrib__lattice) ).
fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).
fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
class_Groups_Osemigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Osemigroup__add) ).
fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Nat_Osemiring__char__0) ).
fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
fof(arity_Int__Oint__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
fof(arity_Int__Oint__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
class_Rings_Osemiring__1(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).
fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
fof(arity_Int__Oint__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Lattices_Olattice) ).
fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
fof(arity_Int__Oint__Divides_Oring__div,axiom,
class_Divides_Oring__div(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Divides_Oring__div) ).
fof(arity_Int__Oint__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
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_Int__Oint__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).
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__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).
fof(arity_Nat__Onat__Nat_Osize,axiom,
class_Nat_Osize(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Nat_Osize) ).
fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice) ).
fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__top) ).
fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).
fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
class_Lattices_Osemilattice__sup(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__sup) ).
fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).
fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Lattices_Odistrib__lattice) ).
fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).
fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
class_Finite__Set_Ofinite(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).
fof(arity_HOL__Obool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).
fof(arity_HOL__Obool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(arity_HOL__Obool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).
fof(arity_HOL__Obool__Orderings_Oord,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(arity_HOL__Obool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
fof(arity_HOL__Obool__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).
fof(arity_HOL__Obool__Groups_Ominus,axiom,
class_Groups_Ominus(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
fof(arity_HOL__Obool__Enum_Oenum,axiom,
class_Enum_Oenum(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Enum_Oenum) ).
fof(arity_HOL__Obool__Nat_Osize,axiom,
class_Nat_Osize(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Nat_Osize) ).
fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom,
! [T_1] :
( class_Lazy__Sequence_Osmall__lazy(T_1)
=> class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ),
file('theBenchmark.p',arity_List__Olist__Lazy__Sequence_Osmall__lazy) ).
fof(arity_List__Olist__Nat_Osize,axiom,
! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)),
file('theBenchmark.p',arity_List__Olist__Nat_Osize) ).
fof(arity_sum__Finite__Set_Ofinite,axiom,
! [T_1,T_2] :
( ( class_Finite__Set_Ofinite(T_1)
& class_Finite__Set_Ofinite(T_2) )
=> class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ),
file('theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).
fof(arity_sum__Enum_Oenum,axiom,
! [T_1,T_2] :
( ( class_Enum_Oenum(T_1)
& class_Enum_Oenum(T_2) )
=> class_Enum_Oenum(tc_sum(T_2,T_1)) ),
file('theBenchmark.p',arity_sum__Enum_Oenum) ).
fof(arity_sum__Nat_Osize,axiom,
! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)),
file('theBenchmark.p',arity_sum__Nat_Osize) ).
fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
! [T_1] :
( class_Finite__Set_Ofinite(T_1)
=> class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ),
file('theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).
fof(arity_Option__Ooption__Enum_Oenum,axiom,
! [T_1] :
( class_Enum_Oenum(T_1)
=> class_Enum_Oenum(tc_Option_Ooption(T_1)) ),
file('theBenchmark.p',arity_Option__Ooption__Enum_Oenum) ).
fof(arity_Option__Ooption__Nat_Osize,axiom,
! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)),
file('theBenchmark.p',arity_Option__Ooption__Nat_Osize) ).
fof(arity_Nitpick__Opair____box__Nat_Osize,axiom,
! [T_1,T_2] : class_Nat_Osize(tc_Nitpick_Opair__box(T_2,T_1)),
file('theBenchmark.p',arity_Nitpick__Opair____box__Nat_Osize) ).
fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom,
! [T_1,T_2] :
( ( class_Lazy__Sequence_Osmall__lazy(T_1)
& class_Lazy__Sequence_Osmall__lazy(T_2) )
=> class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ),
file('theBenchmark.p',arity_prod__Lazy__Sequence_Osmall__lazy) ).
fof(arity_prod__Finite__Set_Ofinite,axiom,
! [T_1,T_2] :
( ( class_Finite__Set_Ofinite(T_1)
& class_Finite__Set_Ofinite(T_2) )
=> class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ),
file('theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).
fof(arity_prod__Enum_Oenum,axiom,
! [T_1,T_2] :
( ( class_Enum_Oenum(T_1)
& class_Enum_Oenum(T_2) )
=> class_Enum_Oenum(tc_prod(T_2,T_1)) ),
file('theBenchmark.p',arity_prod__Enum_Oenum) ).
fof(arity_prod__Nat_Osize,axiom,
! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)),
file('theBenchmark.p',arity_prod__Nat_Osize) ).
fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom,
class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit),
file('theBenchmark.p',arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy) ).
fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).
fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
class_Enum_Oenum(tc_Product__Type_Ounit),
file('theBenchmark.p',arity_Product____Type__Ounit__Enum_Oenum) ).
fof(arity_Product____Type__Ounit__Nat_Osize,axiom,
class_Nat_Osize(tc_Product__Type_Ounit),
file('theBenchmark.p',arity_Product____Type__Ounit__Nat_Osize) ).
fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom,
class_Nat_Osize(tc_Code__Evaluation_Oterm),
file('theBenchmark.p',arity_Code____Evaluation__Oterm__Nat_Osize) ).
fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom,
! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)),
file('theBenchmark.p',arity_Hoare____Mirabelle__Otriple__Nat_Osize) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring) ).
fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one) ).
fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder) ).
fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero) ).
fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Oorder) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring) ).
fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Oord) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ominus) ).
fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Power_Opower) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ozero) ).
fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Int_Onumber) ).
fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oone) ).
fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Odvd) ).
fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom,
class_Nat_Osize(tc_Code__Numeral_Ocode__numeral),
file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Nat_Osize) ).
fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)),
file('theBenchmark.p',arity_Lazy____Sequence__Olazy____sequence__Nat_Osize) ).
fof(help_c__COMBI__1,axiom,
! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P,
file('theBenchmark.p',help_c__COMBI__1) ).
fof(help_c__COMBK__1,axiom,
! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P,
file('theBenchmark.p',help_c__COMBK__1) ).
fof(help_c__COMBB__1,axiom,
! [V_R_2,V_Q_2,V_P_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_P_2),V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)),
file('theBenchmark.p',help_c__COMBB__1) ).
fof(help_c__COMBC__1,axiom,
! [V_R_2,V_Q_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2),
file('theBenchmark.p',help_c__COMBC__1) ).
fof(help_c__COMBS__1,axiom,
! [V_R_2,V_Q_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)),
file('theBenchmark.p',help_c__COMBS__1) ).
fof(help_c__fequal__1,axiom,
! [V_y_2,V_x_2] :
( V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ),
file('theBenchmark.p',help_c__fequal__1) ).
fof(help_c__fequal__2,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
| V_x_2 != V_y_2 ),
file('theBenchmark.p',help_c__fequal__2) ).
fof(help_c__fFalse__1,axiom,
~ hBOOL(c_fFalse),
file('theBenchmark.p',help_c__fFalse__1) ).
fof(help_c__fTrue__1,axiom,
hBOOL(c_fTrue),
file('theBenchmark.p',help_c__fTrue__1) ).
fof(help_c__fNot__1,axiom,
! [V_P_2] :
( ~ hBOOL(V_P_2)
| ~ hBOOL(hAPP(c_fNot,V_P_2)) ),
file('theBenchmark.p',help_c__fNot__1) ).
fof(help_c__fNot__2,axiom,
! [V_P_2] :
( hBOOL(hAPP(c_fNot,V_P_2))
| ~ ~ hBOOL(V_P_2) ),
file('theBenchmark.p',help_c__fNot__2) ).
fof(help_c__fconj__1,axiom,
! [V_Q_2,V_P_2] :
( hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
| ~ hBOOL(V_Q_2)
| ~ hBOOL(V_P_2) ),
file('theBenchmark.p',help_c__fconj__1) ).
fof(help_c__fconj__2,axiom,
! [V_Q_2,V_P_2] :
( hBOOL(V_P_2)
| ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ),
file('theBenchmark.p',help_c__fconj__2) ).
fof(help_c__fconj__3,axiom,
! [V_Q_2,V_P_2] :
( hBOOL(V_Q_2)
| ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ),
file('theBenchmark.p',help_c__fconj__3) ).
fof(help_c__fdisj__1,axiom,
! [V_Q_2,V_P_2] :
( hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
| ~ hBOOL(V_P_2) ),
file('theBenchmark.p',help_c__fdisj__1) ).
fof(help_c__fdisj__2,axiom,
! [V_P_2,V_Q_2] :
( hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
| ~ hBOOL(V_Q_2) ),
file('theBenchmark.p',help_c__fdisj__2) ).
fof(help_c__fdisj__3,axiom,
! [V_Q_2,V_P_2] :
( hBOOL(V_Q_2)
| hBOOL(V_P_2)
| ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ),
file('theBenchmark.p',help_c__fdisj__3) ).
fof(help_c__fimplies__1,axiom,
! [V_Q_2,V_P_2] :
( hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
| hBOOL(V_P_2) ),
file('theBenchmark.p',help_c__fimplies__1) ).
fof(help_c__fimplies__2,axiom,
! [V_P_2,V_Q_2] :
( hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
| ~ hBOOL(V_Q_2) ),
file('theBenchmark.p',help_c__fimplies__2) ).
fof(help_c__fimplies__3,axiom,
! [V_Q_2,V_P_2] :
( hBOOL(V_Q_2)
| ~ hBOOL(V_P_2)
| ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ),
file('theBenchmark.p',help_c__fimplies__3) ).
fof(conj_0,hypothesis,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_G)),
file('theBenchmark.p',conj_0) ).
fof(conj_1,conjecture,
! [B_n] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) )
=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) ) ),
file('theBenchmark.p',conj_1) ).
fof(f_1_1,plain,
! [V_g_2,V_f_2] :
( V_f_2 = V_g_2
| ? [B_x] : hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x) ),
inference(fof_nnf,[status(thm)],[fact_ext]) ).
fof(f_1_2,plain,
! [U_2,U_1] :
( U_1 = U_2
| ? [U_0] : hAPP(U_1,U_0) != hAPP(U_2,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_2,U_1] :
( U_1 = U_2
| hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1(U_2,U_1))],[f_1_2]) ).
cnf(f_1_4,plain,
( U_1 = U_2
| hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [V_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_2_2,plain,
! [U_5,U_4,U_3] :
( U_4 = U_5
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3,tc_HOL_Obool)),U_5),U_4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3,tc_HOL_Obool)),U_4),U_5)) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( U_4 = U_5
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3,tc_HOL_Obool)),U_5),U_4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3,tc_HOL_Obool)),U_4),U_5)) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_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_3_2,plain,
! [U_7,U_6] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6),U_7),U_7))
| ~ class_Orderings_Opreorder(U_6) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6),U_7),U_7))
| ~ class_Orderings_Opreorder(U_6) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [V_tsa_2,V_Ga_2,T_b] :
( ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,V_tsa_2)
| ? [B_n] :
( ? [B_x] :
( ~ c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2)) )
& ! [B_x] :
( c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_Ga_2)) ) ) )
& ( ! [B_n] :
( ! [B_x] :
( c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2)) )
| ? [B_x] :
( ~ c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_Ga_2)) ) )
| ~ c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,V_tsa_2) ) ),
inference(fof_nnf,[status(thm)],[fact_hoare__valids__def]) ).
fof(f_4_2,plain,
! [U_16,U_15,U_14] :
( ( c_Hoare__Mirabelle_Ohoare__valids(U_14,U_15,U_16)
| ? [U_13] :
( ? [U_12] :
( ~ c_Hoare__Mirabelle_Otriple__valid(U_14,U_13,U_12)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14)),U_12),U_16)) )
& ! [U_11] :
( c_Hoare__Mirabelle_Otriple__valid(U_14,U_13,U_11)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14)),U_11),U_15)) ) ) )
& ( ! [U_10] :
( ! [U_9] :
( c_Hoare__Mirabelle_Otriple__valid(U_14,U_10,U_9)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14)),U_9),U_16)) )
| ? [U_8] :
( ~ c_Hoare__Mirabelle_Otriple__valid(U_14,U_10,U_8)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_14)),U_8),U_15)) ) )
| ~ c_Hoare__Mirabelle_Ohoare__valids(U_14,U_15,U_16) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_22,U_20,U_18] :
( c_Hoare__Mirabelle_Ohoare__valids(U_18,U_20,U_22)
| ? [U_13] :
( ? [U_12] :
( ~ c_Hoare__Mirabelle_Otriple__valid(U_18,U_13,U_12)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_18)),U_12),U_22)) )
& ! [U_11] :
( c_Hoare__Mirabelle_Otriple__valid(U_18,U_13,U_11)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_18)),U_11),U_20)) ) ) )
& ! [U_21,U_19,U_17] :
( ! [U_10] :
( ! [U_9] :
( c_Hoare__Mirabelle_Otriple__valid(U_17,U_10,U_9)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_17)),U_9),U_21)) )
| ? [U_8] :
( ~ c_Hoare__Mirabelle_Otriple__valid(U_17,U_10,U_8)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_17)),U_8),U_19)) ) )
| ~ c_Hoare__Mirabelle_Ohoare__valids(U_17,U_19,U_21) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_22,U_20,U_18] :
( c_Hoare__Mirabelle_Ohoare__valids(U_18,U_20,U_22)
| ? [U_13] :
( ? [U_12] :
( ~ c_Hoare__Mirabelle_Otriple__valid(U_18,U_13,U_12)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_18)),U_12),U_22)) )
& ! [U_11] :
( c_Hoare__Mirabelle_Otriple__valid(U_18,U_13,U_11)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_18)),U_11),U_20)) ) ) )
& ! [U_21,U_19,U_17] :
( ! [U_10] :
( ! [U_9] :
( c_Hoare__Mirabelle_Otriple__valid(U_17,U_10,U_9)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_17)),U_9),U_21)) )
| ( ~ c_Hoare__Mirabelle_Otriple__valid(U_17,U_10,sK2(U_21,U_19,U_17,U_10))
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_17)),sK2(U_21,U_19,U_17,U_10)),U_19)) ) )
| ~ c_Hoare__Mirabelle_Ohoare__valids(U_17,U_19,U_21) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_8,sK2(U_21,U_19,U_17,U_10))],[f_4_3]) ).
fof(f_4_5,plain,
( ! [U_22,U_20,U_18] :
( c_Hoare__Mirabelle_Ohoare__valids(U_18,U_20,U_22)
| ( ? [U_12] :
( ~ c_Hoare__Mirabelle_Otriple__valid(U_18,sK3(U_22,U_20,U_18),U_12)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_18)),U_12),U_22)) )
& ! [U_11] :
( c_Hoare__Mirabelle_Otriple__valid(U_18,sK3(U_22,U_20,U_18),U_11)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_18)),U_11),U_20)) ) ) )
& ! [U_21,U_19,U_17] :
( ! [U_10] :
( ! [U_9] :
( c_Hoare__Mirabelle_Otriple__valid(U_17,U_10,U_9)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_17)),U_9),U_21)) )
| ( ~ c_Hoare__Mirabelle_Otriple__valid(U_17,U_10,sK2(U_21,U_19,U_17,U_10))
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_17)),sK2(U_21,U_19,U_17,U_10)),U_19)) ) )
| ~ c_Hoare__Mirabelle_Ohoare__valids(U_17,U_19,U_21) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_13,sK3(U_22,U_20,U_18))],[f_4_4]) ).
fof(f_4_6,plain,
( ! [U_22,U_20,U_18] :
( c_Hoare__Mirabelle_Ohoare__valids(U_18,U_20,U_22)
| ( ~ c_Hoare__Mirabelle_Otriple__valid(U_18,sK3(U_22,U_20,U_18),sK4(U_22,U_20,U_18))
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_18)),sK4(U_22,U_20,U_18)),U_22))
& ! [U_11] :
( c_Hoare__Mirabelle_Otriple__valid(U_18,sK3(U_22,U_20,U_18),U_11)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_18)),U_11),U_20)) ) ) )
& ! [U_21,U_19,U_17] :
( ! [U_10] :
( ! [U_9] :
( c_Hoare__Mirabelle_Otriple__valid(U_17,U_10,U_9)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_17)),U_9),U_21)) )
| ( ~ c_Hoare__Mirabelle_Otriple__valid(U_17,U_10,sK2(U_21,U_19,U_17,U_10))
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_17)),sK2(U_21,U_19,U_17,U_10)),U_19)) ) )
| ~ c_Hoare__Mirabelle_Ohoare__valids(U_17,U_19,U_21) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_12,sK4(U_22,U_20,U_18))],[f_4_5]) ).
cnf(f_4_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_17)),sK2(U_21,U_19,U_17,U_10)),U_19))
| c_Hoare__Mirabelle_Otriple__valid(U_17,U_10,U_9)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_17)),U_9),U_21))
| ~ c_Hoare__Mirabelle_Ohoare__valids(U_17,U_19,U_21) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_8,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(U_17,U_10,sK2(U_21,U_19,U_17,U_10))
| c_Hoare__Mirabelle_Otriple__valid(U_17,U_10,U_9)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_17)),U_9),U_21))
| ~ c_Hoare__Mirabelle_Ohoare__valids(U_17,U_19,U_21) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_9,plain,
( c_Hoare__Mirabelle_Otriple__valid(U_18,sK3(U_22,U_20,U_18),U_11)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_18)),U_11),U_20))
| c_Hoare__Mirabelle_Ohoare__valids(U_18,U_20,U_22) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_10,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_18)),sK4(U_22,U_20,U_18)),U_22))
| c_Hoare__Mirabelle_Ohoare__valids(U_18,U_20,U_22) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_11,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(U_18,sK3(U_22,U_20,U_18),sK4(U_22,U_20,U_18))
| c_Hoare__Mirabelle_Ohoare__valids(U_18,U_20,U_22) ),
inference(clausify,[status(thm)],[f_4_6]) ).
fof(f_5_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_5_2,plain,
! [U_28,U_27,U_26,U_25] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_26,U_25)),U_27),U_28))
| ? [U_24] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_25),hAPP(U_27,U_24)),hAPP(U_28,U_24))) )
& ( ! [U_23] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_25),hAPP(U_27,U_23)),hAPP(U_28,U_23)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_26,U_25)),U_27),U_28)) ) )
| ~ class_Orderings_Oord(U_25) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_28,U_27,U_26,U_25] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_26,U_25)),U_27),U_28))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_25),hAPP(U_27,sK5(U_28,U_27,U_26,U_25))),hAPP(U_28,sK5(U_28,U_27,U_26,U_25)))) )
& ( ! [U_23] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_25),hAPP(U_27,U_23)),hAPP(U_28,U_23)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_26,U_25)),U_27),U_28)) ) )
| ~ class_Orderings_Oord(U_25) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_24,sK5(U_28,U_27,U_26,U_25))],[f_5_2]) ).
cnf(f_5_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_25),hAPP(U_27,U_23)),hAPP(U_28,U_23)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_26,U_25)),U_27),U_28))
| ~ class_Orderings_Oord(U_25) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_26,U_25)),U_27),U_28))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_25),hAPP(U_27,sK5(U_28,U_27,U_26,U_25))),hAPP(U_28,sK5(U_28,U_27,U_26,U_25))))
| ~ class_Orderings_Oord(U_25) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_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_6_2,plain,
! [U_33,U_32,U_31,U_30,U_29] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_29),hAPP(U_31,U_33)),hAPP(U_32,U_33)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_30,U_29)),U_31),U_32))
| ~ class_Orderings_Oord(U_29) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_29),hAPP(U_31,U_33)),hAPP(U_32,U_33)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_30,U_29)),U_31),U_32))
| ~ class_Orderings_Oord(U_29) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_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_7_2,plain,
! [U_38,U_37,U_36,U_35,U_34] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_34),hAPP(U_36,U_38)),hAPP(U_37,U_38)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_35,U_34)),U_36),U_37))
| ~ class_Orderings_Oord(U_34) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_34),hAPP(U_36,U_38)),hAPP(U_37,U_38)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_35,U_34)),U_36),U_37))
| ~ class_Orderings_Oord(U_34) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_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_8_2,plain,
! [U_40,U_39] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_39,tc_HOL_Obool)),U_40),U_40)),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_39,tc_HOL_Obool)),U_40),U_40)),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_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_9_2,plain,
! [U_43,U_42,U_41] :
( ( U_41 = U_42
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_43,tc_HOL_Obool)),U_42),U_41))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_43,tc_HOL_Obool)),U_41),U_42)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_43,tc_HOL_Obool)),U_42),U_41))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_43,tc_HOL_Obool)),U_41),U_42)) )
| U_41 != U_42 ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_49,U_47,U_45] :
( U_45 = U_47
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_49,tc_HOL_Obool)),U_47),U_45))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_49,tc_HOL_Obool)),U_45),U_47)) )
& ! [U_48,U_46,U_44] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_48,tc_HOL_Obool)),U_46),U_44))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_48,tc_HOL_Obool)),U_44),U_46)) )
| U_44 != U_46 ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_48,tc_HOL_Obool)),U_44),U_46))
| U_44 != U_46 ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_48,tc_HOL_Obool)),U_46),U_44))
| U_44 != U_46 ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
( U_45 = U_47
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_49,tc_HOL_Obool)),U_47),U_45))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_49,tc_HOL_Obool)),U_45),U_47)) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [V_Q_2,T_b,V_x_2,V_P_2] :
( hBOOL(hAPP(V_Q_2,V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
| ~ hBOOL(hAPP(V_P_2,V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_rev__predicate1D]) ).
fof(f_10_2,plain,
! [U_53,U_52,U_51,U_50] :
( hBOOL(hAPP(U_53,U_51))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_52,tc_HOL_Obool)),U_50),U_53))
| ~ hBOOL(hAPP(U_50,U_51)) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( hBOOL(hAPP(U_53,U_51))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_52,tc_HOL_Obool)),U_50),U_53))
| ~ hBOOL(hAPP(U_50,U_51)) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_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_11_2,plain,
! [U_56,U_55,U_54] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_56,tc_HOL_Obool)),U_54),U_55))
| U_54 != U_55 ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_56,tc_HOL_Obool)),U_54),U_55))
| U_54 != U_55 ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_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_12_2,plain,
! [U_59,U_58,U_57] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_59,tc_HOL_Obool)),U_58),U_57))
| U_57 != U_58 ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_59,tc_HOL_Obool)),U_58),U_57))
| U_57 != U_58 ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [V_x_2,V_Q_2,V_P_2,T_b] :
( hBOOL(hAPP(V_Q_2,V_x_2))
| ~ hBOOL(hAPP(V_P_2,V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2)) ),
inference(fof_nnf,[status(thm)],[fact_predicate1D]) ).
fof(f_13_2,plain,
! [U_63,U_62,U_61,U_60] :
( hBOOL(hAPP(U_62,U_63))
| ~ hBOOL(hAPP(U_61,U_63))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_60,tc_HOL_Obool)),U_61),U_62)) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_63,U_62,U_61] :
( ! [U_60] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_60,tc_HOL_Obool)),U_61),U_62))
| hBOOL(hAPP(U_62,U_63))
| ~ hBOOL(hAPP(U_61,U_63)) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_60,tc_HOL_Obool)),U_61),U_62))
| hBOOL(hAPP(U_62,U_63))
| ~ hBOOL(hAPP(U_61,U_63)) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_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_14_2,plain,
! [U_66,U_65,U_64] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_64),U_66),U_65))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_64),U_65),U_66))
| ~ class_Orderings_Olinorder(U_64) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_64),U_66),U_65))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_64),U_65),U_66))
| ~ class_Orderings_Olinorder(U_64) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_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_15_2,plain,
! [U_70,U_69,U_68,U_67] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_67),U_70),U_69))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_67),U_70),U_68))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_67),U_68),U_69))
| ~ class_Orderings_Oorder(U_67) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_67),U_70),U_69))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_67),U_70),U_68))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_67),U_68),U_69))
| ~ class_Orderings_Oorder(U_67) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_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_16_2,plain,
! [U_73,U_72,U_71] :
( U_73 = U_72
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_71),U_73),U_72))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_71),U_72),U_73))
| ~ class_Orderings_Oorder(U_71) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( U_73 = U_72
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_71),U_73),U_72))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_71),U_72),U_73))
| ~ class_Orderings_Oorder(U_71) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_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_17_2,plain,
! [U_77,U_76,U_75,U_74] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_74),U_75),U_77))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_74),U_76),U_77))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_74),U_75),U_76))
| ~ class_Orderings_Opreorder(U_74) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_74),U_75),U_77))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_74),U_76),U_77))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_74),U_75),U_76))
| ~ class_Orderings_Opreorder(U_74) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_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_18_2,plain,
! [U_80,U_79,U_78] :
( U_79 = U_80
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_78),U_80),U_79))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_78),U_79),U_80))
| ~ class_Orderings_Oorder(U_78) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( U_79 = U_80
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_78),U_80),U_79))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_78),U_79),U_80))
| ~ class_Orderings_Oorder(U_78) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_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_19_2,plain,
! [U_84,U_83,U_82,U_81] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_81),U_84),U_83))
| U_82 != U_84
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_81),U_82),U_83))
| ~ class_Orderings_Oorder(U_81) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_81),U_84),U_83))
| U_82 != U_84
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_81),U_82),U_83))
| ~ class_Orderings_Oorder(U_81) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_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_20_2,plain,
! [U_88,U_87,U_86,U_85] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_85),U_86),U_88))
| U_87 != U_88
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_85),U_86),U_87))
| ~ class_Orderings_Oord(U_85) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_85),U_86),U_88))
| U_87 != U_88
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_85),U_86),U_87))
| ~ class_Orderings_Oord(U_85) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_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_21_2,plain,
! [U_92,U_91,U_90,U_89] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_89),U_92),U_90))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_89),U_92),U_91))
| U_90 != U_91
| ~ class_Orderings_Oorder(U_89) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_89),U_92),U_90))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_89),U_92),U_91))
| U_90 != U_91
| ~ class_Orderings_Oorder(U_89) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_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_22_2,plain,
! [U_96,U_95,U_94,U_93] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_93),U_94),U_96))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_93),U_95),U_96))
| U_94 != U_95
| ~ class_Orderings_Oord(U_93) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_93),U_94),U_96))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_93),U_95),U_96))
| U_94 != U_95
| ~ class_Orderings_Oord(U_93) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_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_23_2,plain,
! [U_99,U_98,U_97] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_97),U_99),U_98))
| U_99 != U_98 )
& ( U_99 = U_98
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_97),U_99),U_98)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_97),U_98),U_99))
| ~ class_Orderings_Oorder(U_97) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( U_99 = U_98
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_97),U_99),U_98))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_97),U_98),U_99))
| ~ class_Orderings_Oorder(U_97) ),
inference(clausify,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_97),U_99),U_98))
| U_99 != U_98
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_97),U_98),U_99))
| ~ class_Orderings_Oorder(U_97) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_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_24_2,plain,
! [U_102,U_101,U_100] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_100),U_101),U_102))
| U_101 != U_102
| ~ class_Orderings_Opreorder(U_100) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_100),U_101),U_102))
| U_101 != U_102
| ~ class_Orderings_Opreorder(U_100) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_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_25_2,plain,
! [U_105,U_104,U_103] :
( ( ( U_104 = U_105
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_103),U_105),U_104))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_103),U_104),U_105)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_103),U_105),U_104))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_103),U_104),U_105)) )
| U_104 != U_105 ) )
| ~ class_Orderings_Oorder(U_103) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_103),U_104),U_105))
| U_104 != U_105
| ~ class_Orderings_Oorder(U_103) ),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(f_25_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_103),U_105),U_104))
| U_104 != U_105
| ~ class_Orderings_Oorder(U_103) ),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(f_25_5,plain,
( U_104 = U_105
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_103),U_105),U_104))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_103),U_104),U_105))
| ~ class_Orderings_Oorder(U_103) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_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_26_2,plain,
! [U_108,U_107,U_106] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_106),U_108),U_107))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_106),U_107),U_108))
| ~ class_Orderings_Olinorder(U_106) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_106),U_108),U_107))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_106),U_107),U_108))
| ~ class_Orderings_Olinorder(U_106) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_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_27_2,plain,
! [U_111,U_110,U_109] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_111,tc_HOL_Obool)),U_110),U_109))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_111,tc_HOL_Obool)),U_109),U_110)) )
| U_109 != U_110 ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_111,tc_HOL_Obool)),U_109),U_110))
| U_109 != U_110 ),
inference(clausify,[status(thm)],[f_27_2]) ).
cnf(f_27_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_111,tc_HOL_Obool)),U_110),U_109))
| U_109 != U_110 ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_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_28_2,plain,
! [U_115,U_114,U_113,U_112] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_112,tc_HOL_Obool)),U_113),U_115))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_112,tc_HOL_Obool)),U_114),U_115))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_112,tc_HOL_Obool)),U_113),U_114)) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_112,tc_HOL_Obool)),U_113),U_115))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_112,tc_HOL_Obool)),U_114),U_115))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_112,tc_HOL_Obool)),U_113),U_114)) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_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_29_2,plain,
! [U_118,U_117,U_116] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_116,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_116,U_117)),c_Predicate_OPowp(U_116,U_118)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_116,tc_HOL_Obool)),U_117),U_118)) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_116,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_116,U_117)),c_Predicate_OPowp(U_116,U_118)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_116,tc_HOL_Obool)),U_117),U_118)) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [V_n_2,V_tsa_2,T_b] :
( ! [B_x] :
( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,B_x)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2)) )
| ? [B_x] :
( ~ c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),B_x)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_triples__valid__Suc]) ).
fof(f_30_2,plain,
! [U_123,U_122,U_121] :
( ! [U_120] :
( c_Hoare__Mirabelle_Otriple__valid(U_121,U_123,U_120)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_121)),U_120),U_122)) )
| ? [U_119] :
( ~ c_Hoare__Mirabelle_Otriple__valid(U_121,hAPP(c_Nat_OSuc,U_123),U_119)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_121)),U_119),U_122)) ) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_123,U_122,U_121] :
( ! [U_120] :
( c_Hoare__Mirabelle_Otriple__valid(U_121,U_123,U_120)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_121)),U_120),U_122)) )
| ( ~ c_Hoare__Mirabelle_Otriple__valid(U_121,hAPP(c_Nat_OSuc,U_123),sK6(U_123,U_122,U_121))
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_121)),sK6(U_123,U_122,U_121)),U_122)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_119,sK6(U_123,U_122,U_121))],[f_30_2]) ).
cnf(f_30_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_121)),sK6(U_123,U_122,U_121)),U_122))
| c_Hoare__Mirabelle_Otriple__valid(U_121,U_123,U_120)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_121)),U_120),U_122)) ),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_5,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(U_121,hAPP(c_Nat_OSuc,U_123),sK6(U_123,U_122,U_121))
| c_Hoare__Mirabelle_Otriple__valid(U_121,U_123,U_120)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_121)),U_120),U_122)) ),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [T_b,V_g_2,V_f_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
| ? [B_x] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x)))
| ~ class_Orderings_Oord(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__funI]) ).
fof(f_31_2,plain,
! [U_128,U_127,U_126,U_125] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_128,U_125)),U_126),U_127))
| ? [U_124] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_125),hAPP(U_126,U_124)),hAPP(U_127,U_124)))
| ~ class_Orderings_Oord(U_125) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_128,U_127,U_126,U_125] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_128,U_125)),U_126),U_127))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_125),hAPP(U_126,sK7(U_128,U_127,U_126,U_125))),hAPP(U_127,sK7(U_128,U_127,U_126,U_125))))
| ~ class_Orderings_Oord(U_125) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_124,sK7(U_128,U_127,U_126,U_125))],[f_31_2]) ).
cnf(f_31_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_128,U_125)),U_126),U_127))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_125),hAPP(U_126,sK7(U_128,U_127,U_126,U_125))),hAPP(U_127,sK7(U_128,U_127,U_126,U_125))))
| ~ class_Orderings_Oord(U_125) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) )
| ~ c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_strict__mono__less__eq]) ).
fof(f_32_2,plain,
! [U_133,U_132,U_131,U_130,U_129] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_129),hAPP(U_131,U_132)),hAPP(U_131,U_133)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_130),U_132),U_133)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_130),U_132),U_133))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_129),hAPP(U_131,U_132)),hAPP(U_131,U_133))) ) )
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_130,U_129,U_131)
| ~ class_Orderings_Olinorder(U_130)
| ~ class_Orderings_Oorder(U_129) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_130),U_132),U_133))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_129),hAPP(U_131,U_132)),hAPP(U_131,U_133)))
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_130,U_129,U_131)
| ~ class_Orderings_Olinorder(U_130)
| ~ class_Orderings_Oorder(U_129) ),
inference(clausify,[status(thm)],[f_32_2]) ).
cnf(f_32_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_129),hAPP(U_131,U_132)),hAPP(U_131,U_133)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_130),U_132),U_133))
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_130,U_129,U_131)
| ~ class_Orderings_Olinorder(U_130)
| ~ class_Orderings_Oorder(U_129) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [V_Ga_2,V_tsa_2,V_G_H_2,T_b] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_tsa_2) ),
inference(fof_nnf,[status(thm)],[fact_thin]) ).
fof(f_33_2,plain,
! [U_137,U_136,U_135,U_134] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_134,U_137,U_136)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_134),tc_HOL_Obool)),U_135),U_137))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_134,U_135,U_136) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(U_134,U_137,U_136)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_134),tc_HOL_Obool)),U_135),U_137))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_134,U_135,U_136) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
! [V_tsa_2,V_ts_H_2,V_Ga_2,T_b] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2) ),
inference(fof_nnf,[status(thm)],[fact_weaken]) ).
fof(f_34_2,plain,
! [U_141,U_140,U_139,U_138] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_138,U_139,U_141)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_138),tc_HOL_Obool)),U_141),U_140))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_138,U_139,U_140) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(U_138,U_139,U_141)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_138),tc_HOL_Obool)),U_141),U_140))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_138,U_139,U_140) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
! [V_Ga_2,V_tsa_2,T_b] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_Ga_2)) ),
inference(fof_nnf,[status(thm)],[fact_asm]) ).
fof(f_35_2,plain,
! [U_144,U_143,U_142] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_142,U_144,U_143)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_142),tc_HOL_Obool)),U_143),U_144)) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(U_142,U_144,U_143)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_142),tc_HOL_Obool)),U_143),U_144)) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_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_36_2,plain,
! [U_147,U_146,U_145] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_145,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_145),U_146)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_145),U_147)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_145),U_147),U_146)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_145),U_147),U_146))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_145,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_145),U_146)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_145),U_147))) ) )
| ~ class_Orderings_Olinorder(U_145) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_145),U_147),U_146))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_145,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_145),U_146)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_145),U_147)))
| ~ class_Orderings_Olinorder(U_145) ),
inference(clausify,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_145,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_145),U_146)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_145),U_147)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_145),U_147),U_146))
| ~ class_Orderings_Olinorder(U_145) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_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_37_2,plain,
! [U_150,U_149,U_148] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_148,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_148),U_149)),hAPP(c_SetInterval_Oord__class_OlessThan(U_148),U_150)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_148),U_149),U_150)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_148),U_149),U_150))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_148,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_148),U_149)),hAPP(c_SetInterval_Oord__class_OlessThan(U_148),U_150))) ) )
| ~ class_Orderings_Olinorder(U_148) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_148),U_149),U_150))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_148,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_148),U_149)),hAPP(c_SetInterval_Oord__class_OlessThan(U_148),U_150)))
| ~ class_Orderings_Olinorder(U_148) ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_148,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_148),U_149)),hAPP(c_SetInterval_Oord__class_OlessThan(U_148),U_150)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_148),U_149),U_150))
| ~ class_Orderings_Olinorder(U_148) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_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_38_2,plain,
! [U_153,U_152,U_151] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_151,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_151),U_152)),hAPP(c_SetInterval_Oord__class_OatLeast(U_151),U_153)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_151),U_153),U_152)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_151),U_153),U_152))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_151,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_151),U_152)),hAPP(c_SetInterval_Oord__class_OatLeast(U_151),U_153))) ) )
| ~ class_Orderings_Oorder(U_151) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_151),U_153),U_152))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_151,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_151),U_152)),hAPP(c_SetInterval_Oord__class_OatLeast(U_151),U_153)))
| ~ class_Orderings_Oorder(U_151) ),
inference(clausify,[status(thm)],[f_38_2]) ).
cnf(f_38_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_151,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_151),U_152)),hAPP(c_SetInterval_Oord__class_OatLeast(U_151),U_153)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_151),U_153),U_152))
| ~ class_Orderings_Oorder(U_151) ),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_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_39_2,plain,
! [U_156,U_155,U_154] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_154,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_154),U_155)),hAPP(c_SetInterval_Oord__class_OatMost(U_154),U_156)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_154),U_155),U_156)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_154),U_155),U_156))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_154,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_154),U_155)),hAPP(c_SetInterval_Oord__class_OatMost(U_154),U_156))) ) )
| ~ class_Orderings_Oorder(U_154) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_154),U_155),U_156))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_154,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_154),U_155)),hAPP(c_SetInterval_Oord__class_OatMost(U_154),U_156)))
| ~ class_Orderings_Oorder(U_154) ),
inference(clausify,[status(thm)],[f_39_2]) ).
cnf(f_39_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_154,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_154),U_155)),hAPP(c_SetInterval_Oord__class_OatMost(U_154),U_156)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_154),U_155),U_156))
| ~ class_Orderings_Oorder(U_154) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_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_40_2,plain,
! [U_161,U_160,U_159,U_158,U_157] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_157),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_158,U_157),U_159),U_161)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_158,U_157),U_160),U_161)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_158,tc_HOL_Obool)),U_159),U_160))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_157) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_157),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_158,U_157),U_159),U_161)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_158,U_157),U_160),U_161)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_158,tc_HOL_Obool)),U_159),U_160))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_157) ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
! [V_Ga_2,V_tsa_2,V_G_H_2,T_b] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_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_tsa_2) ),
inference(fof_nnf,[status(thm)],[fact_cut]) ).
fof(f_41_2,plain,
! [U_165,U_164,U_163,U_162] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_162,U_165,U_164)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_162,U_165,U_163)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_162,U_163,U_164) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(U_162,U_165,U_164)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_162,U_165,U_163)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_162,U_163,U_164) ),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_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_42_2,plain,
! [U_168,U_167,U_166] :
( ( ( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_166),U_167) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_166),U_168)
| U_167 != U_168 )
& ( U_167 = U_168
| hAPP(c_SetInterval_Oord__class_OgreaterThan(U_166),U_167) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_166),U_168) ) )
| ~ class_Orderings_Olinorder(U_166) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
( U_167 = U_168
| hAPP(c_SetInterval_Oord__class_OgreaterThan(U_166),U_167) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_166),U_168)
| ~ class_Orderings_Olinorder(U_166) ),
inference(clausify,[status(thm)],[f_42_2]) ).
cnf(f_42_4,plain,
( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_166),U_167) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_166),U_168)
| U_167 != U_168
| ~ class_Orderings_Olinorder(U_166) ),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_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_43_2,plain,
! [U_171,U_170,U_169] :
( ( ( hAPP(c_SetInterval_Oord__class_OlessThan(U_169),U_170) = hAPP(c_SetInterval_Oord__class_OlessThan(U_169),U_171)
| U_170 != U_171 )
& ( U_170 = U_171
| hAPP(c_SetInterval_Oord__class_OlessThan(U_169),U_170) != hAPP(c_SetInterval_Oord__class_OlessThan(U_169),U_171) ) )
| ~ class_Orderings_Olinorder(U_169) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
cnf(f_43_3,plain,
( U_170 = U_171
| hAPP(c_SetInterval_Oord__class_OlessThan(U_169),U_170) != hAPP(c_SetInterval_Oord__class_OlessThan(U_169),U_171)
| ~ class_Orderings_Olinorder(U_169) ),
inference(clausify,[status(thm)],[f_43_2]) ).
cnf(f_43_4,plain,
( hAPP(c_SetInterval_Oord__class_OlessThan(U_169),U_170) = hAPP(c_SetInterval_Oord__class_OlessThan(U_169),U_171)
| U_170 != U_171
| ~ class_Orderings_Olinorder(U_169) ),
inference(clausify,[status(thm)],[f_43_2]) ).
fof(f_44_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_44_2,plain,
! [U_174,U_173,U_172] :
( ( ( hAPP(c_SetInterval_Oord__class_OatLeast(U_172),U_173) = hAPP(c_SetInterval_Oord__class_OatLeast(U_172),U_174)
| U_173 != U_174 )
& ( U_173 = U_174
| hAPP(c_SetInterval_Oord__class_OatLeast(U_172),U_173) != hAPP(c_SetInterval_Oord__class_OatLeast(U_172),U_174) ) )
| ~ class_Orderings_Olinorder(U_172) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
( U_173 = U_174
| hAPP(c_SetInterval_Oord__class_OatLeast(U_172),U_173) != hAPP(c_SetInterval_Oord__class_OatLeast(U_172),U_174)
| ~ class_Orderings_Olinorder(U_172) ),
inference(clausify,[status(thm)],[f_44_2]) ).
cnf(f_44_4,plain,
( hAPP(c_SetInterval_Oord__class_OatLeast(U_172),U_173) = hAPP(c_SetInterval_Oord__class_OatLeast(U_172),U_174)
| U_173 != U_174
| ~ class_Orderings_Olinorder(U_172) ),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_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_45_2,plain,
! [U_177,U_176,U_175] :
( ( ( hAPP(c_SetInterval_Oord__class_OatMost(U_175),U_176) = hAPP(c_SetInterval_Oord__class_OatMost(U_175),U_177)
| U_176 != U_177 )
& ( U_176 = U_177
| hAPP(c_SetInterval_Oord__class_OatMost(U_175),U_176) != hAPP(c_SetInterval_Oord__class_OatMost(U_175),U_177) ) )
| ~ class_Orderings_Olinorder(U_175) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
( U_176 = U_177
| hAPP(c_SetInterval_Oord__class_OatMost(U_175),U_176) != hAPP(c_SetInterval_Oord__class_OatMost(U_175),U_177)
| ~ class_Orderings_Olinorder(U_175) ),
inference(clausify,[status(thm)],[f_45_2]) ).
cnf(f_45_4,plain,
( hAPP(c_SetInterval_Oord__class_OatMost(U_175),U_176) = hAPP(c_SetInterval_Oord__class_OatMost(U_175),U_177)
| U_176 != U_177
| ~ class_Orderings_Olinorder(U_175) ),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_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_46_2,plain,
! [U_178] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_178)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_178),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_178)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_178),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_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_47_2,plain,
! [U_179] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_179)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_179),
inference(variable_rename,[status(thm)],[f_47_1]) ).
cnf(f_47_3,plain,
hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_179)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_179),
inference(clausify,[status(thm)],[f_47_2]) ).
fof(f_48_1,plain,
! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
( ( ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) )
| ~ c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_strict__mono__eq]) ).
fof(f_48_2,plain,
! [U_184,U_183,U_182,U_181,U_180] :
( ( ( hAPP(U_182,U_183) = hAPP(U_182,U_184)
| U_183 != U_184 )
& ( U_183 = U_184
| hAPP(U_182,U_183) != hAPP(U_182,U_184) ) )
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_181,U_180,U_182)
| ~ class_Orderings_Olinorder(U_181)
| ~ class_Orderings_Oorder(U_180) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
cnf(f_48_3,plain,
( U_183 = U_184
| hAPP(U_182,U_183) != hAPP(U_182,U_184)
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_181,U_180,U_182)
| ~ class_Orderings_Olinorder(U_181)
| ~ class_Orderings_Oorder(U_180) ),
inference(clausify,[status(thm)],[f_48_2]) ).
cnf(f_48_4,plain,
( hAPP(U_182,U_183) = hAPP(U_182,U_184)
| U_183 != U_184
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_181,U_180,U_182)
| ~ class_Orderings_Olinorder(U_181)
| ~ class_Orderings_Oorder(U_180) ),
inference(clausify,[status(thm)],[f_48_2]) ).
fof(f_49_1,plain,
! [V_t,V_n,T_a] :
( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t)
| ~ c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t) ),
inference(fof_nnf,[status(thm)],[fact_triple__valid__Suc]) ).
fof(f_49_2,plain,
! [U_187,U_186,U_185] :
( c_Hoare__Mirabelle_Otriple__valid(U_185,U_186,U_187)
| ~ c_Hoare__Mirabelle_Otriple__valid(U_185,hAPP(c_Nat_OSuc,U_186),U_187) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
cnf(f_49_3,plain,
( c_Hoare__Mirabelle_Otriple__valid(U_185,U_186,U_187)
| ~ c_Hoare__Mirabelle_Otriple__valid(U_185,hAPP(c_Nat_OSuc,U_186),U_187) ),
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_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_50_2,plain,
! [U_188] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_188)),U_188)),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_188)),U_188)),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_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_51_2,plain,
! [U_190,U_189] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_189),U_190))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_190)),U_189)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_190)),U_189))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_189),U_190)) ) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
( ! [U_194,U_192] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_192),U_194))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_194)),U_192)) )
& ! [U_193,U_191] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_193)),U_191))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_191),U_193)) ) ),
inference(miniscope,[status(thm)],[f_51_2]) ).
cnf(f_51_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_193)),U_191))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_191),U_193)) ),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_192),U_194))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_194)),U_192)) ),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_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_52_2,plain,
! [U_196,U_195] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_195),hAPP(c_Nat_OSuc,U_196)))
| ( U_195 != hAPP(c_Nat_OSuc,U_196)
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_195),U_196)) ) )
& ( U_195 = hAPP(c_Nat_OSuc,U_196)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_195),U_196))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_195),hAPP(c_Nat_OSuc,U_196))) ) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
( ! [U_200,U_198] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_198),hAPP(c_Nat_OSuc,U_200)))
| ( U_198 != hAPP(c_Nat_OSuc,U_200)
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_198),U_200)) ) )
& ! [U_199,U_197] :
( U_197 = hAPP(c_Nat_OSuc,U_199)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_197),U_199))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_197),hAPP(c_Nat_OSuc,U_199))) ) ),
inference(miniscope,[status(thm)],[f_52_2]) ).
cnf(f_52_4,plain,
( U_197 = hAPP(c_Nat_OSuc,U_199)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_197),U_199))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_197),hAPP(c_Nat_OSuc,U_199))) ),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_198),U_200))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_198),hAPP(c_Nat_OSuc,U_200))) ),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_6,plain,
( U_198 != hAPP(c_Nat_OSuc,U_200)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_198),hAPP(c_Nat_OSuc,U_200))) ),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_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_53_2,plain,
! [U_202,U_201] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_201)),hAPP(c_Nat_OSuc,U_202)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_201),U_202)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_201),U_202))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_201)),hAPP(c_Nat_OSuc,U_202))) ) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
( ! [U_206,U_204] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_204)),hAPP(c_Nat_OSuc,U_206)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_204),U_206)) )
& ! [U_205,U_203] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_203),U_205))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_203)),hAPP(c_Nat_OSuc,U_205))) ) ),
inference(miniscope,[status(thm)],[f_53_2]) ).
cnf(f_53_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_203),U_205))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_203)),hAPP(c_Nat_OSuc,U_205))) ),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_204)),hAPP(c_Nat_OSuc,U_206)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_204),U_206)) ),
inference(clausify,[status(thm)],[f_53_3]) ).
fof(f_54_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_54_2,plain,
! [U_208,U_207] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_207),hAPP(c_Nat_OSuc,U_208)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_207),U_208)) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
cnf(f_54_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_207),hAPP(c_Nat_OSuc,U_208)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_207),U_208)) ),
inference(clausify,[status(thm)],[f_54_2]) ).
fof(f_55_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_55_2,plain,
! [U_210,U_209] :
( U_209 = hAPP(c_Nat_OSuc,U_210)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_209),U_210))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_209),hAPP(c_Nat_OSuc,U_210))) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
cnf(f_55_3,plain,
( U_209 = hAPP(c_Nat_OSuc,U_210)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_209),U_210))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_209),hAPP(c_Nat_OSuc,U_210))) ),
inference(clausify,[status(thm)],[f_55_2]) ).
fof(f_56_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_56_2,plain,
! [U_212,U_211] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_211),U_212))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_211)),U_212)) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
cnf(f_56_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_211),U_212))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_211)),U_212)) ),
inference(clausify,[status(thm)],[f_56_2]) ).
fof(f_57_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_57_2,plain,
! [U_214,U_213] :
( U_213 = U_214
| hAPP(c_Nat_OSuc,U_213) != hAPP(c_Nat_OSuc,U_214) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
cnf(f_57_3,plain,
( U_213 = U_214
| hAPP(c_Nat_OSuc,U_213) != hAPP(c_Nat_OSuc,U_214) ),
inference(clausify,[status(thm)],[f_57_2]) ).
fof(f_58_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_58_2,plain,
! [U_216,U_215] :
( ( hAPP(c_Nat_OSuc,U_215) = hAPP(c_Nat_OSuc,U_216)
| U_215 != U_216 )
& ( U_215 = U_216
| hAPP(c_Nat_OSuc,U_215) != hAPP(c_Nat_OSuc,U_216) ) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
( ! [U_220,U_218] :
( hAPP(c_Nat_OSuc,U_218) = hAPP(c_Nat_OSuc,U_220)
| U_218 != U_220 )
& ! [U_219,U_217] :
( U_217 = U_219
| hAPP(c_Nat_OSuc,U_217) != hAPP(c_Nat_OSuc,U_219) ) ),
inference(miniscope,[status(thm)],[f_58_2]) ).
cnf(f_58_4,plain,
( U_217 = U_219
| hAPP(c_Nat_OSuc,U_217) != hAPP(c_Nat_OSuc,U_219) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_5,plain,
( hAPP(c_Nat_OSuc,U_218) = hAPP(c_Nat_OSuc,U_220)
| U_218 != U_220 ),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_1,plain,
! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n,
inference(fof_nnf,[status(thm)],[fact_Suc__n__not__n]) ).
fof(f_59_2,plain,
! [U_221] : hAPP(c_Nat_OSuc,U_221) != U_221,
inference(variable_rename,[status(thm)],[f_59_1]) ).
cnf(f_59_3,plain,
hAPP(c_Nat_OSuc,U_221) != U_221,
inference(clausify,[status(thm)],[f_59_2]) ).
fof(f_60_1,plain,
! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n),
inference(fof_nnf,[status(thm)],[fact_n__not__Suc__n]) ).
fof(f_60_2,plain,
! [U_222] : U_222 != hAPP(c_Nat_OSuc,U_222),
inference(variable_rename,[status(thm)],[f_60_1]) ).
cnf(f_60_3,plain,
U_222 != hAPP(c_Nat_OSuc,U_222),
inference(clausify,[status(thm)],[f_60_2]) ).
fof(f_61_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_61_2,plain,
! [U_223] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_223),U_223)),
inference(variable_rename,[status(thm)],[f_61_1]) ).
cnf(f_61_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_223),U_223)),
inference(clausify,[status(thm)],[f_61_2]) ).
fof(f_62_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_62_2,plain,
! [U_225,U_224] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_225),U_224))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_224),U_225)) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
cnf(f_62_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_225),U_224))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_224),U_225)) ),
inference(clausify,[status(thm)],[f_62_2]) ).
fof(f_63_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_63_2,plain,
! [U_227,U_226] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_226),U_227))
| U_226 != U_227 ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
cnf(f_63_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_226),U_227))
| U_226 != U_227 ),
inference(clausify,[status(thm)],[f_63_2]) ).
fof(f_64_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_64_2,plain,
! [U_230,U_229,U_228] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_228),U_230))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_229),U_230))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_228),U_229)) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
cnf(f_64_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_228),U_230))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_229),U_230))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_228),U_229)) ),
inference(clausify,[status(thm)],[f_64_2]) ).
fof(f_65_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_65_2,plain,
! [U_232,U_231] :
( U_231 = U_232
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_232),U_231))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_231),U_232)) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
cnf(f_65_3,plain,
( U_231 = U_232
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_232),U_231))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_231),U_232)) ),
inference(clausify,[status(thm)],[f_65_2]) ).
fof(f_66_1,plain,
! [V_n_H_2,V_n_2,V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_n_2)),hAPP(V_f_2,V_n_H_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_n_H_2))
| ? [B_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n))))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lift__Suc__mono__le]) ).
fof(f_66_2,plain,
! [U_237,U_236,U_235,U_234] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_234),hAPP(U_235,U_236)),hAPP(U_235,U_237)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_236),U_237))
| ? [U_233] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_234),hAPP(U_235,U_233)),hAPP(U_235,hAPP(c_Nat_OSuc,U_233))))
| ~ class_Orderings_Oorder(U_234) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
! [U_237,U_236,U_235,U_234] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_234),hAPP(U_235,U_236)),hAPP(U_235,U_237)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_236),U_237))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_234),hAPP(U_235,sK8(U_237,U_236,U_235,U_234))),hAPP(U_235,hAPP(c_Nat_OSuc,sK8(U_237,U_236,U_235,U_234)))))
| ~ class_Orderings_Oorder(U_234) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_233,sK8(U_237,U_236,U_235,U_234))],[f_66_2]) ).
cnf(f_66_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_234),hAPP(U_235,U_236)),hAPP(U_235,U_237)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_236),U_237))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_234),hAPP(U_235,sK8(U_237,U_236,U_235,U_234))),hAPP(U_235,hAPP(c_Nat_OSuc,sK8(U_237,U_236,U_235,U_234)))))
| ~ class_Orderings_Oorder(U_234) ),
inference(clausify,[status(thm)],[f_66_3]) ).
fof(f_67_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_67_2,plain,
! [U_241,U_240,U_239,U_238] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(U_238,U_239,hAPP(c_Nat_OSuc,U_240),U_241) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_238,U_239,U_240,hAPP(U_239,U_241))
| ~ class_Rings_Osemiring__1(U_238) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
cnf(f_67_3,plain,
( c_Nat_Osemiring__1__class_Oof__nat__aux(U_238,U_239,hAPP(c_Nat_OSuc,U_240),U_241) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_238,U_239,U_240,hAPP(U_239,U_241))
| ~ class_Rings_Osemiring__1(U_238) ),
inference(clausify,[status(thm)],[f_67_2]) ).
fof(f_68_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_68_2,plain,
! [U_246,U_245,U_244,U_243,U_242] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_242),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_243,U_242),U_245),U_246)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_243,U_242),U_244),U_246)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_243,tc_HOL_Obool)),U_244),U_245))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_242) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
cnf(f_68_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_242),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_243,U_242),U_245),U_246)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_243,U_242),U_244),U_246)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_243,tc_HOL_Obool)),U_244),U_245))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_242) ),
inference(clausify,[status(thm)],[f_68_2]) ).
fof(f_69_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_69_2,plain,
! [U_249,U_248,U_247] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_247,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_247),U_248)),hAPP(c_Set_OPow(U_247),U_249)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_247,tc_HOL_Obool)),U_248),U_249)) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
cnf(f_69_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_247,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_247),U_248)),hAPP(c_Set_OPow(U_247),U_249)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_247,tc_HOL_Obool)),U_248),U_249)) ),
inference(clausify,[status(thm)],[f_69_2]) ).
fof(f_70_1,plain,
! [V_f_2,T_b] :
( ( ( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,T_b,V_f_2)
| ? [B_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n)))) )
& ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n))))
| ~ c_Orderings_Oorder__class_Omono(tc_Nat_Onat,T_b,V_f_2) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_mono__iff__le__Suc]) ).
fof(f_70_2,plain,
! [U_253,U_252] :
( ( ( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,U_252,U_253)
| ? [U_251] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_252),hAPP(U_253,U_251)),hAPP(U_253,hAPP(c_Nat_OSuc,U_251)))) )
& ( ! [U_250] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_252),hAPP(U_253,U_250)),hAPP(U_253,hAPP(c_Nat_OSuc,U_250))))
| ~ c_Orderings_Oorder__class_Omono(tc_Nat_Onat,U_252,U_253) ) )
| ~ class_Orderings_Oorder(U_252) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
! [U_253,U_252] :
( ( ( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,U_252,U_253)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_252),hAPP(U_253,sK9(U_253,U_252))),hAPP(U_253,hAPP(c_Nat_OSuc,sK9(U_253,U_252))))) )
& ( ! [U_250] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_252),hAPP(U_253,U_250)),hAPP(U_253,hAPP(c_Nat_OSuc,U_250))))
| ~ c_Orderings_Oorder__class_Omono(tc_Nat_Onat,U_252,U_253) ) )
| ~ class_Orderings_Oorder(U_252) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_251,sK9(U_253,U_252))],[f_70_2]) ).
cnf(f_70_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_252),hAPP(U_253,U_250)),hAPP(U_253,hAPP(c_Nat_OSuc,U_250))))
| ~ c_Orderings_Oorder__class_Omono(tc_Nat_Onat,U_252,U_253)
| ~ class_Orderings_Oorder(U_252) ),
inference(clausify,[status(thm)],[f_70_3]) ).
cnf(f_70_5,plain,
( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,U_252,U_253)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_252),hAPP(U_253,sK9(U_253,U_252))),hAPP(U_253,hAPP(c_Nat_OSuc,sK9(U_253,U_252)))))
| ~ class_Orderings_Oorder(U_252) ),
inference(clausify,[status(thm)],[f_70_3]) ).
fof(f_71_1,plain,
! [V_m_H,V_n] :
( ? [B_m] : V_m_H = hAPP(c_Nat_OSuc,B_m)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_m_H)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__le__D]) ).
fof(f_71_2,plain,
! [U_256,U_255] :
( ? [U_254] : U_256 = hAPP(c_Nat_OSuc,U_254)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_255)),U_256)) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
! [U_256] :
( ! [U_255] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_255)),U_256))
| ? [U_254] : U_256 = hAPP(c_Nat_OSuc,U_254) ),
inference(miniscope,[status(thm)],[f_71_2]) ).
fof(f_71_4,plain,
! [U_256] :
( ! [U_255] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_255)),U_256))
| U_256 = hAPP(c_Nat_OSuc,sK10(U_256)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_254,sK10(U_256))],[f_71_3]) ).
cnf(f_71_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_255)),U_256))
| U_256 = hAPP(c_Nat_OSuc,sK10(U_256)) ),
inference(clausify,[status(thm)],[f_71_4]) ).
fof(f_72_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_72_2,plain,
! [U_259,U_258,U_257] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_257,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_257,tc_HOL_Obool),U_259)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_257,tc_HOL_Obool),U_258)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_257,tc_HOL_Obool),tc_HOL_Obool)),U_258),U_259)) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
cnf(f_72_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_257,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_257,tc_HOL_Obool),U_259)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_257,tc_HOL_Obool),U_258)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_257,tc_HOL_Obool),tc_HOL_Obool)),U_258),U_259)) ),
inference(clausify,[status(thm)],[f_72_2]) ).
fof(f_73_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_73_2,plain,
! [U_263,U_262,U_261,U_260] : c_Nat_Onat_Onat__case(U_260,U_261,U_262,hAPP(c_Nat_OSuc,U_263)) = hAPP(U_262,U_263),
inference(variable_rename,[status(thm)],[f_73_1]) ).
cnf(f_73_3,plain,
c_Nat_Onat_Onat__case(U_260,U_261,U_262,hAPP(c_Nat_OSuc,U_263)) = hAPP(U_262,U_263),
inference(clausify,[status(thm)],[f_73_2]) ).
fof(f_74_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__subset__iff]) ).
fof(f_74_2,plain,
! [U_268,U_267,U_266,U_265,U_264] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_264),U_266),U_268))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_264),U_267),U_265)) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_264),U_266),U_265))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_264,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_264,U_265),U_266)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_264,U_267),U_268)))
| ~ class_Orderings_Olinorder(U_264) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
cnf(f_74_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_264),U_267),U_265))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_264),U_266),U_265))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_264,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_264,U_265),U_266)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_264,U_267),U_268)))
| ~ class_Orderings_Olinorder(U_264) ),
inference(clausify,[status(thm)],[f_74_2]) ).
cnf(f_74_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_264),U_266),U_268))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_264),U_266),U_265))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_264,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_264,U_265),U_266)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_264,U_267),U_268)))
| ~ class_Orderings_Olinorder(U_264) ),
inference(clausify,[status(thm)],[f_74_2]) ).
fof(f_75_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_75_2,plain,
! [U_270,U_269] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_269,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_269),U_270)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_269),U_270)
| ~ class_Orderings_Olinorder(U_269) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
cnf(f_75_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_269,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_269),U_270)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_269),U_270)
| ~ class_Orderings_Olinorder(U_269) ),
inference(clausify,[status(thm)],[f_75_2]) ).
fof(f_76_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_76_2,plain,
! [U_272,U_271] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_271,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_271),U_272)) = hAPP(c_SetInterval_Oord__class_OatMost(U_271),U_272)
| ~ class_Orderings_Olinorder(U_271) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
cnf(f_76_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_271,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_271),U_272)) = hAPP(c_SetInterval_Oord__class_OatMost(U_271),U_272)
| ~ class_Orderings_Olinorder(U_271) ),
inference(clausify,[status(thm)],[f_76_2]) ).
fof(f_77_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2))) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastatMost__subset__iff]) ).
fof(f_77_2,plain,
! [U_277,U_276,U_275,U_274,U_273] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_273,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_273,U_274,U_275)),c_SetInterval_Oord__class_OatLeastAtMost(U_273,U_276,U_277)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_273),U_275),U_277))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_273),U_276),U_274)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_273),U_274),U_275)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_273),U_275),U_277))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_273),U_276),U_274)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_273),U_274),U_275))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_273,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_273,U_274,U_275)),c_SetInterval_Oord__class_OatLeastAtMost(U_273,U_276,U_277))) ) )
| ~ class_Orderings_Oorder(U_273) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
cnf(f_77_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_273),U_276),U_274))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_273),U_274),U_275))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_273,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_273,U_274,U_275)),c_SetInterval_Oord__class_OatLeastAtMost(U_273,U_276,U_277)))
| ~ class_Orderings_Oorder(U_273) ),
inference(clausify,[status(thm)],[f_77_2]) ).
cnf(f_77_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_273),U_275),U_277))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_273),U_274),U_275))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_273,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_273,U_274,U_275)),c_SetInterval_Oord__class_OatLeastAtMost(U_273,U_276,U_277)))
| ~ class_Orderings_Oorder(U_273) ),
inference(clausify,[status(thm)],[f_77_2]) ).
cnf(f_77_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_273),U_274),U_275))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_273,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_273,U_274,U_275)),c_SetInterval_Oord__class_OatLeastAtMost(U_273,U_276,U_277)))
| ~ class_Orderings_Oorder(U_273) ),
inference(clausify,[status(thm)],[f_77_2]) ).
cnf(f_77_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_273),U_275),U_277))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_273),U_276),U_274))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_273,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_273,U_274,U_275)),c_SetInterval_Oord__class_OatLeastAtMost(U_273,U_276,U_277)))
| ~ class_Orderings_Oorder(U_273) ),
inference(clausify,[status(thm)],[f_77_2]) ).
fof(f_78_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_78_2,plain,
! [U_279,U_278] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_278,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_278,tc_HOL_Obool)),U_279)) = U_279,
inference(variable_rename,[status(thm)],[f_78_1]) ).
cnf(f_78_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_278,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_278,tc_HOL_Obool)),U_279)) = U_279,
inference(clausify,[status(thm)],[f_78_2]) ).
fof(f_79_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_79_2,plain,
! [U_282,U_281,U_280] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_280,tc_HOL_Obool)),U_281) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_280,tc_HOL_Obool)),U_282)
| U_281 != U_282 )
& ( U_281 = U_282
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_280,tc_HOL_Obool)),U_281) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_280,tc_HOL_Obool)),U_282) ) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
fof(f_79_3,plain,
( ! [U_288,U_286] :
( ! [U_284] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_284,tc_HOL_Obool)),U_286) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_284,tc_HOL_Obool)),U_288)
| U_286 != U_288 )
& ! [U_287,U_285] :
( ! [U_283] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_283,tc_HOL_Obool)),U_285) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_283,tc_HOL_Obool)),U_287)
| U_285 = U_287 ) ),
inference(miniscope,[status(thm)],[f_79_2]) ).
cnf(f_79_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_283,tc_HOL_Obool)),U_285) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_283,tc_HOL_Obool)),U_287)
| U_285 = U_287 ),
inference(clausify,[status(thm)],[f_79_3]) ).
cnf(f_79_5,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_284,tc_HOL_Obool)),U_286) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_284,tc_HOL_Obool)),U_288)
| U_286 != U_288 ),
inference(clausify,[status(thm)],[f_79_3]) ).
fof(f_80_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_80_2,plain,
! [U_290,U_289] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_289),hAPP(c_Nat_OSuc,U_290)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_289,U_290),
inference(variable_rename,[status(thm)],[f_80_1]) ).
cnf(f_80_3,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_289),hAPP(c_Nat_OSuc,U_290)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_289,U_290),
inference(clausify,[status(thm)],[f_80_2]) ).
fof(f_81_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_81_2,plain,
! [U_293,U_292,U_291] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_291,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_291,tc_HOL_Obool)),U_292)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_291,tc_HOL_Obool)),U_293)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_291,tc_HOL_Obool)),U_293),U_292)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_291,tc_HOL_Obool)),U_293),U_292))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_291,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_291,tc_HOL_Obool)),U_292)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_291,tc_HOL_Obool)),U_293))) ) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
fof(f_81_3,plain,
( ! [U_299,U_297,U_295] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_295,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_295,tc_HOL_Obool)),U_297)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_295,tc_HOL_Obool)),U_299)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_295,tc_HOL_Obool)),U_299),U_297)) )
& ! [U_298,U_296,U_294] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_294,tc_HOL_Obool)),U_298),U_296))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_294,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_294,tc_HOL_Obool)),U_296)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_294,tc_HOL_Obool)),U_298))) ) ),
inference(miniscope,[status(thm)],[f_81_2]) ).
cnf(f_81_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_294,tc_HOL_Obool)),U_298),U_296))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_294,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_294,tc_HOL_Obool)),U_296)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_294,tc_HOL_Obool)),U_298))) ),
inference(clausify,[status(thm)],[f_81_3]) ).
cnf(f_81_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_295,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_295,tc_HOL_Obool)),U_297)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_295,tc_HOL_Obool)),U_299)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_295,tc_HOL_Obool)),U_299),U_297)) ),
inference(clausify,[status(thm)],[f_81_3]) ).
fof(f_82_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_82_2,plain,
! [U_302,U_301,U_300] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_300,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_300,tc_HOL_Obool)),U_302)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_300,tc_HOL_Obool)),U_301)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_300,tc_HOL_Obool)),U_301),U_302)) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
cnf(f_82_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_300,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_300,tc_HOL_Obool)),U_302)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_300,tc_HOL_Obool)),U_301)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_300,tc_HOL_Obool)),U_301),U_302)) ),
inference(clausify,[status(thm)],[f_82_2]) ).
fof(f_83_1,plain,
! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
| ~ class_Orderings_Oorder(T_b)
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_monoD]) ).
fof(f_83_2,plain,
! [U_307,U_306,U_305,U_304,U_303] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_303),hAPP(U_305,U_306)),hAPP(U_305,U_307)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_304),U_306),U_307))
| ~ c_Orderings_Oorder__class_Omono(U_304,U_303,U_305)
| ~ class_Orderings_Oorder(U_304)
| ~ class_Orderings_Oorder(U_303) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
cnf(f_83_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_303),hAPP(U_305,U_306)),hAPP(U_305,U_307)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_304),U_306),U_307))
| ~ c_Orderings_Oorder__class_Omono(U_304,U_303,U_305)
| ~ class_Orderings_Oorder(U_304)
| ~ class_Orderings_Oorder(U_303) ),
inference(clausify,[status(thm)],[f_83_2]) ).
fof(f_84_1,plain,
c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),
inference(fof_nnf,[status(thm)],[fact_mono__Suc]) ).
cnf(f_84_2,plain,
c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),
inference(clausify,[status(thm)],[f_84_1]) ).
fof(f_85_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_85_2,plain,
! [U_312,U_311,U_310] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_310),U_311),c_Complete__Lattice_OInf__class_OInf(U_310,U_312)))
| ? [U_309] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_310),U_311),U_309))
& hBOOL(hAPP(hAPP(c_member(U_310),U_309),U_312)) ) )
& ( ! [U_308] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_310),U_311),U_308))
| ~ hBOOL(hAPP(hAPP(c_member(U_310),U_308),U_312)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_310),U_311),c_Complete__Lattice_OInf__class_OInf(U_310,U_312))) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_310) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
fof(f_85_3,plain,
! [U_312,U_311,U_310] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_310),U_311),c_Complete__Lattice_OInf__class_OInf(U_310,U_312)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_310),U_311),sK11(U_312,U_311,U_310)))
& hBOOL(hAPP(hAPP(c_member(U_310),sK11(U_312,U_311,U_310)),U_312)) ) )
& ( ! [U_308] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_310),U_311),U_308))
| ~ hBOOL(hAPP(hAPP(c_member(U_310),U_308),U_312)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_310),U_311),c_Complete__Lattice_OInf__class_OInf(U_310,U_312))) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_310) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_309,sK11(U_312,U_311,U_310))],[f_85_2]) ).
cnf(f_85_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_310),U_311),U_308))
| ~ hBOOL(hAPP(hAPP(c_member(U_310),U_308),U_312))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_310),U_311),c_Complete__Lattice_OInf__class_OInf(U_310,U_312)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_310) ),
inference(clausify,[status(thm)],[f_85_3]) ).
cnf(f_85_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_310),sK11(U_312,U_311,U_310)),U_312))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_310),U_311),c_Complete__Lattice_OInf__class_OInf(U_310,U_312)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_310) ),
inference(clausify,[status(thm)],[f_85_3]) ).
cnf(f_85_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_310),U_311),sK11(U_312,U_311,U_310)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_310),U_311),c_Complete__Lattice_OInf__class_OInf(U_310,U_312)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_310) ),
inference(clausify,[status(thm)],[f_85_3]) ).
fof(f_86_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_86_2,plain,
! [U_313] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_313,tc_HOL_Obool) = c_Set_OBall(U_313),
inference(variable_rename,[status(thm)],[f_86_1]) ).
cnf(f_86_3,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_313,tc_HOL_Obool) = c_Set_OBall(U_313),
inference(clausify,[status(thm)],[f_86_2]) ).
fof(f_87_1,plain,
! [V_f_2,T_b,T_c] :
( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
| ~ c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
| ~ class_Orderings_Oorder(T_b)
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_strict__mono__mono]) ).
fof(f_87_2,plain,
! [U_316,U_315,U_314] :
( c_Orderings_Oorder__class_Omono(U_315,U_314,U_316)
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_315,U_314,U_316)
| ~ class_Orderings_Oorder(U_315)
| ~ class_Orderings_Oorder(U_314) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
cnf(f_87_3,plain,
( c_Orderings_Oorder__class_Omono(U_315,U_314,U_316)
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_315,U_314,U_316)
| ~ class_Orderings_Oorder(U_315)
| ~ class_Orderings_Oorder(U_314) ),
inference(clausify,[status(thm)],[f_87_2]) ).
fof(f_88_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_88_2,plain,
! [U_318,U_317] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_317,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_317),U_318)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_317),U_318)
| ~ class_Orderings_Olinorder(U_317) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
cnf(f_88_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_317,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_317),U_318)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_317),U_318)
| ~ class_Orderings_Olinorder(U_317) ),
inference(clausify,[status(thm)],[f_88_2]) ).
fof(f_89_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_89_2,plain,
! [U_320,U_319] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_319,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_319),U_320)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_319),U_320)
| ~ class_Orderings_Olinorder(U_319) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
cnf(f_89_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_319,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_319),U_320)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_319),U_320)
| ~ class_Orderings_Olinorder(U_319) ),
inference(clausify,[status(thm)],[f_89_2]) ).
fof(f_90_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_90_2,plain,
! [U_324,U_323,U_322,U_321] :
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_322,U_321)),U_323),U_324) = hAPP(c_Groups_Ouminus__class_Ouminus(U_321),hAPP(U_323,U_324))
| ~ class_Groups_Ouminus(U_321) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
cnf(f_90_3,plain,
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_322,U_321)),U_323),U_324) = hAPP(c_Groups_Ouminus__class_Ouminus(U_321),hAPP(U_323,U_324))
| ~ class_Groups_Ouminus(U_321) ),
inference(clausify,[status(thm)],[f_90_2]) ).
fof(f_91_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_91_2,plain,
! [U_327,U_326,U_325] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_325),U_326),hAPP(c_Groups_Ouminus__class_Ouminus(U_325),U_327)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_325),U_327),hAPP(c_Groups_Ouminus__class_Ouminus(U_325),U_326))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_325),U_327),hAPP(c_Groups_Ouminus__class_Ouminus(U_325),U_326)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_325),U_326),hAPP(c_Groups_Ouminus__class_Ouminus(U_325),U_327))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_325) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
cnf(f_91_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_325),U_327),hAPP(c_Groups_Ouminus__class_Ouminus(U_325),U_326)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_325),U_326),hAPP(c_Groups_Ouminus__class_Ouminus(U_325),U_327)))
| ~ class_Groups_Oordered__ab__group__add(U_325) ),
inference(clausify,[status(thm)],[f_91_2]) ).
cnf(f_91_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_325),U_326),hAPP(c_Groups_Ouminus__class_Ouminus(U_325),U_327)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_325),U_327),hAPP(c_Groups_Ouminus__class_Ouminus(U_325),U_326)))
| ~ class_Groups_Oordered__ab__group__add(U_325) ),
inference(clausify,[status(thm)],[f_91_2]) ).
fof(f_92_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_92_2,plain,
! [U_330,U_329,U_328] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_328),hAPP(c_Groups_Ouminus__class_Ouminus(U_328),U_329)),U_330))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_328),hAPP(c_Groups_Ouminus__class_Ouminus(U_328),U_330)),U_329)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_328),hAPP(c_Groups_Ouminus__class_Ouminus(U_328),U_330)),U_329))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_328),hAPP(c_Groups_Ouminus__class_Ouminus(U_328),U_329)),U_330)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_328) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
cnf(f_92_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_328),hAPP(c_Groups_Ouminus__class_Ouminus(U_328),U_330)),U_329))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_328),hAPP(c_Groups_Ouminus__class_Ouminus(U_328),U_329)),U_330))
| ~ class_Groups_Oordered__ab__group__add(U_328) ),
inference(clausify,[status(thm)],[f_92_2]) ).
cnf(f_92_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_328),hAPP(c_Groups_Ouminus__class_Ouminus(U_328),U_329)),U_330))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_328),hAPP(c_Groups_Ouminus__class_Ouminus(U_328),U_330)),U_329))
| ~ class_Groups_Oordered__ab__group__add(U_328) ),
inference(clausify,[status(thm)],[f_92_2]) ).
fof(f_93_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_93_2,plain,
! [U_333,U_332,U_331] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_331),hAPP(c_Groups_Ouminus__class_Ouminus(U_331),U_332)),hAPP(c_Groups_Ouminus__class_Ouminus(U_331),U_333)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_331),U_333),U_332)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_331),U_333),U_332))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_331),hAPP(c_Groups_Ouminus__class_Ouminus(U_331),U_332)),hAPP(c_Groups_Ouminus__class_Ouminus(U_331),U_333))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_331) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
cnf(f_93_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_331),U_333),U_332))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_331),hAPP(c_Groups_Ouminus__class_Ouminus(U_331),U_332)),hAPP(c_Groups_Ouminus__class_Ouminus(U_331),U_333)))
| ~ class_Groups_Oordered__ab__group__add(U_331) ),
inference(clausify,[status(thm)],[f_93_2]) ).
cnf(f_93_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_331),hAPP(c_Groups_Ouminus__class_Ouminus(U_331),U_332)),hAPP(c_Groups_Ouminus__class_Ouminus(U_331),U_333)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_331),U_333),U_332))
| ~ class_Groups_Oordered__ab__group__add(U_331) ),
inference(clausify,[status(thm)],[f_93_2]) ).
fof(f_94_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_94_2,plain,
! [U_336,U_335,U_334] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_334),hAPP(c_Groups_Ouminus__class_Ouminus(U_334),U_335)),hAPP(c_Groups_Ouminus__class_Ouminus(U_334),U_336)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_334),U_336),U_335)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_334),U_336),U_335))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_334),hAPP(c_Groups_Ouminus__class_Ouminus(U_334),U_335)),hAPP(c_Groups_Ouminus__class_Ouminus(U_334),U_336))) ) )
| ~ class_Lattices_Oboolean__algebra(U_334) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
cnf(f_94_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_334),U_336),U_335))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_334),hAPP(c_Groups_Ouminus__class_Ouminus(U_334),U_335)),hAPP(c_Groups_Ouminus__class_Ouminus(U_334),U_336)))
| ~ class_Lattices_Oboolean__algebra(U_334) ),
inference(clausify,[status(thm)],[f_94_2]) ).
cnf(f_94_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_334),hAPP(c_Groups_Ouminus__class_Ouminus(U_334),U_335)),hAPP(c_Groups_Ouminus__class_Ouminus(U_334),U_336)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_334),U_336),U_335))
| ~ class_Lattices_Oboolean__algebra(U_334) ),
inference(clausify,[status(thm)],[f_94_2]) ).
fof(f_95_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__imp__neg__le]) ).
fof(f_95_2,plain,
! [U_339,U_338,U_337] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_337),hAPP(c_Groups_Ouminus__class_Ouminus(U_337),U_339)),hAPP(c_Groups_Ouminus__class_Ouminus(U_337),U_338)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_337),U_338),U_339))
| ~ class_Groups_Oordered__ab__group__add(U_337) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
cnf(f_95_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_337),hAPP(c_Groups_Ouminus__class_Ouminus(U_337),U_339)),hAPP(c_Groups_Ouminus__class_Ouminus(U_337),U_338)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_337),U_338),U_339))
| ~ class_Groups_Oordered__ab__group__add(U_337) ),
inference(clausify,[status(thm)],[f_95_2]) ).
fof(f_96_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_96_2,plain,
! [U_342,U_341,U_340] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_340),hAPP(c_Groups_Ouminus__class_Ouminus(U_340),U_342)),hAPP(c_Groups_Ouminus__class_Ouminus(U_340),U_341)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_340),U_341),U_342))
| ~ class_Lattices_Oboolean__algebra(U_340) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
cnf(f_96_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_340),hAPP(c_Groups_Ouminus__class_Ouminus(U_340),U_342)),hAPP(c_Groups_Ouminus__class_Ouminus(U_340),U_341)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_340),U_341),U_342))
| ~ class_Lattices_Oboolean__algebra(U_340) ),
inference(clausify,[status(thm)],[f_96_2]) ).
fof(f_97_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_97_2,plain,
! [U_345,U_344,U_343] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_343,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_343,U_344,U_345)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_343),U_345)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_343),U_344)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_343),U_344),U_345))
| ~ class_Orderings_Olinorder(U_343) ),
inference(variable_rename,[status(thm)],[f_97_1]) ).
cnf(f_97_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_343,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_343,U_344,U_345)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_343),U_345)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_343),U_344)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_343),U_344),U_345))
| ~ class_Orderings_Olinorder(U_343) ),
inference(clausify,[status(thm)],[f_97_2]) ).
fof(f_98_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_98_2,plain,
! [U_348,U_347,U_346] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_346,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_346),U_347)),c_SetInterval_Oord__class_OatLeastAtMost(U_346,U_347,U_348)) = hAPP(c_SetInterval_Oord__class_OatMost(U_346),U_348)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_346),U_347),U_348))
| ~ class_Orderings_Olinorder(U_346) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
cnf(f_98_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_346,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_346),U_347)),c_SetInterval_Oord__class_OatLeastAtMost(U_346,U_347,U_348)) = hAPP(c_SetInterval_Oord__class_OatMost(U_346),U_348)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_346),U_347),U_348))
| ~ class_Orderings_Olinorder(U_346) ),
inference(clausify,[status(thm)],[f_98_2]) ).
fof(f_99_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_99_2,plain,
! [U_351,U_350,U_349] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_349),U_350) = hAPP(c_Groups_Ouminus__class_Ouminus(U_349),U_351)
| U_350 != U_351 )
& ( U_350 = U_351
| hAPP(c_Groups_Ouminus__class_Ouminus(U_349),U_350) != hAPP(c_Groups_Ouminus__class_Ouminus(U_349),U_351) ) )
| ~ class_Lattices_Oboolean__algebra(U_349) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
cnf(f_99_3,plain,
( U_350 = U_351
| hAPP(c_Groups_Ouminus__class_Ouminus(U_349),U_350) != hAPP(c_Groups_Ouminus__class_Ouminus(U_349),U_351)
| ~ class_Lattices_Oboolean__algebra(U_349) ),
inference(clausify,[status(thm)],[f_99_2]) ).
cnf(f_99_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_349),U_350) = hAPP(c_Groups_Ouminus__class_Ouminus(U_349),U_351)
| U_350 != U_351
| ~ class_Lattices_Oboolean__algebra(U_349) ),
inference(clausify,[status(thm)],[f_99_2]) ).
fof(f_100_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_100_2,plain,
! [U_354,U_353,U_352] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_352),U_353) = hAPP(c_Groups_Ouminus__class_Ouminus(U_352),U_354)
| U_353 != U_354 )
& ( U_353 = U_354
| hAPP(c_Groups_Ouminus__class_Ouminus(U_352),U_353) != hAPP(c_Groups_Ouminus__class_Ouminus(U_352),U_354) ) )
| ~ class_Groups_Ogroup__add(U_352) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
cnf(f_100_3,plain,
( U_353 = U_354
| hAPP(c_Groups_Ouminus__class_Ouminus(U_352),U_353) != hAPP(c_Groups_Ouminus__class_Ouminus(U_352),U_354)
| ~ class_Groups_Ogroup__add(U_352) ),
inference(clausify,[status(thm)],[f_100_2]) ).
cnf(f_100_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_352),U_353) = hAPP(c_Groups_Ouminus__class_Ouminus(U_352),U_354)
| U_353 != U_354
| ~ class_Groups_Ogroup__add(U_352) ),
inference(clausify,[status(thm)],[f_100_2]) ).
fof(f_101_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_101_2,plain,
! [U_357,U_356,U_355] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_355),U_356) = U_357
| hAPP(c_Groups_Ouminus__class_Ouminus(U_355),U_357) != U_356 )
& ( hAPP(c_Groups_Ouminus__class_Ouminus(U_355),U_357) = U_356
| hAPP(c_Groups_Ouminus__class_Ouminus(U_355),U_356) != U_357 ) )
| ~ class_Groups_Ogroup__add(U_355) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
cnf(f_101_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_355),U_357) = U_356
| hAPP(c_Groups_Ouminus__class_Ouminus(U_355),U_356) != U_357
| ~ class_Groups_Ogroup__add(U_355) ),
inference(clausify,[status(thm)],[f_101_2]) ).
cnf(f_101_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_355),U_356) = U_357
| hAPP(c_Groups_Ouminus__class_Ouminus(U_355),U_357) != U_356
| ~ class_Groups_Ogroup__add(U_355) ),
inference(clausify,[status(thm)],[f_101_2]) ).
fof(f_102_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_102_2,plain,
! [U_361,U_360,U_359,U_358] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_361,tc_HOL_Obool)),U_360),U_358),U_359))
| ( ~ hBOOL(hAPP(U_360,U_359))
& ~ hBOOL(hAPP(U_358,U_359)) ) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
cnf(f_102_3,plain,
( ~ hBOOL(hAPP(U_358,U_359))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_361,tc_HOL_Obool)),U_360),U_358),U_359)) ),
inference(clausify,[status(thm)],[f_102_2]) ).
cnf(f_102_4,plain,
( ~ hBOOL(hAPP(U_360,U_359))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_361,tc_HOL_Obool)),U_360),U_358),U_359)) ),
inference(clausify,[status(thm)],[f_102_2]) ).
fof(f_103_1,plain,
! [V_x_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(V_B_2,V_x_2))
| hBOOL(hAPP(V_A_2,V_x_2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_sup1E]) ).
fof(f_103_2,plain,
! [U_365,U_364,U_363,U_362] :
( hBOOL(hAPP(U_364,U_365))
| hBOOL(hAPP(U_363,U_365))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_362,tc_HOL_Obool)),U_363),U_364),U_365)) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
fof(f_103_3,plain,
! [U_365,U_364,U_363] :
( ! [U_362] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_362,tc_HOL_Obool)),U_363),U_364),U_365))
| hBOOL(hAPP(U_364,U_365))
| hBOOL(hAPP(U_363,U_365)) ),
inference(miniscope,[status(thm)],[f_103_2]) ).
cnf(f_103_4,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_362,tc_HOL_Obool)),U_363),U_364),U_365))
| hBOOL(hAPP(U_364,U_365))
| hBOOL(hAPP(U_363,U_365)) ),
inference(clausify,[status(thm)],[f_103_3]) ).
fof(f_104_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_104_2,plain,
! [U_367,U_366] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_366),U_367),U_367) = U_367
| ~ class_Lattices_Osemilattice__sup(U_366) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
cnf(f_104_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_366),U_367),U_367) = U_367
| ~ class_Lattices_Osemilattice__sup(U_366) ),
inference(clausify,[status(thm)],[f_104_2]) ).
fof(f_105_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_105_2,plain,
! [U_369,U_368] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_368),U_369),U_369) = U_369
| ~ class_Lattices_Osemilattice__sup(U_368) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
cnf(f_105_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_368),U_369),U_369) = U_369
| ~ class_Lattices_Osemilattice__sup(U_368) ),
inference(clausify,[status(thm)],[f_105_2]) ).
fof(f_106_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_106_2,plain,
! [U_372,U_371,U_370] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_370),U_371),U_372) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_370),U_372),U_371)
| ~ class_Lattices_Osemilattice__sup(U_370) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
cnf(f_106_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_370),U_371),U_372) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_370),U_372),U_371)
| ~ class_Lattices_Osemilattice__sup(U_370) ),
inference(clausify,[status(thm)],[f_106_2]) ).
fof(f_107_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_107_2,plain,
! [U_375,U_374,U_373] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_373),U_374),U_375) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_373),U_375),U_374)
| ~ class_Lattices_Olattice(U_373) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
cnf(f_107_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_373),U_374),U_375) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_373),U_375),U_374)
| ~ class_Lattices_Olattice(U_373) ),
inference(clausify,[status(thm)],[f_107_2]) ).
fof(f_108_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_108_2,plain,
! [U_378,U_377,U_376] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_376),U_377),U_378) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_376),U_378),U_377)
| ~ class_Lattices_Osemilattice__sup(U_376) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
cnf(f_108_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_376),U_377),U_378) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_376),U_378),U_377)
| ~ class_Lattices_Osemilattice__sup(U_376) ),
inference(clausify,[status(thm)],[f_108_2]) ).
fof(f_109_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_109_2,plain,
! [U_381,U_380,U_379] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_379),U_380),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_379),U_380),U_381)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_379),U_380),U_381)
| ~ class_Lattices_Osemilattice__sup(U_379) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
cnf(f_109_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_379),U_380),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_379),U_380),U_381)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_379),U_380),U_381)
| ~ class_Lattices_Osemilattice__sup(U_379) ),
inference(clausify,[status(thm)],[f_109_2]) ).
fof(f_110_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_110_2,plain,
! [U_384,U_383,U_382] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_382),U_383),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_382),U_383),U_384)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_382),U_383),U_384)
| ~ class_Lattices_Olattice(U_382) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
cnf(f_110_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_382),U_383),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_382),U_383),U_384)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_382),U_383),U_384)
| ~ class_Lattices_Olattice(U_382) ),
inference(clausify,[status(thm)],[f_110_2]) ).
fof(f_111_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_111_2,plain,
! [U_387,U_386,U_385] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_385),U_386),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_385),U_386),U_387)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_385),U_386),U_387)
| ~ class_Lattices_Osemilattice__sup(U_385) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
cnf(f_111_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_385),U_386),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_385),U_386),U_387)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_385),U_386),U_387)
| ~ class_Lattices_Osemilattice__sup(U_385) ),
inference(clausify,[status(thm)],[f_111_2]) ).
fof(f_112_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_112_2,plain,
! [U_391,U_390,U_389,U_388] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_388),U_389),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_388),U_390),U_391)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_388),U_390),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_388),U_389),U_391))
| ~ class_Lattices_Osemilattice__sup(U_388) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
cnf(f_112_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_388),U_389),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_388),U_390),U_391)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_388),U_390),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_388),U_389),U_391))
| ~ class_Lattices_Osemilattice__sup(U_388) ),
inference(clausify,[status(thm)],[f_112_2]) ).
fof(f_113_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_113_2,plain,
! [U_395,U_394,U_393,U_392] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_392),U_393),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_392),U_394),U_395)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_392),U_394),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_392),U_393),U_395))
| ~ class_Lattices_Olattice(U_392) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
cnf(f_113_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_392),U_393),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_392),U_394),U_395)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_392),U_394),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_392),U_393),U_395))
| ~ class_Lattices_Olattice(U_392) ),
inference(clausify,[status(thm)],[f_113_2]) ).
fof(f_114_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_114_2,plain,
! [U_399,U_398,U_397,U_396] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_396),U_397),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_396),U_398),U_399)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_396),U_398),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_396),U_397),U_399))
| ~ class_Lattices_Osemilattice__sup(U_396) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
cnf(f_114_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_396),U_397),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_396),U_398),U_399)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_396),U_398),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_396),U_397),U_399))
| ~ class_Lattices_Osemilattice__sup(U_396) ),
inference(clausify,[status(thm)],[f_114_2]) ).
fof(f_115_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_115_2,plain,
! [U_403,U_402,U_401,U_400] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_400),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_400),U_401),U_402)),U_403) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_400),U_401),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_400),U_402),U_403))
| ~ class_Lattices_Osemilattice__sup(U_400) ),
inference(variable_rename,[status(thm)],[f_115_1]) ).
cnf(f_115_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_400),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_400),U_401),U_402)),U_403) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_400),U_401),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_400),U_402),U_403))
| ~ class_Lattices_Osemilattice__sup(U_400) ),
inference(clausify,[status(thm)],[f_115_2]) ).
fof(f_116_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_116_2,plain,
! [U_407,U_406,U_405,U_404] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_404),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_404),U_405),U_406)),U_407) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_404),U_405),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_404),U_406),U_407))
| ~ class_Lattices_Olattice(U_404) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
cnf(f_116_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_404),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_404),U_405),U_406)),U_407) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_404),U_405),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_404),U_406),U_407))
| ~ class_Lattices_Olattice(U_404) ),
inference(clausify,[status(thm)],[f_116_2]) ).
fof(f_117_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_117_2,plain,
! [U_411,U_410,U_409,U_408] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_408),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_408),U_409),U_410)),U_411) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_408),U_409),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_408),U_410),U_411))
| ~ class_Lattices_Osemilattice__sup(U_408) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
cnf(f_117_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_408),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_408),U_409),U_410)),U_411) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_408),U_409),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_408),U_410),U_411))
| ~ class_Lattices_Osemilattice__sup(U_408) ),
inference(clausify,[status(thm)],[f_117_2]) ).
fof(f_118_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_118_2,plain,
! [U_416,U_415,U_414,U_413,U_412] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_413,U_412)),U_414),U_415),U_416) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_412),hAPP(U_414,U_416)),hAPP(U_415,U_416))
| ~ class_Lattices_Olattice(U_412) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
cnf(f_118_3,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_413,U_412)),U_414),U_415),U_416) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_412),hAPP(U_414,U_416)),hAPP(U_415,U_416))
| ~ class_Lattices_Olattice(U_412) ),
inference(clausify,[status(thm)],[f_118_2]) ).
fof(f_119_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_119_2,plain,
! [U_420,U_419,U_418,U_417] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_419,tc_HOL_Obool)),U_420),U_417),U_418))
| ~ hBOOL(hAPP(U_417,U_418)) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
cnf(f_119_3,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_419,tc_HOL_Obool)),U_420),U_417),U_418))
| ~ hBOOL(hAPP(U_417,U_418)) ),
inference(clausify,[status(thm)],[f_119_2]) ).
fof(f_120_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_120_2,plain,
! [U_424,U_423,U_422,U_421] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_423,tc_HOL_Obool)),U_421),U_424),U_422))
| ~ hBOOL(hAPP(U_421,U_422)) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
cnf(f_120_3,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_423,tc_HOL_Obool)),U_421),U_424),U_422))
| ~ hBOOL(hAPP(U_421,U_422)) ),
inference(clausify,[status(thm)],[f_120_2]) ).
fof(f_121_1,plain,
! [V_P_2,V_B_2,V_A_2,T_b] :
( ( ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ( ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
& ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
inference(fof_nnf,[status(thm)],[fact_ball__Un]) ).
fof(f_121_2,plain,
! [U_434,U_433,U_432,U_431] :
( ( ! [U_430] :
( hBOOL(hAPP(U_434,U_430))
| ~ hBOOL(hAPP(hAPP(c_member(U_431),U_430),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_431,tc_HOL_Obool)),U_432),U_433))) )
| ? [U_429] :
( ~ hBOOL(hAPP(U_434,U_429))
& hBOOL(hAPP(hAPP(c_member(U_431),U_429),U_433)) )
| ? [U_428] :
( ~ hBOOL(hAPP(U_434,U_428))
& hBOOL(hAPP(hAPP(c_member(U_431),U_428),U_432)) ) )
& ( ( ! [U_427] :
( hBOOL(hAPP(U_434,U_427))
| ~ hBOOL(hAPP(hAPP(c_member(U_431),U_427),U_433)) )
& ! [U_426] :
( hBOOL(hAPP(U_434,U_426))
| ~ hBOOL(hAPP(hAPP(c_member(U_431),U_426),U_432)) ) )
| ? [U_425] :
( ~ hBOOL(hAPP(U_434,U_425))
& hBOOL(hAPP(hAPP(c_member(U_431),U_425),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_431,tc_HOL_Obool)),U_432),U_433))) ) ) ),
inference(variable_rename,[status(thm)],[f_121_1]) ).
fof(f_121_3,plain,
( ! [U_442,U_440,U_438,U_436] :
( ! [U_430] :
( hBOOL(hAPP(U_442,U_430))
| ~ hBOOL(hAPP(hAPP(c_member(U_436),U_430),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_436,tc_HOL_Obool)),U_438),U_440))) )
| ? [U_429] :
( ~ hBOOL(hAPP(U_442,U_429))
& hBOOL(hAPP(hAPP(c_member(U_436),U_429),U_440)) )
| ? [U_428] :
( ~ hBOOL(hAPP(U_442,U_428))
& hBOOL(hAPP(hAPP(c_member(U_436),U_428),U_438)) ) )
& ! [U_441,U_439,U_437,U_435] :
( ( ! [U_427] :
( hBOOL(hAPP(U_441,U_427))
| ~ hBOOL(hAPP(hAPP(c_member(U_435),U_427),U_439)) )
& ! [U_426] :
( hBOOL(hAPP(U_441,U_426))
| ~ hBOOL(hAPP(hAPP(c_member(U_435),U_426),U_437)) ) )
| ? [U_425] :
( ~ hBOOL(hAPP(U_441,U_425))
& hBOOL(hAPP(hAPP(c_member(U_435),U_425),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_435,tc_HOL_Obool)),U_437),U_439))) ) ) ),
inference(miniscope,[status(thm)],[f_121_2]) ).
fof(f_121_4,plain,
( ! [U_442,U_440,U_438,U_436] :
( ! [U_430] :
( hBOOL(hAPP(U_442,U_430))
| ~ hBOOL(hAPP(hAPP(c_member(U_436),U_430),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_436,tc_HOL_Obool)),U_438),U_440))) )
| ? [U_429] :
( ~ hBOOL(hAPP(U_442,U_429))
& hBOOL(hAPP(hAPP(c_member(U_436),U_429),U_440)) )
| ? [U_428] :
( ~ hBOOL(hAPP(U_442,U_428))
& hBOOL(hAPP(hAPP(c_member(U_436),U_428),U_438)) ) )
& ! [U_441,U_439,U_437,U_435] :
( ( ! [U_427] :
( hBOOL(hAPP(U_441,U_427))
| ~ hBOOL(hAPP(hAPP(c_member(U_435),U_427),U_439)) )
& ! [U_426] :
( hBOOL(hAPP(U_441,U_426))
| ~ hBOOL(hAPP(hAPP(c_member(U_435),U_426),U_437)) ) )
| ( ~ hBOOL(hAPP(U_441,sK12(U_441,U_439,U_437,U_435)))
& hBOOL(hAPP(hAPP(c_member(U_435),sK12(U_441,U_439,U_437,U_435)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_435,tc_HOL_Obool)),U_437),U_439))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_425,sK12(U_441,U_439,U_437,U_435))],[f_121_3]) ).
fof(f_121_5,plain,
( ! [U_442,U_440,U_438,U_436] :
( ! [U_430] :
( hBOOL(hAPP(U_442,U_430))
| ~ hBOOL(hAPP(hAPP(c_member(U_436),U_430),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_436,tc_HOL_Obool)),U_438),U_440))) )
| ? [U_429] :
( ~ hBOOL(hAPP(U_442,U_429))
& hBOOL(hAPP(hAPP(c_member(U_436),U_429),U_440)) )
| ( ~ hBOOL(hAPP(U_442,sK13(U_442,U_440,U_438,U_436)))
& hBOOL(hAPP(hAPP(c_member(U_436),sK13(U_442,U_440,U_438,U_436)),U_438)) ) )
& ! [U_441,U_439,U_437,U_435] :
( ( ! [U_427] :
( hBOOL(hAPP(U_441,U_427))
| ~ hBOOL(hAPP(hAPP(c_member(U_435),U_427),U_439)) )
& ! [U_426] :
( hBOOL(hAPP(U_441,U_426))
| ~ hBOOL(hAPP(hAPP(c_member(U_435),U_426),U_437)) ) )
| ( ~ hBOOL(hAPP(U_441,sK12(U_441,U_439,U_437,U_435)))
& hBOOL(hAPP(hAPP(c_member(U_435),sK12(U_441,U_439,U_437,U_435)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_435,tc_HOL_Obool)),U_437),U_439))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_428,sK13(U_442,U_440,U_438,U_436))],[f_121_4]) ).
fof(f_121_6,plain,
( ! [U_442,U_440,U_438,U_436] :
( ! [U_430] :
( hBOOL(hAPP(U_442,U_430))
| ~ hBOOL(hAPP(hAPP(c_member(U_436),U_430),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_436,tc_HOL_Obool)),U_438),U_440))) )
| ( ~ hBOOL(hAPP(U_442,sK14(U_442,U_440,U_438,U_436)))
& hBOOL(hAPP(hAPP(c_member(U_436),sK14(U_442,U_440,U_438,U_436)),U_440)) )
| ( ~ hBOOL(hAPP(U_442,sK13(U_442,U_440,U_438,U_436)))
& hBOOL(hAPP(hAPP(c_member(U_436),sK13(U_442,U_440,U_438,U_436)),U_438)) ) )
& ! [U_441,U_439,U_437,U_435] :
( ( ! [U_427] :
( hBOOL(hAPP(U_441,U_427))
| ~ hBOOL(hAPP(hAPP(c_member(U_435),U_427),U_439)) )
& ! [U_426] :
( hBOOL(hAPP(U_441,U_426))
| ~ hBOOL(hAPP(hAPP(c_member(U_435),U_426),U_437)) ) )
| ( ~ hBOOL(hAPP(U_441,sK12(U_441,U_439,U_437,U_435)))
& hBOOL(hAPP(hAPP(c_member(U_435),sK12(U_441,U_439,U_437,U_435)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_435,tc_HOL_Obool)),U_437),U_439))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_429,sK14(U_442,U_440,U_438,U_436))],[f_121_5]) ).
cnf(f_121_7,plain,
( hBOOL(hAPP(U_441,U_426))
| ~ hBOOL(hAPP(hAPP(c_member(U_435),U_426),U_437))
| hBOOL(hAPP(hAPP(c_member(U_435),sK12(U_441,U_439,U_437,U_435)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_435,tc_HOL_Obool)),U_437),U_439))) ),
inference(clausify,[status(thm)],[f_121_6]) ).
cnf(f_121_8,plain,
( hBOOL(hAPP(U_441,U_427))
| ~ hBOOL(hAPP(hAPP(c_member(U_435),U_427),U_439))
| hBOOL(hAPP(hAPP(c_member(U_435),sK12(U_441,U_439,U_437,U_435)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_435,tc_HOL_Obool)),U_437),U_439))) ),
inference(clausify,[status(thm)],[f_121_6]) ).
cnf(f_121_9,plain,
( hBOOL(hAPP(U_441,U_426))
| ~ hBOOL(hAPP(hAPP(c_member(U_435),U_426),U_437))
| ~ hBOOL(hAPP(U_441,sK12(U_441,U_439,U_437,U_435))) ),
inference(clausify,[status(thm)],[f_121_6]) ).
cnf(f_121_10,plain,
( hBOOL(hAPP(U_441,U_427))
| ~ hBOOL(hAPP(hAPP(c_member(U_435),U_427),U_439))
| ~ hBOOL(hAPP(U_441,sK12(U_441,U_439,U_437,U_435))) ),
inference(clausify,[status(thm)],[f_121_6]) ).
cnf(f_121_11,plain,
( hBOOL(hAPP(hAPP(c_member(U_436),sK14(U_442,U_440,U_438,U_436)),U_440))
| hBOOL(hAPP(hAPP(c_member(U_436),sK13(U_442,U_440,U_438,U_436)),U_438))
| hBOOL(hAPP(U_442,U_430))
| ~ hBOOL(hAPP(hAPP(c_member(U_436),U_430),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_436,tc_HOL_Obool)),U_438),U_440))) ),
inference(clausify,[status(thm)],[f_121_6]) ).
cnf(f_121_12,plain,
( ~ hBOOL(hAPP(U_442,sK14(U_442,U_440,U_438,U_436)))
| hBOOL(hAPP(hAPP(c_member(U_436),sK13(U_442,U_440,U_438,U_436)),U_438))
| hBOOL(hAPP(U_442,U_430))
| ~ hBOOL(hAPP(hAPP(c_member(U_436),U_430),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_436,tc_HOL_Obool)),U_438),U_440))) ),
inference(clausify,[status(thm)],[f_121_6]) ).
cnf(f_121_13,plain,
( hBOOL(hAPP(hAPP(c_member(U_436),sK14(U_442,U_440,U_438,U_436)),U_440))
| ~ hBOOL(hAPP(U_442,sK13(U_442,U_440,U_438,U_436)))
| hBOOL(hAPP(U_442,U_430))
| ~ hBOOL(hAPP(hAPP(c_member(U_436),U_430),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_436,tc_HOL_Obool)),U_438),U_440))) ),
inference(clausify,[status(thm)],[f_121_6]) ).
cnf(f_121_14,plain,
( ~ hBOOL(hAPP(U_442,sK14(U_442,U_440,U_438,U_436)))
| ~ hBOOL(hAPP(U_442,sK13(U_442,U_440,U_438,U_436)))
| hBOOL(hAPP(U_442,U_430))
| ~ hBOOL(hAPP(hAPP(c_member(U_436),U_430),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_436,tc_HOL_Obool)),U_438),U_440))) ),
inference(clausify,[status(thm)],[f_121_6]) ).
fof(f_122_1,plain,
! [V_P_2,V_B_2,V_A_2,T_b] :
( ( ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
| ( ! [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
& ! [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) )
& ( ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
| ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ! [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
inference(fof_nnf,[status(thm)],[fact_bex__Un]) ).
fof(f_122_2,plain,
! [U_452,U_451,U_450,U_449] :
( ( ? [U_448] :
( hBOOL(hAPP(U_452,U_448))
& hBOOL(hAPP(hAPP(c_member(U_449),U_448),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_449,tc_HOL_Obool)),U_450),U_451))) )
| ( ! [U_447] :
( ~ hBOOL(hAPP(U_452,U_447))
| ~ hBOOL(hAPP(hAPP(c_member(U_449),U_447),U_451)) )
& ! [U_446] :
( ~ hBOOL(hAPP(U_452,U_446))
| ~ hBOOL(hAPP(hAPP(c_member(U_449),U_446),U_450)) ) ) )
& ( ? [U_445] :
( hBOOL(hAPP(U_452,U_445))
& hBOOL(hAPP(hAPP(c_member(U_449),U_445),U_451)) )
| ? [U_444] :
( hBOOL(hAPP(U_452,U_444))
& hBOOL(hAPP(hAPP(c_member(U_449),U_444),U_450)) )
| ! [U_443] :
( ~ hBOOL(hAPP(U_452,U_443))
| ~ hBOOL(hAPP(hAPP(c_member(U_449),U_443),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_449,tc_HOL_Obool)),U_450),U_451))) ) ) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
fof(f_122_3,plain,
( ! [U_460,U_458,U_456,U_454] :
( ? [U_448] :
( hBOOL(hAPP(U_460,U_448))
& hBOOL(hAPP(hAPP(c_member(U_454),U_448),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_454,tc_HOL_Obool)),U_456),U_458))) )
| ( ! [U_447] :
( ~ hBOOL(hAPP(U_460,U_447))
| ~ hBOOL(hAPP(hAPP(c_member(U_454),U_447),U_458)) )
& ! [U_446] :
( ~ hBOOL(hAPP(U_460,U_446))
| ~ hBOOL(hAPP(hAPP(c_member(U_454),U_446),U_456)) ) ) )
& ! [U_459,U_457,U_455,U_453] :
( ? [U_445] :
( hBOOL(hAPP(U_459,U_445))
& hBOOL(hAPP(hAPP(c_member(U_453),U_445),U_457)) )
| ? [U_444] :
( hBOOL(hAPP(U_459,U_444))
& hBOOL(hAPP(hAPP(c_member(U_453),U_444),U_455)) )
| ! [U_443] :
( ~ hBOOL(hAPP(U_459,U_443))
| ~ hBOOL(hAPP(hAPP(c_member(U_453),U_443),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_453,tc_HOL_Obool)),U_455),U_457))) ) ) ),
inference(miniscope,[status(thm)],[f_122_2]) ).
fof(f_122_4,plain,
( ! [U_460,U_458,U_456,U_454] :
( ? [U_448] :
( hBOOL(hAPP(U_460,U_448))
& hBOOL(hAPP(hAPP(c_member(U_454),U_448),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_454,tc_HOL_Obool)),U_456),U_458))) )
| ( ! [U_447] :
( ~ hBOOL(hAPP(U_460,U_447))
| ~ hBOOL(hAPP(hAPP(c_member(U_454),U_447),U_458)) )
& ! [U_446] :
( ~ hBOOL(hAPP(U_460,U_446))
| ~ hBOOL(hAPP(hAPP(c_member(U_454),U_446),U_456)) ) ) )
& ! [U_459,U_457,U_455,U_453] :
( ? [U_445] :
( hBOOL(hAPP(U_459,U_445))
& hBOOL(hAPP(hAPP(c_member(U_453),U_445),U_457)) )
| ( hBOOL(hAPP(U_459,sK15(U_459,U_457,U_455,U_453)))
& hBOOL(hAPP(hAPP(c_member(U_453),sK15(U_459,U_457,U_455,U_453)),U_455)) )
| ! [U_443] :
( ~ hBOOL(hAPP(U_459,U_443))
| ~ hBOOL(hAPP(hAPP(c_member(U_453),U_443),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_453,tc_HOL_Obool)),U_455),U_457))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_444,sK15(U_459,U_457,U_455,U_453))],[f_122_3]) ).
fof(f_122_5,plain,
( ! [U_460,U_458,U_456,U_454] :
( ? [U_448] :
( hBOOL(hAPP(U_460,U_448))
& hBOOL(hAPP(hAPP(c_member(U_454),U_448),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_454,tc_HOL_Obool)),U_456),U_458))) )
| ( ! [U_447] :
( ~ hBOOL(hAPP(U_460,U_447))
| ~ hBOOL(hAPP(hAPP(c_member(U_454),U_447),U_458)) )
& ! [U_446] :
( ~ hBOOL(hAPP(U_460,U_446))
| ~ hBOOL(hAPP(hAPP(c_member(U_454),U_446),U_456)) ) ) )
& ! [U_459,U_457,U_455,U_453] :
( ( hBOOL(hAPP(U_459,sK16(U_459,U_457,U_455,U_453)))
& hBOOL(hAPP(hAPP(c_member(U_453),sK16(U_459,U_457,U_455,U_453)),U_457)) )
| ( hBOOL(hAPP(U_459,sK15(U_459,U_457,U_455,U_453)))
& hBOOL(hAPP(hAPP(c_member(U_453),sK15(U_459,U_457,U_455,U_453)),U_455)) )
| ! [U_443] :
( ~ hBOOL(hAPP(U_459,U_443))
| ~ hBOOL(hAPP(hAPP(c_member(U_453),U_443),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_453,tc_HOL_Obool)),U_455),U_457))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_445,sK16(U_459,U_457,U_455,U_453))],[f_122_4]) ).
fof(f_122_6,plain,
( ! [U_460,U_458,U_456,U_454] :
( ( hBOOL(hAPP(U_460,sK17(U_460,U_458,U_456,U_454)))
& hBOOL(hAPP(hAPP(c_member(U_454),sK17(U_460,U_458,U_456,U_454)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_454,tc_HOL_Obool)),U_456),U_458))) )
| ( ! [U_447] :
( ~ hBOOL(hAPP(U_460,U_447))
| ~ hBOOL(hAPP(hAPP(c_member(U_454),U_447),U_458)) )
& ! [U_446] :
( ~ hBOOL(hAPP(U_460,U_446))
| ~ hBOOL(hAPP(hAPP(c_member(U_454),U_446),U_456)) ) ) )
& ! [U_459,U_457,U_455,U_453] :
( ( hBOOL(hAPP(U_459,sK16(U_459,U_457,U_455,U_453)))
& hBOOL(hAPP(hAPP(c_member(U_453),sK16(U_459,U_457,U_455,U_453)),U_457)) )
| ( hBOOL(hAPP(U_459,sK15(U_459,U_457,U_455,U_453)))
& hBOOL(hAPP(hAPP(c_member(U_453),sK15(U_459,U_457,U_455,U_453)),U_455)) )
| ! [U_443] :
( ~ hBOOL(hAPP(U_459,U_443))
| ~ hBOOL(hAPP(hAPP(c_member(U_453),U_443),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_453,tc_HOL_Obool)),U_455),U_457))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_448,sK17(U_460,U_458,U_456,U_454))],[f_122_5]) ).
cnf(f_122_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_453),sK16(U_459,U_457,U_455,U_453)),U_457))
| hBOOL(hAPP(hAPP(c_member(U_453),sK15(U_459,U_457,U_455,U_453)),U_455))
| ~ hBOOL(hAPP(U_459,U_443))
| ~ hBOOL(hAPP(hAPP(c_member(U_453),U_443),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_453,tc_HOL_Obool)),U_455),U_457))) ),
inference(clausify,[status(thm)],[f_122_6]) ).
cnf(f_122_8,plain,
( hBOOL(hAPP(U_459,sK16(U_459,U_457,U_455,U_453)))
| hBOOL(hAPP(hAPP(c_member(U_453),sK15(U_459,U_457,U_455,U_453)),U_455))
| ~ hBOOL(hAPP(U_459,U_443))
| ~ hBOOL(hAPP(hAPP(c_member(U_453),U_443),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_453,tc_HOL_Obool)),U_455),U_457))) ),
inference(clausify,[status(thm)],[f_122_6]) ).
cnf(f_122_9,plain,
( hBOOL(hAPP(hAPP(c_member(U_453),sK16(U_459,U_457,U_455,U_453)),U_457))
| hBOOL(hAPP(U_459,sK15(U_459,U_457,U_455,U_453)))
| ~ hBOOL(hAPP(U_459,U_443))
| ~ hBOOL(hAPP(hAPP(c_member(U_453),U_443),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_453,tc_HOL_Obool)),U_455),U_457))) ),
inference(clausify,[status(thm)],[f_122_6]) ).
cnf(f_122_10,plain,
( hBOOL(hAPP(U_459,sK16(U_459,U_457,U_455,U_453)))
| hBOOL(hAPP(U_459,sK15(U_459,U_457,U_455,U_453)))
| ~ hBOOL(hAPP(U_459,U_443))
| ~ hBOOL(hAPP(hAPP(c_member(U_453),U_443),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_453,tc_HOL_Obool)),U_455),U_457))) ),
inference(clausify,[status(thm)],[f_122_6]) ).
cnf(f_122_11,plain,
( hBOOL(hAPP(hAPP(c_member(U_454),sK17(U_460,U_458,U_456,U_454)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_454,tc_HOL_Obool)),U_456),U_458)))
| ~ hBOOL(hAPP(U_460,U_446))
| ~ hBOOL(hAPP(hAPP(c_member(U_454),U_446),U_456)) ),
inference(clausify,[status(thm)],[f_122_6]) ).
cnf(f_122_12,plain,
( hBOOL(hAPP(U_460,sK17(U_460,U_458,U_456,U_454)))
| ~ hBOOL(hAPP(U_460,U_446))
| ~ hBOOL(hAPP(hAPP(c_member(U_454),U_446),U_456)) ),
inference(clausify,[status(thm)],[f_122_6]) ).
cnf(f_122_13,plain,
( hBOOL(hAPP(hAPP(c_member(U_454),sK17(U_460,U_458,U_456,U_454)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_454,tc_HOL_Obool)),U_456),U_458)))
| ~ hBOOL(hAPP(U_460,U_447))
| ~ hBOOL(hAPP(hAPP(c_member(U_454),U_447),U_458)) ),
inference(clausify,[status(thm)],[f_122_6]) ).
cnf(f_122_14,plain,
( hBOOL(hAPP(U_460,sK17(U_460,U_458,U_456,U_454)))
| ~ hBOOL(hAPP(U_460,U_447))
| ~ hBOOL(hAPP(hAPP(c_member(U_454),U_447),U_458)) ),
inference(clausify,[status(thm)],[f_122_6]) ).
fof(f_123_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_123_2,plain,
! [U_464,U_463,U_462,U_461] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_461,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_461,tc_HOL_Obool)),U_462),U_463)),U_464) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_461,tc_HOL_Obool)),U_462),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_461,tc_HOL_Obool)),U_463),U_464)),
inference(variable_rename,[status(thm)],[f_123_1]) ).
cnf(f_123_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_461,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_461,tc_HOL_Obool)),U_462),U_463)),U_464) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_461,tc_HOL_Obool)),U_462),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_461,tc_HOL_Obool)),U_463),U_464)),
inference(clausify,[status(thm)],[f_123_2]) ).
fof(f_124_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_124_2,plain,
! [U_468,U_467,U_466,U_465] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_465,tc_HOL_Obool)),U_466),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_465,tc_HOL_Obool)),U_467),U_468)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_465,tc_HOL_Obool)),U_467),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_465,tc_HOL_Obool)),U_466),U_468)),
inference(variable_rename,[status(thm)],[f_124_1]) ).
cnf(f_124_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_465,tc_HOL_Obool)),U_466),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_465,tc_HOL_Obool)),U_467),U_468)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_465,tc_HOL_Obool)),U_467),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_465,tc_HOL_Obool)),U_466),U_468)),
inference(clausify,[status(thm)],[f_124_2]) ).
fof(f_125_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_125_2,plain,
! [U_471,U_470,U_469] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_469,tc_HOL_Obool)),U_470),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_469,tc_HOL_Obool)),U_470),U_471)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_469,tc_HOL_Obool)),U_470),U_471),
inference(variable_rename,[status(thm)],[f_125_1]) ).
cnf(f_125_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_469,tc_HOL_Obool)),U_470),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_469,tc_HOL_Obool)),U_470),U_471)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_469,tc_HOL_Obool)),U_470),U_471),
inference(clausify,[status(thm)],[f_125_2]) ).
fof(f_126_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_126_2,plain,
! [U_474,U_473,U_472] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_472,tc_HOL_Obool)),U_473),U_474) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_472,tc_HOL_Obool)),U_474),U_473),
inference(variable_rename,[status(thm)],[f_126_1]) ).
cnf(f_126_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_472,tc_HOL_Obool)),U_473),U_474) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_472,tc_HOL_Obool)),U_474),U_473),
inference(clausify,[status(thm)],[f_126_2]) ).
fof(f_127_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_127_2,plain,
! [U_476,U_475] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_475,tc_HOL_Obool)),U_476),U_476) = U_476,
inference(variable_rename,[status(thm)],[f_127_1]) ).
cnf(f_127_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_475,tc_HOL_Obool)),U_476),U_476) = U_476,
inference(clausify,[status(thm)],[f_127_2]) ).
fof(f_128_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_128_2,plain,
! [U_480,U_479,U_478,U_477] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_477),U_479),U_480))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_477),U_478),U_480)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_477),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_477),U_478),U_479)),U_480))
| ~ class_Lattices_Osemilattice__sup(U_477) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
cnf(f_128_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_477),U_478),U_480))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_477),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_477),U_478),U_479)),U_480))
| ~ class_Lattices_Osemilattice__sup(U_477) ),
inference(clausify,[status(thm)],[f_128_2]) ).
cnf(f_128_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_477),U_479),U_480))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_477),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_477),U_478),U_479)),U_480))
| ~ class_Lattices_Osemilattice__sup(U_477) ),
inference(clausify,[status(thm)],[f_128_2]) ).
fof(f_129_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_129_2,plain,
! [U_485,U_484,U_483,U_482,U_481] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_481),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_481),U_482),U_484)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_481),U_483),U_485)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_481),U_484),U_485))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_481),U_482),U_483))
| ~ class_Lattices_Osemilattice__sup(U_481) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
cnf(f_129_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_481),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_481),U_482),U_484)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_481),U_483),U_485)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_481),U_484),U_485))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_481),U_482),U_483))
| ~ class_Lattices_Osemilattice__sup(U_481) ),
inference(clausify,[status(thm)],[f_129_2]) ).
fof(f_130_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_130_2,plain,
! [U_489,U_488,U_487,U_486] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_486),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_486),U_487),U_489)),U_488))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_486),U_489),U_488))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_486),U_487),U_488))
| ~ class_Lattices_Osemilattice__sup(U_486) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
cnf(f_130_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_486),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_486),U_487),U_489)),U_488))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_486),U_489),U_488))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_486),U_487),U_488))
| ~ class_Lattices_Osemilattice__sup(U_486) ),
inference(clausify,[status(thm)],[f_130_2]) ).
fof(f_131_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_131_2,plain,
! [U_493,U_492,U_491,U_490] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_490),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_490),U_491),U_493)),U_492))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_490),U_493),U_492))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_490),U_491),U_492))
| ~ class_Lattices_Osemilattice__sup(U_490) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
cnf(f_131_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_490),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_490),U_491),U_493)),U_492))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_490),U_493),U_492))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_490),U_491),U_492))
| ~ class_Lattices_Osemilattice__sup(U_490) ),
inference(clausify,[status(thm)],[f_131_2]) ).
fof(f_132_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_132_2,plain,
! [U_496,U_495,U_494] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_494),U_496),U_495) = U_496
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_494),U_495),U_496))
| ~ class_Lattices_Osemilattice__sup(U_494) ),
inference(variable_rename,[status(thm)],[f_132_1]) ).
cnf(f_132_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_494),U_496),U_495) = U_496
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_494),U_495),U_496))
| ~ class_Lattices_Osemilattice__sup(U_494) ),
inference(clausify,[status(thm)],[f_132_2]) ).
fof(f_133_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_133_2,plain,
! [U_499,U_498,U_497] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_497),U_498),U_499) = U_499
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_497),U_498),U_499))
| ~ class_Lattices_Osemilattice__sup(U_497) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
cnf(f_133_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_497),U_498),U_499) = U_499
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_497),U_498),U_499))
| ~ class_Lattices_Osemilattice__sup(U_497) ),
inference(clausify,[status(thm)],[f_133_2]) ).
fof(f_134_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_134_2,plain,
! [U_503,U_502,U_501,U_500] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_500),U_501),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_500),U_503),U_502)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_500),U_501),U_502))
| ~ class_Lattices_Osemilattice__sup(U_500) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
cnf(f_134_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_500),U_501),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_500),U_503),U_502)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_500),U_501),U_502))
| ~ class_Lattices_Osemilattice__sup(U_500) ),
inference(clausify,[status(thm)],[f_134_2]) ).
fof(f_135_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_135_2,plain,
! [U_507,U_506,U_505,U_504] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_504),U_505),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_504),U_506),U_507)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_504),U_505),U_506))
| ~ class_Lattices_Osemilattice__sup(U_504) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
cnf(f_135_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_504),U_505),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_504),U_506),U_507)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_504),U_505),U_506))
| ~ class_Lattices_Osemilattice__sup(U_504) ),
inference(clausify,[status(thm)],[f_135_2]) ).
fof(f_136_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_136_2,plain,
! [U_511,U_510,U_509,U_508] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_508),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_508),U_509),U_510)),U_511))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_508),U_510),U_511))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_508),U_509),U_511)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_508),U_510),U_511))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_508),U_509),U_511)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_508),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_508),U_509),U_510)),U_511)) ) )
| ~ class_Lattices_Osemilattice__sup(U_508) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
cnf(f_136_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_508),U_509),U_511))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_508),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_508),U_509),U_510)),U_511))
| ~ class_Lattices_Osemilattice__sup(U_508) ),
inference(clausify,[status(thm)],[f_136_2]) ).
cnf(f_136_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_508),U_510),U_511))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_508),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_508),U_509),U_510)),U_511))
| ~ class_Lattices_Osemilattice__sup(U_508) ),
inference(clausify,[status(thm)],[f_136_2]) ).
cnf(f_136_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_508),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_508),U_509),U_510)),U_511))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_508),U_510),U_511))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_508),U_509),U_511))
| ~ class_Lattices_Osemilattice__sup(U_508) ),
inference(clausify,[status(thm)],[f_136_2]) ).
fof(f_137_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_137_2,plain,
! [U_514,U_513,U_512] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_512),U_513),U_514))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_512),U_513),U_514) != U_514 )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_512),U_513),U_514) = U_514
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_512),U_513),U_514)) ) )
| ~ class_Lattices_Osemilattice__sup(U_512) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
cnf(f_137_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_512),U_513),U_514) = U_514
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_512),U_513),U_514))
| ~ class_Lattices_Osemilattice__sup(U_512) ),
inference(clausify,[status(thm)],[f_137_2]) ).
cnf(f_137_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_512),U_513),U_514))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_512),U_513),U_514) != U_514
| ~ class_Lattices_Osemilattice__sup(U_512) ),
inference(clausify,[status(thm)],[f_137_2]) ).
fof(f_138_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_138_2,plain,
! [U_517,U_516,U_515] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_515),U_516),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_515),U_517),U_516)))
| ~ class_Lattices_Osemilattice__sup(U_515) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
cnf(f_138_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_515),U_516),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_515),U_517),U_516)))
| ~ class_Lattices_Osemilattice__sup(U_515) ),
inference(clausify,[status(thm)],[f_138_2]) ).
fof(f_139_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_139_2,plain,
! [U_520,U_519,U_518] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_518),U_519),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_518),U_520),U_519)))
| ~ class_Lattices_Olattice(U_518) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
cnf(f_139_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_518),U_519),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_518),U_520),U_519)))
| ~ class_Lattices_Olattice(U_518) ),
inference(clausify,[status(thm)],[f_139_2]) ).
fof(f_140_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_140_2,plain,
! [U_523,U_522,U_521] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_521),U_522),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_521),U_522),U_523)))
| ~ class_Lattices_Osemilattice__sup(U_521) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
cnf(f_140_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_521),U_522),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_521),U_522),U_523)))
| ~ class_Lattices_Osemilattice__sup(U_521) ),
inference(clausify,[status(thm)],[f_140_2]) ).
fof(f_141_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_141_2,plain,
! [U_526,U_525,U_524] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_524),U_525),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_524),U_525),U_526)))
| ~ class_Lattices_Olattice(U_524) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
cnf(f_141_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_524),U_525),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_524),U_525),U_526)))
| ~ class_Lattices_Olattice(U_524) ),
inference(clausify,[status(thm)],[f_141_2]) ).
fof(f_142_1,plain,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_mono__Un]) ).
fof(f_142_2,plain,
! [U_531,U_530,U_529,U_528,U_527] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_528,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_528,tc_HOL_Obool)),hAPP(U_529,U_530)),hAPP(U_529,U_531))),hAPP(U_529,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_527,tc_HOL_Obool)),U_530),U_531))))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_527,tc_HOL_Obool),tc_fun(U_528,tc_HOL_Obool),U_529) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
cnf(f_142_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_528,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_528,tc_HOL_Obool)),hAPP(U_529,U_530)),hAPP(U_529,U_531))),hAPP(U_529,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_527,tc_HOL_Obool)),U_530),U_531))))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_527,tc_HOL_Obool),tc_fun(U_528,tc_HOL_Obool),U_529) ),
inference(clausify,[status(thm)],[f_142_2]) ).
fof(f_143_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_143_2,plain,
! [U_536,U_535,U_534,U_533,U_532] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_532,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_532,tc_HOL_Obool)),U_533),U_535)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_532,tc_HOL_Obool)),U_534),U_536)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_532,tc_HOL_Obool)),U_535),U_536))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_532,tc_HOL_Obool)),U_533),U_534)) ),
inference(variable_rename,[status(thm)],[f_143_1]) ).
cnf(f_143_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_532,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_532,tc_HOL_Obool)),U_533),U_535)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_532,tc_HOL_Obool)),U_534),U_536)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_532,tc_HOL_Obool)),U_535),U_536))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_532,tc_HOL_Obool)),U_533),U_534)) ),
inference(clausify,[status(thm)],[f_143_2]) ).
fof(f_144_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_144_2,plain,
! [U_540,U_539,U_538,U_537] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_537,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_537,tc_HOL_Obool)),U_538),U_540)),U_539))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_537,tc_HOL_Obool)),U_540),U_539))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_537,tc_HOL_Obool)),U_538),U_539)) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
cnf(f_144_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_537,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_537,tc_HOL_Obool)),U_538),U_540)),U_539))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_537,tc_HOL_Obool)),U_540),U_539))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_537,tc_HOL_Obool)),U_538),U_539)) ),
inference(clausify,[status(thm)],[f_144_2]) ).
fof(f_145_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_145_2,plain,
! [U_543,U_542,U_541] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_541,tc_HOL_Obool)),U_543),U_542) = U_543
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_541,tc_HOL_Obool)),U_542),U_543)) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
cnf(f_145_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_541,tc_HOL_Obool)),U_543),U_542) = U_543
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_541,tc_HOL_Obool)),U_542),U_543)) ),
inference(clausify,[status(thm)],[f_145_2]) ).
fof(f_146_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_146_2,plain,
! [U_546,U_545,U_544] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_544,tc_HOL_Obool)),U_545),U_546) = U_546
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_544,tc_HOL_Obool)),U_545),U_546)) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
cnf(f_146_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_544,tc_HOL_Obool)),U_545),U_546) = U_546
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_544,tc_HOL_Obool)),U_545),U_546)) ),
inference(clausify,[status(thm)],[f_146_2]) ).
fof(f_147_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_147_2,plain,
! [U_549,U_548,U_547] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_547,tc_HOL_Obool)),U_548),U_549))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_547,tc_HOL_Obool)),U_548),U_549) != U_549 )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_547,tc_HOL_Obool)),U_548),U_549) = U_549
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_547,tc_HOL_Obool)),U_548),U_549)) ) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
fof(f_147_3,plain,
( ! [U_555,U_553,U_551] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_551,tc_HOL_Obool)),U_553),U_555))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_551,tc_HOL_Obool)),U_553),U_555) != U_555 )
& ! [U_554,U_552,U_550] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_550,tc_HOL_Obool)),U_552),U_554) = U_554
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_550,tc_HOL_Obool)),U_552),U_554)) ) ),
inference(miniscope,[status(thm)],[f_147_2]) ).
cnf(f_147_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_550,tc_HOL_Obool)),U_552),U_554) = U_554
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_550,tc_HOL_Obool)),U_552),U_554)) ),
inference(clausify,[status(thm)],[f_147_3]) ).
cnf(f_147_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_551,tc_HOL_Obool)),U_553),U_555))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_551,tc_HOL_Obool)),U_553),U_555) != U_555 ),
inference(clausify,[status(thm)],[f_147_3]) ).
fof(f_148_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_148_2,plain,
! [U_558,U_557,U_556] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_556,tc_HOL_Obool)),U_557),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_556,tc_HOL_Obool)),U_558),U_557))),
inference(variable_rename,[status(thm)],[f_148_1]) ).
cnf(f_148_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_556,tc_HOL_Obool)),U_557),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_556,tc_HOL_Obool)),U_558),U_557))),
inference(clausify,[status(thm)],[f_148_2]) ).
fof(f_149_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_149_2,plain,
! [U_561,U_560,U_559] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_559,tc_HOL_Obool)),U_560),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_559,tc_HOL_Obool)),U_560),U_561))),
inference(variable_rename,[status(thm)],[f_149_1]) ).
cnf(f_149_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_559,tc_HOL_Obool)),U_560),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_559,tc_HOL_Obool)),U_560),U_561))),
inference(clausify,[status(thm)],[f_149_2]) ).
fof(f_150_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_150_2,plain,
! [U_564,U_563,U_562] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_562,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_562,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_562),U_563)),hAPP(c_Set_OPow(U_562),U_564))),hAPP(c_Set_OPow(U_562),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_562,tc_HOL_Obool)),U_563),U_564)))),
inference(variable_rename,[status(thm)],[f_150_1]) ).
cnf(f_150_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_562,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_562,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_562),U_563)),hAPP(c_Set_OPow(U_562),U_564))),hAPP(c_Set_OPow(U_562),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_562,tc_HOL_Obool)),U_563),U_564)))),
inference(clausify,[status(thm)],[f_150_2]) ).
fof(f_151_1,plain,
! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_A_2),V_B_2))))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
| ~ class_Lattices_Osemilattice__sup(T_b)
| ~ class_Lattices_Osemilattice__sup(T_c) ),
inference(fof_nnf,[status(thm)],[fact_mono__sup]) ).
fof(f_151_2,plain,
! [U_569,U_568,U_567,U_566,U_565] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_565),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_565),hAPP(U_567,U_568)),hAPP(U_567,U_569))),hAPP(U_567,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_566),U_568),U_569))))
| ~ c_Orderings_Oorder__class_Omono(U_566,U_565,U_567)
| ~ class_Lattices_Osemilattice__sup(U_566)
| ~ class_Lattices_Osemilattice__sup(U_565) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
cnf(f_151_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_565),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_565),hAPP(U_567,U_568)),hAPP(U_567,U_569))),hAPP(U_567,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_566),U_568),U_569))))
| ~ c_Orderings_Oorder__class_Omono(U_566,U_565,U_567)
| ~ class_Lattices_Osemilattice__sup(U_566)
| ~ class_Lattices_Osemilattice__sup(U_565) ),
inference(clausify,[status(thm)],[f_151_2]) ).
fof(f_152_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_152_2,plain,
! [U_573,U_572,U_571,U_570] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_570,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_570,U_571),U_572)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_570,U_572),U_573)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_570,U_571),U_573)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_570),U_572),U_573))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_570),U_571),U_572))
| ~ class_Orderings_Olinorder(U_570) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
cnf(f_152_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_570,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_570,U_571),U_572)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_570,U_572),U_573)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_570,U_571),U_573)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_570),U_572),U_573))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_570),U_571),U_572))
| ~ class_Orderings_Olinorder(U_570) ),
inference(clausify,[status(thm)],[f_152_2]) ).
fof(f_153_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_153_2,plain,
! [U_577,U_576,U_575,U_574] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_574,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_574,U_575),U_576)),c_SetInterval_Oord__class_OatLeastAtMost(U_574,U_576,U_577)) = c_SetInterval_Oord__class_OatLeastAtMost(U_574,U_575,U_577)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_574),U_576),U_577))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_574),U_575),U_576))
| ~ class_Orderings_Olinorder(U_574) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
cnf(f_153_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_574,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_574,U_575),U_576)),c_SetInterval_Oord__class_OatLeastAtMost(U_574,U_576,U_577)) = c_SetInterval_Oord__class_OatLeastAtMost(U_574,U_575,U_577)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_574),U_576),U_577))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_574),U_575),U_576))
| ~ class_Orderings_Olinorder(U_574) ),
inference(clausify,[status(thm)],[f_153_2]) ).
fof(f_154_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_154_2,plain,
! [U_580,U_579,U_578] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_578,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_578),U_579)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_578,U_579),U_580)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_578),U_580)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_578),U_579),U_580))
| ~ class_Orderings_Olinorder(U_578) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
cnf(f_154_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_578,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_578),U_579)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_578,U_579),U_580)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_578),U_580)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_578),U_579),U_580))
| ~ class_Orderings_Olinorder(U_578) ),
inference(clausify,[status(thm)],[f_154_2]) ).
fof(f_155_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_155_2,plain,
! [U_583,U_582,U_581] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_581,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_581,U_582),U_583)),hAPP(c_SetInterval_Oord__class_OatLeast(U_581),U_583)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_581),U_582)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_581),U_582),U_583))
| ~ class_Orderings_Olinorder(U_581) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
cnf(f_155_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_581,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_581,U_582),U_583)),hAPP(c_SetInterval_Oord__class_OatLeast(U_581),U_583)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_581),U_582)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_581),U_582),U_583))
| ~ class_Orderings_Olinorder(U_581) ),
inference(clausify,[status(thm)],[f_155_2]) ).
fof(f_156_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_156_2,plain,
! [U_585,U_584] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_584),hAPP(c_Groups_Ouminus__class_Ouminus(U_584),U_585)) = U_585
| ~ class_Groups_Ogroup__add(U_584) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
cnf(f_156_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_584),hAPP(c_Groups_Ouminus__class_Ouminus(U_584),U_585)) = U_585
| ~ class_Groups_Ogroup__add(U_584) ),
inference(clausify,[status(thm)],[f_156_2]) ).
fof(f_157_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_157_2,plain,
! [U_587,U_586] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_586),hAPP(c_Groups_Ouminus__class_Ouminus(U_586),U_587)) = U_587
| ~ class_Lattices_Oboolean__algebra(U_586) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
cnf(f_157_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_586),hAPP(c_Groups_Ouminus__class_Ouminus(U_586),U_587)) = U_587
| ~ class_Lattices_Oboolean__algebra(U_586) ),
inference(clausify,[status(thm)],[f_157_2]) ).
fof(f_158_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_158_2,plain,
! [U_590,U_589,U_588] :
( ( ( U_589 = hAPP(c_Groups_Ouminus__class_Ouminus(U_588),U_590)
| U_590 != hAPP(c_Groups_Ouminus__class_Ouminus(U_588),U_589) )
& ( U_590 = hAPP(c_Groups_Ouminus__class_Ouminus(U_588),U_589)
| U_589 != hAPP(c_Groups_Ouminus__class_Ouminus(U_588),U_590) ) )
| ~ class_Groups_Ogroup__add(U_588) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
cnf(f_158_3,plain,
( U_590 = hAPP(c_Groups_Ouminus__class_Ouminus(U_588),U_589)
| U_589 != hAPP(c_Groups_Ouminus__class_Ouminus(U_588),U_590)
| ~ class_Groups_Ogroup__add(U_588) ),
inference(clausify,[status(thm)],[f_158_2]) ).
cnf(f_158_4,plain,
( U_589 = hAPP(c_Groups_Ouminus__class_Ouminus(U_588),U_590)
| U_590 != hAPP(c_Groups_Ouminus__class_Ouminus(U_588),U_589)
| ~ class_Groups_Ogroup__add(U_588) ),
inference(clausify,[status(thm)],[f_158_2]) ).
fof(f_159_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_159_2,plain,
! [U_593,U_592,U_591] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_591,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_591,U_592,U_593)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_591),U_593)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_591),U_592)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_591),U_592),U_593))
| ~ class_Orderings_Olinorder(U_591) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
cnf(f_159_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_591,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_591,U_592,U_593)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_591),U_593)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_591),U_592)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_591),U_592),U_593))
| ~ class_Orderings_Olinorder(U_591) ),
inference(clausify,[status(thm)],[f_159_2]) ).
fof(f_160_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_160_2,plain,
! [U_596,U_595,U_594] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_594,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_594),U_595)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_594,U_595,U_596)) = hAPP(c_SetInterval_Oord__class_OatMost(U_594),U_596)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_594),U_595),U_596))
| ~ class_Orderings_Olinorder(U_594) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
cnf(f_160_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_594,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_594),U_595)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_594,U_595,U_596)) = hAPP(c_SetInterval_Oord__class_OatMost(U_594),U_596)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_594),U_595),U_596))
| ~ class_Orderings_Olinorder(U_594) ),
inference(clausify,[status(thm)],[f_160_2]) ).
fof(f_161_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_161_2,plain,
! [U_600,U_599,U_598,U_597] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_597,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_597,U_598,U_599)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_597,U_599,U_600)) = c_SetInterval_Oord__class_OatLeastAtMost(U_597,U_598,U_600)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_597),U_599),U_600))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_597),U_598),U_599))
| ~ class_Orderings_Olinorder(U_597) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
cnf(f_161_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_597,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_597,U_598,U_599)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_597,U_599,U_600)) = c_SetInterval_Oord__class_OatLeastAtMost(U_597,U_598,U_600)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_597),U_599),U_600))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_597),U_598),U_599))
| ~ class_Orderings_Olinorder(U_597) ),
inference(clausify,[status(thm)],[f_161_2]) ).
fof(f_162_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_162_2,plain,
! [U_602,U_601] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_601),U_602),U_602) = U_602
| ~ class_Lattices_Olattice(U_601) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
cnf(f_162_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_601),U_602),U_602) = U_602
| ~ class_Lattices_Olattice(U_601) ),
inference(clausify,[status(thm)],[f_162_2]) ).
fof(f_163_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_163_2,plain,
! [U_605,U_604,U_603] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_603,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_603,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_603,tc_HOL_Obool),U_604)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_603,tc_HOL_Obool),U_605))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_603,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_603,tc_HOL_Obool),tc_HOL_Obool)),U_604),U_605)))),
inference(variable_rename,[status(thm)],[f_163_1]) ).
cnf(f_163_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_603,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_603,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_603,tc_HOL_Obool),U_604)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_603,tc_HOL_Obool),U_605))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_603,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_603,tc_HOL_Obool),tc_HOL_Obool)),U_604),U_605)))),
inference(clausify,[status(thm)],[f_163_2]) ).
fof(f_164_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_164_2,plain,
! [U_607,U_606] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_606,hAPP(c_Nat_OSuc,U_607)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_607)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_606,U_607))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_606),hAPP(c_Nat_OSuc,U_607))) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
cnf(f_164_3,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_606,hAPP(c_Nat_OSuc,U_607)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_607)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_606,U_607))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_606),hAPP(c_Nat_OSuc,U_607))) ),
inference(clausify,[status(thm)],[f_164_2]) ).
fof(f_165_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_165_2,plain,
! [U_609,U_608] :
( hAPP(c_Set_Oimage(U_608,U_608,c_Groups_Ouminus__class_Ouminus(U_608)),hAPP(c_SetInterval_Oord__class_OatMost(U_608),U_609)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_608),hAPP(c_Groups_Ouminus__class_Ouminus(U_608),U_609))
| ~ class_Groups_Oordered__ab__group__add(U_608) ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
cnf(f_165_3,plain,
( hAPP(c_Set_Oimage(U_608,U_608,c_Groups_Ouminus__class_Ouminus(U_608)),hAPP(c_SetInterval_Oord__class_OatMost(U_608),U_609)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_608),hAPP(c_Groups_Ouminus__class_Ouminus(U_608),U_609))
| ~ class_Groups_Oordered__ab__group__add(U_608) ),
inference(clausify,[status(thm)],[f_165_2]) ).
fof(f_166_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_166_2,plain,
! [U_611,U_610] :
( hAPP(c_Set_Oimage(U_610,U_610,c_Groups_Ouminus__class_Ouminus(U_610)),hAPP(c_SetInterval_Oord__class_OatLeast(U_610),U_611)) = hAPP(c_SetInterval_Oord__class_OatMost(U_610),hAPP(c_Groups_Ouminus__class_Ouminus(U_610),U_611))
| ~ class_Groups_Oordered__ab__group__add(U_610) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
cnf(f_166_3,plain,
( hAPP(c_Set_Oimage(U_610,U_610,c_Groups_Ouminus__class_Ouminus(U_610)),hAPP(c_SetInterval_Oord__class_OatLeast(U_610),U_611)) = hAPP(c_SetInterval_Oord__class_OatMost(U_610),hAPP(c_Groups_Ouminus__class_Ouminus(U_610),U_611))
| ~ class_Groups_Oordered__ab__group__add(U_610) ),
inference(clausify,[status(thm)],[f_166_2]) ).
fof(f_167_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_167_2,plain,
! [U_613,U_612] :
( hAPP(c_Set_Oimage(U_612,U_612,c_Groups_Ouminus__class_Ouminus(U_612)),hAPP(c_SetInterval_Oord__class_OlessThan(U_612),U_613)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_612),hAPP(c_Groups_Ouminus__class_Ouminus(U_612),U_613))
| ~ class_Groups_Oordered__ab__group__add(U_612) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
cnf(f_167_3,plain,
( hAPP(c_Set_Oimage(U_612,U_612,c_Groups_Ouminus__class_Ouminus(U_612)),hAPP(c_SetInterval_Oord__class_OlessThan(U_612),U_613)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_612),hAPP(c_Groups_Ouminus__class_Ouminus(U_612),U_613))
| ~ class_Groups_Oordered__ab__group__add(U_612) ),
inference(clausify,[status(thm)],[f_167_2]) ).
fof(f_168_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_168_2,plain,
! [U_615,U_614] :
( hAPP(c_Set_Oimage(U_614,U_614,c_Groups_Ouminus__class_Ouminus(U_614)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_614),U_615)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_614),hAPP(c_Groups_Ouminus__class_Ouminus(U_614),U_615))
| ~ class_Groups_Oordered__ab__group__add(U_614) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
cnf(f_168_3,plain,
( hAPP(c_Set_Oimage(U_614,U_614,c_Groups_Ouminus__class_Ouminus(U_614)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_614),U_615)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_614),hAPP(c_Groups_Ouminus__class_Ouminus(U_614),U_615))
| ~ class_Groups_Oordered__ab__group__add(U_614) ),
inference(clausify,[status(thm)],[f_168_2]) ).
fof(f_169_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_169_2,plain,
! [U_617,U_616] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_616),hAPP(c_Groups_Ouminus__class_Ouminus(U_616),U_617)),U_617) = c_Orderings_Otop__class_Otop(U_616)
| ~ class_Lattices_Oboolean__algebra(U_616) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
cnf(f_169_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_616),hAPP(c_Groups_Ouminus__class_Ouminus(U_616),U_617)),U_617) = c_Orderings_Otop__class_Otop(U_616)
| ~ class_Lattices_Oboolean__algebra(U_616) ),
inference(clausify,[status(thm)],[f_169_2]) ).
fof(f_170_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_170_2,plain,
! [U_621,U_620,U_619,U_618] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_621,tc_HOL_Obool)),U_618),U_620),U_619))
| ~ hBOOL(hAPP(U_620,U_619))
| ~ hBOOL(hAPP(U_618,U_619)) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
cnf(f_170_3,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_621,tc_HOL_Obool)),U_618),U_620),U_619))
| ~ hBOOL(hAPP(U_620,U_619))
| ~ hBOOL(hAPP(U_618,U_619)) ),
inference(clausify,[status(thm)],[f_170_2]) ).
fof(f_171_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_171_2,plain,
! [U_625,U_624,U_623,U_622] :
( ( hBOOL(hAPP(U_624,U_625))
& hBOOL(hAPP(U_623,U_625)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_622,tc_HOL_Obool)),U_623),U_624),U_625)) ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
fof(f_171_3,plain,
! [U_625,U_624,U_623] :
( ! [U_622] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_622,tc_HOL_Obool)),U_623),U_624),U_625))
| ( hBOOL(hAPP(U_624,U_625))
& hBOOL(hAPP(U_623,U_625)) ) ),
inference(miniscope,[status(thm)],[f_171_2]) ).
cnf(f_171_4,plain,
( hBOOL(hAPP(U_623,U_625))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_622,tc_HOL_Obool)),U_623),U_624),U_625)) ),
inference(clausify,[status(thm)],[f_171_3]) ).
cnf(f_171_5,plain,
( hBOOL(hAPP(U_624,U_625))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_622,tc_HOL_Obool)),U_623),U_624),U_625)) ),
inference(clausify,[status(thm)],[f_171_3]) ).
fof(f_172_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_172_2,plain,
! [U_627,U_626] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_626),c_Orderings_Otop__class_Otop(U_626)),U_627) = U_627
| ~ class_Lattices_Obounded__lattice__top(U_626) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
cnf(f_172_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_626),c_Orderings_Otop__class_Otop(U_626)),U_627) = U_627
| ~ class_Lattices_Obounded__lattice__top(U_626) ),
inference(clausify,[status(thm)],[f_172_2]) ).
fof(f_173_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_173_2,plain,
! [U_629,U_628] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_628),U_629),c_Orderings_Otop__class_Otop(U_628)) = U_629
| ~ class_Lattices_Obounded__lattice__top(U_628) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
cnf(f_173_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_628),U_629),c_Orderings_Otop__class_Otop(U_628)) = U_629
| ~ class_Lattices_Obounded__lattice__top(U_628) ),
inference(clausify,[status(thm)],[f_173_2]) ).
fof(f_174_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_174_2,plain,
! [U_631,U_630] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_630),U_631),U_631) = U_631
| ~ class_Lattices_Osemilattice__inf(U_630) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
cnf(f_174_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_630),U_631),U_631) = U_631
| ~ class_Lattices_Osemilattice__inf(U_630) ),
inference(clausify,[status(thm)],[f_174_2]) ).
fof(f_175_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_175_2,plain,
! [U_633,U_632] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_632),U_633),U_633) = U_633
| ~ class_Lattices_Osemilattice__inf(U_632) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
cnf(f_175_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_632),U_633),U_633) = U_633
| ~ class_Lattices_Osemilattice__inf(U_632) ),
inference(clausify,[status(thm)],[f_175_2]) ).
fof(f_176_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_176_2,plain,
! [U_636,U_635,U_634] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_634),U_635),U_636) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_634),U_636),U_635)
| ~ class_Lattices_Osemilattice__inf(U_634) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
cnf(f_176_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_634),U_635),U_636) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_634),U_636),U_635)
| ~ class_Lattices_Osemilattice__inf(U_634) ),
inference(clausify,[status(thm)],[f_176_2]) ).
fof(f_177_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_177_2,plain,
! [U_639,U_638,U_637] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_637),U_638),U_639) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_637),U_639),U_638)
| ~ class_Lattices_Olattice(U_637) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
cnf(f_177_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_637),U_638),U_639) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_637),U_639),U_638)
| ~ class_Lattices_Olattice(U_637) ),
inference(clausify,[status(thm)],[f_177_2]) ).
fof(f_178_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_178_2,plain,
! [U_642,U_641,U_640] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_640),U_641),U_642) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_640),U_642),U_641)
| ~ class_Lattices_Osemilattice__inf(U_640) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
cnf(f_178_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_640),U_641),U_642) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_640),U_642),U_641)
| ~ class_Lattices_Osemilattice__inf(U_640) ),
inference(clausify,[status(thm)],[f_178_2]) ).
fof(f_179_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_179_2,plain,
! [U_645,U_644,U_643] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_643),U_644),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_643),U_644),U_645)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_643),U_644),U_645)
| ~ class_Lattices_Osemilattice__inf(U_643) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
cnf(f_179_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_643),U_644),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_643),U_644),U_645)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_643),U_644),U_645)
| ~ class_Lattices_Osemilattice__inf(U_643) ),
inference(clausify,[status(thm)],[f_179_2]) ).
fof(f_180_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_180_2,plain,
! [U_648,U_647,U_646] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_646),U_647),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_646),U_647),U_648)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_646),U_647),U_648)
| ~ class_Lattices_Olattice(U_646) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
cnf(f_180_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_646),U_647),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_646),U_647),U_648)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_646),U_647),U_648)
| ~ class_Lattices_Olattice(U_646) ),
inference(clausify,[status(thm)],[f_180_2]) ).
fof(f_181_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_181_2,plain,
! [U_651,U_650,U_649] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_649),U_650),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_649),U_650),U_651)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_649),U_650),U_651)
| ~ class_Lattices_Osemilattice__inf(U_649) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
cnf(f_181_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_649),U_650),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_649),U_650),U_651)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_649),U_650),U_651)
| ~ class_Lattices_Osemilattice__inf(U_649) ),
inference(clausify,[status(thm)],[f_181_2]) ).
fof(f_182_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_182_2,plain,
! [U_655,U_654,U_653,U_652] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_652),U_653),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_652),U_654),U_655)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_652),U_654),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_652),U_653),U_655))
| ~ class_Lattices_Osemilattice__inf(U_652) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
cnf(f_182_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_652),U_653),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_652),U_654),U_655)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_652),U_654),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_652),U_653),U_655))
| ~ class_Lattices_Osemilattice__inf(U_652) ),
inference(clausify,[status(thm)],[f_182_2]) ).
fof(f_183_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_183_2,plain,
! [U_659,U_658,U_657,U_656] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_656),U_657),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_656),U_658),U_659)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_656),U_658),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_656),U_657),U_659))
| ~ class_Lattices_Olattice(U_656) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
cnf(f_183_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_656),U_657),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_656),U_658),U_659)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_656),U_658),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_656),U_657),U_659))
| ~ class_Lattices_Olattice(U_656) ),
inference(clausify,[status(thm)],[f_183_2]) ).
fof(f_184_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_184_2,plain,
! [U_663,U_662,U_661,U_660] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_660),U_661),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_660),U_662),U_663)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_660),U_662),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_660),U_661),U_663))
| ~ class_Lattices_Osemilattice__inf(U_660) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
cnf(f_184_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_660),U_661),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_660),U_662),U_663)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_660),U_662),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_660),U_661),U_663))
| ~ class_Lattices_Osemilattice__inf(U_660) ),
inference(clausify,[status(thm)],[f_184_2]) ).
fof(f_185_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_185_2,plain,
! [U_666,U_665,U_664] :
( ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_664),U_665),U_666) = c_Orderings_Otop__class_Otop(U_664)
| U_666 != c_Orderings_Otop__class_Otop(U_664)
| U_665 != c_Orderings_Otop__class_Otop(U_664) )
& ( ( U_666 = c_Orderings_Otop__class_Otop(U_664)
& U_665 = c_Orderings_Otop__class_Otop(U_664) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_664),U_665),U_666) != c_Orderings_Otop__class_Otop(U_664) ) )
| ~ class_Lattices_Obounded__lattice__top(U_664) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
cnf(f_185_3,plain,
( U_665 = c_Orderings_Otop__class_Otop(U_664)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_664),U_665),U_666) != c_Orderings_Otop__class_Otop(U_664)
| ~ class_Lattices_Obounded__lattice__top(U_664) ),
inference(clausify,[status(thm)],[f_185_2]) ).
cnf(f_185_4,plain,
( U_666 = c_Orderings_Otop__class_Otop(U_664)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_664),U_665),U_666) != c_Orderings_Otop__class_Otop(U_664)
| ~ class_Lattices_Obounded__lattice__top(U_664) ),
inference(clausify,[status(thm)],[f_185_2]) ).
cnf(f_185_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_664),U_665),U_666) = c_Orderings_Otop__class_Otop(U_664)
| U_666 != c_Orderings_Otop__class_Otop(U_664)
| U_665 != c_Orderings_Otop__class_Otop(U_664)
| ~ class_Lattices_Obounded__lattice__top(U_664) ),
inference(clausify,[status(thm)],[f_185_2]) ).
fof(f_186_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_186_2,plain,
! [U_670,U_669,U_668,U_667] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_667),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_667),U_668),U_669)),U_670) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_667),U_668),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_667),U_669),U_670))
| ~ class_Lattices_Osemilattice__inf(U_667) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
cnf(f_186_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_667),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_667),U_668),U_669)),U_670) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_667),U_668),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_667),U_669),U_670))
| ~ class_Lattices_Osemilattice__inf(U_667) ),
inference(clausify,[status(thm)],[f_186_2]) ).
fof(f_187_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_187_2,plain,
! [U_674,U_673,U_672,U_671] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_671),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_671),U_672),U_673)),U_674) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_671),U_672),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_671),U_673),U_674))
| ~ class_Lattices_Olattice(U_671) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
cnf(f_187_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_671),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_671),U_672),U_673)),U_674) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_671),U_672),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_671),U_673),U_674))
| ~ class_Lattices_Olattice(U_671) ),
inference(clausify,[status(thm)],[f_187_2]) ).
fof(f_188_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_188_2,plain,
! [U_678,U_677,U_676,U_675] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_675),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_675),U_676),U_677)),U_678) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_675),U_676),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_675),U_677),U_678))
| ~ class_Lattices_Osemilattice__inf(U_675) ),
inference(variable_rename,[status(thm)],[f_188_1]) ).
cnf(f_188_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_675),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_675),U_676),U_677)),U_678) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_675),U_676),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_675),U_677),U_678))
| ~ class_Lattices_Osemilattice__inf(U_675) ),
inference(clausify,[status(thm)],[f_188_2]) ).
fof(f_189_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_189_2,plain,
! [U_683,U_682,U_681,U_680,U_679] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_680,U_679)),U_681),U_682),U_683) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_679),hAPP(U_681,U_683)),hAPP(U_682,U_683))
| ~ class_Lattices_Olattice(U_679) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
cnf(f_189_3,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_680,U_679)),U_681),U_682),U_683) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_679),hAPP(U_681,U_683)),hAPP(U_682,U_683))
| ~ class_Lattices_Olattice(U_679) ),
inference(clausify,[status(thm)],[f_189_2]) ).
fof(f_190_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_190_2,plain,
! [U_686,U_685,U_684] :
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_685,U_684)),U_686) = c_Orderings_Otop__class_Otop(U_684)
| ~ class_Orderings_Otop(U_684) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
cnf(f_190_3,plain,
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_685,U_684)),U_686) = c_Orderings_Otop__class_Otop(U_684)
| ~ class_Orderings_Otop(U_684) ),
inference(clausify,[status(thm)],[f_190_2]) ).
fof(f_191_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_191_2,plain,
! [U_688,U_687] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_687,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_687,tc_HOL_Obool))),U_688) = U_688,
inference(variable_rename,[status(thm)],[f_191_1]) ).
cnf(f_191_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_687,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_687,tc_HOL_Obool))),U_688) = U_688,
inference(clausify,[status(thm)],[f_191_2]) ).
fof(f_192_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_192_2,plain,
! [U_690,U_689] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_689,tc_HOL_Obool)),U_690),c_Orderings_Otop__class_Otop(tc_fun(U_689,tc_HOL_Obool))) = U_690,
inference(variable_rename,[status(thm)],[f_192_1]) ).
cnf(f_192_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_689,tc_HOL_Obool)),U_690),c_Orderings_Otop__class_Otop(tc_fun(U_689,tc_HOL_Obool))) = U_690,
inference(clausify,[status(thm)],[f_192_2]) ).
fof(f_193_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_193_2,plain,
! [U_692,U_691] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_691,tc_HOL_Obool)),U_692),U_692) = U_692,
inference(variable_rename,[status(thm)],[f_193_1]) ).
cnf(f_193_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_691,tc_HOL_Obool)),U_692),U_692) = U_692,
inference(clausify,[status(thm)],[f_193_2]) ).
fof(f_194_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_194_2,plain,
! [U_695,U_694,U_693] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_693,tc_HOL_Obool)),U_694),U_695) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_693,tc_HOL_Obool)),U_695),U_694),
inference(variable_rename,[status(thm)],[f_194_1]) ).
cnf(f_194_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_693,tc_HOL_Obool)),U_694),U_695) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_693,tc_HOL_Obool)),U_695),U_694),
inference(clausify,[status(thm)],[f_194_2]) ).
fof(f_195_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_195_2,plain,
! [U_698,U_697,U_696] : hAPP(hAPP(c_Set_Oinsert(U_696),U_697),hAPP(hAPP(c_Set_Oinsert(U_696),U_697),U_698)) = hAPP(hAPP(c_Set_Oinsert(U_696),U_697),U_698),
inference(variable_rename,[status(thm)],[f_195_1]) ).
cnf(f_195_3,plain,
hAPP(hAPP(c_Set_Oinsert(U_696),U_697),hAPP(hAPP(c_Set_Oinsert(U_696),U_697),U_698)) = hAPP(hAPP(c_Set_Oinsert(U_696),U_697),U_698),
inference(clausify,[status(thm)],[f_195_2]) ).
fof(f_196_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_196_2,plain,
! [U_701,U_700,U_699] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_699,tc_HOL_Obool)),U_700),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_699,tc_HOL_Obool)),U_700),U_701)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_699,tc_HOL_Obool)),U_700),U_701),
inference(variable_rename,[status(thm)],[f_196_1]) ).
cnf(f_196_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_699,tc_HOL_Obool)),U_700),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_699,tc_HOL_Obool)),U_700),U_701)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_699,tc_HOL_Obool)),U_700),U_701),
inference(clausify,[status(thm)],[f_196_2]) ).
fof(f_197_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_197_2,plain,
! [U_705,U_704,U_703,U_702] : hAPP(hAPP(c_Set_Oinsert(U_702),U_703),hAPP(hAPP(c_Set_Oinsert(U_702),U_704),U_705)) = hAPP(hAPP(c_Set_Oinsert(U_702),U_704),hAPP(hAPP(c_Set_Oinsert(U_702),U_703),U_705)),
inference(variable_rename,[status(thm)],[f_197_1]) ).
cnf(f_197_3,plain,
hAPP(hAPP(c_Set_Oinsert(U_702),U_703),hAPP(hAPP(c_Set_Oinsert(U_702),U_704),U_705)) = hAPP(hAPP(c_Set_Oinsert(U_702),U_704),hAPP(hAPP(c_Set_Oinsert(U_702),U_703),U_705)),
inference(clausify,[status(thm)],[f_197_2]) ).
fof(f_198_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_198_2,plain,
! [U_709,U_708,U_707,U_706] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_706,tc_HOL_Obool)),U_707),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_706,tc_HOL_Obool)),U_708),U_709)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_706,tc_HOL_Obool)),U_708),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_706,tc_HOL_Obool)),U_707),U_709)),
inference(variable_rename,[status(thm)],[f_198_1]) ).
cnf(f_198_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_706,tc_HOL_Obool)),U_707),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_706,tc_HOL_Obool)),U_708),U_709)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_706,tc_HOL_Obool)),U_708),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_706,tc_HOL_Obool)),U_707),U_709)),
inference(clausify,[status(thm)],[f_198_2]) ).
fof(f_199_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_199_2,plain,
! [U_714,U_713,U_712,U_711,U_710] : hAPP(c_Set_Oimage(U_710,U_711,U_712),hAPP(hAPP(c_Set_Oinsert(U_710),U_713),U_714)) = hAPP(hAPP(c_Set_Oinsert(U_711),hAPP(U_712,U_713)),hAPP(c_Set_Oimage(U_710,U_711,U_712),U_714)),
inference(variable_rename,[status(thm)],[f_199_1]) ).
cnf(f_199_3,plain,
hAPP(c_Set_Oimage(U_710,U_711,U_712),hAPP(hAPP(c_Set_Oinsert(U_710),U_713),U_714)) = hAPP(hAPP(c_Set_Oinsert(U_711),hAPP(U_712,U_713)),hAPP(c_Set_Oimage(U_710,U_711,U_712),U_714)),
inference(clausify,[status(thm)],[f_199_2]) ).
fof(f_200_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_200_2,plain,
! [U_718,U_717,U_716,U_715] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_715,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_715,tc_HOL_Obool)),U_716),U_717)),U_718) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_715,tc_HOL_Obool)),U_716),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_715,tc_HOL_Obool)),U_717),U_718)),
inference(variable_rename,[status(thm)],[f_200_1]) ).
cnf(f_200_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_715,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_715,tc_HOL_Obool)),U_716),U_717)),U_718) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_715,tc_HOL_Obool)),U_716),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_715,tc_HOL_Obool)),U_717),U_718)),
inference(clausify,[status(thm)],[f_200_2]) ).
fof(f_201_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_201_2,plain,
! [U_722,U_721,U_720,U_719] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_719,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_719),U_720),U_721)),hAPP(hAPP(c_Set_Oinsert(U_719),U_720),U_722)) = hAPP(hAPP(c_Set_Oinsert(U_719),U_720),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_719,tc_HOL_Obool)),U_721),U_722)),
inference(variable_rename,[status(thm)],[f_201_1]) ).
cnf(f_201_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_719,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_719),U_720),U_721)),hAPP(hAPP(c_Set_Oinsert(U_719),U_720),U_722)) = hAPP(hAPP(c_Set_Oinsert(U_719),U_720),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_719,tc_HOL_Obool)),U_721),U_722)),
inference(clausify,[status(thm)],[f_201_2]) ).
fof(f_202_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_202_2,plain,
! [U_726,U_725,U_724,U_723] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_723),U_724),U_725),U_726))
| ( ~ hBOOL(hAPP(U_725,U_726))
& U_724 != U_726 ) )
& ( hBOOL(hAPP(U_725,U_726))
| U_724 = U_726
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_723),U_724),U_725),U_726)) ) ),
inference(variable_rename,[status(thm)],[f_202_1]) ).
fof(f_202_3,plain,
( ! [U_734,U_732,U_730] :
( ! [U_728] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_728),U_730),U_732),U_734))
| ( ~ hBOOL(hAPP(U_732,U_734))
& U_730 != U_734 ) )
& ! [U_733,U_731,U_729] :
( ! [U_727] : ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_727),U_729),U_731),U_733))
| hBOOL(hAPP(U_731,U_733))
| U_729 = U_733 ) ),
inference(miniscope,[status(thm)],[f_202_2]) ).
cnf(f_202_4,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_727),U_729),U_731),U_733))
| hBOOL(hAPP(U_731,U_733))
| U_729 = U_733 ),
inference(clausify,[status(thm)],[f_202_3]) ).
cnf(f_202_5,plain,
( U_730 != U_734
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_728),U_730),U_732),U_734)) ),
inference(clausify,[status(thm)],[f_202_3]) ).
cnf(f_202_6,plain,
( ~ hBOOL(hAPP(U_732,U_734))
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_728),U_730),U_732),U_734)) ),
inference(clausify,[status(thm)],[f_202_3]) ).
fof(f_203_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_203_2,plain,
! [U_738,U_737,U_736,U_735] :
( hBOOL(hAPP(U_736,U_738))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_735,tc_HOL_Obool)),U_736),U_737),U_738)) ),
inference(variable_rename,[status(thm)],[f_203_1]) ).
fof(f_203_3,plain,
! [U_738,U_737,U_736] :
( ! [U_735] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_735,tc_HOL_Obool)),U_736),U_737),U_738))
| hBOOL(hAPP(U_736,U_738)) ),
inference(miniscope,[status(thm)],[f_203_2]) ).
cnf(f_203_4,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_735,tc_HOL_Obool)),U_736),U_737),U_738))
| hBOOL(hAPP(U_736,U_738)) ),
inference(clausify,[status(thm)],[f_203_3]) ).
fof(f_204_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_204_2,plain,
! [U_742,U_741,U_740,U_739] :
( hBOOL(hAPP(U_741,U_742))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_739,tc_HOL_Obool)),U_740),U_741),U_742)) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
fof(f_204_3,plain,
! [U_742,U_741] :
( ! [U_740,U_739] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_739,tc_HOL_Obool)),U_740),U_741),U_742))
| hBOOL(hAPP(U_741,U_742)) ),
inference(miniscope,[status(thm)],[f_204_2]) ).
cnf(f_204_4,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_739,tc_HOL_Obool)),U_740),U_741),U_742))
| hBOOL(hAPP(U_741,U_742)) ),
inference(clausify,[status(thm)],[f_204_3]) ).
fof(f_205_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_205_2,plain,
! [U_744,U_743] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_743),U_744),U_744) = U_744
| ~ class_Lattices_Olattice(U_743) ),
inference(variable_rename,[status(thm)],[f_205_1]) ).
cnf(f_205_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_743),U_744),U_744) = U_744
| ~ class_Lattices_Olattice(U_743) ),
inference(clausify,[status(thm)],[f_205_2]) ).
fof(f_206_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_206_2,plain,
! [U_749,U_748,U_747,U_746,U_745] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_745,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_746,U_745,U_747),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_746,tc_HOL_Obool)),U_748),U_749))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_745,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_746,U_745,U_747),U_748)),hAPP(c_Set_Oimage(U_746,U_745,U_747),U_749)))),
inference(variable_rename,[status(thm)],[f_206_1]) ).
cnf(f_206_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_745,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_746,U_745,U_747),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_746,tc_HOL_Obool)),U_748),U_749))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_745,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_746,U_745,U_747),U_748)),hAPP(c_Set_Oimage(U_746,U_745,U_747),U_749)))),
inference(clausify,[status(thm)],[f_206_2]) ).
fof(f_207_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_207_2,plain,
! [U_754,U_753,U_752,U_751,U_750] :
( hAPP(c_Set_Oimage(tc_fun(U_750,tc_HOL_Obool),tc_fun(U_751,tc_HOL_Obool),c_Set_Oimage(U_750,U_751,U_752)),hAPP(c_Set_OPow(U_750),U_753)) = hAPP(c_Set_OPow(U_751),U_754)
| hAPP(c_Set_Oimage(U_750,U_751,U_752),U_753) != U_754 ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
cnf(f_207_3,plain,
( hAPP(c_Set_Oimage(tc_fun(U_750,tc_HOL_Obool),tc_fun(U_751,tc_HOL_Obool),c_Set_Oimage(U_750,U_751,U_752)),hAPP(c_Set_OPow(U_750),U_753)) = hAPP(c_Set_OPow(U_751),U_754)
| hAPP(c_Set_Oimage(U_750,U_751,U_752),U_753) != U_754 ),
inference(clausify,[status(thm)],[f_207_2]) ).
fof(f_208_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_208_2,plain,
! [U_757,U_756,U_755] :
( c_Complete__Lattice_OInf__class_OInf(U_755,hAPP(hAPP(c_Set_Oinsert(U_755),U_756),U_757)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_755),U_756),c_Complete__Lattice_OInf__class_OInf(U_755,U_757))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_755) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
cnf(f_208_3,plain,
( c_Complete__Lattice_OInf__class_OInf(U_755,hAPP(hAPP(c_Set_Oinsert(U_755),U_756),U_757)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_755),U_756),c_Complete__Lattice_OInf__class_OInf(U_755,U_757))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_755) ),
inference(clausify,[status(thm)],[f_208_2]) ).
fof(f_209_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_209_2,plain,
! [U_760,U_759,U_758] : hAPP(c_Set_OPow(U_758),hAPP(hAPP(c_Set_Oinsert(U_758),U_759),U_760)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_758,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_758),U_760)),hAPP(c_Set_Oimage(tc_fun(U_758,tc_HOL_Obool),tc_fun(U_758,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_758),U_759)),hAPP(c_Set_OPow(U_758),U_760))),
inference(variable_rename,[status(thm)],[f_209_1]) ).
cnf(f_209_3,plain,
hAPP(c_Set_OPow(U_758),hAPP(hAPP(c_Set_Oinsert(U_758),U_759),U_760)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_758,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_758),U_760)),hAPP(c_Set_Oimage(tc_fun(U_758,tc_HOL_Obool),tc_fun(U_758,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_758),U_759)),hAPP(c_Set_OPow(U_758),U_760))),
inference(clausify,[status(thm)],[f_209_2]) ).
fof(f_210_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_210_2,plain,
! [U_763,U_762,U_761] : hAPP(c_Set_OPow(U_761),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_761,tc_HOL_Obool)),U_762),U_763)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_761,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_761),U_762)),hAPP(c_Set_OPow(U_761),U_763)),
inference(variable_rename,[status(thm)],[f_210_1]) ).
cnf(f_210_3,plain,
hAPP(c_Set_OPow(U_761),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_761,tc_HOL_Obool)),U_762),U_763)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_761,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_761),U_762)),hAPP(c_Set_OPow(U_761),U_763)),
inference(clausify,[status(thm)],[f_210_2]) ).
fof(f_211_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_211_2,plain,
! [U_764] : hAPP(c_Set_OPow(U_764),c_Orderings_Otop__class_Otop(tc_fun(U_764,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_764,tc_HOL_Obool),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_211_1]) ).
cnf(f_211_3,plain,
hAPP(c_Set_OPow(U_764),c_Orderings_Otop__class_Otop(tc_fun(U_764,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_764,tc_HOL_Obool),tc_HOL_Obool)),
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__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_212_2,plain,
! [U_767,U_766,U_765] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_765),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_765),U_766),U_767)),U_766))
| ~ class_Lattices_Olattice(U_765) ),
inference(variable_rename,[status(thm)],[f_212_1]) ).
cnf(f_212_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_765),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_765),U_766),U_767)),U_766))
| ~ class_Lattices_Olattice(U_765) ),
inference(clausify,[status(thm)],[f_212_2]) ).
fof(f_213_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_213_2,plain,
! [U_770,U_769,U_768] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_768),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_768),U_769),U_770)),U_769))
| ~ class_Lattices_Osemilattice__inf(U_768) ),
inference(variable_rename,[status(thm)],[f_213_1]) ).
cnf(f_213_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_768),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_768),U_769),U_770)),U_769))
| ~ class_Lattices_Osemilattice__inf(U_768) ),
inference(clausify,[status(thm)],[f_213_2]) ).
fof(f_214_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_214_2,plain,
! [U_773,U_772,U_771] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_771),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_771),U_772),U_773)),U_773))
| ~ class_Lattices_Olattice(U_771) ),
inference(variable_rename,[status(thm)],[f_214_1]) ).
cnf(f_214_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_771),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_771),U_772),U_773)),U_773))
| ~ class_Lattices_Olattice(U_771) ),
inference(clausify,[status(thm)],[f_214_2]) ).
fof(f_215_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_215_2,plain,
! [U_776,U_775,U_774] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_774),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_774),U_775),U_776)),U_776))
| ~ class_Lattices_Osemilattice__inf(U_774) ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
cnf(f_215_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_774),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_774),U_775),U_776)),U_776))
| ~ class_Lattices_Osemilattice__inf(U_774) ),
inference(clausify,[status(thm)],[f_215_2]) ).
fof(f_216_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_216_2,plain,
! [U_779,U_778,U_777] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_777),U_778),U_779))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_777),U_778),U_779) != U_778 )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_777),U_778),U_779) = U_778
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_777),U_778),U_779)) ) )
| ~ class_Lattices_Osemilattice__inf(U_777) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
cnf(f_216_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_777),U_778),U_779) = U_778
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_777),U_778),U_779))
| ~ class_Lattices_Osemilattice__inf(U_777) ),
inference(clausify,[status(thm)],[f_216_2]) ).
cnf(f_216_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_777),U_778),U_779))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_777),U_778),U_779) != U_778
| ~ class_Lattices_Osemilattice__inf(U_777) ),
inference(clausify,[status(thm)],[f_216_2]) ).
fof(f_217_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_217_2,plain,
! [U_783,U_782,U_781,U_780] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_780),U_781),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_780),U_782),U_783)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_780),U_781),U_783))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_780),U_781),U_782)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_780),U_781),U_783))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_780),U_781),U_782)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_780),U_781),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_780),U_782),U_783))) ) )
| ~ class_Lattices_Osemilattice__inf(U_780) ),
inference(variable_rename,[status(thm)],[f_217_1]) ).
cnf(f_217_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_780),U_781),U_782))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_780),U_781),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_780),U_782),U_783)))
| ~ class_Lattices_Osemilattice__inf(U_780) ),
inference(clausify,[status(thm)],[f_217_2]) ).
cnf(f_217_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_780),U_781),U_783))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_780),U_781),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_780),U_782),U_783)))
| ~ class_Lattices_Osemilattice__inf(U_780) ),
inference(clausify,[status(thm)],[f_217_2]) ).
cnf(f_217_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_780),U_781),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_780),U_782),U_783)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_780),U_781),U_783))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_780),U_781),U_782))
| ~ class_Lattices_Osemilattice__inf(U_780) ),
inference(clausify,[status(thm)],[f_217_2]) ).
fof(f_218_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_218_2,plain,
! [U_787,U_786,U_785,U_784] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_784),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_784),U_785),U_787)),U_786))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_784),U_785),U_786))
| ~ class_Lattices_Osemilattice__inf(U_784) ),
inference(variable_rename,[status(thm)],[f_218_1]) ).
cnf(f_218_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_784),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_784),U_785),U_787)),U_786))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_784),U_785),U_786))
| ~ class_Lattices_Osemilattice__inf(U_784) ),
inference(clausify,[status(thm)],[f_218_2]) ).
fof(f_219_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_219_2,plain,
! [U_791,U_790,U_789,U_788] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_788),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_788),U_791),U_789)),U_790))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_788),U_789),U_790))
| ~ class_Lattices_Osemilattice__inf(U_788) ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
cnf(f_219_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_788),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_788),U_791),U_789)),U_790))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_788),U_789),U_790))
| ~ class_Lattices_Osemilattice__inf(U_788) ),
inference(clausify,[status(thm)],[f_219_2]) ).
fof(f_220_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_220_2,plain,
! [U_794,U_793,U_792] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_792),U_793),U_794) = U_793
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_792),U_793),U_794))
| ~ class_Lattices_Osemilattice__inf(U_792) ),
inference(variable_rename,[status(thm)],[f_220_1]) ).
cnf(f_220_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_792),U_793),U_794) = U_793
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_792),U_793),U_794))
| ~ class_Lattices_Osemilattice__inf(U_792) ),
inference(clausify,[status(thm)],[f_220_2]) ).
fof(f_221_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_221_2,plain,
! [U_797,U_796,U_795] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_795),U_797),U_796) = U_796
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_795),U_796),U_797))
| ~ class_Lattices_Osemilattice__inf(U_795) ),
inference(variable_rename,[status(thm)],[f_221_1]) ).
cnf(f_221_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_795),U_797),U_796) = U_796
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_795),U_796),U_797))
| ~ class_Lattices_Osemilattice__inf(U_795) ),
inference(clausify,[status(thm)],[f_221_2]) ).
fof(f_222_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_222_2,plain,
! [U_801,U_800,U_799,U_798] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_798),U_799),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_798),U_800),U_801)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_798),U_799),U_801))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_798),U_799),U_800))
| ~ class_Lattices_Osemilattice__inf(U_798) ),
inference(variable_rename,[status(thm)],[f_222_1]) ).
cnf(f_222_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_798),U_799),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_798),U_800),U_801)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_798),U_799),U_801))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_798),U_799),U_800))
| ~ class_Lattices_Osemilattice__inf(U_798) ),
inference(clausify,[status(thm)],[f_222_2]) ).
fof(f_223_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_223_2,plain,
! [U_805,U_804,U_803,U_802] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_802),U_803),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_802),U_804),U_805)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_802),U_803),U_805))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_802),U_803),U_804))
| ~ class_Lattices_Osemilattice__inf(U_802) ),
inference(variable_rename,[status(thm)],[f_223_1]) ).
cnf(f_223_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_802),U_803),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_802),U_804),U_805)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_802),U_803),U_805))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_802),U_803),U_804))
| ~ class_Lattices_Osemilattice__inf(U_802) ),
inference(clausify,[status(thm)],[f_223_2]) ).
fof(f_224_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_224_2,plain,
! [U_810,U_809,U_808,U_807,U_806] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_806),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_806),U_807),U_809)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_806),U_808),U_810)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_806),U_809),U_810))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_806),U_807),U_808))
| ~ class_Lattices_Osemilattice__inf(U_806) ),
inference(variable_rename,[status(thm)],[f_224_1]) ).
cnf(f_224_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_806),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_806),U_807),U_809)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_806),U_808),U_810)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_806),U_809),U_810))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_806),U_807),U_808))
| ~ class_Lattices_Osemilattice__inf(U_806) ),
inference(clausify,[status(thm)],[f_224_2]) ).
fof(f_225_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_225_2,plain,
! [U_814,U_813,U_812,U_811] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_811),U_812),U_814))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_811),U_812),U_813)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_811),U_812),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_811),U_813),U_814)))
| ~ class_Lattices_Osemilattice__inf(U_811) ),
inference(variable_rename,[status(thm)],[f_225_1]) ).
cnf(f_225_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_811),U_812),U_813))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_811),U_812),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_811),U_813),U_814)))
| ~ class_Lattices_Osemilattice__inf(U_811) ),
inference(clausify,[status(thm)],[f_225_2]) ).
cnf(f_225_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_811),U_812),U_814))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_811),U_812),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_811),U_813),U_814)))
| ~ class_Lattices_Osemilattice__inf(U_811) ),
inference(clausify,[status(thm)],[f_225_2]) ).
fof(f_226_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_226_2,plain,
! [U_821,U_820,U_819,U_818,U_817] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_817,tc_HOL_Obool)),U_818),hAPP(c_Set_Oimage(U_819,U_817,U_820),U_821)))
| ! [U_816] :
( U_818 != hAPP(c_Set_Oimage(U_819,U_817,U_820),U_816)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_819,tc_HOL_Obool)),U_816),U_821)) ) )
& ( ? [U_815] :
( U_818 = hAPP(c_Set_Oimage(U_819,U_817,U_820),U_815)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_819,tc_HOL_Obool)),U_815),U_821)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_817,tc_HOL_Obool)),U_818),hAPP(c_Set_Oimage(U_819,U_817,U_820),U_821))) ) ),
inference(variable_rename,[status(thm)],[f_226_1]) ).
fof(f_226_3,plain,
( ! [U_831,U_829,U_827,U_825,U_823] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_823,tc_HOL_Obool)),U_825),hAPP(c_Set_Oimage(U_827,U_823,U_829),U_831)))
| ! [U_816] :
( U_825 != hAPP(c_Set_Oimage(U_827,U_823,U_829),U_816)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_827,tc_HOL_Obool)),U_816),U_831)) ) )
& ! [U_830,U_828,U_826,U_824,U_822] :
( ? [U_815] :
( U_824 = hAPP(c_Set_Oimage(U_826,U_822,U_828),U_815)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_826,tc_HOL_Obool)),U_815),U_830)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_822,tc_HOL_Obool)),U_824),hAPP(c_Set_Oimage(U_826,U_822,U_828),U_830))) ) ),
inference(miniscope,[status(thm)],[f_226_2]) ).
fof(f_226_4,plain,
( ! [U_831,U_829,U_827,U_825,U_823] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_823,tc_HOL_Obool)),U_825),hAPP(c_Set_Oimage(U_827,U_823,U_829),U_831)))
| ! [U_816] :
( U_825 != hAPP(c_Set_Oimage(U_827,U_823,U_829),U_816)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_827,tc_HOL_Obool)),U_816),U_831)) ) )
& ! [U_830,U_828,U_826,U_824,U_822] :
( ( U_824 = hAPP(c_Set_Oimage(U_826,U_822,U_828),sK18(U_830,U_828,U_826,U_824,U_822))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_826,tc_HOL_Obool)),sK18(U_830,U_828,U_826,U_824,U_822)),U_830)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_822,tc_HOL_Obool)),U_824),hAPP(c_Set_Oimage(U_826,U_822,U_828),U_830))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_815,sK18(U_830,U_828,U_826,U_824,U_822))],[f_226_3]) ).
cnf(f_226_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_826,tc_HOL_Obool)),sK18(U_830,U_828,U_826,U_824,U_822)),U_830))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_822,tc_HOL_Obool)),U_824),hAPP(c_Set_Oimage(U_826,U_822,U_828),U_830))) ),
inference(clausify,[status(thm)],[f_226_4]) ).
cnf(f_226_6,plain,
( U_824 = hAPP(c_Set_Oimage(U_826,U_822,U_828),sK18(U_830,U_828,U_826,U_824,U_822))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_822,tc_HOL_Obool)),U_824),hAPP(c_Set_Oimage(U_826,U_822,U_828),U_830))) ),
inference(clausify,[status(thm)],[f_226_4]) ).
cnf(f_226_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_823,tc_HOL_Obool)),U_825),hAPP(c_Set_Oimage(U_827,U_823,U_829),U_831)))
| U_825 != hAPP(c_Set_Oimage(U_827,U_823,U_829),U_816)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_827,tc_HOL_Obool)),U_816),U_831)) ),
inference(clausify,[status(thm)],[f_226_4]) ).
fof(f_227_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_227_2,plain,
! [U_836,U_835,U_834,U_833,U_832] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_835,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_832,U_835,U_836),U_833)),hAPP(c_Set_Oimage(U_832,U_835,U_836),U_834)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_832,tc_HOL_Obool)),U_833),U_834)) ),
inference(variable_rename,[status(thm)],[f_227_1]) ).
cnf(f_227_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_835,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_832,U_835,U_836),U_833)),hAPP(c_Set_Oimage(U_832,U_835,U_836),U_834)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_832,tc_HOL_Obool)),U_833),U_834)) ),
inference(clausify,[status(thm)],[f_227_2]) ).
fof(f_228_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_228_2,plain,
! [U_841,U_840,U_839,U_838,U_837] : hAPP(c_Set_Oimage(U_837,U_838,U_839),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_837,tc_HOL_Obool)),U_840),U_841)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_838,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_837,U_838,U_839),U_840)),hAPP(c_Set_Oimage(U_837,U_838,U_839),U_841)),
inference(variable_rename,[status(thm)],[f_228_1]) ).
cnf(f_228_3,plain,
hAPP(c_Set_Oimage(U_837,U_838,U_839),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_837,tc_HOL_Obool)),U_840),U_841)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_838,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_837,U_838,U_839),U_840)),hAPP(c_Set_Oimage(U_837,U_838,U_839),U_841)),
inference(clausify,[status(thm)],[f_228_2]) ).
fof(f_229_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_229_2,plain,
! [U_845,U_844,U_843,U_842] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_842),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_842),U_843),U_844)),U_845) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_842),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_842),U_843),U_845)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_842),U_844),U_845))
| ~ class_Lattices_Odistrib__lattice(U_842) ),
inference(variable_rename,[status(thm)],[f_229_1]) ).
cnf(f_229_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_842),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_842),U_843),U_844)),U_845) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_842),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_842),U_843),U_845)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_842),U_844),U_845))
| ~ class_Lattices_Odistrib__lattice(U_842) ),
inference(clausify,[status(thm)],[f_229_2]) ).
fof(f_230_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_230_2,plain,
! [U_849,U_848,U_847,U_846] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_846),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_846),U_847),U_848)),U_849) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_846),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_846),U_847),U_849)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_846),U_848),U_849))
| ~ class_Lattices_Odistrib__lattice(U_846) ),
inference(variable_rename,[status(thm)],[f_230_1]) ).
cnf(f_230_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_846),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_846),U_847),U_848)),U_849) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_846),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_846),U_847),U_849)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_846),U_848),U_849))
| ~ class_Lattices_Odistrib__lattice(U_846) ),
inference(clausify,[status(thm)],[f_230_2]) ).
fof(f_231_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_231_2,plain,
! [U_853,U_852,U_851,U_850] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_850),U_851),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_850),U_852),U_853)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_850),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_850),U_851),U_852)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_850),U_851),U_853))
| ~ class_Lattices_Odistrib__lattice(U_850) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
cnf(f_231_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_850),U_851),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_850),U_852),U_853)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_850),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_850),U_851),U_852)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_850),U_851),U_853))
| ~ class_Lattices_Odistrib__lattice(U_850) ),
inference(clausify,[status(thm)],[f_231_2]) ).
fof(f_232_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_232_2,plain,
! [U_857,U_856,U_855,U_854] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_854),U_855),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_854),U_856),U_857)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_854),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_854),U_855),U_856)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_854),U_855),U_857))
| ~ class_Lattices_Odistrib__lattice(U_854) ),
inference(variable_rename,[status(thm)],[f_232_1]) ).
cnf(f_232_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_854),U_855),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_854),U_856),U_857)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_854),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_854),U_855),U_856)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_854),U_855),U_857))
| ~ class_Lattices_Odistrib__lattice(U_854) ),
inference(clausify,[status(thm)],[f_232_2]) ).
fof(f_233_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_233_2,plain,
! [U_860,U_859,U_858] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_858),U_859),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_858),U_859),U_860)) = U_859
| ~ class_Lattices_Olattice(U_858) ),
inference(variable_rename,[status(thm)],[f_233_1]) ).
cnf(f_233_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_858),U_859),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_858),U_859),U_860)) = U_859
| ~ class_Lattices_Olattice(U_858) ),
inference(clausify,[status(thm)],[f_233_2]) ).
fof(f_234_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_234_2,plain,
! [U_863,U_862,U_861] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_861),U_862),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_861),U_862),U_863)) = U_862
| ~ class_Lattices_Olattice(U_861) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
cnf(f_234_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_861),U_862),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_861),U_862),U_863)) = U_862
| ~ class_Lattices_Olattice(U_861) ),
inference(clausify,[status(thm)],[f_234_2]) ).
fof(f_235_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_235_2,plain,
! [U_866,U_865,U_864] :
( hAPP(c_Set_Oimage(U_864,U_864,c_Groups_Ouminus__class_Ouminus(U_864)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_864,U_865),U_866)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_864,hAPP(c_Groups_Ouminus__class_Ouminus(U_864),U_866),hAPP(c_Groups_Ouminus__class_Ouminus(U_864),U_865))
| ~ class_Groups_Oordered__ab__group__add(U_864) ),
inference(variable_rename,[status(thm)],[f_235_1]) ).
cnf(f_235_3,plain,
( hAPP(c_Set_Oimage(U_864,U_864,c_Groups_Ouminus__class_Ouminus(U_864)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_864,U_865),U_866)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_864,hAPP(c_Groups_Ouminus__class_Ouminus(U_864),U_866),hAPP(c_Groups_Ouminus__class_Ouminus(U_864),U_865))
| ~ class_Groups_Oordered__ab__group__add(U_864) ),
inference(clausify,[status(thm)],[f_235_2]) ).
fof(f_236_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_236_2,plain,
! [U_869,U_868,U_867] :
( hAPP(c_Set_Oimage(U_867,U_867,c_Groups_Ouminus__class_Ouminus(U_867)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_867,U_868,U_869)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_867,hAPP(c_Groups_Ouminus__class_Ouminus(U_867),U_869)),hAPP(c_Groups_Ouminus__class_Ouminus(U_867),U_868))
| ~ class_Groups_Oordered__ab__group__add(U_867) ),
inference(variable_rename,[status(thm)],[f_236_1]) ).
cnf(f_236_3,plain,
( hAPP(c_Set_Oimage(U_867,U_867,c_Groups_Ouminus__class_Ouminus(U_867)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_867,U_868,U_869)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_867,hAPP(c_Groups_Ouminus__class_Ouminus(U_867),U_869)),hAPP(c_Groups_Ouminus__class_Ouminus(U_867),U_868))
| ~ class_Groups_Oordered__ab__group__add(U_867) ),
inference(clausify,[status(thm)],[f_236_2]) ).
fof(f_237_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_237_2,plain,
! [U_872,U_871,U_870] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_870,tc_HOL_Obool)),U_871),hAPP(hAPP(c_Set_Oinsert(U_870),U_872),U_871))),
inference(variable_rename,[status(thm)],[f_237_1]) ).
cnf(f_237_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_870,tc_HOL_Obool)),U_871),hAPP(hAPP(c_Set_Oinsert(U_870),U_872),U_871))),
inference(clausify,[status(thm)],[f_237_2]) ).
fof(f_238_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_238_2,plain,
! [U_876,U_875,U_874,U_873] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_873,tc_HOL_Obool)),U_874),hAPP(hAPP(c_Set_Oinsert(U_873),U_876),U_875)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_873,tc_HOL_Obool)),U_874),U_875)) ),
inference(variable_rename,[status(thm)],[f_238_1]) ).
cnf(f_238_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_873,tc_HOL_Obool)),U_874),hAPP(hAPP(c_Set_Oinsert(U_873),U_876),U_875)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_873,tc_HOL_Obool)),U_874),U_875)) ),
inference(clausify,[status(thm)],[f_238_2]) ).
fof(f_239_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_239_2,plain,
! [U_880,U_879,U_878,U_877] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_877,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_877),U_880),U_878)),hAPP(hAPP(c_Set_Oinsert(U_877),U_880),U_879)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_877,tc_HOL_Obool)),U_878),U_879)) ),
inference(variable_rename,[status(thm)],[f_239_1]) ).
cnf(f_239_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_877,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_877),U_880),U_878)),hAPP(hAPP(c_Set_Oinsert(U_877),U_880),U_879)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_877,tc_HOL_Obool)),U_878),U_879)) ),
inference(clausify,[status(thm)],[f_239_2]) ).
fof(f_240_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_240_2,plain,
! [U_883,U_882,U_881] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_881,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_881,tc_HOL_Obool)),U_882),U_883)),U_882)),
inference(variable_rename,[status(thm)],[f_240_1]) ).
cnf(f_240_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_881,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_881,tc_HOL_Obool)),U_882),U_883)),U_882)),
inference(clausify,[status(thm)],[f_240_2]) ).
fof(f_241_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_241_2,plain,
! [U_886,U_885,U_884] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_884,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_884,tc_HOL_Obool)),U_885),U_886)),U_886)),
inference(variable_rename,[status(thm)],[f_241_1]) ).
cnf(f_241_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_884,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_884,tc_HOL_Obool)),U_885),U_886)),U_886)),
inference(clausify,[status(thm)],[f_241_2]) ).
fof(f_242_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_242_2,plain,
! [U_889,U_888,U_887] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_887,tc_HOL_Obool)),U_888),U_889) = U_888
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_887,tc_HOL_Obool)),U_888),U_889)) ),
inference(variable_rename,[status(thm)],[f_242_1]) ).
cnf(f_242_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_887,tc_HOL_Obool)),U_888),U_889) = U_888
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_887,tc_HOL_Obool)),U_888),U_889)) ),
inference(clausify,[status(thm)],[f_242_2]) ).
fof(f_243_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_243_2,plain,
! [U_892,U_891,U_890] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_890,tc_HOL_Obool)),U_892),U_891) = U_891
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_890,tc_HOL_Obool)),U_891),U_892)) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
cnf(f_243_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_890,tc_HOL_Obool)),U_892),U_891) = U_891
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_890,tc_HOL_Obool)),U_891),U_892)) ),
inference(clausify,[status(thm)],[f_243_2]) ).
fof(f_244_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_244_2,plain,
! [U_896,U_895,U_894,U_893] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_893,tc_HOL_Obool)),U_894),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_893,tc_HOL_Obool)),U_895),U_896)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_893,tc_HOL_Obool)),U_894),U_896))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_893,tc_HOL_Obool)),U_894),U_895)) ),
inference(variable_rename,[status(thm)],[f_244_1]) ).
cnf(f_244_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_893,tc_HOL_Obool)),U_894),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_893,tc_HOL_Obool)),U_895),U_896)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_893,tc_HOL_Obool)),U_894),U_896))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_893,tc_HOL_Obool)),U_894),U_895)) ),
inference(clausify,[status(thm)],[f_244_2]) ).
fof(f_245_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_245_2,plain,
! [U_901,U_900,U_899,U_898,U_897] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_897,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_897,tc_HOL_Obool)),U_898),U_900)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_897,tc_HOL_Obool)),U_899),U_901)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_897,tc_HOL_Obool)),U_900),U_901))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_897,tc_HOL_Obool)),U_898),U_899)) ),
inference(variable_rename,[status(thm)],[f_245_1]) ).
cnf(f_245_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_897,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_897,tc_HOL_Obool)),U_898),U_900)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_897,tc_HOL_Obool)),U_899),U_901)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_897,tc_HOL_Obool)),U_900),U_901))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_897,tc_HOL_Obool)),U_898),U_899)) ),
inference(clausify,[status(thm)],[f_245_2]) ).
fof(f_246_1,plain,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_mono__Int]) ).
fof(f_246_2,plain,
! [U_906,U_905,U_904,U_903,U_902] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_903,tc_HOL_Obool)),hAPP(U_904,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_902,tc_HOL_Obool)),U_905),U_906))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_903,tc_HOL_Obool)),hAPP(U_904,U_905)),hAPP(U_904,U_906))))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_902,tc_HOL_Obool),tc_fun(U_903,tc_HOL_Obool),U_904) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
cnf(f_246_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_903,tc_HOL_Obool)),hAPP(U_904,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_902,tc_HOL_Obool)),U_905),U_906))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_903,tc_HOL_Obool)),hAPP(U_904,U_905)),hAPP(U_904,U_906))))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_902,tc_HOL_Obool),tc_fun(U_903,tc_HOL_Obool),U_904) ),
inference(clausify,[status(thm)],[f_246_2]) ).
fof(f_247_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_247_2,plain,
! [U_910,U_909,U_908,U_907] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_907,tc_HOL_Obool)),U_908),hAPP(hAPP(c_Set_Oinsert(U_907),U_909),U_910)) = hAPP(hAPP(c_Set_Oinsert(U_907),U_909),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_907,tc_HOL_Obool)),U_908),U_910)),
inference(variable_rename,[status(thm)],[f_247_1]) ).
cnf(f_247_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_907,tc_HOL_Obool)),U_908),hAPP(hAPP(c_Set_Oinsert(U_907),U_909),U_910)) = hAPP(hAPP(c_Set_Oinsert(U_907),U_909),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_907,tc_HOL_Obool)),U_908),U_910)),
inference(clausify,[status(thm)],[f_247_2]) ).
fof(f_248_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_248_2,plain,
! [U_914,U_913,U_912,U_911] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_911,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_911),U_912),U_913)),U_914) = hAPP(hAPP(c_Set_Oinsert(U_911),U_912),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_911,tc_HOL_Obool)),U_913),U_914)),
inference(variable_rename,[status(thm)],[f_248_1]) ).
cnf(f_248_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_911,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_911),U_912),U_913)),U_914) = hAPP(hAPP(c_Set_Oinsert(U_911),U_912),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_911,tc_HOL_Obool)),U_913),U_914)),
inference(clausify,[status(thm)],[f_248_2]) ).
fof(f_249_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_249_2,plain,
! [U_918,U_917,U_916,U_915] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_915,tc_HOL_Obool)),U_916),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_915,tc_HOL_Obool)),U_917),U_918)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_915,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_915,tc_HOL_Obool)),U_916),U_917)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_915,tc_HOL_Obool)),U_916),U_918)),
inference(variable_rename,[status(thm)],[f_249_1]) ).
cnf(f_249_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_915,tc_HOL_Obool)),U_916),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_915,tc_HOL_Obool)),U_917),U_918)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_915,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_915,tc_HOL_Obool)),U_916),U_917)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_915,tc_HOL_Obool)),U_916),U_918)),
inference(clausify,[status(thm)],[f_249_2]) ).
fof(f_250_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_250_2,plain,
! [U_922,U_921,U_920,U_919] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_919,tc_HOL_Obool)),U_920),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_919,tc_HOL_Obool)),U_921),U_922)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_919,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_919,tc_HOL_Obool)),U_920),U_921)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_919,tc_HOL_Obool)),U_920),U_922)),
inference(variable_rename,[status(thm)],[f_250_1]) ).
cnf(f_250_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_919,tc_HOL_Obool)),U_920),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_919,tc_HOL_Obool)),U_921),U_922)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_919,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_919,tc_HOL_Obool)),U_920),U_921)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_919,tc_HOL_Obool)),U_920),U_922)),
inference(clausify,[status(thm)],[f_250_2]) ).
fof(f_251_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_251_2,plain,
! [U_926,U_925,U_924,U_923] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_923,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_923,tc_HOL_Obool)),U_924),U_925)),U_926) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_923,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_923,tc_HOL_Obool)),U_924),U_926)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_923,tc_HOL_Obool)),U_925),U_926)),
inference(variable_rename,[status(thm)],[f_251_1]) ).
cnf(f_251_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_923,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_923,tc_HOL_Obool)),U_924),U_925)),U_926) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_923,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_923,tc_HOL_Obool)),U_924),U_926)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_923,tc_HOL_Obool)),U_925),U_926)),
inference(clausify,[status(thm)],[f_251_2]) ).
fof(f_252_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_252_2,plain,
! [U_930,U_929,U_928,U_927] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_927,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_927,tc_HOL_Obool)),U_928),U_929)),U_930) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_927,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_927,tc_HOL_Obool)),U_928),U_930)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_927,tc_HOL_Obool)),U_929),U_930)),
inference(variable_rename,[status(thm)],[f_252_1]) ).
cnf(f_252_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_927,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_927,tc_HOL_Obool)),U_928),U_929)),U_930) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_927,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_927,tc_HOL_Obool)),U_928),U_930)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_927,tc_HOL_Obool)),U_929),U_930)),
inference(clausify,[status(thm)],[f_252_2]) ).
fof(f_253_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_253_2,plain,
! [U_934,U_933,U_932,U_931] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_931,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_931,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_931,tc_HOL_Obool)),U_932),U_933)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_931,tc_HOL_Obool)),U_933),U_934))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_931,tc_HOL_Obool)),U_934),U_932)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_931,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_931,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_931,tc_HOL_Obool)),U_932),U_933)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_931,tc_HOL_Obool)),U_933),U_934))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_931,tc_HOL_Obool)),U_934),U_932)),
inference(variable_rename,[status(thm)],[f_253_1]) ).
cnf(f_253_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_931,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_931,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_931,tc_HOL_Obool)),U_932),U_933)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_931,tc_HOL_Obool)),U_933),U_934))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_931,tc_HOL_Obool)),U_934),U_932)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_931,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_931,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_931,tc_HOL_Obool)),U_932),U_933)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_931,tc_HOL_Obool)),U_933),U_934))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_931,tc_HOL_Obool)),U_934),U_932)),
inference(clausify,[status(thm)],[f_253_2]) ).
fof(f_254_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_254_2,plain,
! [U_936,U_935] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_935,tc_HOL_Obool)),U_936),c_Orderings_Otop__class_Otop(tc_fun(U_935,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_254_1]) ).
cnf(f_254_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_935,tc_HOL_Obool)),U_936),c_Orderings_Otop__class_Otop(tc_fun(U_935,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_254_2]) ).
fof(f_255_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_255_2,plain,
! [U_938,U_937] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_937,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_937,tc_HOL_Obool))),U_938) = c_Orderings_Otop__class_Otop(tc_fun(U_937,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_255_1]) ).
cnf(f_255_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_937,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_937,tc_HOL_Obool))),U_938) = c_Orderings_Otop__class_Otop(tc_fun(U_937,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_255_2]) ).
fof(f_256_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_256_2,plain,
! [U_940,U_939] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_939,tc_HOL_Obool)),U_940),c_Orderings_Otop__class_Otop(tc_fun(U_939,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_939,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_256_1]) ).
cnf(f_256_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_939,tc_HOL_Obool)),U_940),c_Orderings_Otop__class_Otop(tc_fun(U_939,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_939,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_256_2]) ).
fof(f_257_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_257_2,plain,
! [U_943,U_942,U_941] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_941,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_941,tc_HOL_Obool),tc_HOL_Obool)),U_942),U_943)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_941,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_941,tc_HOL_Obool),U_942)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_941,tc_HOL_Obool),U_943)),
inference(variable_rename,[status(thm)],[f_257_1]) ).
cnf(f_257_3,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_941,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_941,tc_HOL_Obool),tc_HOL_Obool)),U_942),U_943)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_941,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_941,tc_HOL_Obool),U_942)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_941,tc_HOL_Obool),U_943)),
inference(clausify,[status(thm)],[f_257_2]) ).
fof(f_258_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_258_2,plain,
! [U_948,U_947,U_946,U_945,U_944] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_944,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_945,tc_HOL_Obool),tc_fun(U_944,tc_HOL_Obool),c_Set_Oimage(U_945,U_944,U_946)),hAPP(c_Set_OPow(U_945),U_947))),hAPP(c_Set_OPow(U_944),U_948)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_944,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_945,U_944,U_946),U_947)),U_948)) ),
inference(variable_rename,[status(thm)],[f_258_1]) ).
cnf(f_258_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_944,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_945,tc_HOL_Obool),tc_fun(U_944,tc_HOL_Obool),c_Set_Oimage(U_945,U_944,U_946)),hAPP(c_Set_OPow(U_945),U_947))),hAPP(c_Set_OPow(U_944),U_948)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_944,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_945,U_944,U_946),U_947)),U_948)) ),
inference(clausify,[status(thm)],[f_258_2]) ).
fof(f_259_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_259_2,plain,
! [U_950,U_949] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_949),U_950),c_Orderings_Otop__class_Otop(U_949)))
| ~ class_Orderings_Otop(U_949) ),
inference(variable_rename,[status(thm)],[f_259_1]) ).
cnf(f_259_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_949),U_950),c_Orderings_Otop__class_Otop(U_949)))
| ~ class_Orderings_Otop(U_949) ),
inference(clausify,[status(thm)],[f_259_2]) ).
fof(f_260_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_260_2,plain,
! [U_952,U_951] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_951),U_952),c_Orderings_Otop__class_Otop(U_951)) = c_Orderings_Otop__class_Otop(U_951)
| ~ class_Lattices_Obounded__lattice__top(U_951) ),
inference(variable_rename,[status(thm)],[f_260_1]) ).
cnf(f_260_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_951),U_952),c_Orderings_Otop__class_Otop(U_951)) = c_Orderings_Otop__class_Otop(U_951)
| ~ class_Lattices_Obounded__lattice__top(U_951) ),
inference(clausify,[status(thm)],[f_260_2]) ).
fof(f_261_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_261_2,plain,
! [U_954,U_953] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_953),c_Orderings_Otop__class_Otop(U_953)),U_954) = c_Orderings_Otop__class_Otop(U_953)
| ~ class_Lattices_Obounded__lattice__top(U_953) ),
inference(variable_rename,[status(thm)],[f_261_1]) ).
cnf(f_261_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_953),c_Orderings_Otop__class_Otop(U_953)),U_954) = c_Orderings_Otop__class_Otop(U_953)
| ~ class_Lattices_Obounded__lattice__top(U_953) ),
inference(clausify,[status(thm)],[f_261_2]) ).
fof(f_262_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_262_2,plain,
! [U_958,U_957,U_956,U_955] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_955),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_955),U_956),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_955),U_957),U_958))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_955),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_955),U_956),U_957)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_955),U_956),U_958))))
| ~ class_Lattices_Olattice(U_955) ),
inference(variable_rename,[status(thm)],[f_262_1]) ).
cnf(f_262_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_955),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_955),U_956),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_955),U_957),U_958))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_955),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_955),U_956),U_957)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_955),U_956),U_958))))
| ~ class_Lattices_Olattice(U_955) ),
inference(clausify,[status(thm)],[f_262_2]) ).
fof(f_263_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_263_2,plain,
! [U_962,U_961,U_960,U_959] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_959),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_959),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_959),U_960),U_961)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_959),U_960),U_962))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_959),U_960),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_959),U_961),U_962))))
| ~ class_Lattices_Olattice(U_959) ),
inference(variable_rename,[status(thm)],[f_263_1]) ).
cnf(f_263_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_959),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_959),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_959),U_960),U_961)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_959),U_960),U_962))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_959),U_960),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_959),U_961),U_962))))
| ~ class_Lattices_Olattice(U_959) ),
inference(clausify,[status(thm)],[f_263_2]) ).
fof(f_264_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_264_2,plain,
! [U_965,U_964,U_963] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_963),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_963),U_964),U_965)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_963),hAPP(c_Groups_Ouminus__class_Ouminus(U_963),U_964)),hAPP(c_Groups_Ouminus__class_Ouminus(U_963),U_965))
| ~ class_Lattices_Oboolean__algebra(U_963) ),
inference(variable_rename,[status(thm)],[f_264_1]) ).
cnf(f_264_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_963),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_963),U_964),U_965)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_963),hAPP(c_Groups_Ouminus__class_Ouminus(U_963),U_964)),hAPP(c_Groups_Ouminus__class_Ouminus(U_963),U_965))
| ~ class_Lattices_Oboolean__algebra(U_963) ),
inference(clausify,[status(thm)],[f_264_2]) ).
fof(f_265_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_265_2,plain,
! [U_968,U_967,U_966] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_966),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_966),U_967),U_968)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_966),hAPP(c_Groups_Ouminus__class_Ouminus(U_966),U_967)),hAPP(c_Groups_Ouminus__class_Ouminus(U_966),U_968))
| ~ class_Lattices_Oboolean__algebra(U_966) ),
inference(variable_rename,[status(thm)],[f_265_1]) ).
cnf(f_265_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_966),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_966),U_967),U_968)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_966),hAPP(c_Groups_Ouminus__class_Ouminus(U_966),U_967)),hAPP(c_Groups_Ouminus__class_Ouminus(U_966),U_968))
| ~ class_Lattices_Oboolean__algebra(U_966) ),
inference(clausify,[status(thm)],[f_265_2]) ).
fof(f_266_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_266_2,plain,
! [U_971,U_970,U_969] :
( hAPP(c_Set_Oimage(U_969,U_969,c_Groups_Ouminus__class_Ouminus(U_969)),c_SetInterval_Oord__class_OatLeastAtMost(U_969,U_970,U_971)) = c_SetInterval_Oord__class_OatLeastAtMost(U_969,hAPP(c_Groups_Ouminus__class_Ouminus(U_969),U_971),hAPP(c_Groups_Ouminus__class_Ouminus(U_969),U_970))
| ~ class_Groups_Oordered__ab__group__add(U_969) ),
inference(variable_rename,[status(thm)],[f_266_1]) ).
cnf(f_266_3,plain,
( hAPP(c_Set_Oimage(U_969,U_969,c_Groups_Ouminus__class_Ouminus(U_969)),c_SetInterval_Oord__class_OatLeastAtMost(U_969,U_970,U_971)) = c_SetInterval_Oord__class_OatLeastAtMost(U_969,hAPP(c_Groups_Ouminus__class_Ouminus(U_969),U_971),hAPP(c_Groups_Ouminus__class_Ouminus(U_969),U_970))
| ~ class_Groups_Oordered__ab__group__add(U_969) ),
inference(clausify,[status(thm)],[f_266_2]) ).
fof(f_267_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_267_2,plain,
! [U_973,U_972] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_972),U_973)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_972)),hAPP(c_Nat_OSuc,U_973)),
inference(variable_rename,[status(thm)],[f_267_1]) ).
cnf(f_267_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_972),U_973)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_972)),hAPP(c_Nat_OSuc,U_973)),
inference(clausify,[status(thm)],[f_267_2]) ).
fof(f_268_1,plain,
! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
| ~ class_Lattices_Osemilattice__inf(T_b)
| ~ class_Lattices_Osemilattice__inf(T_c) ),
inference(fof_nnf,[status(thm)],[fact_mono__inf]) ).
fof(f_268_2,plain,
! [U_978,U_977,U_976,U_975,U_974] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_974),hAPP(U_976,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_975),U_977),U_978))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_974),hAPP(U_976,U_977)),hAPP(U_976,U_978))))
| ~ c_Orderings_Oorder__class_Omono(U_975,U_974,U_976)
| ~ class_Lattices_Osemilattice__inf(U_975)
| ~ class_Lattices_Osemilattice__inf(U_974) ),
inference(variable_rename,[status(thm)],[f_268_1]) ).
cnf(f_268_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_974),hAPP(U_976,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_975),U_977),U_978))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_974),hAPP(U_976,U_977)),hAPP(U_976,U_978))))
| ~ c_Orderings_Oorder__class_Omono(U_975,U_974,U_976)
| ~ class_Lattices_Osemilattice__inf(U_975)
| ~ class_Lattices_Osemilattice__inf(U_974) ),
inference(clausify,[status(thm)],[f_268_2]) ).
fof(f_269_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_269_2,plain,
! [U_980,U_979] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_979,U_980)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_979),hAPP(c_Nat_OSuc,U_980)),
inference(variable_rename,[status(thm)],[f_269_1]) ).
cnf(f_269_3,plain,
hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_979,U_980)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_979),hAPP(c_Nat_OSuc,U_980)),
inference(clausify,[status(thm)],[f_269_2]) ).
fof(f_270_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_270_2,plain,
! [U_984,U_983,U_982,U_981] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_981,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_981,tc_HOL_Obool)),U_982),U_983)),U_984) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_981,tc_HOL_Obool)),U_982),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_981,tc_HOL_Obool)),U_983),U_984))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_981,tc_HOL_Obool)),U_984),U_982)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_981,tc_HOL_Obool)),U_984),U_982))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_981,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_981,tc_HOL_Obool)),U_982),U_983)),U_984) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_981,tc_HOL_Obool)),U_982),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_981,tc_HOL_Obool)),U_983),U_984)) ) ),
inference(variable_rename,[status(thm)],[f_270_1]) ).
fof(f_270_3,plain,
( ! [U_992,U_990,U_988,U_986] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_986,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_986,tc_HOL_Obool)),U_988),U_990)),U_992) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_986,tc_HOL_Obool)),U_988),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_986,tc_HOL_Obool)),U_990),U_992))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_986,tc_HOL_Obool)),U_992),U_988)) )
& ! [U_991,U_989,U_987,U_985] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_985,tc_HOL_Obool)),U_991),U_987))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_985,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_985,tc_HOL_Obool)),U_987),U_989)),U_991) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_985,tc_HOL_Obool)),U_987),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_985,tc_HOL_Obool)),U_989),U_991)) ) ),
inference(miniscope,[status(thm)],[f_270_2]) ).
cnf(f_270_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_985,tc_HOL_Obool)),U_991),U_987))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_985,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_985,tc_HOL_Obool)),U_987),U_989)),U_991) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_985,tc_HOL_Obool)),U_987),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_985,tc_HOL_Obool)),U_989),U_991)) ),
inference(clausify,[status(thm)],[f_270_3]) ).
cnf(f_270_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_986,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_986,tc_HOL_Obool)),U_988),U_990)),U_992) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_986,tc_HOL_Obool)),U_988),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_986,tc_HOL_Obool)),U_990),U_992))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_986,tc_HOL_Obool)),U_992),U_988)) ),
inference(clausify,[status(thm)],[f_270_3]) ).
fof(f_271_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_271_2,plain,
! [U_995,U_994,U_993] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_993,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_993,tc_HOL_Obool)),U_994),U_995)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_993,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_993,tc_HOL_Obool)),U_994)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_993,tc_HOL_Obool)),U_995)),
inference(variable_rename,[status(thm)],[f_271_1]) ).
cnf(f_271_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_993,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_993,tc_HOL_Obool)),U_994),U_995)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_993,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_993,tc_HOL_Obool)),U_994)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_993,tc_HOL_Obool)),U_995)),
inference(clausify,[status(thm)],[f_271_2]) ).
fof(f_272_1,plain,
! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(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_272_2,plain,
! [U_998,U_997,U_996] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_996,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_996,tc_HOL_Obool)),U_997),U_998)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_996,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_996,tc_HOL_Obool)),U_997)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_996,tc_HOL_Obool)),U_998)),
inference(variable_rename,[status(thm)],[f_272_1]) ).
cnf(f_272_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_996,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_996,tc_HOL_Obool)),U_997),U_998)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_996,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_996,tc_HOL_Obool)),U_997)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_996,tc_HOL_Obool)),U_998)),
inference(clausify,[status(thm)],[f_272_2]) ).
fof(f_273_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_273_2,plain,
! [U_1000,U_999] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_999,tc_HOL_Obool)),U_1000),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_999,tc_HOL_Obool)),U_1000)) = c_Orderings_Otop__class_Otop(tc_fun(U_999,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_273_1]) ).
cnf(f_273_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_999,tc_HOL_Obool)),U_1000),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_999,tc_HOL_Obool)),U_1000)) = c_Orderings_Otop__class_Otop(tc_fun(U_999,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_273_2]) ).
fof(f_274_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_274_2,plain,
! [U_1002,U_1001] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1001,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1001,tc_HOL_Obool)),U_1002)),U_1002) = c_Orderings_Otop__class_Otop(tc_fun(U_1001,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_274_1]) ).
cnf(f_274_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1001,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1001,tc_HOL_Obool)),U_1002)),U_1002) = c_Orderings_Otop__class_Otop(tc_fun(U_1001,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_274_2]) ).
fof(f_275_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_275_2,plain,
! [U_1003] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1003)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_1003),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_1003)),
inference(variable_rename,[status(thm)],[f_275_1]) ).
cnf(f_275_3,plain,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1003)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_1003),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_1003)),
inference(clausify,[status(thm)],[f_275_2]) ).
fof(f_276_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_276_2,plain,
! [U_1004] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1004)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1004)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_1004)),
inference(variable_rename,[status(thm)],[f_276_1]) ).
cnf(f_276_3,plain,
hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1004)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1004)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_1004)),
inference(clausify,[status(thm)],[f_276_2]) ).
fof(f_277_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_277_2,plain,
! [U_1008,U_1007,U_1006,U_1005] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1005,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1005,U_1006,U_1007)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1005,U_1007,U_1008)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1005,U_1006,U_1008)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1005),U_1007),U_1008))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1005),U_1006),U_1007))
| ~ class_Orderings_Olinorder(U_1005) ),
inference(variable_rename,[status(thm)],[f_277_1]) ).
cnf(f_277_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1005,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1005,U_1006,U_1007)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1005,U_1007,U_1008)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1005,U_1006,U_1008)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1005),U_1007),U_1008))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1005),U_1006),U_1007))
| ~ class_Orderings_Olinorder(U_1005) ),
inference(clausify,[status(thm)],[f_277_2]) ).
fof(f_278_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_278_2,plain,
! [U_1010,U_1009] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_1009),U_1010) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_1009,U_1010),
inference(variable_rename,[status(thm)],[f_278_1]) ).
cnf(f_278_3,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_1009),U_1010) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_1009,U_1010),
inference(clausify,[status(thm)],[f_278_2]) ).
fof(f_279_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_279_2,plain,
! [U_1012,U_1011] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1011),U_1012),hAPP(c_Groups_Ouminus__class_Ouminus(U_1011),U_1012)) = c_Orderings_Otop__class_Otop(U_1011)
| ~ class_Lattices_Oboolean__algebra(U_1011) ),
inference(variable_rename,[status(thm)],[f_279_1]) ).
cnf(f_279_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1011),U_1012),hAPP(c_Groups_Ouminus__class_Ouminus(U_1011),U_1012)) = c_Orderings_Otop__class_Otop(U_1011)
| ~ class_Lattices_Oboolean__algebra(U_1011) ),
inference(clausify,[status(thm)],[f_279_2]) ).
fof(f_280_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_280_2,plain,
! [U_1016,U_1015,U_1014,U_1013] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1014,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1014,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1013,U_1014,U_1015),U_1016))),hAPP(c_Set_Oimage(U_1013,U_1014,U_1015),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1013,tc_HOL_Obool)),U_1016))))
| hAPP(c_Set_Oimage(U_1013,U_1014,U_1015),c_Orderings_Otop__class_Otop(tc_fun(U_1013,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_1014,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_280_1]) ).
cnf(f_280_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1014,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1014,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1013,U_1014,U_1015),U_1016))),hAPP(c_Set_Oimage(U_1013,U_1014,U_1015),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1013,tc_HOL_Obool)),U_1016))))
| hAPP(c_Set_Oimage(U_1013,U_1014,U_1015),c_Orderings_Otop__class_Otop(tc_fun(U_1013,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_1014,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_280_2]) ).
fof(f_281_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_281_2,plain,
! [U_1019,U_1018,U_1017] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1017),U_1018) = U_1019
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1017),U_1018),U_1019) != c_Orderings_Otop__class_Otop(U_1017)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1017),U_1018),U_1019) != c_Orderings_Obot__class_Obot(U_1017)
| ~ class_Lattices_Oboolean__algebra(U_1017) ),
inference(variable_rename,[status(thm)],[f_281_1]) ).
cnf(f_281_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1017),U_1018) = U_1019
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1017),U_1018),U_1019) != c_Orderings_Otop__class_Otop(U_1017)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1017),U_1018),U_1019) != c_Orderings_Obot__class_Obot(U_1017)
| ~ class_Lattices_Oboolean__algebra(U_1017) ),
inference(clausify,[status(thm)],[f_281_2]) ).
fof(f_282_1,plain,
! [V_u_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),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_282_2,plain,
! [U_1022,U_1021,U_1020] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1020,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1020),U_1021),c_Orderings_Obot__class_Obot(tc_fun(U_1020,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1020,U_1021,U_1022)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1020,U_1021,U_1022)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1020),U_1021),U_1022))
| ~ class_Orderings_Olinorder(U_1020) ),
inference(variable_rename,[status(thm)],[f_282_1]) ).
cnf(f_282_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1020,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1020),U_1021),c_Orderings_Obot__class_Obot(tc_fun(U_1020,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1020,U_1021,U_1022)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1020,U_1021,U_1022)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1020),U_1021),U_1022))
| ~ class_Orderings_Olinorder(U_1020) ),
inference(clausify,[status(thm)],[f_282_2]) ).
fof(f_283_1,plain,
! [V_u_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_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_283_2,plain,
! [U_1025,U_1024,U_1023] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1023,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1023,U_1024),U_1025)),hAPP(hAPP(c_Set_Oinsert(U_1023),U_1025),c_Orderings_Obot__class_Obot(tc_fun(U_1023,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_1023,U_1024,U_1025)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1023),U_1024),U_1025))
| ~ class_Orderings_Olinorder(U_1023) ),
inference(variable_rename,[status(thm)],[f_283_1]) ).
cnf(f_283_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1023,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1023,U_1024),U_1025)),hAPP(hAPP(c_Set_Oinsert(U_1023),U_1025),c_Orderings_Obot__class_Obot(tc_fun(U_1023,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_1023,U_1024,U_1025)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1023),U_1024),U_1025))
| ~ class_Orderings_Olinorder(U_1023) ),
inference(clausify,[status(thm)],[f_283_2]) ).
fof(f_284_1,plain,
! [V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I1_J]) ).
fof(f_284_2,plain,
! [U_1027,U_1026] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1026,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1026),U_1027),c_Orderings_Obot__class_Obot(tc_fun(U_1026,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1026),U_1027)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_1026),U_1027)
| ~ class_Orderings_Olinorder(U_1026) ),
inference(variable_rename,[status(thm)],[f_284_1]) ).
cnf(f_284_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1026,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1026),U_1027),c_Orderings_Obot__class_Obot(tc_fun(U_1026,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1026),U_1027)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_1026),U_1027)
| ~ class_Orderings_Olinorder(U_1026) ),
inference(clausify,[status(thm)],[f_284_2]) ).
fof(f_285_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_285_2,plain,
! [U_1029,U_1028] :
( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_1028),hAPP(c_Nat_OSuc,U_1029)) = 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_1028),U_1029)) )
& ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_1028),hAPP(c_Nat_OSuc,U_1029)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_1029),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_1028),U_1029))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1028),U_1029)) ) ),
inference(variable_rename,[status(thm)],[f_285_1]) ).
fof(f_285_3,plain,
( ! [U_1033,U_1031] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_1031),hAPP(c_Nat_OSuc,U_1033)) = 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_1031),U_1033)) )
& ! [U_1032,U_1030] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_1030),hAPP(c_Nat_OSuc,U_1032)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_1032),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_1030),U_1032))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1030),U_1032)) ) ),
inference(miniscope,[status(thm)],[f_285_2]) ).
cnf(f_285_4,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_1030),hAPP(c_Nat_OSuc,U_1032)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_1032),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_1030),U_1032))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1030),U_1032)) ),
inference(clausify,[status(thm)],[f_285_3]) ).
cnf(f_285_5,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_1031),hAPP(c_Nat_OSuc,U_1033)) = 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_1031),U_1033)) ),
inference(clausify,[status(thm)],[f_285_3]) ).
fof(f_286_1,plain,
! [V_n_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atMost__Int__atLeast]) ).
fof(f_286_2,plain,
! [U_1035,U_1034] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1034,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_1034),U_1035)),hAPP(c_SetInterval_Oord__class_OatLeast(U_1034),U_1035)) = hAPP(hAPP(c_Set_Oinsert(U_1034),U_1035),c_Orderings_Obot__class_Obot(tc_fun(U_1034,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_1034) ),
inference(variable_rename,[status(thm)],[f_286_1]) ).
cnf(f_286_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1034,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_1034),U_1035)),hAPP(c_SetInterval_Oord__class_OatLeast(U_1034),U_1035)) = hAPP(hAPP(c_Set_Oinsert(U_1034),U_1035),c_Orderings_Obot__class_Obot(tc_fun(U_1034,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_1034) ),
inference(clausify,[status(thm)],[f_286_2]) ).
fof(f_287_1,plain,
! [V_u_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I2_J]) ).
fof(f_287_2,plain,
! [U_1037,U_1036] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1036,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1036),U_1037)),hAPP(hAPP(c_Set_Oinsert(U_1036),U_1037),c_Orderings_Obot__class_Obot(tc_fun(U_1036,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_1036),U_1037)
| ~ class_Orderings_Olinorder(U_1036) ),
inference(variable_rename,[status(thm)],[f_287_1]) ).
cnf(f_287_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1036,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1036),U_1037)),hAPP(hAPP(c_Set_Oinsert(U_1036),U_1037),c_Orderings_Obot__class_Obot(tc_fun(U_1036,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_1036),U_1037)
| ~ class_Orderings_Olinorder(U_1036) ),
inference(clausify,[status(thm)],[f_287_2]) ).
fof(f_288_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_288_2,plain,
! [U_1040,U_1039,U_1038] : hAPP(c_Set_Oimage(U_1039,tc_fun(U_1039,tc_HOL_Obool),U_1038),U_1040) != hAPP(c_Set_OPow(U_1039),U_1040),
inference(variable_rename,[status(thm)],[f_288_1]) ).
cnf(f_288_3,plain,
hAPP(c_Set_Oimage(U_1039,tc_fun(U_1039,tc_HOL_Obool),U_1038),U_1040) != hAPP(c_Set_OPow(U_1039),U_1040),
inference(clausify,[status(thm)],[f_288_2]) ).
fof(f_289_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_289_2,plain,
! [U_1041] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1041)) = 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_1041))),
inference(variable_rename,[status(thm)],[f_289_1]) ).
cnf(f_289_3,plain,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1041)) = 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_1041))),
inference(clausify,[status(thm)],[f_289_2]) ).
fof(f_290_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_290_2,plain,
! [U_1044,U_1043,U_1042] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1042,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1042,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_1042,tc_HOL_Obool),tc_HOL_Obool)),U_1043),U_1044))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1042,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1042,tc_HOL_Obool),U_1043)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1042,tc_HOL_Obool),U_1044)))),
inference(variable_rename,[status(thm)],[f_290_1]) ).
cnf(f_290_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1042,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1042,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_1042,tc_HOL_Obool),tc_HOL_Obool)),U_1043),U_1044))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1042,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1042,tc_HOL_Obool),U_1043)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1042,tc_HOL_Obool),U_1044)))),
inference(clausify,[status(thm)],[f_290_2]) ).
fof(f_291_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_291_2,plain,
! [U_1046,U_1045] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_1045,tc_HOL_Obool)),U_1046)),
inference(variable_rename,[status(thm)],[f_291_1]) ).
cnf(f_291_3,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_1045,tc_HOL_Obool)),U_1046)),
inference(clausify,[status(thm)],[f_291_2]) ).
fof(f_292_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_292_2,plain,
! [U_1048,U_1047] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1047,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1047,tc_HOL_Obool))),U_1048)),
inference(variable_rename,[status(thm)],[f_292_1]) ).
cnf(f_292_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1047,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1047,tc_HOL_Obool))),U_1048)),
inference(clausify,[status(thm)],[f_292_2]) ).
fof(f_293_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_293_2,plain,
! [U_1049] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1049)),
inference(variable_rename,[status(thm)],[f_293_1]) ).
cnf(f_293_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1049)),
inference(clausify,[status(thm)],[f_293_2]) ).
fof(f_294_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_294_2,plain,
! [U_1052,U_1051,U_1050] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1050,tc_HOL_Obool)),U_1051),U_1052) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1050,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1050,tc_HOL_Obool)),U_1051),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1050,tc_HOL_Obool)),U_1052),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_1050,tc_HOL_Obool),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_294_1]) ).
cnf(f_294_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1050,tc_HOL_Obool)),U_1051),U_1052) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1050,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1050,tc_HOL_Obool)),U_1051),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1050,tc_HOL_Obool)),U_1052),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_1050,tc_HOL_Obool),tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_294_2]) ).
fof(f_295_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_295_2,plain,
! [U_1053] : c_Orderings_Otop__class_Otop(tc_fun(U_1053,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_1053,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_295_1]) ).
cnf(f_295_3,plain,
c_Orderings_Otop__class_Otop(tc_fun(U_1053,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_1053,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_295_2]) ).
fof(f_296_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_296_2,plain,
! [U_1054] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1054,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_1054,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_1054,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_296_1]) ).
cnf(f_296_3,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1054,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_1054,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_1054,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_296_2]) ).
fof(f_297_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_297_2,plain,
! [U_1055] : hAPP(c_Set_OPow(U_1055),c_Orderings_Obot__class_Obot(tc_fun(U_1055,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1055,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1055,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_1055,tc_HOL_Obool),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_297_1]) ).
cnf(f_297_3,plain,
hAPP(c_Set_OPow(U_1055),c_Orderings_Obot__class_Obot(tc_fun(U_1055,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1055,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1055,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_1055,tc_HOL_Obool),tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_297_2]) ).
fof(f_298_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_298_2,plain,
! [U_1056] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1056,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_1056,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_1056,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_298_1]) ).
cnf(f_298_3,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1056,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_1056,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_1056,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_298_2]) ).
fof(f_299_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_299_2,plain,
! [U_1057] :
( c_Complete__Lattice_OSup__class_OSup(U_1057,c_Orderings_Obot__class_Obot(tc_fun(U_1057,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_1057)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1057) ),
inference(variable_rename,[status(thm)],[f_299_1]) ).
cnf(f_299_3,plain,
( c_Complete__Lattice_OSup__class_OSup(U_1057,c_Orderings_Obot__class_Obot(tc_fun(U_1057,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_1057)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1057) ),
inference(clausify,[status(thm)],[f_299_2]) ).
fof(f_300_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_300_2,plain,
! [U_1060,U_1059,U_1058] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_1059,U_1058)),U_1060) = c_Orderings_Obot__class_Obot(U_1058)
| ~ class_Orderings_Obot(U_1058) ),
inference(variable_rename,[status(thm)],[f_300_1]) ).
cnf(f_300_3,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_1059,U_1058)),U_1060) = c_Orderings_Obot__class_Obot(U_1058)
| ~ class_Orderings_Obot(U_1058) ),
inference(clausify,[status(thm)],[f_300_2]) ).
fof(f_301_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_301_2,plain,
c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_301_1]) ).
fof(f_302_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_302_2,plain,
! [U_1062,U_1061] :
( ( ( c_Groups_Ozero__class_Ozero(U_1061) = U_1062
| U_1062 != c_Groups_Ozero__class_Ozero(U_1061) )
& ( U_1062 = c_Groups_Ozero__class_Ozero(U_1061)
| c_Groups_Ozero__class_Ozero(U_1061) != U_1062 ) )
| ~ class_Groups_Ozero(U_1061) ),
inference(variable_rename,[status(thm)],[f_302_1]) ).
cnf(f_302_3,plain,
( U_1062 = c_Groups_Ozero__class_Ozero(U_1061)
| c_Groups_Ozero__class_Ozero(U_1061) != U_1062
| ~ class_Groups_Ozero(U_1061) ),
inference(clausify,[status(thm)],[f_302_2]) ).
cnf(f_302_4,plain,
( c_Groups_Ozero__class_Ozero(U_1061) = U_1062
| U_1062 != c_Groups_Ozero__class_Ozero(U_1061)
| ~ class_Groups_Ozero(U_1061) ),
inference(clausify,[status(thm)],[f_302_2]) ).
fof(f_303_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_303_2,plain,
! [U_1065,U_1064,U_1063] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1063,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1063,tc_HOL_Obool)),U_1064),U_1065)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1063,tc_HOL_Obool)),U_1064),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1063,tc_HOL_Obool),U_1065)),
inference(variable_rename,[status(thm)],[f_303_1]) ).
cnf(f_303_3,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1063,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1063,tc_HOL_Obool)),U_1064),U_1065)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1063,tc_HOL_Obool)),U_1064),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1063,tc_HOL_Obool),U_1065)),
inference(clausify,[status(thm)],[f_303_2]) ).
fof(f_304_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_304_2,plain,
! [U_1070,U_1069,U_1068] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1068,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1068,tc_HOL_Obool),U_1069)),U_1070) = c_Orderings_Obot__class_Obot(tc_fun(U_1068,tc_HOL_Obool))
| ? [U_1067] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1068,tc_HOL_Obool)),U_1067),U_1070) != c_Orderings_Obot__class_Obot(tc_fun(U_1068,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_1068,tc_HOL_Obool)),U_1067),U_1069)) ) )
& ( ! [U_1066] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1068,tc_HOL_Obool)),U_1066),U_1070) = c_Orderings_Obot__class_Obot(tc_fun(U_1068,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_1068,tc_HOL_Obool)),U_1066),U_1069)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1068,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1068,tc_HOL_Obool),U_1069)),U_1070) != c_Orderings_Obot__class_Obot(tc_fun(U_1068,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_304_1]) ).
fof(f_304_3,plain,
( ! [U_1076,U_1074,U_1072] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1072,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1072,tc_HOL_Obool),U_1074)),U_1076) = c_Orderings_Obot__class_Obot(tc_fun(U_1072,tc_HOL_Obool))
| ? [U_1067] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1072,tc_HOL_Obool)),U_1067),U_1076) != c_Orderings_Obot__class_Obot(tc_fun(U_1072,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_1072,tc_HOL_Obool)),U_1067),U_1074)) ) )
& ! [U_1075,U_1073,U_1071] :
( ! [U_1066] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1071,tc_HOL_Obool)),U_1066),U_1075) = c_Orderings_Obot__class_Obot(tc_fun(U_1071,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_1071,tc_HOL_Obool)),U_1066),U_1073)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1071,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1071,tc_HOL_Obool),U_1073)),U_1075) != c_Orderings_Obot__class_Obot(tc_fun(U_1071,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_304_2]) ).
fof(f_304_4,plain,
( ! [U_1076,U_1074,U_1072] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1072,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1072,tc_HOL_Obool),U_1074)),U_1076) = c_Orderings_Obot__class_Obot(tc_fun(U_1072,tc_HOL_Obool))
| ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1072,tc_HOL_Obool)),sK19(U_1076,U_1074,U_1072)),U_1076) != c_Orderings_Obot__class_Obot(tc_fun(U_1072,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_1072,tc_HOL_Obool)),sK19(U_1076,U_1074,U_1072)),U_1074)) ) )
& ! [U_1075,U_1073,U_1071] :
( ! [U_1066] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1071,tc_HOL_Obool)),U_1066),U_1075) = c_Orderings_Obot__class_Obot(tc_fun(U_1071,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_1071,tc_HOL_Obool)),U_1066),U_1073)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1071,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1071,tc_HOL_Obool),U_1073)),U_1075) != c_Orderings_Obot__class_Obot(tc_fun(U_1071,tc_HOL_Obool)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_1067,sK19(U_1076,U_1074,U_1072))],[f_304_3]) ).
cnf(f_304_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1071,tc_HOL_Obool)),U_1066),U_1075) = c_Orderings_Obot__class_Obot(tc_fun(U_1071,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_1071,tc_HOL_Obool)),U_1066),U_1073))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1071,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1071,tc_HOL_Obool),U_1073)),U_1075) != c_Orderings_Obot__class_Obot(tc_fun(U_1071,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_304_4]) ).
cnf(f_304_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_1072,tc_HOL_Obool)),sK19(U_1076,U_1074,U_1072)),U_1074))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1072,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1072,tc_HOL_Obool),U_1074)),U_1076) = c_Orderings_Obot__class_Obot(tc_fun(U_1072,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_304_4]) ).
cnf(f_304_7,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1072,tc_HOL_Obool)),sK19(U_1076,U_1074,U_1072)),U_1076) != c_Orderings_Obot__class_Obot(tc_fun(U_1072,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1072,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1072,tc_HOL_Obool),U_1074)),U_1076) = c_Orderings_Obot__class_Obot(tc_fun(U_1072,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_304_4]) ).
fof(f_305_1,plain,
! [V_tsa_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_tsa_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_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_305_2,plain,
! [U_1080,U_1079,U_1078,U_1077] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_1077,U_1078,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_1077)),U_1079),U_1080))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_1077,U_1078,U_1080)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_1077,U_1078,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_1077)),U_1079),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_1077),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_305_1]) ).
cnf(f_305_3,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(U_1077,U_1078,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_1077)),U_1079),U_1080))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_1077,U_1078,U_1080)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_1077,U_1078,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_1077)),U_1079),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_1077),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_305_2]) ).
fof(f_306_1,plain,
! [V_tsa_2,V_t_2,V_Ga_2,T_b] :
( ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_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)))) )
| ~ 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_tsa_2)) ),
inference(fof_nnf,[status(thm)],[fact_derivs__insertD]) ).
fof(f_306_2,plain,
! [U_1084,U_1083,U_1082,U_1081] :
( ( c_Hoare__Mirabelle_Ohoare__derivs(U_1081,U_1082,U_1084)
& c_Hoare__Mirabelle_Ohoare__derivs(U_1081,U_1082,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_1081)),U_1083),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_1081),tc_HOL_Obool)))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_1081,U_1082,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_1081)),U_1083),U_1084)) ),
inference(variable_rename,[status(thm)],[f_306_1]) ).
cnf(f_306_3,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(U_1081,U_1082,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_1081)),U_1083),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_1081),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_1081,U_1082,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_1081)),U_1083),U_1084)) ),
inference(clausify,[status(thm)],[f_306_2]) ).
cnf(f_306_4,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(U_1081,U_1082,U_1084)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_1081,U_1082,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_1081)),U_1083),U_1084)) ),
inference(clausify,[status(thm)],[f_306_2]) ).
fof(f_307_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_307_2,plain,
! [U_1085] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_1085),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_307_1]) ).
cnf(f_307_3,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_1085),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_307_2]) ).
fof(f_308_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_308_2,plain,
! [U_1087,U_1086] :
( c_Complete__Lattice_OSup__class_OSup(U_1086,hAPP(hAPP(c_Set_Oinsert(U_1086),U_1087),c_Orderings_Obot__class_Obot(tc_fun(U_1086,tc_HOL_Obool)))) = U_1087
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1086) ),
inference(variable_rename,[status(thm)],[f_308_1]) ).
cnf(f_308_3,plain,
( c_Complete__Lattice_OSup__class_OSup(U_1086,hAPP(hAPP(c_Set_Oinsert(U_1086),U_1087),c_Orderings_Obot__class_Obot(tc_fun(U_1086,tc_HOL_Obool)))) = U_1087
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1086) ),
inference(clausify,[status(thm)],[f_308_2]) ).
fof(f_309_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_309_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_309_1]) ).
fof(f_310_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_310_2,plain,
! [U_1090,U_1089,U_1088] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1088,tc_HOL_Obool)),U_1089),U_1090) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1088,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1088,tc_HOL_Obool)),U_1089),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1088,tc_HOL_Obool)),U_1090),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_1088,tc_HOL_Obool),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_310_1]) ).
cnf(f_310_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1088,tc_HOL_Obool)),U_1089),U_1090) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1088,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1088,tc_HOL_Obool)),U_1089),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1088,tc_HOL_Obool)),U_1090),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_1088,tc_HOL_Obool),tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_310_2]) ).
fof(f_311_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_311_2,plain,
! [U_1093,U_1092,U_1091] :
( c_Complete__Lattice_OSup__class_OSup(U_1091,hAPP(hAPP(c_Set_Oinsert(U_1091),U_1092),hAPP(hAPP(c_Set_Oinsert(U_1091),U_1093),c_Orderings_Obot__class_Obot(tc_fun(U_1091,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1091),U_1092),U_1093)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1091) ),
inference(variable_rename,[status(thm)],[f_311_1]) ).
cnf(f_311_3,plain,
( c_Complete__Lattice_OSup__class_OSup(U_1091,hAPP(hAPP(c_Set_Oinsert(U_1091),U_1092),hAPP(hAPP(c_Set_Oinsert(U_1091),U_1093),c_Orderings_Obot__class_Obot(tc_fun(U_1091,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1091),U_1092),U_1093)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1091) ),
inference(clausify,[status(thm)],[f_311_2]) ).
fof(f_312_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_312_2,plain,
! [U_1096,U_1095,U_1094] :
( U_1095 = U_1096
| hAPP(hAPP(c_Set_Oinsert(U_1094),U_1095),c_Orderings_Obot__class_Obot(tc_fun(U_1094,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_1094),U_1096),c_Orderings_Obot__class_Obot(tc_fun(U_1094,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_312_1]) ).
fof(f_312_3,plain,
! [U_1096,U_1095] :
( ! [U_1094] : hAPP(hAPP(c_Set_Oinsert(U_1094),U_1095),c_Orderings_Obot__class_Obot(tc_fun(U_1094,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_1094),U_1096),c_Orderings_Obot__class_Obot(tc_fun(U_1094,tc_HOL_Obool)))
| U_1095 = U_1096 ),
inference(miniscope,[status(thm)],[f_312_2]) ).
cnf(f_312_4,plain,
( hAPP(hAPP(c_Set_Oinsert(U_1094),U_1095),c_Orderings_Obot__class_Obot(tc_fun(U_1094,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_1094),U_1096),c_Orderings_Obot__class_Obot(tc_fun(U_1094,tc_HOL_Obool)))
| U_1095 = U_1096 ),
inference(clausify,[status(thm)],[f_312_3]) ).
fof(f_313_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
| ( ( V_b_2 != V_c_2
| V_a_2 != V_d_2 )
& ( V_b_2 != V_d_2
| V_a_2 != V_c_2 ) ) )
& ( ( V_b_2 = V_c_2
& V_a_2 = V_d_2 )
| ( V_b_2 = V_d_2
& V_a_2 = V_c_2 )
| hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ),
inference(fof_nnf,[status(thm)],[fact_doubleton__eq__iff]) ).
fof(f_313_2,plain,
! [U_1101,U_1100,U_1099,U_1098,U_1097] :
( ( hAPP(hAPP(c_Set_Oinsert(U_1097),U_1098),hAPP(hAPP(c_Set_Oinsert(U_1097),U_1099),c_Orderings_Obot__class_Obot(tc_fun(U_1097,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_1097),U_1100),hAPP(hAPP(c_Set_Oinsert(U_1097),U_1101),c_Orderings_Obot__class_Obot(tc_fun(U_1097,tc_HOL_Obool))))
| ( ( U_1099 != U_1100
| U_1098 != U_1101 )
& ( U_1099 != U_1101
| U_1098 != U_1100 ) ) )
& ( ( U_1099 = U_1100
& U_1098 = U_1101 )
| ( U_1099 = U_1101
& U_1098 = U_1100 )
| hAPP(hAPP(c_Set_Oinsert(U_1097),U_1098),hAPP(hAPP(c_Set_Oinsert(U_1097),U_1099),c_Orderings_Obot__class_Obot(tc_fun(U_1097,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_1097),U_1100),hAPP(hAPP(c_Set_Oinsert(U_1097),U_1101),c_Orderings_Obot__class_Obot(tc_fun(U_1097,tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[f_313_1]) ).
fof(f_313_3,plain,
( ! [U_1111,U_1109,U_1107,U_1105] :
( ! [U_1103] : hAPP(hAPP(c_Set_Oinsert(U_1103),U_1105),hAPP(hAPP(c_Set_Oinsert(U_1103),U_1107),c_Orderings_Obot__class_Obot(tc_fun(U_1103,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_1103),U_1109),hAPP(hAPP(c_Set_Oinsert(U_1103),U_1111),c_Orderings_Obot__class_Obot(tc_fun(U_1103,tc_HOL_Obool))))
| ( ( U_1107 != U_1109
| U_1105 != U_1111 )
& ( U_1107 != U_1111
| U_1105 != U_1109 ) ) )
& ! [U_1110,U_1108,U_1106,U_1104] :
( ! [U_1102] : hAPP(hAPP(c_Set_Oinsert(U_1102),U_1104),hAPP(hAPP(c_Set_Oinsert(U_1102),U_1106),c_Orderings_Obot__class_Obot(tc_fun(U_1102,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_1102),U_1108),hAPP(hAPP(c_Set_Oinsert(U_1102),U_1110),c_Orderings_Obot__class_Obot(tc_fun(U_1102,tc_HOL_Obool))))
| ( U_1106 = U_1108
& U_1104 = U_1110 )
| ( U_1106 = U_1110
& U_1104 = U_1108 ) ) ),
inference(miniscope,[status(thm)],[f_313_2]) ).
cnf(f_313_4,plain,
( U_1104 = U_1110
| U_1104 = U_1108
| hAPP(hAPP(c_Set_Oinsert(U_1102),U_1104),hAPP(hAPP(c_Set_Oinsert(U_1102),U_1106),c_Orderings_Obot__class_Obot(tc_fun(U_1102,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_1102),U_1108),hAPP(hAPP(c_Set_Oinsert(U_1102),U_1110),c_Orderings_Obot__class_Obot(tc_fun(U_1102,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_313_3]) ).
cnf(f_313_5,plain,
( U_1106 = U_1108
| U_1104 = U_1108
| hAPP(hAPP(c_Set_Oinsert(U_1102),U_1104),hAPP(hAPP(c_Set_Oinsert(U_1102),U_1106),c_Orderings_Obot__class_Obot(tc_fun(U_1102,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_1102),U_1108),hAPP(hAPP(c_Set_Oinsert(U_1102),U_1110),c_Orderings_Obot__class_Obot(tc_fun(U_1102,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_313_3]) ).
cnf(f_313_6,plain,
( U_1104 = U_1110
| U_1106 = U_1110
| hAPP(hAPP(c_Set_Oinsert(U_1102),U_1104),hAPP(hAPP(c_Set_Oinsert(U_1102),U_1106),c_Orderings_Obot__class_Obot(tc_fun(U_1102,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_1102),U_1108),hAPP(hAPP(c_Set_Oinsert(U_1102),U_1110),c_Orderings_Obot__class_Obot(tc_fun(U_1102,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_313_3]) ).
cnf(f_313_7,plain,
( U_1106 = U_1108
| U_1106 = U_1110
| hAPP(hAPP(c_Set_Oinsert(U_1102),U_1104),hAPP(hAPP(c_Set_Oinsert(U_1102),U_1106),c_Orderings_Obot__class_Obot(tc_fun(U_1102,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_1102),U_1108),hAPP(hAPP(c_Set_Oinsert(U_1102),U_1110),c_Orderings_Obot__class_Obot(tc_fun(U_1102,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_313_3]) ).
cnf(f_313_8,plain,
( U_1107 != U_1111
| U_1105 != U_1109
| hAPP(hAPP(c_Set_Oinsert(U_1103),U_1105),hAPP(hAPP(c_Set_Oinsert(U_1103),U_1107),c_Orderings_Obot__class_Obot(tc_fun(U_1103,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_1103),U_1109),hAPP(hAPP(c_Set_Oinsert(U_1103),U_1111),c_Orderings_Obot__class_Obot(tc_fun(U_1103,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_313_3]) ).
cnf(f_313_9,plain,
( U_1107 != U_1109
| U_1105 != U_1111
| hAPP(hAPP(c_Set_Oinsert(U_1103),U_1105),hAPP(hAPP(c_Set_Oinsert(U_1103),U_1107),c_Orderings_Obot__class_Obot(tc_fun(U_1103,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_1103),U_1109),hAPP(hAPP(c_Set_Oinsert(U_1103),U_1111),c_Orderings_Obot__class_Obot(tc_fun(U_1103,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_313_3]) ).
fof(f_314_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_314_2,plain,
! [U_1114,U_1113,U_1112] : hAPP(hAPP(c_Set_Oinsert(U_1112),U_1113),U_1114) != c_Orderings_Obot__class_Obot(tc_fun(U_1112,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_314_1]) ).
cnf(f_314_3,plain,
hAPP(hAPP(c_Set_Oinsert(U_1112),U_1113),U_1114) != c_Orderings_Obot__class_Obot(tc_fun(U_1112,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_314_2]) ).
fof(f_315_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_315_2,plain,
! [U_1117,U_1116,U_1115] : c_Orderings_Obot__class_Obot(tc_fun(U_1115,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_1115),U_1116),U_1117),
inference(variable_rename,[status(thm)],[f_315_1]) ).
cnf(f_315_3,plain,
c_Orderings_Obot__class_Obot(tc_fun(U_1115,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_1115),U_1116),U_1117),
inference(clausify,[status(thm)],[f_315_2]) ).
fof(f_316_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_316_2,plain,
! [U_1119,U_1118] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1118,tc_HOL_Obool)),U_1119),c_Orderings_Obot__class_Obot(tc_fun(U_1118,tc_HOL_Obool))))
| U_1119 != c_Orderings_Obot__class_Obot(tc_fun(U_1118,tc_HOL_Obool)) )
& ( U_1119 = c_Orderings_Obot__class_Obot(tc_fun(U_1118,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1118,tc_HOL_Obool)),U_1119),c_Orderings_Obot__class_Obot(tc_fun(U_1118,tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[f_316_1]) ).
fof(f_316_3,plain,
( ! [U_1123,U_1121] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1121,tc_HOL_Obool)),U_1123),c_Orderings_Obot__class_Obot(tc_fun(U_1121,tc_HOL_Obool))))
| U_1123 != c_Orderings_Obot__class_Obot(tc_fun(U_1121,tc_HOL_Obool)) )
& ! [U_1122,U_1120] :
( U_1122 = c_Orderings_Obot__class_Obot(tc_fun(U_1120,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1120,tc_HOL_Obool)),U_1122),c_Orderings_Obot__class_Obot(tc_fun(U_1120,tc_HOL_Obool)))) ) ),
inference(miniscope,[status(thm)],[f_316_2]) ).
cnf(f_316_4,plain,
( U_1122 = c_Orderings_Obot__class_Obot(tc_fun(U_1120,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1120,tc_HOL_Obool)),U_1122),c_Orderings_Obot__class_Obot(tc_fun(U_1120,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_316_3]) ).
cnf(f_316_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1121,tc_HOL_Obool)),U_1123),c_Orderings_Obot__class_Obot(tc_fun(U_1121,tc_HOL_Obool))))
| U_1123 != c_Orderings_Obot__class_Obot(tc_fun(U_1121,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_316_3]) ).
fof(f_317_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_317_2,plain,
! [U_1127,U_1126,U_1125,U_1124] :
( ( hAPP(c_Set_Oimage(U_1124,U_1125,U_1126),U_1127) = c_Orderings_Obot__class_Obot(tc_fun(U_1125,tc_HOL_Obool))
| U_1127 != c_Orderings_Obot__class_Obot(tc_fun(U_1124,tc_HOL_Obool)) )
& ( U_1127 = c_Orderings_Obot__class_Obot(tc_fun(U_1124,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_1124,U_1125,U_1126),U_1127) != c_Orderings_Obot__class_Obot(tc_fun(U_1125,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_317_1]) ).
fof(f_317_3,plain,
( ! [U_1135,U_1133,U_1131,U_1129] :
( hAPP(c_Set_Oimage(U_1129,U_1131,U_1133),U_1135) = c_Orderings_Obot__class_Obot(tc_fun(U_1131,tc_HOL_Obool))
| U_1135 != c_Orderings_Obot__class_Obot(tc_fun(U_1129,tc_HOL_Obool)) )
& ! [U_1134,U_1132,U_1130,U_1128] :
( U_1134 = c_Orderings_Obot__class_Obot(tc_fun(U_1128,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_1128,U_1130,U_1132),U_1134) != c_Orderings_Obot__class_Obot(tc_fun(U_1130,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_317_2]) ).
cnf(f_317_4,plain,
( U_1134 = c_Orderings_Obot__class_Obot(tc_fun(U_1128,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_1128,U_1130,U_1132),U_1134) != c_Orderings_Obot__class_Obot(tc_fun(U_1130,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_317_3]) ).
cnf(f_317_5,plain,
( hAPP(c_Set_Oimage(U_1129,U_1131,U_1133),U_1135) = c_Orderings_Obot__class_Obot(tc_fun(U_1131,tc_HOL_Obool))
| U_1135 != c_Orderings_Obot__class_Obot(tc_fun(U_1129,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_317_3]) ).
fof(f_318_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_318_2,plain,
! [U_1138,U_1137,U_1136] : hAPP(c_Set_Oimage(U_1136,U_1137,U_1138),c_Orderings_Obot__class_Obot(tc_fun(U_1136,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_1137,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_318_1]) ).
cnf(f_318_3,plain,
hAPP(c_Set_Oimage(U_1136,U_1137,U_1138),c_Orderings_Obot__class_Obot(tc_fun(U_1136,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_1137,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_318_2]) ).
fof(f_319_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_319_2,plain,
! [U_1142,U_1141,U_1140,U_1139] :
( ( c_Orderings_Obot__class_Obot(tc_fun(U_1139,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_1140,U_1139,U_1141),U_1142)
| U_1142 != c_Orderings_Obot__class_Obot(tc_fun(U_1140,tc_HOL_Obool)) )
& ( U_1142 = c_Orderings_Obot__class_Obot(tc_fun(U_1140,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(U_1139,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_1140,U_1139,U_1141),U_1142) ) ),
inference(variable_rename,[status(thm)],[f_319_1]) ).
fof(f_319_3,plain,
( ! [U_1150,U_1148,U_1146] :
( ! [U_1144] : c_Orderings_Obot__class_Obot(tc_fun(U_1144,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_1146,U_1144,U_1148),U_1150)
| U_1150 != c_Orderings_Obot__class_Obot(tc_fun(U_1146,tc_HOL_Obool)) )
& ! [U_1149,U_1147,U_1145] :
( ! [U_1143] : c_Orderings_Obot__class_Obot(tc_fun(U_1143,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_1145,U_1143,U_1147),U_1149)
| U_1149 = c_Orderings_Obot__class_Obot(tc_fun(U_1145,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_319_2]) ).
cnf(f_319_4,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_1143,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_1145,U_1143,U_1147),U_1149)
| U_1149 = c_Orderings_Obot__class_Obot(tc_fun(U_1145,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_319_3]) ).
cnf(f_319_5,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_1144,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_1146,U_1144,U_1148),U_1150)
| U_1150 != c_Orderings_Obot__class_Obot(tc_fun(U_1146,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_319_3]) ).
fof(f_320_1,plain,
! [V_P_2,T_b,B_x] :
( hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[fact_ball__empty]) ).
fof(f_320_2,plain,
! [U_1153,U_1152,U_1151] :
( hBOOL(hAPP(U_1153,U_1151))
| ~ hBOOL(hAPP(hAPP(c_member(U_1152),U_1151),c_Orderings_Obot__class_Obot(tc_fun(U_1152,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_320_1]) ).
cnf(f_320_3,plain,
( hBOOL(hAPP(U_1153,U_1151))
| ~ hBOOL(hAPP(hAPP(c_member(U_1152),U_1151),c_Orderings_Obot__class_Obot(tc_fun(U_1152,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_320_2]) ).
fof(f_321_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_321_2,plain,
! [U_1154] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1154),c_Groups_Ozero__class_Ozero(U_1154)) = c_Groups_Ozero__class_Ozero(U_1154)
| ~ class_Groups_Ogroup__add(U_1154) ),
inference(variable_rename,[status(thm)],[f_321_1]) ).
cnf(f_321_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1154),c_Groups_Ozero__class_Ozero(U_1154)) = c_Groups_Ozero__class_Ozero(U_1154)
| ~ class_Groups_Ogroup__add(U_1154) ),
inference(clausify,[status(thm)],[f_321_2]) ).
fof(f_322_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_322_2,plain,
! [U_1156,U_1155] :
( ( ( c_Groups_Ozero__class_Ozero(U_1155) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1155),U_1156)
| c_Groups_Ozero__class_Ozero(U_1155) != U_1156 )
& ( c_Groups_Ozero__class_Ozero(U_1155) = U_1156
| c_Groups_Ozero__class_Ozero(U_1155) != hAPP(c_Groups_Ouminus__class_Ouminus(U_1155),U_1156) ) )
| ~ class_Groups_Ogroup__add(U_1155) ),
inference(variable_rename,[status(thm)],[f_322_1]) ).
cnf(f_322_3,plain,
( c_Groups_Ozero__class_Ozero(U_1155) = U_1156
| c_Groups_Ozero__class_Ozero(U_1155) != hAPP(c_Groups_Ouminus__class_Ouminus(U_1155),U_1156)
| ~ class_Groups_Ogroup__add(U_1155) ),
inference(clausify,[status(thm)],[f_322_2]) ).
cnf(f_322_4,plain,
( c_Groups_Ozero__class_Ozero(U_1155) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1155),U_1156)
| c_Groups_Ozero__class_Ozero(U_1155) != U_1156
| ~ class_Groups_Ogroup__add(U_1155) ),
inference(clausify,[status(thm)],[f_322_2]) ).
fof(f_323_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_323_2,plain,
! [U_1158,U_1157] :
( ( ( U_1158 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1157),U_1158)
| U_1158 != c_Groups_Ozero__class_Ozero(U_1157) )
& ( U_1158 = c_Groups_Ozero__class_Ozero(U_1157)
| U_1158 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1157),U_1158) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1157) ),
inference(variable_rename,[status(thm)],[f_323_1]) ).
cnf(f_323_3,plain,
( U_1158 = c_Groups_Ozero__class_Ozero(U_1157)
| U_1158 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1157),U_1158)
| ~ class_Groups_Olinordered__ab__group__add(U_1157) ),
inference(clausify,[status(thm)],[f_323_2]) ).
cnf(f_323_4,plain,
( U_1158 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1157),U_1158)
| U_1158 != c_Groups_Ozero__class_Ozero(U_1157)
| ~ class_Groups_Olinordered__ab__group__add(U_1157) ),
inference(clausify,[status(thm)],[f_323_2]) ).
fof(f_324_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_324_2,plain,
! [U_1160,U_1159] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1159),U_1160) = c_Groups_Ozero__class_Ozero(U_1159)
| U_1160 != c_Groups_Ozero__class_Ozero(U_1159) )
& ( U_1160 = c_Groups_Ozero__class_Ozero(U_1159)
| hAPP(c_Groups_Ouminus__class_Ouminus(U_1159),U_1160) != c_Groups_Ozero__class_Ozero(U_1159) ) )
| ~ class_Groups_Ogroup__add(U_1159) ),
inference(variable_rename,[status(thm)],[f_324_1]) ).
cnf(f_324_3,plain,
( U_1160 = c_Groups_Ozero__class_Ozero(U_1159)
| hAPP(c_Groups_Ouminus__class_Ouminus(U_1159),U_1160) != c_Groups_Ozero__class_Ozero(U_1159)
| ~ class_Groups_Ogroup__add(U_1159) ),
inference(clausify,[status(thm)],[f_324_2]) ).
cnf(f_324_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1159),U_1160) = c_Groups_Ozero__class_Ozero(U_1159)
| U_1160 != c_Groups_Ozero__class_Ozero(U_1159)
| ~ class_Groups_Ogroup__add(U_1159) ),
inference(clausify,[status(thm)],[f_324_2]) ).
fof(f_325_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_325_2,plain,
! [U_1162,U_1161] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1161),U_1162) = U_1162
| U_1162 != c_Groups_Ozero__class_Ozero(U_1161) )
& ( U_1162 = c_Groups_Ozero__class_Ozero(U_1161)
| hAPP(c_Groups_Ouminus__class_Ouminus(U_1161),U_1162) != U_1162 ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1161) ),
inference(variable_rename,[status(thm)],[f_325_1]) ).
cnf(f_325_3,plain,
( U_1162 = c_Groups_Ozero__class_Ozero(U_1161)
| hAPP(c_Groups_Ouminus__class_Ouminus(U_1161),U_1162) != U_1162
| ~ class_Groups_Olinordered__ab__group__add(U_1161) ),
inference(clausify,[status(thm)],[f_325_2]) ).
cnf(f_325_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1161),U_1162) = U_1162
| U_1162 != c_Groups_Ozero__class_Ozero(U_1161)
| ~ class_Groups_Olinordered__ab__group__add(U_1161) ),
inference(clausify,[status(thm)],[f_325_2]) ).
fof(f_326_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_326_2,plain,
! [U_1165,U_1164,U_1163] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1163,tc_HOL_Obool)),U_1164),U_1165) = c_Orderings_Obot__class_Obot(tc_fun(U_1163,tc_HOL_Obool))
| U_1165 != c_Orderings_Obot__class_Obot(tc_fun(U_1163,tc_HOL_Obool))
| U_1164 != c_Orderings_Obot__class_Obot(tc_fun(U_1163,tc_HOL_Obool)) )
& ( ( U_1165 = c_Orderings_Obot__class_Obot(tc_fun(U_1163,tc_HOL_Obool))
& U_1164 = c_Orderings_Obot__class_Obot(tc_fun(U_1163,tc_HOL_Obool)) )
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1163,tc_HOL_Obool)),U_1164),U_1165) != c_Orderings_Obot__class_Obot(tc_fun(U_1163,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_326_1]) ).
fof(f_326_3,plain,
( ! [U_1171,U_1169,U_1167] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1167,tc_HOL_Obool)),U_1169),U_1171) = c_Orderings_Obot__class_Obot(tc_fun(U_1167,tc_HOL_Obool))
| U_1171 != c_Orderings_Obot__class_Obot(tc_fun(U_1167,tc_HOL_Obool))
| U_1169 != c_Orderings_Obot__class_Obot(tc_fun(U_1167,tc_HOL_Obool)) )
& ! [U_1170,U_1168,U_1166] :
( ( U_1170 = c_Orderings_Obot__class_Obot(tc_fun(U_1166,tc_HOL_Obool))
& U_1168 = c_Orderings_Obot__class_Obot(tc_fun(U_1166,tc_HOL_Obool)) )
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1166,tc_HOL_Obool)),U_1168),U_1170) != c_Orderings_Obot__class_Obot(tc_fun(U_1166,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_326_2]) ).
cnf(f_326_4,plain,
( U_1168 = c_Orderings_Obot__class_Obot(tc_fun(U_1166,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1166,tc_HOL_Obool)),U_1168),U_1170) != c_Orderings_Obot__class_Obot(tc_fun(U_1166,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_326_3]) ).
cnf(f_326_5,plain,
( U_1170 = c_Orderings_Obot__class_Obot(tc_fun(U_1166,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1166,tc_HOL_Obool)),U_1168),U_1170) != c_Orderings_Obot__class_Obot(tc_fun(U_1166,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_326_3]) ).
cnf(f_326_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1167,tc_HOL_Obool)),U_1169),U_1171) = c_Orderings_Obot__class_Obot(tc_fun(U_1167,tc_HOL_Obool))
| U_1171 != c_Orderings_Obot__class_Obot(tc_fun(U_1167,tc_HOL_Obool))
| U_1169 != c_Orderings_Obot__class_Obot(tc_fun(U_1167,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_326_3]) ).
fof(f_327_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_327_2,plain,
! [U_1173,U_1172] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1172,tc_HOL_Obool)),U_1173),c_Orderings_Obot__class_Obot(tc_fun(U_1172,tc_HOL_Obool))) = U_1173,
inference(variable_rename,[status(thm)],[f_327_1]) ).
cnf(f_327_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1172,tc_HOL_Obool)),U_1173),c_Orderings_Obot__class_Obot(tc_fun(U_1172,tc_HOL_Obool))) = U_1173,
inference(clausify,[status(thm)],[f_327_2]) ).
fof(f_328_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_328_2,plain,
! [U_1175,U_1174] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1174,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1174,tc_HOL_Obool))),U_1175) = U_1175,
inference(variable_rename,[status(thm)],[f_328_1]) ).
cnf(f_328_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1174,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1174,tc_HOL_Obool))),U_1175) = U_1175,
inference(clausify,[status(thm)],[f_328_2]) ).
fof(f_329_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_329_2,plain,
! [U_1182,U_1181,U_1180] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1180,tc_HOL_Obool)),U_1181),U_1182) = c_Orderings_Obot__class_Obot(tc_fun(U_1180,tc_HOL_Obool))
| ? [U_1179] :
( ? [U_1178] :
( U_1179 = U_1178
& hBOOL(hAPP(hAPP(c_member(U_1180),U_1178),U_1182)) )
& hBOOL(hAPP(hAPP(c_member(U_1180),U_1179),U_1181)) ) )
& ( ! [U_1177] :
( ! [U_1176] :
( U_1177 != U_1176
| ~ hBOOL(hAPP(hAPP(c_member(U_1180),U_1176),U_1182)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1180),U_1177),U_1181)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1180,tc_HOL_Obool)),U_1181),U_1182) != c_Orderings_Obot__class_Obot(tc_fun(U_1180,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_329_1]) ).
fof(f_329_3,plain,
( ! [U_1188,U_1186,U_1184] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1184,tc_HOL_Obool)),U_1186),U_1188) = c_Orderings_Obot__class_Obot(tc_fun(U_1184,tc_HOL_Obool))
| ? [U_1179] :
( ? [U_1178] :
( U_1179 = U_1178
& hBOOL(hAPP(hAPP(c_member(U_1184),U_1178),U_1188)) )
& hBOOL(hAPP(hAPP(c_member(U_1184),U_1179),U_1186)) ) )
& ! [U_1187,U_1185,U_1183] :
( ! [U_1177] :
( ! [U_1176] :
( U_1177 != U_1176
| ~ hBOOL(hAPP(hAPP(c_member(U_1183),U_1176),U_1187)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1183),U_1177),U_1185)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1183,tc_HOL_Obool)),U_1185),U_1187) != c_Orderings_Obot__class_Obot(tc_fun(U_1183,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_329_2]) ).
fof(f_329_4,plain,
( ! [U_1188,U_1186,U_1184] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1184,tc_HOL_Obool)),U_1186),U_1188) = c_Orderings_Obot__class_Obot(tc_fun(U_1184,tc_HOL_Obool))
| ( ? [U_1178] :
( sK20(U_1188,U_1186,U_1184) = U_1178
& hBOOL(hAPP(hAPP(c_member(U_1184),U_1178),U_1188)) )
& hBOOL(hAPP(hAPP(c_member(U_1184),sK20(U_1188,U_1186,U_1184)),U_1186)) ) )
& ! [U_1187,U_1185,U_1183] :
( ! [U_1177] :
( ! [U_1176] :
( U_1177 != U_1176
| ~ hBOOL(hAPP(hAPP(c_member(U_1183),U_1176),U_1187)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1183),U_1177),U_1185)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1183,tc_HOL_Obool)),U_1185),U_1187) != c_Orderings_Obot__class_Obot(tc_fun(U_1183,tc_HOL_Obool)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_1179,sK20(U_1188,U_1186,U_1184))],[f_329_3]) ).
fof(f_329_5,plain,
( ! [U_1188,U_1186,U_1184] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1184,tc_HOL_Obool)),U_1186),U_1188) = c_Orderings_Obot__class_Obot(tc_fun(U_1184,tc_HOL_Obool))
| ( sK20(U_1188,U_1186,U_1184) = sK21(U_1188,U_1186,U_1184)
& hBOOL(hAPP(hAPP(c_member(U_1184),sK21(U_1188,U_1186,U_1184)),U_1188))
& hBOOL(hAPP(hAPP(c_member(U_1184),sK20(U_1188,U_1186,U_1184)),U_1186)) ) )
& ! [U_1187,U_1185,U_1183] :
( ! [U_1177] :
( ! [U_1176] :
( U_1177 != U_1176
| ~ hBOOL(hAPP(hAPP(c_member(U_1183),U_1176),U_1187)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1183),U_1177),U_1185)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1183,tc_HOL_Obool)),U_1185),U_1187) != c_Orderings_Obot__class_Obot(tc_fun(U_1183,tc_HOL_Obool)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_1178,sK21(U_1188,U_1186,U_1184))],[f_329_4]) ).
cnf(f_329_6,plain,
( U_1177 != U_1176
| ~ hBOOL(hAPP(hAPP(c_member(U_1183),U_1176),U_1187))
| ~ hBOOL(hAPP(hAPP(c_member(U_1183),U_1177),U_1185))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1183,tc_HOL_Obool)),U_1185),U_1187) != c_Orderings_Obot__class_Obot(tc_fun(U_1183,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_329_5]) ).
cnf(f_329_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_1184),sK20(U_1188,U_1186,U_1184)),U_1186))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1184,tc_HOL_Obool)),U_1186),U_1188) = c_Orderings_Obot__class_Obot(tc_fun(U_1184,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_329_5]) ).
cnf(f_329_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_1184),sK21(U_1188,U_1186,U_1184)),U_1188))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1184,tc_HOL_Obool)),U_1186),U_1188) = c_Orderings_Obot__class_Obot(tc_fun(U_1184,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_329_5]) ).
cnf(f_329_9,plain,
( sK20(U_1188,U_1186,U_1184) = sK21(U_1188,U_1186,U_1184)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1184,tc_HOL_Obool)),U_1186),U_1188) = c_Orderings_Obot__class_Obot(tc_fun(U_1184,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_329_5]) ).
fof(f_330_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_330_2,plain,
! [U_1190,U_1189] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1189,tc_HOL_Obool)),U_1190),c_Orderings_Obot__class_Obot(tc_fun(U_1189,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_1189,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_330_1]) ).
cnf(f_330_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1189,tc_HOL_Obool)),U_1190),c_Orderings_Obot__class_Obot(tc_fun(U_1189,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_1189,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_330_2]) ).
fof(f_331_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_331_2,plain,
! [U_1192,U_1191] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1191,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1191,tc_HOL_Obool))),U_1192) = c_Orderings_Obot__class_Obot(tc_fun(U_1191,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_331_1]) ).
cnf(f_331_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1191,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1191,tc_HOL_Obool))),U_1192) = c_Orderings_Obot__class_Obot(tc_fun(U_1191,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_331_2]) ).
fof(f_332_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_332_2,plain,
! [U_1193] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_1193),
inference(variable_rename,[status(thm)],[f_332_1]) ).
cnf(f_332_3,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_1193),
inference(clausify,[status(thm)],[f_332_2]) ).
fof(f_333_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_333_2,plain,
! [U_1194] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_1194),
inference(variable_rename,[status(thm)],[f_333_1]) ).
cnf(f_333_3,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_1194),
inference(clausify,[status(thm)],[f_333_2]) ).
fof(f_334_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_334_2,plain,
! [U_1195] : hAPP(c_Nat_OSuc,U_1195) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_334_1]) ).
cnf(f_334_3,plain,
hAPP(c_Nat_OSuc,U_1195) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_334_2]) ).
fof(f_335_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_335_2,plain,
! [U_1196] : hAPP(c_Nat_OSuc,U_1196) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_335_1]) ).
cnf(f_335_3,plain,
hAPP(c_Nat_OSuc,U_1196) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_335_2]) ).
fof(f_336_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_336_2,plain,
! [U_1197] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_1197),
inference(variable_rename,[status(thm)],[f_336_1]) ).
cnf(f_336_3,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_1197),
inference(clausify,[status(thm)],[f_336_2]) ).
fof(f_337_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_337_2,plain,
! [U_1198] : hAPP(c_Nat_OSuc,U_1198) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_337_1]) ).
cnf(f_337_3,plain,
hAPP(c_Nat_OSuc,U_1198) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_337_2]) ).
fof(f_338_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_338_2,plain,
! [U_1199] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1199)),
inference(variable_rename,[status(thm)],[f_338_1]) ).
cnf(f_338_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1199)),
inference(clausify,[status(thm)],[f_338_2]) ).
fof(f_339_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_339_2,plain,
! [U_1200] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1200),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_1200 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_1200 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1200),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[f_339_1]) ).
fof(f_339_3,plain,
( ! [U_1202] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1202),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_1202 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1201] :
( U_1201 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1201),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(miniscope,[status(thm)],[f_339_2]) ).
cnf(f_339_4,plain,
( U_1201 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1201),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_339_3]) ).
cnf(f_339_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1202),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_1202 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_339_3]) ).
fof(f_340_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_340_2,plain,
! [U_1204,U_1203] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1203,tc_HOL_Obool),hAPP(c_Set_OPow(U_1203),U_1204)) = U_1204,
inference(variable_rename,[status(thm)],[f_340_1]) ).
cnf(f_340_3,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1203,tc_HOL_Obool),hAPP(c_Set_OPow(U_1203),U_1204)) = U_1204,
inference(clausify,[status(thm)],[f_340_2]) ).
fof(f_341_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_341_2,plain,
! [U_1205] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1205,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_1205,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_1205,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_341_1]) ).
cnf(f_341_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1205,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_1205,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_1205,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_341_2]) ).
fof(f_342_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_342_2,plain,
! [U_1206] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1206,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1206,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_1206,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_342_1]) ).
cnf(f_342_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1206,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1206,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_1206,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_342_2]) ).
fof(f_343_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_343_2,plain,
! [U_1208,U_1207] : c_Hoare__Mirabelle_Ohoare__derivs(U_1207,U_1208,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_1207),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_343_1]) ).
cnf(f_343_3,plain,
c_Hoare__Mirabelle_Ohoare__derivs(U_1207,U_1208,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_1207),tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_343_2]) ).
fof(f_344_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_344_2,plain,
! [U_1210,U_1209] : c_Hoare__Mirabelle_Ohoare__derivs(U_1209,U_1210,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_1209),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_344_1]) ).
cnf(f_344_3,plain,
c_Hoare__Mirabelle_Ohoare__derivs(U_1209,U_1210,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_1209),tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_344_2]) ).
fof(f_345_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_345_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_345_1]) ).
fof(f_346_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_346_2,plain,
! [U_1212,U_1211] : hAPP(c_Set_OPow(U_1211),U_1212) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_1211,tc_HOL_Obool),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_346_1]) ).
cnf(f_346_3,plain,
hAPP(c_Set_OPow(U_1211),U_1212) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_1211,tc_HOL_Obool),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_346_2]) ).
fof(f_347_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_347_2,plain,
! [U_1213] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1213,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_1213,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_1213,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_347_1]) ).
cnf(f_347_3,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1213,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_1213,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_1213,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_347_2]) ).
fof(f_348_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_348_2,plain,
! [U_1214] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1214,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_1214,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_1214,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_348_1]) ).
cnf(f_348_3,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1214,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_1214,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_1214,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_348_2]) ).
fof(f_349_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_349_2,plain,
! [U_1217,U_1216,U_1215] : c_Nat_Onat_Onat__case(U_1215,U_1216,U_1217,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1216,
inference(variable_rename,[status(thm)],[f_349_1]) ).
cnf(f_349_3,plain,
c_Nat_Onat_Onat__case(U_1215,U_1216,U_1217,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1216,
inference(clausify,[status(thm)],[f_349_2]) ).
fof(f_350_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_350_2,plain,
! [U_1222,U_1221,U_1220] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1220),c_Complete__Lattice_OSup__class_OSup(U_1220,U_1221)),U_1222))
| ? [U_1219] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1220),U_1219),U_1222))
& hBOOL(hAPP(hAPP(c_member(U_1220),U_1219),U_1221)) ) )
& ( ! [U_1218] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1220),U_1218),U_1222))
| ~ hBOOL(hAPP(hAPP(c_member(U_1220),U_1218),U_1221)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1220),c_Complete__Lattice_OSup__class_OSup(U_1220,U_1221)),U_1222)) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1220) ),
inference(variable_rename,[status(thm)],[f_350_1]) ).
fof(f_350_3,plain,
! [U_1222,U_1221,U_1220] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1220),c_Complete__Lattice_OSup__class_OSup(U_1220,U_1221)),U_1222))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1220),sK22(U_1222,U_1221,U_1220)),U_1222))
& hBOOL(hAPP(hAPP(c_member(U_1220),sK22(U_1222,U_1221,U_1220)),U_1221)) ) )
& ( ! [U_1218] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1220),U_1218),U_1222))
| ~ hBOOL(hAPP(hAPP(c_member(U_1220),U_1218),U_1221)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1220),c_Complete__Lattice_OSup__class_OSup(U_1220,U_1221)),U_1222)) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1220) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_1219,sK22(U_1222,U_1221,U_1220))],[f_350_2]) ).
cnf(f_350_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1220),U_1218),U_1222))
| ~ hBOOL(hAPP(hAPP(c_member(U_1220),U_1218),U_1221))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1220),c_Complete__Lattice_OSup__class_OSup(U_1220,U_1221)),U_1222))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1220) ),
inference(clausify,[status(thm)],[f_350_3]) ).
cnf(f_350_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_1220),sK22(U_1222,U_1221,U_1220)),U_1221))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1220),c_Complete__Lattice_OSup__class_OSup(U_1220,U_1221)),U_1222))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1220) ),
inference(clausify,[status(thm)],[f_350_3]) ).
cnf(f_350_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1220),sK22(U_1222,U_1221,U_1220)),U_1222))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1220),c_Complete__Lattice_OSup__class_OSup(U_1220,U_1221)),U_1222))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1220) ),
inference(clausify,[status(thm)],[f_350_3]) ).
fof(f_351_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_351_2,plain,
! [U_1224,U_1223] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1223),c_Orderings_Obot__class_Obot(U_1223)),U_1224))
| ~ class_Orderings_Obot(U_1223) ),
inference(variable_rename,[status(thm)],[f_351_1]) ).
cnf(f_351_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1223),c_Orderings_Obot__class_Obot(U_1223)),U_1224))
| ~ class_Orderings_Obot(U_1223) ),
inference(clausify,[status(thm)],[f_351_2]) ).
fof(f_352_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_352_2,plain,
! [U_1225] :
( c_Complete__Lattice_OSup__class_OSup(U_1225,c_Orderings_Otop__class_Otop(tc_fun(U_1225,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_1225)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1225) ),
inference(variable_rename,[status(thm)],[f_352_1]) ).
cnf(f_352_3,plain,
( c_Complete__Lattice_OSup__class_OSup(U_1225,c_Orderings_Otop__class_Otop(tc_fun(U_1225,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_1225)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1225) ),
inference(clausify,[status(thm)],[f_352_2]) ).
fof(f_353_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_353_2,plain,
! [U_1227,U_1226] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1226),c_Orderings_Obot__class_Obot(U_1226)),U_1227) = U_1227
| ~ class_Lattices_Obounded__lattice__bot(U_1226) ),
inference(variable_rename,[status(thm)],[f_353_1]) ).
cnf(f_353_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1226),c_Orderings_Obot__class_Obot(U_1226)),U_1227) = U_1227
| ~ class_Lattices_Obounded__lattice__bot(U_1226) ),
inference(clausify,[status(thm)],[f_353_2]) ).
fof(f_354_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_354_2,plain,
! [U_1229,U_1228] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1228),U_1229),c_Orderings_Obot__class_Obot(U_1228)) = U_1229
| ~ class_Lattices_Obounded__lattice__bot(U_1228) ),
inference(variable_rename,[status(thm)],[f_354_1]) ).
cnf(f_354_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1228),U_1229),c_Orderings_Obot__class_Obot(U_1228)) = U_1229
| ~ class_Lattices_Obounded__lattice__bot(U_1228) ),
inference(clausify,[status(thm)],[f_354_2]) ).
fof(f_355_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_355_2,plain,
! [U_1232,U_1231,U_1230] :
( ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1230),U_1231),U_1232) = c_Orderings_Obot__class_Obot(U_1230)
| U_1232 != c_Orderings_Obot__class_Obot(U_1230)
| U_1231 != c_Orderings_Obot__class_Obot(U_1230) )
& ( ( U_1232 = c_Orderings_Obot__class_Obot(U_1230)
& U_1231 = c_Orderings_Obot__class_Obot(U_1230) )
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1230),U_1231),U_1232) != c_Orderings_Obot__class_Obot(U_1230) ) )
| ~ class_Lattices_Obounded__lattice__bot(U_1230) ),
inference(variable_rename,[status(thm)],[f_355_1]) ).
cnf(f_355_3,plain,
( U_1231 = c_Orderings_Obot__class_Obot(U_1230)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1230),U_1231),U_1232) != c_Orderings_Obot__class_Obot(U_1230)
| ~ class_Lattices_Obounded__lattice__bot(U_1230) ),
inference(clausify,[status(thm)],[f_355_2]) ).
cnf(f_355_4,plain,
( U_1232 = c_Orderings_Obot__class_Obot(U_1230)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1230),U_1231),U_1232) != c_Orderings_Obot__class_Obot(U_1230)
| ~ class_Lattices_Obounded__lattice__bot(U_1230) ),
inference(clausify,[status(thm)],[f_355_2]) ).
cnf(f_355_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1230),U_1231),U_1232) = c_Orderings_Obot__class_Obot(U_1230)
| U_1232 != c_Orderings_Obot__class_Obot(U_1230)
| U_1231 != c_Orderings_Obot__class_Obot(U_1230)
| ~ class_Lattices_Obounded__lattice__bot(U_1230) ),
inference(clausify,[status(thm)],[f_355_2]) ).
fof(f_356_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_356_2,plain,
! [U_1234,U_1233] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1233),U_1234),c_Orderings_Obot__class_Obot(U_1233)) = c_Orderings_Obot__class_Obot(U_1233)
| ~ class_Lattices_Obounded__lattice__bot(U_1233) ),
inference(variable_rename,[status(thm)],[f_356_1]) ).
cnf(f_356_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1233),U_1234),c_Orderings_Obot__class_Obot(U_1233)) = c_Orderings_Obot__class_Obot(U_1233)
| ~ class_Lattices_Obounded__lattice__bot(U_1233) ),
inference(clausify,[status(thm)],[f_356_2]) ).
fof(f_357_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_357_2,plain,
! [U_1236,U_1235] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1235),c_Orderings_Obot__class_Obot(U_1235)),U_1236) = c_Orderings_Obot__class_Obot(U_1235)
| ~ class_Lattices_Obounded__lattice__bot(U_1235) ),
inference(variable_rename,[status(thm)],[f_357_1]) ).
cnf(f_357_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1235),c_Orderings_Obot__class_Obot(U_1235)),U_1236) = c_Orderings_Obot__class_Obot(U_1235)
| ~ class_Lattices_Obounded__lattice__bot(U_1235) ),
inference(clausify,[status(thm)],[f_357_2]) ).
fof(f_358_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_358_2,plain,
! [U_1237] :
( c_Complete__Lattice_OInf__class_OInf(U_1237,c_Orderings_Otop__class_Otop(tc_fun(U_1237,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_1237)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1237) ),
inference(variable_rename,[status(thm)],[f_358_1]) ).
cnf(f_358_3,plain,
( c_Complete__Lattice_OInf__class_OInf(U_1237,c_Orderings_Otop__class_Otop(tc_fun(U_1237,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_1237)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1237) ),
inference(clausify,[status(thm)],[f_358_2]) ).
fof(f_359_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_359_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_359_1]) ).
fof(f_360_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_360_2,plain,
! [U_1240,U_1239,U_1238] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(U_1238,U_1239,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1240) = U_1240
| ~ class_Rings_Osemiring__1(U_1238) ),
inference(variable_rename,[status(thm)],[f_360_1]) ).
cnf(f_360_3,plain,
( c_Nat_Osemiring__1__class_Oof__nat__aux(U_1238,U_1239,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1240) = U_1240
| ~ class_Rings_Osemiring__1(U_1238) ),
inference(clausify,[status(thm)],[f_360_2]) ).
fof(f_361_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_361_2,plain,
! [U_1242,U_1241] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1241),hAPP(c_Groups_Ouminus__class_Ouminus(U_1241),U_1242)),U_1242))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1241),c_Groups_Ozero__class_Ozero(U_1241)),U_1242)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1241),c_Groups_Ozero__class_Ozero(U_1241)),U_1242))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1241),hAPP(c_Groups_Ouminus__class_Ouminus(U_1241),U_1242)),U_1242)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1241) ),
inference(variable_rename,[status(thm)],[f_361_1]) ).
cnf(f_361_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1241),c_Groups_Ozero__class_Ozero(U_1241)),U_1242))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1241),hAPP(c_Groups_Ouminus__class_Ouminus(U_1241),U_1242)),U_1242))
| ~ class_Groups_Olinordered__ab__group__add(U_1241) ),
inference(clausify,[status(thm)],[f_361_2]) ).
cnf(f_361_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1241),hAPP(c_Groups_Ouminus__class_Ouminus(U_1241),U_1242)),U_1242))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1241),c_Groups_Ozero__class_Ozero(U_1241)),U_1242))
| ~ class_Groups_Olinordered__ab__group__add(U_1241) ),
inference(clausify,[status(thm)],[f_361_2]) ).
fof(f_362_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_362_2,plain,
! [U_1244,U_1243] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1243),hAPP(c_Groups_Ouminus__class_Ouminus(U_1243),U_1244)),c_Groups_Ozero__class_Ozero(U_1243)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1243),c_Groups_Ozero__class_Ozero(U_1243)),U_1244)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1243),c_Groups_Ozero__class_Ozero(U_1243)),U_1244))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1243),hAPP(c_Groups_Ouminus__class_Ouminus(U_1243),U_1244)),c_Groups_Ozero__class_Ozero(U_1243))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1243) ),
inference(variable_rename,[status(thm)],[f_362_1]) ).
cnf(f_362_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1243),c_Groups_Ozero__class_Ozero(U_1243)),U_1244))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1243),hAPP(c_Groups_Ouminus__class_Ouminus(U_1243),U_1244)),c_Groups_Ozero__class_Ozero(U_1243)))
| ~ class_Groups_Oordered__ab__group__add(U_1243) ),
inference(clausify,[status(thm)],[f_362_2]) ).
cnf(f_362_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1243),hAPP(c_Groups_Ouminus__class_Ouminus(U_1243),U_1244)),c_Groups_Ozero__class_Ozero(U_1243)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1243),c_Groups_Ozero__class_Ozero(U_1243)),U_1244))
| ~ class_Groups_Oordered__ab__group__add(U_1243) ),
inference(clausify,[status(thm)],[f_362_2]) ).
fof(f_363_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_363_2,plain,
! [U_1246,U_1245] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1245),U_1246),hAPP(c_Groups_Ouminus__class_Ouminus(U_1245),U_1246)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1245),U_1246),c_Groups_Ozero__class_Ozero(U_1245))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1245),U_1246),c_Groups_Ozero__class_Ozero(U_1245)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1245),U_1246),hAPP(c_Groups_Ouminus__class_Ouminus(U_1245),U_1246))) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1245) ),
inference(variable_rename,[status(thm)],[f_363_1]) ).
cnf(f_363_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1245),U_1246),c_Groups_Ozero__class_Ozero(U_1245)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1245),U_1246),hAPP(c_Groups_Ouminus__class_Ouminus(U_1245),U_1246)))
| ~ class_Groups_Olinordered__ab__group__add(U_1245) ),
inference(clausify,[status(thm)],[f_363_2]) ).
cnf(f_363_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1245),U_1246),hAPP(c_Groups_Ouminus__class_Ouminus(U_1245),U_1246)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1245),U_1246),c_Groups_Ozero__class_Ozero(U_1245)))
| ~ class_Groups_Olinordered__ab__group__add(U_1245) ),
inference(clausify,[status(thm)],[f_363_2]) ).
fof(f_364_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_364_2,plain,
! [U_1248,U_1247] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1247),c_Groups_Ozero__class_Ozero(U_1247)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1247),U_1248)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1247),U_1248),c_Groups_Ozero__class_Ozero(U_1247))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1247),U_1248),c_Groups_Ozero__class_Ozero(U_1247)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1247),c_Groups_Ozero__class_Ozero(U_1247)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1247),U_1248))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1247) ),
inference(variable_rename,[status(thm)],[f_364_1]) ).
cnf(f_364_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1247),U_1248),c_Groups_Ozero__class_Ozero(U_1247)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1247),c_Groups_Ozero__class_Ozero(U_1247)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1247),U_1248)))
| ~ class_Groups_Oordered__ab__group__add(U_1247) ),
inference(clausify,[status(thm)],[f_364_2]) ).
cnf(f_364_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1247),c_Groups_Ozero__class_Ozero(U_1247)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1247),U_1248)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1247),U_1248),c_Groups_Ozero__class_Ozero(U_1247)))
| ~ class_Groups_Oordered__ab__group__add(U_1247) ),
inference(clausify,[status(thm)],[f_364_2]) ).
fof(f_365_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_365_2,plain,
! [U_1251,U_1250,U_1249] :
( U_1250 = hAPP(hAPP(c_Set_Oinsert(U_1249),U_1251),c_Orderings_Obot__class_Obot(tc_fun(U_1249,tc_HOL_Obool)))
| U_1250 = c_Orderings_Obot__class_Obot(tc_fun(U_1249,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1249,tc_HOL_Obool)),U_1250),hAPP(hAPP(c_Set_Oinsert(U_1249),U_1251),c_Orderings_Obot__class_Obot(tc_fun(U_1249,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[f_365_1]) ).
cnf(f_365_3,plain,
( U_1250 = hAPP(hAPP(c_Set_Oinsert(U_1249),U_1251),c_Orderings_Obot__class_Obot(tc_fun(U_1249,tc_HOL_Obool)))
| U_1250 = c_Orderings_Obot__class_Obot(tc_fun(U_1249,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1249,tc_HOL_Obool)),U_1250),hAPP(hAPP(c_Set_Oinsert(U_1249),U_1251),c_Orderings_Obot__class_Obot(tc_fun(U_1249,tc_HOL_Obool))))) ),
inference(clausify,[status(thm)],[f_365_2]) ).
fof(f_366_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_366_2,plain,
! [U_1254,U_1253,U_1252] : hAPP(hAPP(c_Set_Oinsert(U_1252),U_1253),U_1254) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1252,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1252),U_1253),c_Orderings_Obot__class_Obot(tc_fun(U_1252,tc_HOL_Obool)))),U_1254),
inference(variable_rename,[status(thm)],[f_366_1]) ).
cnf(f_366_3,plain,
hAPP(hAPP(c_Set_Oinsert(U_1252),U_1253),U_1254) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1252,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1252),U_1253),c_Orderings_Obot__class_Obot(tc_fun(U_1252,tc_HOL_Obool)))),U_1254),
inference(clausify,[status(thm)],[f_366_2]) ).
fof(f_367_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_367_2,plain,
! [U_1257,U_1256,U_1255] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost(U_1255,U_1256,U_1257) = c_Orderings_Obot__class_Obot(tc_fun(U_1255,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1255),U_1256),U_1257)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1255),U_1256),U_1257))
| c_SetInterval_Oord__class_OatLeastAtMost(U_1255,U_1256,U_1257) != c_Orderings_Obot__class_Obot(tc_fun(U_1255,tc_HOL_Obool)) ) )
| ~ class_Orderings_Oorder(U_1255) ),
inference(variable_rename,[status(thm)],[f_367_1]) ).
cnf(f_367_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1255),U_1256),U_1257))
| c_SetInterval_Oord__class_OatLeastAtMost(U_1255,U_1256,U_1257) != c_Orderings_Obot__class_Obot(tc_fun(U_1255,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1255) ),
inference(clausify,[status(thm)],[f_367_2]) ).
cnf(f_367_4,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(U_1255,U_1256,U_1257) = c_Orderings_Obot__class_Obot(tc_fun(U_1255,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1255),U_1256),U_1257))
| ~ class_Orderings_Oorder(U_1255) ),
inference(clausify,[status(thm)],[f_367_2]) ).
fof(f_368_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_368_2,plain,
! [U_1260,U_1259,U_1258] :
( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_1258,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1258,U_1259,U_1260)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1258),U_1259),U_1260)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1258),U_1259),U_1260))
| c_Orderings_Obot__class_Obot(tc_fun(U_1258,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_1258,U_1259,U_1260) ) )
| ~ class_Orderings_Oorder(U_1258) ),
inference(variable_rename,[status(thm)],[f_368_1]) ).
cnf(f_368_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1258),U_1259),U_1260))
| c_Orderings_Obot__class_Obot(tc_fun(U_1258,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_1258,U_1259,U_1260)
| ~ class_Orderings_Oorder(U_1258) ),
inference(clausify,[status(thm)],[f_368_2]) ).
cnf(f_368_4,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_1258,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1258,U_1259,U_1260)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1258),U_1259),U_1260))
| ~ class_Orderings_Oorder(U_1258) ),
inference(clausify,[status(thm)],[f_368_2]) ).
fof(f_369_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_369_2,plain,
! [U_1263,U_1262,U_1261] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1261,U_1263),U_1262) = c_Orderings_Obot__class_Obot(tc_fun(U_1261,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1261),U_1262),U_1263))
| ~ class_Orderings_Oorder(U_1261) ),
inference(variable_rename,[status(thm)],[f_369_1]) ).
cnf(f_369_3,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1261,U_1263),U_1262) = c_Orderings_Obot__class_Obot(tc_fun(U_1261,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1261),U_1262),U_1263))
| ~ class_Orderings_Oorder(U_1261) ),
inference(clausify,[status(thm)],[f_369_2]) ).
fof(f_370_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_370_2,plain,
! [U_1266,U_1265,U_1264] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1264,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1264,tc_HOL_Obool)),U_1265),U_1266)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1264,tc_HOL_Obool)),U_1265),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1264,tc_HOL_Obool),U_1266)),
inference(variable_rename,[status(thm)],[f_370_1]) ).
cnf(f_370_3,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1264,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1264,tc_HOL_Obool)),U_1265),U_1266)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1264,tc_HOL_Obool)),U_1265),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1264,tc_HOL_Obool),U_1266)),
inference(clausify,[status(thm)],[f_370_2]) ).
fof(f_371_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_371_2,plain,
! [U_1269,U_1268,U_1267] :
( c_SetInterval_Oord__class_OatLeastAtMost(U_1267,U_1268,U_1269) = hAPP(hAPP(c_Set_Oinsert(U_1267),U_1268),c_Orderings_Obot__class_Obot(tc_fun(U_1267,tc_HOL_Obool)))
| U_1268 != U_1269
| ~ class_Orderings_Oorder(U_1267) ),
inference(variable_rename,[status(thm)],[f_371_1]) ).
cnf(f_371_3,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(U_1267,U_1268,U_1269) = hAPP(hAPP(c_Set_Oinsert(U_1267),U_1268),c_Orderings_Obot__class_Obot(tc_fun(U_1267,tc_HOL_Obool)))
| U_1268 != U_1269
| ~ class_Orderings_Oorder(U_1267) ),
inference(clausify,[status(thm)],[f_371_2]) ).
fof(f_372_1,plain,
! [V_c_2,V_b_2,V_a_2,T_b] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
| V_b_2 != V_c_2
| V_a_2 != V_b_2 )
& ( ( V_b_2 = V_c_2
& V_a_2 = V_b_2 )
| c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) != hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton__iff]) ).
fof(f_372_2,plain,
! [U_1273,U_1272,U_1271,U_1270] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost(U_1270,U_1271,U_1272) = hAPP(hAPP(c_Set_Oinsert(U_1270),U_1273),c_Orderings_Obot__class_Obot(tc_fun(U_1270,tc_HOL_Obool)))
| U_1272 != U_1273
| U_1271 != U_1272 )
& ( ( U_1272 = U_1273
& U_1271 = U_1272 )
| c_SetInterval_Oord__class_OatLeastAtMost(U_1270,U_1271,U_1272) != hAPP(hAPP(c_Set_Oinsert(U_1270),U_1273),c_Orderings_Obot__class_Obot(tc_fun(U_1270,tc_HOL_Obool))) ) )
| ~ class_Orderings_Oorder(U_1270) ),
inference(variable_rename,[status(thm)],[f_372_1]) ).
cnf(f_372_3,plain,
( U_1271 = U_1272
| c_SetInterval_Oord__class_OatLeastAtMost(U_1270,U_1271,U_1272) != hAPP(hAPP(c_Set_Oinsert(U_1270),U_1273),c_Orderings_Obot__class_Obot(tc_fun(U_1270,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_1270) ),
inference(clausify,[status(thm)],[f_372_2]) ).
cnf(f_372_4,plain,
( U_1272 = U_1273
| c_SetInterval_Oord__class_OatLeastAtMost(U_1270,U_1271,U_1272) != hAPP(hAPP(c_Set_Oinsert(U_1270),U_1273),c_Orderings_Obot__class_Obot(tc_fun(U_1270,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_1270) ),
inference(clausify,[status(thm)],[f_372_2]) ).
cnf(f_372_5,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(U_1270,U_1271,U_1272) = hAPP(hAPP(c_Set_Oinsert(U_1270),U_1273),c_Orderings_Obot__class_Obot(tc_fun(U_1270,tc_HOL_Obool)))
| U_1272 != U_1273
| U_1271 != U_1272
| ~ class_Orderings_Oorder(U_1270) ),
inference(clausify,[status(thm)],[f_372_2]) ).
fof(f_373_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_373_2,plain,
! [U_1275,U_1274] :
( c_SetInterval_Oord__class_OatLeastAtMost(U_1274,U_1275,U_1275) = hAPP(hAPP(c_Set_Oinsert(U_1274),U_1275),c_Orderings_Obot__class_Obot(tc_fun(U_1274,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_1274) ),
inference(variable_rename,[status(thm)],[f_373_1]) ).
cnf(f_373_3,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(U_1274,U_1275,U_1275) = hAPP(hAPP(c_Set_Oinsert(U_1274),U_1275),c_Orderings_Obot__class_Obot(tc_fun(U_1274,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_1274) ),
inference(clausify,[status(thm)],[f_373_2]) ).
fof(f_374_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_374_2,plain,
! [U_1279,U_1278,U_1277,U_1276] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1276,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1276,U_1277),U_1278)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1276,U_1278),U_1279)) = c_Orderings_Obot__class_Obot(tc_fun(U_1276,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1276) ),
inference(variable_rename,[status(thm)],[f_374_1]) ).
cnf(f_374_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1276,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1276,U_1277),U_1278)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1276,U_1278),U_1279)) = c_Orderings_Obot__class_Obot(tc_fun(U_1276,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1276) ),
inference(clausify,[status(thm)],[f_374_2]) ).
fof(f_375_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_375_2,plain,
! [U_1281,U_1280] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1280,tc_HOL_Obool)),U_1281),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1280,tc_HOL_Obool)),U_1281)))
| U_1281 != c_Orderings_Obot__class_Obot(tc_fun(U_1280,tc_HOL_Obool)) )
& ( U_1281 = c_Orderings_Obot__class_Obot(tc_fun(U_1280,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1280,tc_HOL_Obool)),U_1281),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1280,tc_HOL_Obool)),U_1281))) ) ),
inference(variable_rename,[status(thm)],[f_375_1]) ).
fof(f_375_3,plain,
( ! [U_1285,U_1283] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1283,tc_HOL_Obool)),U_1285),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1283,tc_HOL_Obool)),U_1285)))
| U_1285 != c_Orderings_Obot__class_Obot(tc_fun(U_1283,tc_HOL_Obool)) )
& ! [U_1284,U_1282] :
( U_1284 = c_Orderings_Obot__class_Obot(tc_fun(U_1282,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1282,tc_HOL_Obool)),U_1284),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1282,tc_HOL_Obool)),U_1284))) ) ),
inference(miniscope,[status(thm)],[f_375_2]) ).
cnf(f_375_4,plain,
( U_1284 = c_Orderings_Obot__class_Obot(tc_fun(U_1282,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1282,tc_HOL_Obool)),U_1284),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1282,tc_HOL_Obool)),U_1284))) ),
inference(clausify,[status(thm)],[f_375_3]) ).
cnf(f_375_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1283,tc_HOL_Obool)),U_1285),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1283,tc_HOL_Obool)),U_1285)))
| U_1285 != c_Orderings_Obot__class_Obot(tc_fun(U_1283,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_375_3]) ).
fof(f_376_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_376_2,plain,
! [U_1287,U_1286] :
( c_Complete__Lattice_OInf__class_OInf(U_1286,hAPP(hAPP(c_Set_Oinsert(U_1286),U_1287),c_Orderings_Obot__class_Obot(tc_fun(U_1286,tc_HOL_Obool)))) = U_1287
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1286) ),
inference(variable_rename,[status(thm)],[f_376_1]) ).
cnf(f_376_3,plain,
( c_Complete__Lattice_OInf__class_OInf(U_1286,hAPP(hAPP(c_Set_Oinsert(U_1286),U_1287),c_Orderings_Obot__class_Obot(tc_fun(U_1286,tc_HOL_Obool)))) = U_1287
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1286) ),
inference(clausify,[status(thm)],[f_376_2]) ).
fof(f_377_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_377_2,plain,
! [U_1289,U_1288] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1288,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1288,tc_HOL_Obool)),U_1289)),U_1289) = c_Orderings_Obot__class_Obot(tc_fun(U_1288,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_377_1]) ).
cnf(f_377_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1288,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1288,tc_HOL_Obool)),U_1289)),U_1289) = c_Orderings_Obot__class_Obot(tc_fun(U_1288,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_377_2]) ).
fof(f_378_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_378_2,plain,
! [U_1291,U_1290] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1290,tc_HOL_Obool)),U_1291),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1290,tc_HOL_Obool)),U_1291)) = c_Orderings_Obot__class_Obot(tc_fun(U_1290,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_378_1]) ).
cnf(f_378_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1290,tc_HOL_Obool)),U_1291),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1290,tc_HOL_Obool)),U_1291)) = c_Orderings_Obot__class_Obot(tc_fun(U_1290,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_378_2]) ).
fof(f_379_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_379_2,plain,
! [U_1294,U_1293,U_1292] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1292,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1292,tc_HOL_Obool),U_1293)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1292,tc_HOL_Obool),U_1294)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_1292,tc_HOL_Obool),tc_HOL_Obool)),U_1293),U_1294)) ),
inference(variable_rename,[status(thm)],[f_379_1]) ).
cnf(f_379_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1292,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1292,tc_HOL_Obool),U_1293)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1292,tc_HOL_Obool),U_1294)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_1292,tc_HOL_Obool),tc_HOL_Obool)),U_1293),U_1294)) ),
inference(clausify,[status(thm)],[f_379_2]) ).
fof(f_380_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_380_2,plain,
! [U_1297,U_1296,U_1295] :
( c_SetInterval_Oord__class_OgreaterThanAtMost(U_1295,U_1297,U_1296) = c_Orderings_Obot__class_Obot(tc_fun(U_1295,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1295),U_1296),U_1297))
| ~ class_Orderings_Oorder(U_1295) ),
inference(variable_rename,[status(thm)],[f_380_1]) ).
cnf(f_380_3,plain,
( c_SetInterval_Oord__class_OgreaterThanAtMost(U_1295,U_1297,U_1296) = c_Orderings_Obot__class_Obot(tc_fun(U_1295,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1295),U_1296),U_1297))
| ~ class_Orderings_Oorder(U_1295) ),
inference(clausify,[status(thm)],[f_380_2]) ).
fof(f_381_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_381_2,plain,
! [U_1298] :
( c_Complete__Lattice_OInf__class_OInf(U_1298,c_Orderings_Obot__class_Obot(tc_fun(U_1298,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_1298)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1298) ),
inference(variable_rename,[status(thm)],[f_381_1]) ).
cnf(f_381_3,plain,
( c_Complete__Lattice_OInf__class_OInf(U_1298,c_Orderings_Obot__class_Obot(tc_fun(U_1298,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_1298)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1298) ),
inference(clausify,[status(thm)],[f_381_2]) ).
fof(f_382_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_382_2,plain,
! [U_1302,U_1301,U_1300,U_1299] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1299,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1299,U_1300,U_1301)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1299,U_1301,U_1302)) = c_Orderings_Obot__class_Obot(tc_fun(U_1299,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1299) ),
inference(variable_rename,[status(thm)],[f_382_1]) ).
cnf(f_382_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1299,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1299,U_1300,U_1301)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1299,U_1301,U_1302)) = c_Orderings_Obot__class_Obot(tc_fun(U_1299,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1299) ),
inference(clausify,[status(thm)],[f_382_2]) ).
fof(f_383_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_383_2,plain,
! [U_1304,U_1303] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_1303,tc_HOL_Obool),tc_HOL_Obool)),U_1304),hAPP(c_Set_OPow(U_1303),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1303,tc_HOL_Obool),U_1304)))),
inference(variable_rename,[status(thm)],[f_383_1]) ).
cnf(f_383_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_1303,tc_HOL_Obool),tc_HOL_Obool)),U_1304),hAPP(c_Set_OPow(U_1303),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1303,tc_HOL_Obool),U_1304)))),
inference(clausify,[status(thm)],[f_383_2]) ).
fof(f_384_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_384_2,plain,
! [U_1307,U_1306,U_1305] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1305,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_1305,tc_HOL_Obool),tc_HOL_Obool)),U_1306),U_1307)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1305,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1305,tc_HOL_Obool),U_1306)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1305,tc_HOL_Obool),U_1307)),
inference(variable_rename,[status(thm)],[f_384_1]) ).
cnf(f_384_3,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1305,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_1305,tc_HOL_Obool),tc_HOL_Obool)),U_1306),U_1307)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1305,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1305,tc_HOL_Obool),U_1306)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1305,tc_HOL_Obool),U_1307)),
inference(clausify,[status(thm)],[f_384_2]) ).
fof(f_385_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_385_2,plain,
! [U_1308] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1308) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_1308),
inference(variable_rename,[status(thm)],[f_385_1]) ).
cnf(f_385_3,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1308) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_1308),
inference(clausify,[status(thm)],[f_385_2]) ).
fof(f_386_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_386_2,plain,
! [U_1309] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1309) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_1309),
inference(variable_rename,[status(thm)],[f_386_1]) ).
cnf(f_386_3,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1309) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_1309),
inference(clausify,[status(thm)],[f_386_2]) ).
fof(f_387_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_387_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_387_1]) ).
fof(f_388_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_388_2,plain,
! [U_1312,U_1311,U_1310] :
( c_Complete__Lattice_OSup__class_OSup(U_1310,hAPP(hAPP(c_Set_Oinsert(U_1310),U_1311),U_1312)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1310),U_1311),c_Complete__Lattice_OSup__class_OSup(U_1310,U_1312))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1310) ),
inference(variable_rename,[status(thm)],[f_388_1]) ).
cnf(f_388_3,plain,
( c_Complete__Lattice_OSup__class_OSup(U_1310,hAPP(hAPP(c_Set_Oinsert(U_1310),U_1311),U_1312)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1310),U_1311),c_Complete__Lattice_OSup__class_OSup(U_1310,U_1312))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1310) ),
inference(clausify,[status(thm)],[f_388_2]) ).
fof(f_389_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_389_2,plain,
! [U_1314,U_1313] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1313),hAPP(c_Groups_Ouminus__class_Ouminus(U_1313),U_1314)),U_1314) = c_Orderings_Obot__class_Obot(U_1313)
| ~ class_Lattices_Oboolean__algebra(U_1313) ),
inference(variable_rename,[status(thm)],[f_389_1]) ).
cnf(f_389_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1313),hAPP(c_Groups_Ouminus__class_Ouminus(U_1313),U_1314)),U_1314) = c_Orderings_Obot__class_Obot(U_1313)
| ~ class_Lattices_Oboolean__algebra(U_1313) ),
inference(clausify,[status(thm)],[f_389_2]) ).
fof(f_390_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_390_2,plain,
! [U_1316,U_1315] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1315),U_1316),hAPP(c_Groups_Ouminus__class_Ouminus(U_1315),U_1316)) = c_Orderings_Obot__class_Obot(U_1315)
| ~ class_Lattices_Oboolean__algebra(U_1315) ),
inference(variable_rename,[status(thm)],[f_390_1]) ).
cnf(f_390_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1315),U_1316),hAPP(c_Groups_Ouminus__class_Ouminus(U_1315),U_1316)) = c_Orderings_Obot__class_Obot(U_1315)
| ~ class_Lattices_Oboolean__algebra(U_1315) ),
inference(clausify,[status(thm)],[f_390_2]) ).
fof(f_391_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_391_2,plain,
! [U_1317] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1317),c_Orderings_Obot__class_Obot(U_1317)) = c_Orderings_Otop__class_Otop(U_1317)
| ~ class_Lattices_Oboolean__algebra(U_1317) ),
inference(variable_rename,[status(thm)],[f_391_1]) ).
cnf(f_391_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1317),c_Orderings_Obot__class_Obot(U_1317)) = c_Orderings_Otop__class_Otop(U_1317)
| ~ class_Lattices_Oboolean__algebra(U_1317) ),
inference(clausify,[status(thm)],[f_391_2]) ).
fof(f_392_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_392_2,plain,
! [U_1318] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1318),c_Orderings_Otop__class_Otop(U_1318)) = c_Orderings_Obot__class_Obot(U_1318)
| ~ class_Lattices_Oboolean__algebra(U_1318) ),
inference(variable_rename,[status(thm)],[f_392_1]) ).
cnf(f_392_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1318),c_Orderings_Otop__class_Otop(U_1318)) = c_Orderings_Obot__class_Obot(U_1318)
| ~ class_Lattices_Oboolean__algebra(U_1318) ),
inference(clausify,[status(thm)],[f_392_2]) ).
fof(f_393_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_393_2,plain,
! [U_1321,U_1320,U_1319] :
( c_Complete__Lattice_OInf__class_OInf(U_1319,hAPP(hAPP(c_Set_Oinsert(U_1319),U_1320),hAPP(hAPP(c_Set_Oinsert(U_1319),U_1321),c_Orderings_Obot__class_Obot(tc_fun(U_1319,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1319),U_1320),U_1321)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1319) ),
inference(variable_rename,[status(thm)],[f_393_1]) ).
cnf(f_393_3,plain,
( c_Complete__Lattice_OInf__class_OInf(U_1319,hAPP(hAPP(c_Set_Oinsert(U_1319),U_1320),hAPP(hAPP(c_Set_Oinsert(U_1319),U_1321),c_Orderings_Obot__class_Obot(tc_fun(U_1319,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1319),U_1320),U_1321)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_1319) ),
inference(clausify,[status(thm)],[f_393_2]) ).
fof(f_394_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_394_2,plain,
! [U_1324,U_1323,U_1322] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1322,tc_HOL_Obool)),U_1323),U_1324) = c_Orderings_Obot__class_Obot(tc_fun(U_1322,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1322,tc_HOL_Obool)),U_1323),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1322,tc_HOL_Obool)),U_1324))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1322,tc_HOL_Obool)),U_1323),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1322,tc_HOL_Obool)),U_1324)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1322,tc_HOL_Obool)),U_1323),U_1324) != c_Orderings_Obot__class_Obot(tc_fun(U_1322,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_394_1]) ).
fof(f_394_3,plain,
( ! [U_1330,U_1328,U_1326] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1326,tc_HOL_Obool)),U_1328),U_1330) = c_Orderings_Obot__class_Obot(tc_fun(U_1326,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1326,tc_HOL_Obool)),U_1328),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1326,tc_HOL_Obool)),U_1330))) )
& ! [U_1329,U_1327,U_1325] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1325,tc_HOL_Obool)),U_1327),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1325,tc_HOL_Obool)),U_1329)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1325,tc_HOL_Obool)),U_1327),U_1329) != c_Orderings_Obot__class_Obot(tc_fun(U_1325,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_394_2]) ).
cnf(f_394_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1325,tc_HOL_Obool)),U_1327),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1325,tc_HOL_Obool)),U_1329)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1325,tc_HOL_Obool)),U_1327),U_1329) != c_Orderings_Obot__class_Obot(tc_fun(U_1325,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_394_3]) ).
cnf(f_394_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1326,tc_HOL_Obool)),U_1328),U_1330) = c_Orderings_Obot__class_Obot(tc_fun(U_1326,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1326,tc_HOL_Obool)),U_1328),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1326,tc_HOL_Obool)),U_1330))) ),
inference(clausify,[status(thm)],[f_394_3]) ).
fof(f_395_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_395_2,plain,
! [U_1334,U_1333,U_1332,U_1331] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1331,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1331,U_1332),U_1333)),c_SetInterval_Oord__class_OatLeastAtMost(U_1331,U_1333,U_1334)) = c_Orderings_Obot__class_Obot(tc_fun(U_1331,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1331) ),
inference(variable_rename,[status(thm)],[f_395_1]) ).
cnf(f_395_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1331,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1331,U_1332),U_1333)),c_SetInterval_Oord__class_OatLeastAtMost(U_1331,U_1333,U_1334)) = c_Orderings_Obot__class_Obot(tc_fun(U_1331,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1331) ),
inference(clausify,[status(thm)],[f_395_2]) ).
fof(f_396_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_396_2,plain,
! [U_1337,U_1336,U_1335] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1335,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1335),U_1336)),c_SetInterval_Oord__class_OatLeastAtMost(U_1335,U_1336,U_1337)) = c_Orderings_Obot__class_Obot(tc_fun(U_1335,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1335) ),
inference(variable_rename,[status(thm)],[f_396_1]) ).
cnf(f_396_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1335,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1335),U_1336)),c_SetInterval_Oord__class_OatLeastAtMost(U_1335,U_1336,U_1337)) = c_Orderings_Obot__class_Obot(tc_fun(U_1335,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1335) ),
inference(clausify,[status(thm)],[f_396_2]) ).
fof(f_397_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_397_2,plain,
! [U_1340,U_1339,U_1338] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1338,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1338),U_1339)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1338,U_1339),U_1340)) = c_Orderings_Obot__class_Obot(tc_fun(U_1338,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1338) ),
inference(variable_rename,[status(thm)],[f_397_1]) ).
cnf(f_397_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1338,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1338),U_1339)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1338,U_1339),U_1340)) = c_Orderings_Obot__class_Obot(tc_fun(U_1338,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1338) ),
inference(clausify,[status(thm)],[f_397_2]) ).
fof(f_398_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_398_2,plain,
! [U_1344,U_1343,U_1342,U_1341] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1341,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1341,U_1342,U_1343)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1341,U_1343,U_1344)) = c_Orderings_Obot__class_Obot(tc_fun(U_1341,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1341) ),
inference(variable_rename,[status(thm)],[f_398_1]) ).
cnf(f_398_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1341,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1341,U_1342,U_1343)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1341,U_1343,U_1344)) = c_Orderings_Obot__class_Obot(tc_fun(U_1341,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1341) ),
inference(clausify,[status(thm)],[f_398_2]) ).
fof(f_399_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_399_2,plain,
! [U_1347,U_1346,U_1345] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1345,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1345,U_1346),U_1347)),hAPP(c_SetInterval_Oord__class_OatLeast(U_1345),U_1347)) = c_Orderings_Obot__class_Obot(tc_fun(U_1345,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1345) ),
inference(variable_rename,[status(thm)],[f_399_1]) ).
cnf(f_399_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1345,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1345,U_1346),U_1347)),hAPP(c_SetInterval_Oord__class_OatLeast(U_1345),U_1347)) = c_Orderings_Obot__class_Obot(tc_fun(U_1345,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1345) ),
inference(clausify,[status(thm)],[f_399_2]) ).
fof(f_400_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_400_2,plain,
! [U_1350,U_1349,U_1348] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1348,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1348,U_1349,U_1350)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1348),U_1350)) = c_Orderings_Obot__class_Obot(tc_fun(U_1348,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1348) ),
inference(variable_rename,[status(thm)],[f_400_1]) ).
cnf(f_400_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1348,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1348,U_1349,U_1350)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1348),U_1350)) = c_Orderings_Obot__class_Obot(tc_fun(U_1348,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1348) ),
inference(clausify,[status(thm)],[f_400_2]) ).
fof(f_401_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_401_2,plain,
! [U_1353,U_1352,U_1351] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1351,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_1351),U_1352)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1351,U_1352,U_1353)) = c_Orderings_Obot__class_Obot(tc_fun(U_1351,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1351) ),
inference(variable_rename,[status(thm)],[f_401_1]) ).
cnf(f_401_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1351,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_1351),U_1352)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1351,U_1352,U_1353)) = c_Orderings_Obot__class_Obot(tc_fun(U_1351,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1351) ),
inference(clausify,[status(thm)],[f_401_2]) ).
fof(f_402_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_402_2,plain,
! [U_1356,U_1355,U_1354] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1354,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1354,U_1355,U_1356)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1354),U_1356)) = c_Orderings_Obot__class_Obot(tc_fun(U_1354,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1354) ),
inference(variable_rename,[status(thm)],[f_402_1]) ).
cnf(f_402_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1354,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1354,U_1355,U_1356)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1354),U_1356)) = c_Orderings_Obot__class_Obot(tc_fun(U_1354,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1354) ),
inference(clausify,[status(thm)],[f_402_2]) ).
fof(f_403_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_403_2,plain,
! [U_1357] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_1357),hAPP(c_Nat_OSuc,U_1357)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_1357),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_403_1]) ).
cnf(f_403_3,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_1357),hAPP(c_Nat_OSuc,U_1357)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_1357),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_403_2]) ).
fof(f_404_1,plain,
! [V_P_2,V_n_2] :
( ( ! [B_m] :
( hBOOL(hAPP(V_P_2,B_m))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) )
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) ) )
& ( ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) )
| ? [B_m] :
( ~ hBOOL(hAPP(V_P_2,B_m))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_all__nat__less]) ).
fof(f_404_2,plain,
! [U_1363,U_1362] :
( ( ! [U_1361] :
( hBOOL(hAPP(U_1363,U_1361))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1361),U_1362)) )
| ? [U_1360] :
( ~ hBOOL(hAPP(U_1363,U_1360))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_1360),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1362))) ) )
& ( ! [U_1359] :
( hBOOL(hAPP(U_1363,U_1359))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_1359),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1362))) )
| ? [U_1358] :
( ~ hBOOL(hAPP(U_1363,U_1358))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1358),U_1362)) ) ) ),
inference(variable_rename,[status(thm)],[f_404_1]) ).
fof(f_404_3,plain,
( ! [U_1367,U_1365] :
( ! [U_1361] :
( hBOOL(hAPP(U_1367,U_1361))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1361),U_1365)) )
| ? [U_1360] :
( ~ hBOOL(hAPP(U_1367,U_1360))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_1360),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1365))) ) )
& ! [U_1366,U_1364] :
( ! [U_1359] :
( hBOOL(hAPP(U_1366,U_1359))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_1359),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1364))) )
| ? [U_1358] :
( ~ hBOOL(hAPP(U_1366,U_1358))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1358),U_1364)) ) ) ),
inference(miniscope,[status(thm)],[f_404_2]) ).
fof(f_404_4,plain,
( ! [U_1367,U_1365] :
( ! [U_1361] :
( hBOOL(hAPP(U_1367,U_1361))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1361),U_1365)) )
| ? [U_1360] :
( ~ hBOOL(hAPP(U_1367,U_1360))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_1360),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1365))) ) )
& ! [U_1366,U_1364] :
( ! [U_1359] :
( hBOOL(hAPP(U_1366,U_1359))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_1359),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1364))) )
| ( ~ hBOOL(hAPP(U_1366,sK23(U_1366,U_1364)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK23(U_1366,U_1364)),U_1364)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_1358,sK23(U_1366,U_1364))],[f_404_3]) ).
fof(f_404_5,plain,
( ! [U_1367,U_1365] :
( ! [U_1361] :
( hBOOL(hAPP(U_1367,U_1361))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1361),U_1365)) )
| ( ~ hBOOL(hAPP(U_1367,sK24(U_1367,U_1365)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK24(U_1367,U_1365)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1365))) ) )
& ! [U_1366,U_1364] :
( ! [U_1359] :
( hBOOL(hAPP(U_1366,U_1359))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_1359),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1364))) )
| ( ~ hBOOL(hAPP(U_1366,sK23(U_1366,U_1364)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK23(U_1366,U_1364)),U_1364)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_1360,sK24(U_1367,U_1365))],[f_404_4]) ).
cnf(f_404_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK23(U_1366,U_1364)),U_1364))
| hBOOL(hAPP(U_1366,U_1359))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_1359),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1364))) ),
inference(clausify,[status(thm)],[f_404_5]) ).
cnf(f_404_7,plain,
( ~ hBOOL(hAPP(U_1366,sK23(U_1366,U_1364)))
| hBOOL(hAPP(U_1366,U_1359))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_1359),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1364))) ),
inference(clausify,[status(thm)],[f_404_5]) ).
cnf(f_404_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK24(U_1367,U_1365)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1365)))
| hBOOL(hAPP(U_1367,U_1361))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1361),U_1365)) ),
inference(clausify,[status(thm)],[f_404_5]) ).
cnf(f_404_9,plain,
( ~ hBOOL(hAPP(U_1367,sK24(U_1367,U_1365)))
| hBOOL(hAPP(U_1367,U_1361))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1361),U_1365)) ),
inference(clausify,[status(thm)],[f_404_5]) ).
fof(f_405_1,plain,
! [V_P_2,V_n_2] :
( ( ? [B_m] :
( hBOOL(hAPP(V_P_2,B_m))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) )
| ! [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) ) )
& ( ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) )
| ! [B_m] :
( ~ hBOOL(hAPP(V_P_2,B_m))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_ex__nat__less]) ).
fof(f_405_2,plain,
! [U_1373,U_1372] :
( ( ? [U_1371] :
( hBOOL(hAPP(U_1373,U_1371))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1371),U_1372)) )
| ! [U_1370] :
( ~ hBOOL(hAPP(U_1373,U_1370))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_1370),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1372))) ) )
& ( ? [U_1369] :
( hBOOL(hAPP(U_1373,U_1369))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_1369),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1372))) )
| ! [U_1368] :
( ~ hBOOL(hAPP(U_1373,U_1368))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1368),U_1372)) ) ) ),
inference(variable_rename,[status(thm)],[f_405_1]) ).
fof(f_405_3,plain,
( ! [U_1377,U_1375] :
( ? [U_1371] :
( hBOOL(hAPP(U_1377,U_1371))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1371),U_1375)) )
| ! [U_1370] :
( ~ hBOOL(hAPP(U_1377,U_1370))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_1370),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1375))) ) )
& ! [U_1376,U_1374] :
( ? [U_1369] :
( hBOOL(hAPP(U_1376,U_1369))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_1369),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1374))) )
| ! [U_1368] :
( ~ hBOOL(hAPP(U_1376,U_1368))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1368),U_1374)) ) ) ),
inference(miniscope,[status(thm)],[f_405_2]) ).
fof(f_405_4,plain,
( ! [U_1377,U_1375] :
( ? [U_1371] :
( hBOOL(hAPP(U_1377,U_1371))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1371),U_1375)) )
| ! [U_1370] :
( ~ hBOOL(hAPP(U_1377,U_1370))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_1370),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1375))) ) )
& ! [U_1376,U_1374] :
( ( hBOOL(hAPP(U_1376,sK25(U_1376,U_1374)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK25(U_1376,U_1374)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1374))) )
| ! [U_1368] :
( ~ hBOOL(hAPP(U_1376,U_1368))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1368),U_1374)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_1369,sK25(U_1376,U_1374))],[f_405_3]) ).
fof(f_405_5,plain,
( ! [U_1377,U_1375] :
( ( hBOOL(hAPP(U_1377,sK26(U_1377,U_1375)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK26(U_1377,U_1375)),U_1375)) )
| ! [U_1370] :
( ~ hBOOL(hAPP(U_1377,U_1370))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_1370),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1375))) ) )
& ! [U_1376,U_1374] :
( ( hBOOL(hAPP(U_1376,sK25(U_1376,U_1374)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK25(U_1376,U_1374)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1374))) )
| ! [U_1368] :
( ~ hBOOL(hAPP(U_1376,U_1368))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1368),U_1374)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_1371,sK26(U_1377,U_1375))],[f_405_4]) ).
cnf(f_405_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK25(U_1376,U_1374)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1374)))
| ~ hBOOL(hAPP(U_1376,U_1368))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1368),U_1374)) ),
inference(clausify,[status(thm)],[f_405_5]) ).
cnf(f_405_7,plain,
( hBOOL(hAPP(U_1376,sK25(U_1376,U_1374)))
| ~ hBOOL(hAPP(U_1376,U_1368))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1368),U_1374)) ),
inference(clausify,[status(thm)],[f_405_5]) ).
cnf(f_405_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK26(U_1377,U_1375)),U_1375))
| ~ hBOOL(hAPP(U_1377,U_1370))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_1370),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1375))) ),
inference(clausify,[status(thm)],[f_405_5]) ).
cnf(f_405_9,plain,
( hBOOL(hAPP(U_1377,sK26(U_1377,U_1375)))
| ~ hBOOL(hAPP(U_1377,U_1370))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_1370),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1375))) ),
inference(clausify,[status(thm)],[f_405_5]) ).
fof(f_406_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_406_2,plain,
! [U_1379,U_1378] : c_Set_Othe__elem(U_1378,hAPP(hAPP(c_Set_Oinsert(U_1378),U_1379),c_Orderings_Obot__class_Obot(tc_fun(U_1378,tc_HOL_Obool)))) = U_1379,
inference(variable_rename,[status(thm)],[f_406_1]) ).
cnf(f_406_3,plain,
c_Set_Othe__elem(U_1378,hAPP(hAPP(c_Set_Oinsert(U_1378),U_1379),c_Orderings_Obot__class_Obot(tc_fun(U_1378,tc_HOL_Obool)))) = U_1379,
inference(clausify,[status(thm)],[f_406_2]) ).
fof(f_407_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_407_2,plain,
! [U_1380] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1380)) = 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_1380)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1380)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_407_1]) ).
cnf(f_407_3,plain,
hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1380)) = 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_1380)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1380)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_407_2]) ).
fof(f_408_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_408_2,plain,
! [U_1381] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1381)) = 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_1381)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_1381),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_408_1]) ).
cnf(f_408_3,plain,
hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1381)) = 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_1381)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_1381),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_408_2]) ).
fof(f_409_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_409_2,plain,
! [U_1384,U_1383,U_1382] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1382,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1382,U_1383,U_1384)),hAPP(c_SetInterval_Oord__class_OatLeast(U_1382),U_1384)) = c_Orderings_Obot__class_Obot(tc_fun(U_1382,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1382) ),
inference(variable_rename,[status(thm)],[f_409_1]) ).
cnf(f_409_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1382,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1382,U_1383,U_1384)),hAPP(c_SetInterval_Oord__class_OatLeast(U_1382),U_1384)) = c_Orderings_Obot__class_Obot(tc_fun(U_1382,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1382) ),
inference(clausify,[status(thm)],[f_409_2]) ).
fof(f_410_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_410_2,plain,
! [U_1388,U_1387,U_1386,U_1385] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1385,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1385,U_1386,U_1387)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1385,U_1387,U_1388)) = c_Orderings_Obot__class_Obot(tc_fun(U_1385,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1385) ),
inference(variable_rename,[status(thm)],[f_410_1]) ).
cnf(f_410_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1385,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1385,U_1386,U_1387)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1385,U_1387,U_1388)) = c_Orderings_Obot__class_Obot(tc_fun(U_1385,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1385) ),
inference(clausify,[status(thm)],[f_410_2]) ).
fof(f_411_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_411_2,plain,
! [U_1391,U_1390,U_1389] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1389,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_1389),U_1390)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1389,U_1390,U_1391)) = c_Orderings_Obot__class_Obot(tc_fun(U_1389,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1389) ),
inference(variable_rename,[status(thm)],[f_411_1]) ).
cnf(f_411_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1389,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_1389),U_1390)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1389,U_1390,U_1391)) = c_Orderings_Obot__class_Obot(tc_fun(U_1389,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1389) ),
inference(clausify,[status(thm)],[f_411_2]) ).
fof(f_412_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_412_2,plain,
! [U_1395,U_1394,U_1393,U_1392] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1392,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1392,U_1393,U_1394)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1392,U_1394),U_1395)) = c_Orderings_Obot__class_Obot(tc_fun(U_1392,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1392) ),
inference(variable_rename,[status(thm)],[f_412_1]) ).
cnf(f_412_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1392,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1392,U_1393,U_1394)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1392,U_1394),U_1395)) = c_Orderings_Obot__class_Obot(tc_fun(U_1392,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1392) ),
inference(clausify,[status(thm)],[f_412_2]) ).
fof(f_413_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_413_2,plain,
! [U_1399,U_1398,U_1397,U_1396] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1396,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1396,U_1397,U_1398)),c_SetInterval_Oord__class_OatLeastAtMost(U_1396,U_1398,U_1399)) = c_Orderings_Obot__class_Obot(tc_fun(U_1396,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1396) ),
inference(variable_rename,[status(thm)],[f_413_1]) ).
cnf(f_413_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1396,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1396,U_1397,U_1398)),c_SetInterval_Oord__class_OatLeastAtMost(U_1396,U_1398,U_1399)) = c_Orderings_Obot__class_Obot(tc_fun(U_1396,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1396) ),
inference(clausify,[status(thm)],[f_413_2]) ).
fof(f_414_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_414_2,plain,
! [U_1404,U_1403,U_1402,U_1401,U_1400] :
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1401,U_1400)),U_1402),U_1403),U_1404) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1400),hAPP(U_1402,U_1404)),hAPP(U_1403,U_1404))
| ~ class_Groups_Ominus(U_1400) ),
inference(variable_rename,[status(thm)],[f_414_1]) ).
cnf(f_414_3,plain,
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1401,U_1400)),U_1402),U_1403),U_1404) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1400),hAPP(U_1402,U_1404)),hAPP(U_1403,U_1404))
| ~ class_Groups_Ominus(U_1400) ),
inference(clausify,[status(thm)],[f_414_2]) ).
fof(f_415_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( ( ( V_a_2 = V_b_2
| V_c_2 != V_d_2 )
& ( V_c_2 = V_d_2
| V_a_2 != V_b_2 ) )
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
| ~ class_Groups_Oab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq]) ).
fof(f_415_2,plain,
! [U_1409,U_1408,U_1407,U_1406,U_1405] :
( ( ( U_1406 = U_1407
| U_1408 != U_1409 )
& ( U_1408 = U_1409
| U_1406 != U_1407 ) )
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1405),U_1406),U_1407) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1405),U_1408),U_1409)
| ~ class_Groups_Oab__group__add(U_1405) ),
inference(variable_rename,[status(thm)],[f_415_1]) ).
cnf(f_415_3,plain,
( U_1408 = U_1409
| U_1406 != U_1407
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1405),U_1406),U_1407) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1405),U_1408),U_1409)
| ~ class_Groups_Oab__group__add(U_1405) ),
inference(clausify,[status(thm)],[f_415_2]) ).
cnf(f_415_4,plain,
( U_1406 = U_1407
| U_1408 != U_1409
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1405),U_1406),U_1407) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1405),U_1408),U_1409)
| ~ class_Groups_Oab__group__add(U_1405) ),
inference(clausify,[status(thm)],[f_415_2]) ).
fof(f_416_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_416_2,plain,
! [U_1412,U_1411,U_1410] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1410,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1410,tc_HOL_Obool)),U_1411),U_1412)),U_1412) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1410,tc_HOL_Obool)),U_1411),U_1412),
inference(variable_rename,[status(thm)],[f_416_1]) ).
cnf(f_416_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1410,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1410,tc_HOL_Obool)),U_1411),U_1412)),U_1412) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1410,tc_HOL_Obool)),U_1411),U_1412),
inference(clausify,[status(thm)],[f_416_2]) ).
fof(f_417_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) )
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq]) ).
fof(f_417_2,plain,
! [U_1417,U_1416,U_1415,U_1414,U_1413] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1413),U_1414),U_1415))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1413),U_1416),U_1417)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1413),U_1416),U_1417))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1413),U_1414),U_1415)) ) )
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1413),U_1414),U_1415) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1413),U_1416),U_1417)
| ~ class_Groups_Oordered__ab__group__add(U_1413) ),
inference(variable_rename,[status(thm)],[f_417_1]) ).
cnf(f_417_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1413),U_1416),U_1417))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1413),U_1414),U_1415))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1413),U_1414),U_1415) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1413),U_1416),U_1417)
| ~ class_Groups_Oordered__ab__group__add(U_1413) ),
inference(clausify,[status(thm)],[f_417_2]) ).
cnf(f_417_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1413),U_1414),U_1415))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1413),U_1416),U_1417))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1413),U_1414),U_1415) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1413),U_1416),U_1417)
| ~ class_Groups_Oordered__ab__group__add(U_1413) ),
inference(clausify,[status(thm)],[f_417_2]) ).
fof(f_418_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_418_2,plain,
! [U_1419,U_1418] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1418),U_1419),c_Groups_Ozero__class_Ozero(U_1418)) = U_1419
| ~ class_Groups_Ogroup__add(U_1418) ),
inference(variable_rename,[status(thm)],[f_418_1]) ).
cnf(f_418_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1418),U_1419),c_Groups_Ozero__class_Ozero(U_1418)) = U_1419
| ~ class_Groups_Ogroup__add(U_1418) ),
inference(clausify,[status(thm)],[f_418_2]) ).
fof(f_419_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_419_2,plain,
! [U_1421,U_1420] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1420),U_1421),U_1421) = c_Groups_Ozero__class_Ozero(U_1420)
| ~ class_Groups_Ogroup__add(U_1420) ),
inference(variable_rename,[status(thm)],[f_419_1]) ).
cnf(f_419_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1420),U_1421),U_1421) = c_Groups_Ozero__class_Ozero(U_1420)
| ~ class_Groups_Ogroup__add(U_1420) ),
inference(clausify,[status(thm)],[f_419_2]) ).
fof(f_420_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_420_2,plain,
! [U_1424,U_1423,U_1422] :
( ( ( U_1423 = U_1424
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1422),U_1423),U_1424) != c_Groups_Ozero__class_Ozero(U_1422) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1422),U_1423),U_1424) = c_Groups_Ozero__class_Ozero(U_1422)
| U_1423 != U_1424 ) )
| ~ class_Groups_Oab__group__add(U_1422) ),
inference(variable_rename,[status(thm)],[f_420_1]) ).
cnf(f_420_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1422),U_1423),U_1424) = c_Groups_Ozero__class_Ozero(U_1422)
| U_1423 != U_1424
| ~ class_Groups_Oab__group__add(U_1422) ),
inference(clausify,[status(thm)],[f_420_2]) ).
cnf(f_420_4,plain,
( U_1423 = U_1424
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1422),U_1423),U_1424) != c_Groups_Ozero__class_Ozero(U_1422)
| ~ class_Groups_Oab__group__add(U_1422) ),
inference(clausify,[status(thm)],[f_420_2]) ).
fof(f_421_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_421_2,plain,
! [U_1427,U_1426,U_1425] :
( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1425),U_1426),U_1427) = c_Groups_Ozero__class_Ozero(U_1425)
| U_1426 != U_1427 )
& ( U_1426 = U_1427
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1425),U_1426),U_1427) != c_Groups_Ozero__class_Ozero(U_1425) ) )
| ~ class_Groups_Ogroup__add(U_1425) ),
inference(variable_rename,[status(thm)],[f_421_1]) ).
cnf(f_421_3,plain,
( U_1426 = U_1427
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1425),U_1426),U_1427) != c_Groups_Ozero__class_Ozero(U_1425)
| ~ class_Groups_Ogroup__add(U_1425) ),
inference(clausify,[status(thm)],[f_421_2]) ).
cnf(f_421_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1425),U_1426),U_1427) = c_Groups_Ozero__class_Ozero(U_1425)
| U_1426 != U_1427
| ~ class_Groups_Ogroup__add(U_1425) ),
inference(clausify,[status(thm)],[f_421_2]) ).
fof(f_422_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_422_2,plain,
! [U_1430,U_1429,U_1428] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1428),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1428),U_1429),U_1430)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1428),U_1430),U_1429)
| ~ class_Groups_Oab__group__add(U_1428) ),
inference(variable_rename,[status(thm)],[f_422_1]) ).
cnf(f_422_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1428),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1428),U_1429),U_1430)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1428),U_1430),U_1429)
| ~ class_Groups_Oab__group__add(U_1428) ),
inference(clausify,[status(thm)],[f_422_2]) ).
fof(f_423_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_423_2,plain,
! [U_1432,U_1431] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1431,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1431,tc_HOL_Obool))),U_1432) = c_Orderings_Obot__class_Obot(tc_fun(U_1431,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_423_1]) ).
cnf(f_423_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1431,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1431,tc_HOL_Obool))),U_1432) = c_Orderings_Obot__class_Obot(tc_fun(U_1431,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_423_2]) ).
fof(f_424_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_424_2,plain,
! [U_1434,U_1433] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1433,tc_HOL_Obool)),U_1434),c_Orderings_Obot__class_Obot(tc_fun(U_1433,tc_HOL_Obool))) = U_1434,
inference(variable_rename,[status(thm)],[f_424_1]) ).
cnf(f_424_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1433,tc_HOL_Obool)),U_1434),c_Orderings_Obot__class_Obot(tc_fun(U_1433,tc_HOL_Obool))) = U_1434,
inference(clausify,[status(thm)],[f_424_2]) ).
fof(f_425_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_425_2,plain,
! [U_1436,U_1435] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1435,tc_HOL_Obool)),U_1436),U_1436) = c_Orderings_Obot__class_Obot(tc_fun(U_1435,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_425_1]) ).
cnf(f_425_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1435,tc_HOL_Obool)),U_1436),U_1436) = c_Orderings_Obot__class_Obot(tc_fun(U_1435,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_425_2]) ).
fof(f_426_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_426_2,plain,
! [U_1439,U_1438,U_1437] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1437,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1437,tc_HOL_Obool)),U_1438),U_1439)),U_1438)),
inference(variable_rename,[status(thm)],[f_426_1]) ).
cnf(f_426_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1437,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1437,tc_HOL_Obool)),U_1438),U_1439)),U_1438)),
inference(clausify,[status(thm)],[f_426_2]) ).
fof(f_427_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_427_2,plain,
! [U_1444,U_1443,U_1442,U_1441,U_1440] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1440,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1440,tc_HOL_Obool)),U_1441),U_1444)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1440,tc_HOL_Obool)),U_1442),U_1443)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1440,tc_HOL_Obool)),U_1443),U_1444))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1440,tc_HOL_Obool)),U_1441),U_1442)) ),
inference(variable_rename,[status(thm)],[f_427_1]) ).
cnf(f_427_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1440,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1440,tc_HOL_Obool)),U_1441),U_1444)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1440,tc_HOL_Obool)),U_1442),U_1443)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1440,tc_HOL_Obool)),U_1443),U_1444))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1440,tc_HOL_Obool)),U_1441),U_1442)) ),
inference(clausify,[status(thm)],[f_427_2]) ).
fof(f_428_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_428_2,plain,
! [U_1448,U_1447,U_1446,U_1445] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1445,tc_HOL_Obool)),U_1447),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1445,tc_HOL_Obool)),U_1448),U_1446)) = U_1446
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1445,tc_HOL_Obool)),U_1447),U_1448))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1445,tc_HOL_Obool)),U_1446),U_1447)) ),
inference(variable_rename,[status(thm)],[f_428_1]) ).
cnf(f_428_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1445,tc_HOL_Obool)),U_1447),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1445,tc_HOL_Obool)),U_1448),U_1446)) = U_1446
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1445,tc_HOL_Obool)),U_1447),U_1448))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1445,tc_HOL_Obool)),U_1446),U_1447)) ),
inference(clausify,[status(thm)],[f_428_2]) ).
fof(f_429_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_429_2,plain,
! [U_1451,U_1450,U_1449] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1449,tc_HOL_Obool)),U_1450),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1449,tc_HOL_Obool)),U_1451),U_1450)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1449,tc_HOL_Obool)),U_1450),U_1451),
inference(variable_rename,[status(thm)],[f_429_1]) ).
cnf(f_429_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1449,tc_HOL_Obool)),U_1450),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1449,tc_HOL_Obool)),U_1451),U_1450)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1449,tc_HOL_Obool)),U_1450),U_1451),
inference(clausify,[status(thm)],[f_429_2]) ).
fof(f_430_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_430_2,plain,
! [U_1454,U_1453,U_1452] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1452,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1452,tc_HOL_Obool)),U_1453),U_1454)),U_1454) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1452,tc_HOL_Obool)),U_1453),U_1454),
inference(variable_rename,[status(thm)],[f_430_1]) ).
cnf(f_430_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1452,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1452,tc_HOL_Obool)),U_1453),U_1454)),U_1454) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1452,tc_HOL_Obool)),U_1453),U_1454),
inference(clausify,[status(thm)],[f_430_2]) ).
fof(f_431_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_431_2,plain,
! [U_1458,U_1457,U_1456,U_1455] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1455,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1455,tc_HOL_Obool)),U_1456),U_1457)),U_1458) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1455,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1455,tc_HOL_Obool)),U_1456),U_1458)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1455,tc_HOL_Obool)),U_1457),U_1458)),
inference(variable_rename,[status(thm)],[f_431_1]) ).
cnf(f_431_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1455,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1455,tc_HOL_Obool)),U_1456),U_1457)),U_1458) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1455,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1455,tc_HOL_Obool)),U_1456),U_1458)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1455,tc_HOL_Obool)),U_1457),U_1458)),
inference(clausify,[status(thm)],[f_431_2]) ).
fof(f_432_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_432_2,plain,
! [U_1462,U_1461,U_1460,U_1459] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1459,tc_HOL_Obool)),U_1460),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1459,tc_HOL_Obool)),U_1461),U_1462)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1459,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1459,tc_HOL_Obool)),U_1460),U_1461)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1459,tc_HOL_Obool)),U_1460),U_1462)),
inference(variable_rename,[status(thm)],[f_432_1]) ).
cnf(f_432_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1459,tc_HOL_Obool)),U_1460),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1459,tc_HOL_Obool)),U_1461),U_1462)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1459,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1459,tc_HOL_Obool)),U_1460),U_1461)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1459,tc_HOL_Obool)),U_1460),U_1462)),
inference(clausify,[status(thm)],[f_432_2]) ).
fof(f_433_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_433_2,plain,
! [U_1466,U_1465,U_1464,U_1463] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1463,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1463,tc_HOL_Obool)),U_1464),U_1465)),U_1466) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1463,tc_HOL_Obool)),U_1464),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1463,tc_HOL_Obool)),U_1465),U_1466)),
inference(variable_rename,[status(thm)],[f_433_1]) ).
cnf(f_433_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1463,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1463,tc_HOL_Obool)),U_1464),U_1465)),U_1466) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1463,tc_HOL_Obool)),U_1464),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1463,tc_HOL_Obool)),U_1465),U_1466)),
inference(clausify,[status(thm)],[f_433_2]) ).
fof(f_434_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_434_2,plain,
! [U_1470,U_1469,U_1468,U_1467] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1467,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1467,tc_HOL_Obool)),U_1468),U_1469)),U_1470) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1467,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1467,tc_HOL_Obool)),U_1468),U_1470)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1467,tc_HOL_Obool)),U_1469),U_1470)),
inference(variable_rename,[status(thm)],[f_434_1]) ).
cnf(f_434_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1467,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1467,tc_HOL_Obool)),U_1468),U_1469)),U_1470) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1467,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1467,tc_HOL_Obool)),U_1468),U_1470)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1467,tc_HOL_Obool)),U_1469),U_1470)),
inference(clausify,[status(thm)],[f_434_2]) ).
fof(f_435_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_435_2,plain,
! [U_1474,U_1473,U_1472,U_1471] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1471,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1471,tc_HOL_Obool)),U_1472),U_1473)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1471,tc_HOL_Obool)),U_1474),U_1473)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1471,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1471,tc_HOL_Obool)),U_1472),U_1473)),U_1474),
inference(variable_rename,[status(thm)],[f_435_1]) ).
cnf(f_435_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1471,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1471,tc_HOL_Obool)),U_1472),U_1473)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1471,tc_HOL_Obool)),U_1474),U_1473)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1471,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1471,tc_HOL_Obool)),U_1472),U_1473)),U_1474),
inference(clausify,[status(thm)],[f_435_2]) ).
fof(f_436_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_436_2,plain,
! [U_1477,U_1476,U_1475] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1475),U_1476),U_1477))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1475),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1475),U_1476),U_1477)),c_Groups_Ozero__class_Ozero(U_1475))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1475),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1475),U_1476),U_1477)),c_Groups_Ozero__class_Ozero(U_1475)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1475),U_1476),U_1477)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1475) ),
inference(variable_rename,[status(thm)],[f_436_1]) ).
cnf(f_436_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1475),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1475),U_1476),U_1477)),c_Groups_Ozero__class_Ozero(U_1475)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1475),U_1476),U_1477))
| ~ class_Groups_Oordered__ab__group__add(U_1475) ),
inference(clausify,[status(thm)],[f_436_2]) ).
cnf(f_436_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1475),U_1476),U_1477))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1475),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1475),U_1476),U_1477)),c_Groups_Ozero__class_Ozero(U_1475)))
| ~ class_Groups_Oordered__ab__group__add(U_1475) ),
inference(clausify,[status(thm)],[f_436_2]) ).
fof(f_437_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_437_2,plain,
! [U_1479,U_1478] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1478),c_Groups_Ozero__class_Ozero(U_1478)),U_1479) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1478),U_1479)
| ~ class_Groups_Ogroup__add(U_1478) ),
inference(variable_rename,[status(thm)],[f_437_1]) ).
cnf(f_437_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1478),c_Groups_Ozero__class_Ozero(U_1478)),U_1479) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1478),U_1479)
| ~ class_Groups_Ogroup__add(U_1478) ),
inference(clausify,[status(thm)],[f_437_2]) ).
fof(f_438_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_438_2,plain,
! [U_1482,U_1481,U_1480] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1480),U_1481),U_1482) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1480),U_1481),hAPP(c_Groups_Ouminus__class_Ouminus(U_1480),U_1482))
| ~ class_Lattices_Oboolean__algebra(U_1480) ),
inference(variable_rename,[status(thm)],[f_438_1]) ).
cnf(f_438_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1480),U_1481),U_1482) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1480),U_1481),hAPP(c_Groups_Ouminus__class_Ouminus(U_1480),U_1482))
| ~ class_Lattices_Oboolean__algebra(U_1480) ),
inference(clausify,[status(thm)],[f_438_2]) ).
fof(f_439_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_439_2,plain,
! [U_1486,U_1485,U_1484,U_1483] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1483,tc_HOL_Obool)),U_1484),hAPP(hAPP(c_Set_Oinsert(U_1483),U_1485),U_1486)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1483,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1483,tc_HOL_Obool)),U_1484),U_1486)),hAPP(hAPP(c_Set_Oinsert(U_1483),U_1485),c_Orderings_Obot__class_Obot(tc_fun(U_1483,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_439_1]) ).
cnf(f_439_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1483,tc_HOL_Obool)),U_1484),hAPP(hAPP(c_Set_Oinsert(U_1483),U_1485),U_1486)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1483,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1483,tc_HOL_Obool)),U_1484),U_1486)),hAPP(hAPP(c_Set_Oinsert(U_1483),U_1485),c_Orderings_Obot__class_Obot(tc_fun(U_1483,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_439_2]) ).
fof(f_440_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_440_2,plain,
! [U_1490,U_1489,U_1488,U_1487] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1487,tc_HOL_Obool)),U_1488),hAPP(hAPP(c_Set_Oinsert(U_1487),U_1489),U_1490)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1487,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1487,tc_HOL_Obool)),U_1488),hAPP(hAPP(c_Set_Oinsert(U_1487),U_1489),c_Orderings_Obot__class_Obot(tc_fun(U_1487,tc_HOL_Obool))))),U_1490),
inference(variable_rename,[status(thm)],[f_440_1]) ).
cnf(f_440_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1487,tc_HOL_Obool)),U_1488),hAPP(hAPP(c_Set_Oinsert(U_1487),U_1489),U_1490)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1487,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1487,tc_HOL_Obool)),U_1488),hAPP(hAPP(c_Set_Oinsert(U_1487),U_1489),c_Orderings_Obot__class_Obot(tc_fun(U_1487,tc_HOL_Obool))))),U_1490),
inference(clausify,[status(thm)],[f_440_2]) ).
fof(f_441_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_441_2,plain,
! [U_1493,U_1492,U_1491] : hAPP(hAPP(c_Set_Oinsert(U_1491),U_1492),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1491,tc_HOL_Obool)),U_1493),hAPP(hAPP(c_Set_Oinsert(U_1491),U_1492),c_Orderings_Obot__class_Obot(tc_fun(U_1491,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_1491),U_1492),U_1493),
inference(variable_rename,[status(thm)],[f_441_1]) ).
cnf(f_441_3,plain,
hAPP(hAPP(c_Set_Oinsert(U_1491),U_1492),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1491,tc_HOL_Obool)),U_1493),hAPP(hAPP(c_Set_Oinsert(U_1491),U_1492),c_Orderings_Obot__class_Obot(tc_fun(U_1491,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_1491),U_1492),U_1493),
inference(clausify,[status(thm)],[f_441_2]) ).
fof(f_442_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_442_2,plain,
! [U_1495,U_1494] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1494,tc_HOL_Obool)),U_1495),c_Orderings_Otop__class_Otop(tc_fun(U_1494,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_1494,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_442_1]) ).
cnf(f_442_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1494,tc_HOL_Obool)),U_1495),c_Orderings_Otop__class_Otop(tc_fun(U_1494,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_1494,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_442_2]) ).
fof(f_443_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_443_2,plain,
! [U_1498,U_1497,U_1496] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1496,tc_HOL_Obool)),U_1497),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1496,tc_HOL_Obool)),U_1498),U_1497)) = c_Orderings_Obot__class_Obot(tc_fun(U_1496,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_443_1]) ).
cnf(f_443_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1496,tc_HOL_Obool)),U_1497),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1496,tc_HOL_Obool)),U_1498),U_1497)) = c_Orderings_Obot__class_Obot(tc_fun(U_1496,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_443_2]) ).
fof(f_444_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_444_2,plain,
! [U_1501,U_1500,U_1499] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1499,tc_HOL_Obool)),U_1500),U_1501) = U_1500
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1499,tc_HOL_Obool)),U_1500),U_1501) != c_Orderings_Obot__class_Obot(tc_fun(U_1499,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_444_1]) ).
cnf(f_444_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1499,tc_HOL_Obool)),U_1500),U_1501) = U_1500
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1499,tc_HOL_Obool)),U_1500),U_1501) != c_Orderings_Obot__class_Obot(tc_fun(U_1499,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_444_2]) ).
fof(f_445_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_445_2,plain,
! [U_1506,U_1505,U_1504,U_1503,U_1502] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1502,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1502,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1503,U_1502,U_1504),U_1505)),hAPP(c_Set_Oimage(U_1503,U_1502,U_1504),U_1506))),hAPP(c_Set_Oimage(U_1503,U_1502,U_1504),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1503,tc_HOL_Obool)),U_1505),U_1506)))),
inference(variable_rename,[status(thm)],[f_445_1]) ).
cnf(f_445_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1502,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1502,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1503,U_1502,U_1504),U_1505)),hAPP(c_Set_Oimage(U_1503,U_1502,U_1504),U_1506))),hAPP(c_Set_Oimage(U_1503,U_1502,U_1504),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1503,tc_HOL_Obool)),U_1505),U_1506)))),
inference(clausify,[status(thm)],[f_445_2]) ).
fof(f_446_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_446_2,plain,
! [U_1509,U_1508,U_1507] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1507,tc_HOL_Obool)),U_1508),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1507,tc_HOL_Obool)),U_1509),U_1508)) = U_1509
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1507,tc_HOL_Obool)),U_1508),U_1509)) ),
inference(variable_rename,[status(thm)],[f_446_1]) ).
cnf(f_446_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1507,tc_HOL_Obool)),U_1508),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1507,tc_HOL_Obool)),U_1509),U_1508)) = U_1509
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1507,tc_HOL_Obool)),U_1508),U_1509)) ),
inference(clausify,[status(thm)],[f_446_2]) ).
fof(f_447_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_447_2,plain,
! [U_1513,U_1512,U_1511,U_1510] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1510,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1510,tc_HOL_Obool)),U_1511),U_1512)),U_1513))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1510,tc_HOL_Obool)),U_1511),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1510,tc_HOL_Obool)),U_1512),U_1513))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1510,tc_HOL_Obool)),U_1511),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1510,tc_HOL_Obool)),U_1512),U_1513)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1510,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1510,tc_HOL_Obool)),U_1511),U_1512)),U_1513)) ) ),
inference(variable_rename,[status(thm)],[f_447_1]) ).
fof(f_447_3,plain,
( ! [U_1521,U_1519,U_1517,U_1515] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1515,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1515,tc_HOL_Obool)),U_1517),U_1519)),U_1521))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1515,tc_HOL_Obool)),U_1517),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1515,tc_HOL_Obool)),U_1519),U_1521))) )
& ! [U_1520,U_1518,U_1516,U_1514] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1514,tc_HOL_Obool)),U_1516),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1514,tc_HOL_Obool)),U_1518),U_1520)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1514,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1514,tc_HOL_Obool)),U_1516),U_1518)),U_1520)) ) ),
inference(miniscope,[status(thm)],[f_447_2]) ).
cnf(f_447_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1514,tc_HOL_Obool)),U_1516),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1514,tc_HOL_Obool)),U_1518),U_1520)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1514,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1514,tc_HOL_Obool)),U_1516),U_1518)),U_1520)) ),
inference(clausify,[status(thm)],[f_447_3]) ).
cnf(f_447_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1515,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1515,tc_HOL_Obool)),U_1517),U_1519)),U_1521))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1515,tc_HOL_Obool)),U_1517),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1515,tc_HOL_Obool)),U_1519),U_1521))) ),
inference(clausify,[status(thm)],[f_447_3]) ).
fof(f_448_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_448_2,plain,
! [U_1525,U_1524,U_1523,U_1522] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1522,tc_HOL_Obool)),U_1523),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1522,tc_HOL_Obool)),U_1524),U_1525)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1522,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1522,tc_HOL_Obool)),U_1523),U_1524)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1522,tc_HOL_Obool)),U_1523),U_1525)),
inference(variable_rename,[status(thm)],[f_448_1]) ).
cnf(f_448_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1522,tc_HOL_Obool)),U_1523),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1522,tc_HOL_Obool)),U_1524),U_1525)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1522,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1522,tc_HOL_Obool)),U_1523),U_1524)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1522,tc_HOL_Obool)),U_1523),U_1525)),
inference(clausify,[status(thm)],[f_448_2]) ).
fof(f_449_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_449_2,plain,
! [U_1529,U_1528,U_1527,U_1526] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1526,tc_HOL_Obool)),U_1527),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1526,tc_HOL_Obool)),U_1528),U_1529)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1526,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1526,tc_HOL_Obool)),U_1527),U_1528)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1526,tc_HOL_Obool)),U_1527),U_1529)),
inference(variable_rename,[status(thm)],[f_449_1]) ).
cnf(f_449_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1526,tc_HOL_Obool)),U_1527),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1526,tc_HOL_Obool)),U_1528),U_1529)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1526,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1526,tc_HOL_Obool)),U_1527),U_1528)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1526,tc_HOL_Obool)),U_1527),U_1529)),
inference(clausify,[status(thm)],[f_449_2]) ).
fof(f_450_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_450_2,plain,
! [U_1532,U_1531,U_1530] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1530,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1530,tc_HOL_Obool)),U_1531),U_1532)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1530,tc_HOL_Obool)),U_1531),U_1532)) = U_1531,
inference(variable_rename,[status(thm)],[f_450_1]) ).
cnf(f_450_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1530,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1530,tc_HOL_Obool)),U_1531),U_1532)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1530,tc_HOL_Obool)),U_1531),U_1532)) = U_1531,
inference(clausify,[status(thm)],[f_450_2]) ).
fof(f_451_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_451_2,plain,
! [U_1536,U_1535,U_1534,U_1533] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1533,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1533,U_1534),U_1536)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1533,U_1534),U_1535)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1533,U_1535),U_1536)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1533),U_1534),U_1535))
| ~ class_Orderings_Olinorder(U_1533) ),
inference(variable_rename,[status(thm)],[f_451_1]) ).
cnf(f_451_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1533,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1533,U_1534),U_1536)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1533,U_1534),U_1535)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1533,U_1535),U_1536)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1533),U_1534),U_1535))
| ~ class_Orderings_Olinorder(U_1533) ),
inference(clausify,[status(thm)],[f_451_2]) ).
fof(f_452_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_452_2,plain,
! [U_1538,U_1537] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1537,tc_HOL_Obool)),U_1538) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1537,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_1537,tc_HOL_Obool))),U_1538),
inference(variable_rename,[status(thm)],[f_452_1]) ).
cnf(f_452_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1537,tc_HOL_Obool)),U_1538) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1537,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_1537,tc_HOL_Obool))),U_1538),
inference(clausify,[status(thm)],[f_452_2]) ).
fof(f_453_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_453_2,plain,
! [U_1541,U_1540,U_1539] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1539,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1539,tc_HOL_Obool)),U_1540),U_1541)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1539,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1539,tc_HOL_Obool)),U_1540)),U_1541),
inference(variable_rename,[status(thm)],[f_453_1]) ).
cnf(f_453_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1539,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1539,tc_HOL_Obool)),U_1540),U_1541)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1539,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1539,tc_HOL_Obool)),U_1540)),U_1541),
inference(clausify,[status(thm)],[f_453_2]) ).
fof(f_454_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_454_2,plain,
! [U_1544,U_1543,U_1542] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1542,tc_HOL_Obool)),U_1543),U_1544) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1542,tc_HOL_Obool)),U_1543),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1542,tc_HOL_Obool)),U_1544)),
inference(variable_rename,[status(thm)],[f_454_1]) ).
cnf(f_454_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1542,tc_HOL_Obool)),U_1543),U_1544) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1542,tc_HOL_Obool)),U_1543),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1542,tc_HOL_Obool)),U_1544)),
inference(clausify,[status(thm)],[f_454_2]) ).
fof(f_455_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_455_2,plain,
! [U_1547,U_1546,U_1545] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1545,tc_HOL_Obool)),U_1546),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1545,tc_HOL_Obool)),U_1547)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1545,tc_HOL_Obool)),U_1546),U_1547),
inference(variable_rename,[status(thm)],[f_455_1]) ).
cnf(f_455_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1545,tc_HOL_Obool)),U_1546),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1545,tc_HOL_Obool)),U_1547)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1545,tc_HOL_Obool)),U_1546),U_1547),
inference(clausify,[status(thm)],[f_455_2]) ).
fof(f_456_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_456_2,plain,
! [U_1550,U_1549,U_1548] :
( c_SetInterval_Oord__class_OgreaterThanLessThan(U_1548,U_1550,U_1549) = c_Orderings_Obot__class_Obot(tc_fun(U_1548,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1548),U_1549),U_1550))
| ~ class_Orderings_Oorder(U_1548) ),
inference(variable_rename,[status(thm)],[f_456_1]) ).
cnf(f_456_3,plain,
( c_SetInterval_Oord__class_OgreaterThanLessThan(U_1548,U_1550,U_1549) = c_Orderings_Obot__class_Obot(tc_fun(U_1548,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1548),U_1549),U_1550))
| ~ class_Orderings_Oorder(U_1548) ),
inference(clausify,[status(thm)],[f_456_2]) ).
fof(f_457_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_457_2,plain,
! [U_1552,U_1551] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_1551)),U_1552) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_1551,U_1552),
inference(variable_rename,[status(thm)],[f_457_1]) ).
cnf(f_457_3,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_1551)),U_1552) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_1551,U_1552),
inference(clausify,[status(thm)],[f_457_2]) ).
fof(f_458_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_458_2,plain,
! [U_1555,U_1554,U_1553] :
( hAPP(c_Set_Oimage(U_1553,U_1553,c_Groups_Ouminus__class_Ouminus(U_1553)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1553,U_1554,U_1555)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_1553,hAPP(c_Groups_Ouminus__class_Ouminus(U_1553),U_1555),hAPP(c_Groups_Ouminus__class_Ouminus(U_1553),U_1554))
| ~ class_Groups_Oordered__ab__group__add(U_1553) ),
inference(variable_rename,[status(thm)],[f_458_1]) ).
cnf(f_458_3,plain,
( hAPP(c_Set_Oimage(U_1553,U_1553,c_Groups_Ouminus__class_Ouminus(U_1553)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1553,U_1554,U_1555)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_1553,hAPP(c_Groups_Ouminus__class_Ouminus(U_1553),U_1555),hAPP(c_Groups_Ouminus__class_Ouminus(U_1553),U_1554))
| ~ class_Groups_Oordered__ab__group__add(U_1553) ),
inference(clausify,[status(thm)],[f_458_2]) ).
fof(f_459_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_459_2,plain,
! [U_1557,U_1556] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1556,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1556),U_1557),c_Orderings_Obot__class_Obot(tc_fun(U_1556,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_1556),U_1557)) = hAPP(hAPP(c_Set_Oinsert(U_1556),U_1557),c_Orderings_Obot__class_Obot(tc_fun(U_1556,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_1556) ),
inference(variable_rename,[status(thm)],[f_459_1]) ).
cnf(f_459_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1556,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1556),U_1557),c_Orderings_Obot__class_Obot(tc_fun(U_1556,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_1556),U_1557)) = hAPP(hAPP(c_Set_Oinsert(U_1556),U_1557),c_Orderings_Obot__class_Obot(tc_fun(U_1556,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_1556) ),
inference(clausify,[status(thm)],[f_459_2]) ).
fof(f_460_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_460_2,plain,
! [U_1561,U_1560,U_1559,U_1558] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1558,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1558,U_1559,U_1560)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1558,U_1560,U_1561)) = c_Orderings_Obot__class_Obot(tc_fun(U_1558,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1558) ),
inference(variable_rename,[status(thm)],[f_460_1]) ).
cnf(f_460_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1558,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1558,U_1559,U_1560)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1558,U_1560,U_1561)) = c_Orderings_Obot__class_Obot(tc_fun(U_1558,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_1558) ),
inference(clausify,[status(thm)],[f_460_2]) ).
fof(f_461_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_461_2,plain,
! [U_1565,U_1564,U_1563,U_1562] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1562,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1562,U_1563,U_1564)),c_SetInterval_Oord__class_OatLeastAtMost(U_1562,U_1564,U_1565)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1562,U_1563,U_1565)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1562),U_1564),U_1565))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1562),U_1563),U_1564))
| ~ class_Orderings_Olinorder(U_1562) ),
inference(variable_rename,[status(thm)],[f_461_1]) ).
cnf(f_461_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1562,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1562,U_1563,U_1564)),c_SetInterval_Oord__class_OatLeastAtMost(U_1562,U_1564,U_1565)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1562,U_1563,U_1565)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1562),U_1564),U_1565))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1562),U_1563),U_1564))
| ~ class_Orderings_Olinorder(U_1562) ),
inference(clausify,[status(thm)],[f_461_2]) ).
fof(f_462_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_462_2,plain,
! [U_1568,U_1567,U_1566] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1566,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1566,U_1567,U_1568)),hAPP(hAPP(c_Set_Oinsert(U_1566),U_1568),c_Orderings_Obot__class_Obot(tc_fun(U_1566,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1566,U_1567,U_1568)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1566),U_1567),U_1568))
| ~ class_Orderings_Olinorder(U_1566) ),
inference(variable_rename,[status(thm)],[f_462_1]) ).
cnf(f_462_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1566,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1566,U_1567,U_1568)),hAPP(hAPP(c_Set_Oinsert(U_1566),U_1568),c_Orderings_Obot__class_Obot(tc_fun(U_1566,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1566,U_1567,U_1568)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1566),U_1567),U_1568))
| ~ class_Orderings_Olinorder(U_1566) ),
inference(clausify,[status(thm)],[f_462_2]) ).
fof(f_463_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_463_2,plain,
! [U_1572,U_1571,U_1570,U_1569] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1569,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1569,U_1570,U_1571)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1569,U_1571,U_1572)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1569,U_1570),U_1572)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1569),U_1571),U_1572))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1569),U_1570),U_1571))
| ~ class_Orderings_Olinorder(U_1569) ),
inference(variable_rename,[status(thm)],[f_463_1]) ).
cnf(f_463_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1569,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1569,U_1570,U_1571)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1569,U_1571,U_1572)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1569,U_1570),U_1572)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1569),U_1571),U_1572))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1569),U_1570),U_1571))
| ~ class_Orderings_Olinorder(U_1569) ),
inference(clausify,[status(thm)],[f_463_2]) ).
fof(f_464_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_464_2,plain,
! [U_1575,U_1574,U_1573] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1573,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1573),U_1574),c_Orderings_Obot__class_Obot(tc_fun(U_1573,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1573,U_1574,U_1575)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1573,U_1574),U_1575)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1573),U_1574),U_1575))
| ~ class_Orderings_Olinorder(U_1573) ),
inference(variable_rename,[status(thm)],[f_464_1]) ).
cnf(f_464_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1573,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1573),U_1574),c_Orderings_Obot__class_Obot(tc_fun(U_1573,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1573,U_1574,U_1575)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1573,U_1574),U_1575)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1573),U_1574),U_1575))
| ~ class_Orderings_Olinorder(U_1573) ),
inference(clausify,[status(thm)],[f_464_2]) ).
fof(f_465_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_465_2,plain,
! [U_1578,U_1577,U_1576] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1576,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1576,U_1577,U_1578)),hAPP(c_SetInterval_Oord__class_OatLeast(U_1576),U_1578)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1576),U_1577)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1576),U_1577),U_1578))
| ~ class_Orderings_Olinorder(U_1576) ),
inference(variable_rename,[status(thm)],[f_465_1]) ).
cnf(f_465_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1576,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1576,U_1577,U_1578)),hAPP(c_SetInterval_Oord__class_OatLeast(U_1576),U_1578)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1576),U_1577)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1576),U_1577),U_1578))
| ~ class_Orderings_Olinorder(U_1576) ),
inference(clausify,[status(thm)],[f_465_2]) ).
fof(f_466_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_466_2,plain,
! [U_1581,U_1580,U_1579] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1579,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_1579),U_1580)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1579,U_1580,U_1581)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_1579),U_1581)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1579),U_1580),U_1581))
| ~ class_Orderings_Olinorder(U_1579) ),
inference(variable_rename,[status(thm)],[f_466_1]) ).
cnf(f_466_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1579,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_1579),U_1580)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1579,U_1580,U_1581)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_1579),U_1581)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1579),U_1580),U_1581))
| ~ class_Orderings_Olinorder(U_1579) ),
inference(clausify,[status(thm)],[f_466_2]) ).
fof(f_467_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_467_2,plain,
! [U_1586,U_1585,U_1584,U_1583,U_1582] :
( ( c_Fun_Oinj__on(U_1582,U_1583,U_1584,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1582,tc_HOL_Obool)),U_1585),U_1586))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1583,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1582,U_1583,U_1584),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1582,tc_HOL_Obool)),U_1585),U_1586))),hAPP(c_Set_Oimage(U_1582,U_1583,U_1584),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1582,tc_HOL_Obool)),U_1586),U_1585))) != c_Orderings_Obot__class_Obot(tc_fun(U_1583,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(U_1582,U_1583,U_1584,U_1586)
| ~ c_Fun_Oinj__on(U_1582,U_1583,U_1584,U_1585) )
& ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1583,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1582,U_1583,U_1584),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1582,tc_HOL_Obool)),U_1585),U_1586))),hAPP(c_Set_Oimage(U_1582,U_1583,U_1584),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1582,tc_HOL_Obool)),U_1586),U_1585))) = c_Orderings_Obot__class_Obot(tc_fun(U_1583,tc_HOL_Obool))
& c_Fun_Oinj__on(U_1582,U_1583,U_1584,U_1586)
& c_Fun_Oinj__on(U_1582,U_1583,U_1584,U_1585) )
| ~ c_Fun_Oinj__on(U_1582,U_1583,U_1584,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1582,tc_HOL_Obool)),U_1585),U_1586)) ) ),
inference(variable_rename,[status(thm)],[f_467_1]) ).
fof(f_467_3,plain,
( ! [U_1596,U_1594,U_1592,U_1590,U_1588] :
( c_Fun_Oinj__on(U_1588,U_1590,U_1592,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1588,tc_HOL_Obool)),U_1594),U_1596))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1590,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1588,U_1590,U_1592),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1588,tc_HOL_Obool)),U_1594),U_1596))),hAPP(c_Set_Oimage(U_1588,U_1590,U_1592),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1588,tc_HOL_Obool)),U_1596),U_1594))) != c_Orderings_Obot__class_Obot(tc_fun(U_1590,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(U_1588,U_1590,U_1592,U_1596)
| ~ c_Fun_Oinj__on(U_1588,U_1590,U_1592,U_1594) )
& ! [U_1595,U_1593,U_1591,U_1589,U_1587] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1589,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1587,U_1589,U_1591),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1587,tc_HOL_Obool)),U_1593),U_1595))),hAPP(c_Set_Oimage(U_1587,U_1589,U_1591),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1587,tc_HOL_Obool)),U_1595),U_1593))) = c_Orderings_Obot__class_Obot(tc_fun(U_1589,tc_HOL_Obool))
& c_Fun_Oinj__on(U_1587,U_1589,U_1591,U_1595)
& c_Fun_Oinj__on(U_1587,U_1589,U_1591,U_1593) )
| ~ c_Fun_Oinj__on(U_1587,U_1589,U_1591,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1587,tc_HOL_Obool)),U_1593),U_1595)) ) ),
inference(miniscope,[status(thm)],[f_467_2]) ).
cnf(f_467_4,plain,
( c_Fun_Oinj__on(U_1587,U_1589,U_1591,U_1593)
| ~ c_Fun_Oinj__on(U_1587,U_1589,U_1591,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1587,tc_HOL_Obool)),U_1593),U_1595)) ),
inference(clausify,[status(thm)],[f_467_3]) ).
cnf(f_467_5,plain,
( c_Fun_Oinj__on(U_1587,U_1589,U_1591,U_1595)
| ~ c_Fun_Oinj__on(U_1587,U_1589,U_1591,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1587,tc_HOL_Obool)),U_1593),U_1595)) ),
inference(clausify,[status(thm)],[f_467_3]) ).
cnf(f_467_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1589,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1587,U_1589,U_1591),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1587,tc_HOL_Obool)),U_1593),U_1595))),hAPP(c_Set_Oimage(U_1587,U_1589,U_1591),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1587,tc_HOL_Obool)),U_1595),U_1593))) = c_Orderings_Obot__class_Obot(tc_fun(U_1589,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(U_1587,U_1589,U_1591,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1587,tc_HOL_Obool)),U_1593),U_1595)) ),
inference(clausify,[status(thm)],[f_467_3]) ).
cnf(f_467_7,plain,
( c_Fun_Oinj__on(U_1588,U_1590,U_1592,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1588,tc_HOL_Obool)),U_1594),U_1596))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1590,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1588,U_1590,U_1592),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1588,tc_HOL_Obool)),U_1594),U_1596))),hAPP(c_Set_Oimage(U_1588,U_1590,U_1592),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1588,tc_HOL_Obool)),U_1596),U_1594))) != c_Orderings_Obot__class_Obot(tc_fun(U_1590,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(U_1588,U_1590,U_1592,U_1596)
| ~ c_Fun_Oinj__on(U_1588,U_1590,U_1592,U_1594) ),
inference(clausify,[status(thm)],[f_467_3]) ).
fof(f_468_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_468_2,plain,
! [U_1600,U_1599,U_1598,U_1597] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1597,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1597,U_1598,U_1599)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1597,U_1599,U_1600)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_1597,U_1598,U_1600)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1597),U_1599),U_1600))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1597),U_1598),U_1599))
| ~ class_Orderings_Olinorder(U_1597) ),
inference(variable_rename,[status(thm)],[f_468_1]) ).
cnf(f_468_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1597,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1597,U_1598,U_1599)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1597,U_1599,U_1600)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_1597,U_1598,U_1600)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1597),U_1599),U_1600))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1597),U_1598),U_1599))
| ~ class_Orderings_Olinorder(U_1597) ),
inference(clausify,[status(thm)],[f_468_2]) ).
fof(f_469_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_469_2,plain,
! [U_1604,U_1603,U_1602,U_1601] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1601,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1601,U_1602,U_1603)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1601,U_1603),U_1604)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_1601,U_1602,U_1604)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1601),U_1603),U_1604))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1601),U_1602),U_1603))
| ~ class_Orderings_Olinorder(U_1601) ),
inference(variable_rename,[status(thm)],[f_469_1]) ).
cnf(f_469_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1601,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1601,U_1602,U_1603)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1601,U_1603),U_1604)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_1601,U_1602,U_1604)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1601),U_1603),U_1604))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1601),U_1602),U_1603))
| ~ class_Orderings_Olinorder(U_1601) ),
inference(clausify,[status(thm)],[f_469_2]) ).
fof(f_470_1,plain,
! [V_j_2,V_i_2,V_P_2] :
( ( c_List_Oall__interval__nat(V_P_2,V_i_2,V_j_2)
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2))) ) )
& ( ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2))) )
| ~ c_List_Oall__interval__nat(V_P_2,V_i_2,V_j_2) ) ),
inference(fof_nnf,[status(thm)],[fact_all__interval__nat__def]) ).
fof(f_470_2,plain,
! [U_1609,U_1608,U_1607] :
( ( c_List_Oall__interval__nat(U_1607,U_1608,U_1609)
| ? [U_1606] :
( ~ hBOOL(hAPP(U_1607,U_1606))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_1606),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_1608),U_1609))) ) )
& ( ! [U_1605] :
( hBOOL(hAPP(U_1607,U_1605))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_1605),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_1608),U_1609))) )
| ~ c_List_Oall__interval__nat(U_1607,U_1608,U_1609) ) ),
inference(variable_rename,[status(thm)],[f_470_1]) ).
fof(f_470_3,plain,
( ! [U_1615,U_1613,U_1611] :
( c_List_Oall__interval__nat(U_1611,U_1613,U_1615)
| ? [U_1606] :
( ~ hBOOL(hAPP(U_1611,U_1606))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_1606),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_1613),U_1615))) ) )
& ! [U_1614,U_1612,U_1610] :
( ! [U_1605] :
( hBOOL(hAPP(U_1610,U_1605))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_1605),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_1612),U_1614))) )
| ~ c_List_Oall__interval__nat(U_1610,U_1612,U_1614) ) ),
inference(miniscope,[status(thm)],[f_470_2]) ).
fof(f_470_4,plain,
( ! [U_1615,U_1613,U_1611] :
( c_List_Oall__interval__nat(U_1611,U_1613,U_1615)
| ( ~ hBOOL(hAPP(U_1611,sK27(U_1615,U_1613,U_1611)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK27(U_1615,U_1613,U_1611)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_1613),U_1615))) ) )
& ! [U_1614,U_1612,U_1610] :
( ! [U_1605] :
( hBOOL(hAPP(U_1610,U_1605))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_1605),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_1612),U_1614))) )
| ~ c_List_Oall__interval__nat(U_1610,U_1612,U_1614) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_1606,sK27(U_1615,U_1613,U_1611))],[f_470_3]) ).
cnf(f_470_5,plain,
( hBOOL(hAPP(U_1610,U_1605))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_1605),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_1612),U_1614)))
| ~ c_List_Oall__interval__nat(U_1610,U_1612,U_1614) ),
inference(clausify,[status(thm)],[f_470_4]) ).
cnf(f_470_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK27(U_1615,U_1613,U_1611)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_1613),U_1615)))
| c_List_Oall__interval__nat(U_1611,U_1613,U_1615) ),
inference(clausify,[status(thm)],[f_470_4]) ).
cnf(f_470_7,plain,
( ~ hBOOL(hAPP(U_1611,sK27(U_1615,U_1613,U_1611)))
| c_List_Oall__interval__nat(U_1611,U_1613,U_1615) ),
inference(clausify,[status(thm)],[f_470_4]) ).
fof(f_471_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_471_2,plain,
! [U_1616] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1616),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_471_1]) ).
cnf(f_471_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1616),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_471_2]) ).
fof(f_472_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_472_2,plain,
! [U_1617] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1617),hAPP(c_Nat_OSuc,U_1617))),
inference(variable_rename,[status(thm)],[f_472_1]) ).
cnf(f_472_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1617),hAPP(c_Nat_OSuc,U_1617))),
inference(clausify,[status(thm)],[f_472_2]) ).
fof(f_473_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_473_2,plain,
! [U_1619,U_1618] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1618)),hAPP(c_Nat_OSuc,U_1619)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1618),U_1619)) ),
inference(variable_rename,[status(thm)],[f_473_1]) ).
cnf(f_473_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1618)),hAPP(c_Nat_OSuc,U_1619)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1618),U_1619)) ),
inference(clausify,[status(thm)],[f_473_2]) ).
fof(f_474_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_474_2,plain,
! [U_1620] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_1620))),
inference(variable_rename,[status(thm)],[f_474_1]) ).
cnf(f_474_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_1620))),
inference(clausify,[status(thm)],[f_474_2]) ).
fof(f_475_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_475_2,plain,
! [U_1623,U_1622,U_1621] : c_Fun_Oinj__on(U_1621,U_1622,U_1623,c_Orderings_Obot__class_Obot(tc_fun(U_1621,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_475_1]) ).
cnf(f_475_3,plain,
c_Fun_Oinj__on(U_1621,U_1622,U_1623,c_Orderings_Obot__class_Obot(tc_fun(U_1621,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_475_2]) ).
fof(f_476_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_476_2,plain,
! [U_1625,U_1624] :
( c_Fun_Oinj__on(U_1624,U_1624,c_Groups_Ouminus__class_Ouminus(U_1624),U_1625)
| ~ class_Groups_Oordered__ab__group__add(U_1624) ),
inference(variable_rename,[status(thm)],[f_476_1]) ).
cnf(f_476_3,plain,
( c_Fun_Oinj__on(U_1624,U_1624,c_Groups_Ouminus__class_Ouminus(U_1624),U_1625)
| ~ class_Groups_Oordered__ab__group__add(U_1624) ),
inference(clausify,[status(thm)],[f_476_2]) ).
fof(f_477_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_477_2,plain,
! [U_1627,U_1626] :
( ( 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_1626),U_1627)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1627),U_1626)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1627),U_1626))
| ~ 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_1626),U_1627))) ) ),
inference(variable_rename,[status(thm)],[f_477_1]) ).
fof(f_477_3,plain,
( ! [U_1631,U_1629] :
( 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_1629),U_1631)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1631),U_1629)) )
& ! [U_1630,U_1628] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1630),U_1628))
| ~ 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_1628),U_1630))) ) ),
inference(miniscope,[status(thm)],[f_477_2]) ).
cnf(f_477_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1630),U_1628))
| ~ 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_1628),U_1630))) ),
inference(clausify,[status(thm)],[f_477_3]) ).
cnf(f_477_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_1629),U_1631)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1631),U_1629)) ),
inference(clausify,[status(thm)],[f_477_3]) ).
fof(f_478_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_478_2,plain,
! [U_1633,U_1632] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1633),U_1632)),U_1633))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1633))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1632)) ),
inference(variable_rename,[status(thm)],[f_478_1]) ).
cnf(f_478_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1633),U_1632)),U_1633))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1633))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1632)) ),
inference(clausify,[status(thm)],[f_478_2]) ).
fof(f_479_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_479_2,plain,
! [U_1635,U_1634] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1634),U_1635)),hAPP(c_Nat_OSuc,U_1634))),
inference(variable_rename,[status(thm)],[f_479_1]) ).
cnf(f_479_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1634),U_1635)),hAPP(c_Nat_OSuc,U_1634))),
inference(clausify,[status(thm)],[f_479_2]) ).
fof(f_480_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_480_2,plain,
! [U_1638,U_1637,U_1636] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1637),U_1636)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1638),U_1636)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1637),U_1638)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1637),U_1638))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1637),U_1636)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1638),U_1636))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1636),U_1638))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1636),U_1637)) ),
inference(variable_rename,[status(thm)],[f_480_1]) ).
cnf(f_480_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1637),U_1638))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1637),U_1636)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1638),U_1636)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1636),U_1638))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1636),U_1637)) ),
inference(clausify,[status(thm)],[f_480_2]) ).
cnf(f_480_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1637),U_1636)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1638),U_1636)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1637),U_1638))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1636),U_1638))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1636),U_1637)) ),
inference(clausify,[status(thm)],[f_480_2]) ).
fof(f_481_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_481_2,plain,
! [U_1641,U_1640,U_1639] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1639),U_1641)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1640),U_1641)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1641),U_1639))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1639),U_1640)) ),
inference(variable_rename,[status(thm)],[f_481_1]) ).
cnf(f_481_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1639),U_1641)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1640),U_1641)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1641),U_1639))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1639),U_1640)) ),
inference(clausify,[status(thm)],[f_481_2]) ).
fof(f_482_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_482_2,plain,
! [U_1644,U_1643,U_1642] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1642),U_1644),U_1643))
| U_1643 = U_1644
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1642),U_1643),U_1644))
| ~ class_Orderings_Olinorder(U_1642) ),
inference(variable_rename,[status(thm)],[f_482_1]) ).
cnf(f_482_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1642),U_1644),U_1643))
| U_1643 = U_1644
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1642),U_1643),U_1644))
| ~ class_Orderings_Olinorder(U_1642) ),
inference(clausify,[status(thm)],[f_482_2]) ).
fof(f_483_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_483_2,plain,
! [U_1647,U_1646,U_1645] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1645),U_1647),U_1646))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1645),U_1646),U_1647))
| ~ class_Orderings_Opreorder(U_1645) ),
inference(variable_rename,[status(thm)],[f_483_1]) ).
cnf(f_483_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1645),U_1647),U_1646))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1645),U_1646),U_1647))
| ~ class_Orderings_Opreorder(U_1645) ),
inference(clausify,[status(thm)],[f_483_2]) ).
fof(f_484_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_484_2,plain,
! [U_1651,U_1650,U_1649,U_1648] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1648),U_1651),U_1650))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1648),U_1651),U_1649))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1648),U_1649),U_1650))
| ~ class_Orderings_Oorder(U_1648) ),
inference(variable_rename,[status(thm)],[f_484_1]) ).
cnf(f_484_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1648),U_1651),U_1650))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1648),U_1651),U_1649))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1648),U_1649),U_1650))
| ~ class_Orderings_Oorder(U_1648) ),
inference(clausify,[status(thm)],[f_484_2]) ).
fof(f_485_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_485_2,plain,
! [U_1655,U_1654,U_1653,U_1652] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1652),U_1653),U_1655))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1652),U_1654),U_1655))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1652),U_1653),U_1654))
| ~ class_Orderings_Opreorder(U_1652) ),
inference(variable_rename,[status(thm)],[f_485_1]) ).
cnf(f_485_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1652),U_1653),U_1655))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1652),U_1654),U_1655))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1652),U_1653),U_1654))
| ~ class_Orderings_Opreorder(U_1652) ),
inference(clausify,[status(thm)],[f_485_2]) ).
fof(f_486_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_486_2,plain,
! [U_1659,U_1658,U_1657,U_1656] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1656),U_1659),U_1658))
| U_1657 != U_1659
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1656),U_1657),U_1658))
| ~ class_Orderings_Oorder(U_1656) ),
inference(variable_rename,[status(thm)],[f_486_1]) ).
cnf(f_486_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1656),U_1659),U_1658))
| U_1657 != U_1659
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1656),U_1657),U_1658))
| ~ class_Orderings_Oorder(U_1656) ),
inference(clausify,[status(thm)],[f_486_2]) ).
fof(f_487_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_487_2,plain,
! [U_1663,U_1662,U_1661,U_1660] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1660),U_1661),U_1663))
| U_1662 != U_1663
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1660),U_1661),U_1662))
| ~ class_Orderings_Oord(U_1660) ),
inference(variable_rename,[status(thm)],[f_487_1]) ).
cnf(f_487_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1660),U_1661),U_1663))
| U_1662 != U_1663
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1660),U_1661),U_1662))
| ~ class_Orderings_Oord(U_1660) ),
inference(clausify,[status(thm)],[f_487_2]) ).
fof(f_488_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_488_2,plain,
! [U_1667,U_1666,U_1665,U_1664] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1664),U_1667),U_1665))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1664),U_1667),U_1666))
| U_1665 != U_1666
| ~ class_Orderings_Oorder(U_1664) ),
inference(variable_rename,[status(thm)],[f_488_1]) ).
cnf(f_488_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1664),U_1667),U_1665))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1664),U_1667),U_1666))
| U_1665 != U_1666
| ~ class_Orderings_Oorder(U_1664) ),
inference(clausify,[status(thm)],[f_488_2]) ).
fof(f_489_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_489_2,plain,
! [U_1671,U_1670,U_1669,U_1668] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1668),U_1669),U_1671))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1668),U_1670),U_1671))
| U_1669 != U_1670
| ~ class_Orderings_Oord(U_1668) ),
inference(variable_rename,[status(thm)],[f_489_1]) ).
cnf(f_489_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1668),U_1669),U_1671))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1668),U_1670),U_1671))
| U_1669 != U_1670
| ~ class_Orderings_Oord(U_1668) ),
inference(clausify,[status(thm)],[f_489_2]) ).
fof(f_490_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_490_2,plain,
! [U_1674,U_1673,U_1672] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1672),U_1674),U_1673))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1672),U_1673),U_1674))
| ~ class_Orderings_Oorder(U_1672) ),
inference(variable_rename,[status(thm)],[f_490_1]) ).
cnf(f_490_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1672),U_1674),U_1673))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1672),U_1673),U_1674))
| ~ class_Orderings_Oorder(U_1672) ),
inference(clausify,[status(thm)],[f_490_2]) ).
fof(f_491_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_491_2,plain,
! [U_1677,U_1676,U_1675] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1675),U_1677),U_1676))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1675),U_1676),U_1677))
| ~ class_Orderings_Opreorder(U_1675) ),
inference(variable_rename,[status(thm)],[f_491_1]) ).
cnf(f_491_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1675),U_1677),U_1676))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1675),U_1676),U_1677))
| ~ class_Orderings_Opreorder(U_1675) ),
inference(clausify,[status(thm)],[f_491_2]) ).
fof(f_492_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_492_2,plain,
! [U_1680,U_1679,U_1678] :
( U_1680 != U_1679
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1678),U_1679),U_1680))
| ~ class_Orderings_Oorder(U_1678) ),
inference(variable_rename,[status(thm)],[f_492_1]) ).
cnf(f_492_3,plain,
( U_1680 != U_1679
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1678),U_1679),U_1680))
| ~ class_Orderings_Oorder(U_1678) ),
inference(clausify,[status(thm)],[f_492_2]) ).
fof(f_493_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_493_2,plain,
! [U_1683,U_1682,U_1681] :
( U_1682 != U_1683
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1681),U_1682),U_1683))
| ~ class_Orderings_Oorder(U_1681) ),
inference(variable_rename,[status(thm)],[f_493_1]) ).
cnf(f_493_3,plain,
( U_1682 != U_1683
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1681),U_1682),U_1683))
| ~ class_Orderings_Oorder(U_1681) ),
inference(clausify,[status(thm)],[f_493_2]) ).
fof(f_494_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_494_2,plain,
! [U_1686,U_1685,U_1684] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1684),U_1686),U_1685))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1684),U_1685),U_1686))
| ~ class_Orderings_Opreorder(U_1684) ),
inference(variable_rename,[status(thm)],[f_494_1]) ).
cnf(f_494_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1684),U_1686),U_1685))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1684),U_1685),U_1686))
| ~ class_Orderings_Opreorder(U_1684) ),
inference(clausify,[status(thm)],[f_494_2]) ).
fof(f_495_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_495_2,plain,
! [U_1689,U_1688,U_1687] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1687),U_1689),U_1688))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1687),U_1688),U_1689))
| ~ class_Orderings_Opreorder(U_1687) ),
inference(variable_rename,[status(thm)],[f_495_1]) ).
cnf(f_495_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1687),U_1689),U_1688))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1687),U_1688),U_1689))
| ~ class_Orderings_Opreorder(U_1687) ),
inference(clausify,[status(thm)],[f_495_2]) ).
fof(f_496_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_496_2,plain,
! [U_1692,U_1691,U_1690] :
( U_1691 != U_1692
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1690),U_1691),U_1692))
| ~ class_Orderings_Oorder(U_1690) ),
inference(variable_rename,[status(thm)],[f_496_1]) ).
cnf(f_496_3,plain,
( U_1691 != U_1692
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1690),U_1691),U_1692))
| ~ class_Orderings_Oorder(U_1690) ),
inference(clausify,[status(thm)],[f_496_2]) ).
fof(f_497_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_497_2,plain,
! [U_1695,U_1694,U_1693] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1693),U_1695),U_1694))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1693),U_1694),U_1695))
| U_1694 = U_1695
| ~ class_Orderings_Olinorder(U_1693) ),
inference(variable_rename,[status(thm)],[f_497_1]) ).
cnf(f_497_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1693),U_1695),U_1694))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1693),U_1694),U_1695))
| U_1694 = U_1695
| ~ class_Orderings_Olinorder(U_1693) ),
inference(clausify,[status(thm)],[f_497_2]) ).
fof(f_498_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_498_2,plain,
! [U_1698,U_1697,U_1696] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1696),U_1698),U_1697))
| U_1698 != U_1697 )
& ( U_1698 = U_1697
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1696),U_1698),U_1697)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1696),U_1697),U_1698))
| ~ class_Orderings_Olinorder(U_1696) ),
inference(variable_rename,[status(thm)],[f_498_1]) ).
cnf(f_498_3,plain,
( U_1698 = U_1697
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1696),U_1698),U_1697))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1696),U_1697),U_1698))
| ~ class_Orderings_Olinorder(U_1696) ),
inference(clausify,[status(thm)],[f_498_2]) ).
cnf(f_498_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1696),U_1698),U_1697))
| U_1698 != U_1697
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1696),U_1697),U_1698))
| ~ class_Orderings_Olinorder(U_1696) ),
inference(clausify,[status(thm)],[f_498_2]) ).
fof(f_499_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_499_2,plain,
! [U_1701,U_1700,U_1699] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1699),U_1701),U_1700))
| U_1700 = U_1701
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1699),U_1700),U_1701))
| ~ class_Orderings_Olinorder(U_1699) ),
inference(variable_rename,[status(thm)],[f_499_1]) ).
cnf(f_499_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1699),U_1701),U_1700))
| U_1700 = U_1701
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1699),U_1700),U_1701))
| ~ class_Orderings_Olinorder(U_1699) ),
inference(clausify,[status(thm)],[f_499_2]) ).
fof(f_500_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_500_2,plain,
! [U_1704,U_1703,U_1702] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1702),U_1703),U_1704))
| ( U_1703 != U_1704
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1702),U_1704),U_1703)) ) )
& ( U_1703 = U_1704
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1702),U_1704),U_1703))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1702),U_1703),U_1704)) ) )
| ~ class_Orderings_Olinorder(U_1702) ),
inference(variable_rename,[status(thm)],[f_500_1]) ).
cnf(f_500_3,plain,
( U_1703 = U_1704
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1702),U_1704),U_1703))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1702),U_1703),U_1704))
| ~ class_Orderings_Olinorder(U_1702) ),
inference(clausify,[status(thm)],[f_500_2]) ).
cnf(f_500_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1702),U_1704),U_1703))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1702),U_1703),U_1704))
| ~ class_Orderings_Olinorder(U_1702) ),
inference(clausify,[status(thm)],[f_500_2]) ).
cnf(f_500_5,plain,
( U_1703 != U_1704
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1702),U_1703),U_1704))
| ~ class_Orderings_Olinorder(U_1702) ),
inference(clausify,[status(thm)],[f_500_2]) ).
fof(f_501_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_501_2,plain,
! [U_1707,U_1706,U_1705] :
( ( ( U_1706 != U_1707
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1705),U_1707),U_1706))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1705),U_1706),U_1707)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1705),U_1707),U_1706))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1705),U_1706),U_1707))
| U_1706 = U_1707 ) )
| ~ class_Orderings_Olinorder(U_1705) ),
inference(variable_rename,[status(thm)],[f_501_1]) ).
cnf(f_501_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1705),U_1707),U_1706))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1705),U_1706),U_1707))
| U_1706 = U_1707
| ~ class_Orderings_Olinorder(U_1705) ),
inference(clausify,[status(thm)],[f_501_2]) ).
cnf(f_501_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1705),U_1706),U_1707))
| U_1706 != U_1707
| ~ class_Orderings_Olinorder(U_1705) ),
inference(clausify,[status(thm)],[f_501_2]) ).
cnf(f_501_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1705),U_1707),U_1706))
| U_1706 != U_1707
| ~ class_Orderings_Olinorder(U_1705) ),
inference(clausify,[status(thm)],[f_501_2]) ).
fof(f_502_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_502_2,plain,
! [U_1709,U_1708] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1708),U_1709),U_1709))
| ~ class_Orderings_Opreorder(U_1708) ),
inference(variable_rename,[status(thm)],[f_502_1]) ).
cnf(f_502_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1708),U_1709),U_1709))
| ~ class_Orderings_Opreorder(U_1708) ),
inference(clausify,[status(thm)],[f_502_2]) ).
fof(f_503_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_503_2,plain,
! [U_1717,U_1716,U_1715,U_1714] :
( ( c_Fun_Oinj__on(U_1714,U_1715,U_1716,U_1717)
| ? [U_1713] :
( ? [U_1712] :
( U_1713 != U_1712
& hAPP(U_1716,U_1713) = hAPP(U_1716,U_1712)
& hBOOL(hAPP(hAPP(c_member(U_1714),U_1712),U_1717)) )
& hBOOL(hAPP(hAPP(c_member(U_1714),U_1713),U_1717)) ) )
& ( ! [U_1711] :
( ! [U_1710] :
( U_1711 = U_1710
| hAPP(U_1716,U_1711) != hAPP(U_1716,U_1710)
| ~ hBOOL(hAPP(hAPP(c_member(U_1714),U_1710),U_1717)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1714),U_1711),U_1717)) )
| ~ c_Fun_Oinj__on(U_1714,U_1715,U_1716,U_1717) ) ),
inference(variable_rename,[status(thm)],[f_503_1]) ).
fof(f_503_3,plain,
( ! [U_1725,U_1723,U_1721,U_1719] :
( c_Fun_Oinj__on(U_1719,U_1721,U_1723,U_1725)
| ? [U_1713] :
( ? [U_1712] :
( U_1713 != U_1712
& hAPP(U_1723,U_1713) = hAPP(U_1723,U_1712)
& hBOOL(hAPP(hAPP(c_member(U_1719),U_1712),U_1725)) )
& hBOOL(hAPP(hAPP(c_member(U_1719),U_1713),U_1725)) ) )
& ! [U_1724,U_1722,U_1720,U_1718] :
( ! [U_1711] :
( ! [U_1710] :
( U_1711 = U_1710
| hAPP(U_1722,U_1711) != hAPP(U_1722,U_1710)
| ~ hBOOL(hAPP(hAPP(c_member(U_1718),U_1710),U_1724)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1718),U_1711),U_1724)) )
| ~ c_Fun_Oinj__on(U_1718,U_1720,U_1722,U_1724) ) ),
inference(miniscope,[status(thm)],[f_503_2]) ).
fof(f_503_4,plain,
( ! [U_1725,U_1723,U_1721,U_1719] :
( c_Fun_Oinj__on(U_1719,U_1721,U_1723,U_1725)
| ( ? [U_1712] :
( sK28(U_1725,U_1723,U_1721,U_1719) != U_1712
& hAPP(U_1723,sK28(U_1725,U_1723,U_1721,U_1719)) = hAPP(U_1723,U_1712)
& hBOOL(hAPP(hAPP(c_member(U_1719),U_1712),U_1725)) )
& hBOOL(hAPP(hAPP(c_member(U_1719),sK28(U_1725,U_1723,U_1721,U_1719)),U_1725)) ) )
& ! [U_1724,U_1722,U_1720,U_1718] :
( ! [U_1711] :
( ! [U_1710] :
( U_1711 = U_1710
| hAPP(U_1722,U_1711) != hAPP(U_1722,U_1710)
| ~ hBOOL(hAPP(hAPP(c_member(U_1718),U_1710),U_1724)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1718),U_1711),U_1724)) )
| ~ c_Fun_Oinj__on(U_1718,U_1720,U_1722,U_1724) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_1713,sK28(U_1725,U_1723,U_1721,U_1719))],[f_503_3]) ).
fof(f_503_5,plain,
( ! [U_1725,U_1723,U_1721,U_1719] :
( c_Fun_Oinj__on(U_1719,U_1721,U_1723,U_1725)
| ( sK28(U_1725,U_1723,U_1721,U_1719) != sK29(U_1725,U_1723,U_1721,U_1719)
& hAPP(U_1723,sK28(U_1725,U_1723,U_1721,U_1719)) = hAPP(U_1723,sK29(U_1725,U_1723,U_1721,U_1719))
& hBOOL(hAPP(hAPP(c_member(U_1719),sK29(U_1725,U_1723,U_1721,U_1719)),U_1725))
& hBOOL(hAPP(hAPP(c_member(U_1719),sK28(U_1725,U_1723,U_1721,U_1719)),U_1725)) ) )
& ! [U_1724,U_1722,U_1720,U_1718] :
( ! [U_1711] :
( ! [U_1710] :
( U_1711 = U_1710
| hAPP(U_1722,U_1711) != hAPP(U_1722,U_1710)
| ~ hBOOL(hAPP(hAPP(c_member(U_1718),U_1710),U_1724)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1718),U_1711),U_1724)) )
| ~ c_Fun_Oinj__on(U_1718,U_1720,U_1722,U_1724) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_1712,sK29(U_1725,U_1723,U_1721,U_1719))],[f_503_4]) ).
cnf(f_503_6,plain,
( U_1711 = U_1710
| hAPP(U_1722,U_1711) != hAPP(U_1722,U_1710)
| ~ hBOOL(hAPP(hAPP(c_member(U_1718),U_1710),U_1724))
| ~ hBOOL(hAPP(hAPP(c_member(U_1718),U_1711),U_1724))
| ~ c_Fun_Oinj__on(U_1718,U_1720,U_1722,U_1724) ),
inference(clausify,[status(thm)],[f_503_5]) ).
cnf(f_503_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_1719),sK28(U_1725,U_1723,U_1721,U_1719)),U_1725))
| c_Fun_Oinj__on(U_1719,U_1721,U_1723,U_1725) ),
inference(clausify,[status(thm)],[f_503_5]) ).
cnf(f_503_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_1719),sK29(U_1725,U_1723,U_1721,U_1719)),U_1725))
| c_Fun_Oinj__on(U_1719,U_1721,U_1723,U_1725) ),
inference(clausify,[status(thm)],[f_503_5]) ).
cnf(f_503_9,plain,
( hAPP(U_1723,sK28(U_1725,U_1723,U_1721,U_1719)) = hAPP(U_1723,sK29(U_1725,U_1723,U_1721,U_1719))
| c_Fun_Oinj__on(U_1719,U_1721,U_1723,U_1725) ),
inference(clausify,[status(thm)],[f_503_5]) ).
cnf(f_503_10,plain,
( sK28(U_1725,U_1723,U_1721,U_1719) != sK29(U_1725,U_1723,U_1721,U_1719)
| c_Fun_Oinj__on(U_1719,U_1721,U_1723,U_1725) ),
inference(clausify,[status(thm)],[f_503_5]) ).
fof(f_504_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_504_2,plain,
! [U_1730,U_1729,U_1728,U_1727,U_1726] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1727,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1726,U_1727,U_1728),U_1730)),hAPP(c_Set_Oimage(U_1726,U_1727,U_1728),U_1729)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1726,tc_HOL_Obool)),U_1730),U_1729))
| ~ c_Fun_Oinj__on(U_1726,U_1727,U_1728,U_1729) ),
inference(variable_rename,[status(thm)],[f_504_1]) ).
cnf(f_504_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1727,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1726,U_1727,U_1728),U_1730)),hAPP(c_Set_Oimage(U_1726,U_1727,U_1728),U_1729)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1726,tc_HOL_Obool)),U_1730),U_1729))
| ~ c_Fun_Oinj__on(U_1726,U_1727,U_1728,U_1729) ),
inference(clausify,[status(thm)],[f_504_2]) ).
fof(f_505_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_505_2,plain,
! [U_1733,U_1732,U_1731] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1731,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1731),U_1732)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1731),U_1733)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1731),U_1732),U_1733)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1731),U_1732),U_1733))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1731,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1731),U_1732)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1731),U_1733))) ) )
| ~ class_Orderings_Olinorder(U_1731) ),
inference(variable_rename,[status(thm)],[f_505_1]) ).
cnf(f_505_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1731),U_1732),U_1733))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1731,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1731),U_1732)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1731),U_1733)))
| ~ class_Orderings_Olinorder(U_1731) ),
inference(clausify,[status(thm)],[f_505_2]) ).
cnf(f_505_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1731,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1731),U_1732)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1731),U_1733)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1731),U_1732),U_1733))
| ~ class_Orderings_Olinorder(U_1731) ),
inference(clausify,[status(thm)],[f_505_2]) ).
fof(f_506_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_506_2,plain,
! [U_1734] :
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1734),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_1734
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1734)) ),
inference(variable_rename,[status(thm)],[f_506_1]) ).
cnf(f_506_3,plain,
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1734),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_1734
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1734)) ),
inference(clausify,[status(thm)],[f_506_2]) ).
fof(f_507_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_507_2,plain,
! [U_1736,U_1735] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1735),hAPP(c_Nat_OSuc,U_1736))),U_1735))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1735)) ),
inference(variable_rename,[status(thm)],[f_507_1]) ).
cnf(f_507_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1735),hAPP(c_Nat_OSuc,U_1736))),U_1735))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1735)) ),
inference(clausify,[status(thm)],[f_507_2]) ).
fof(f_508_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2))
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2))) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastatMost__psubset__iff]) ).
fof(f_508_2,plain,
! [U_1741,U_1740,U_1739,U_1738,U_1737] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1737,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1737,U_1738,U_1739)),c_SetInterval_Oord__class_OatLeastAtMost(U_1737,U_1740,U_1741)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1740),U_1741))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1737),U_1739),U_1741))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1737),U_1740),U_1738)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1739),U_1741))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1740),U_1738)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1738),U_1739)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1740),U_1741))
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1737),U_1739),U_1741))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1737),U_1740),U_1738)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1739),U_1741))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1740),U_1738)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1738),U_1739)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1737,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1737,U_1738,U_1739)),c_SetInterval_Oord__class_OatLeastAtMost(U_1737,U_1740,U_1741))) ) )
| ~ class_Orderings_Oorder(U_1737) ),
inference(variable_rename,[status(thm)],[f_508_1]) ).
cnf(f_508_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1740),U_1738))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1738),U_1739))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1737,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1737,U_1738,U_1739)),c_SetInterval_Oord__class_OatLeastAtMost(U_1737,U_1740,U_1741)))
| ~ class_Orderings_Oorder(U_1737) ),
inference(clausify,[status(thm)],[f_508_2]) ).
cnf(f_508_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1739),U_1741))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1738),U_1739))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1737,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1737,U_1738,U_1739)),c_SetInterval_Oord__class_OatLeastAtMost(U_1737,U_1740,U_1741)))
| ~ class_Orderings_Oorder(U_1737) ),
inference(clausify,[status(thm)],[f_508_2]) ).
cnf(f_508_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1737),U_1739),U_1741))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1737),U_1740),U_1738))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1738),U_1739))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1737,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1737,U_1738,U_1739)),c_SetInterval_Oord__class_OatLeastAtMost(U_1737,U_1740,U_1741)))
| ~ class_Orderings_Oorder(U_1737) ),
inference(clausify,[status(thm)],[f_508_2]) ).
cnf(f_508_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1740),U_1741))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1737,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1737,U_1738,U_1739)),c_SetInterval_Oord__class_OatLeastAtMost(U_1737,U_1740,U_1741)))
| ~ class_Orderings_Oorder(U_1737) ),
inference(clausify,[status(thm)],[f_508_2]) ).
cnf(f_508_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1738),U_1739))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1740),U_1741))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1737,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1737,U_1738,U_1739)),c_SetInterval_Oord__class_OatLeastAtMost(U_1737,U_1740,U_1741)))
| ~ class_Orderings_Oorder(U_1737) ),
inference(clausify,[status(thm)],[f_508_2]) ).
cnf(f_508_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1737),U_1740),U_1738))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1739),U_1741))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1740),U_1738))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1740),U_1741))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1737,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1737,U_1738,U_1739)),c_SetInterval_Oord__class_OatLeastAtMost(U_1737,U_1740,U_1741)))
| ~ class_Orderings_Oorder(U_1737) ),
inference(clausify,[status(thm)],[f_508_2]) ).
cnf(f_508_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1737),U_1739),U_1741))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1739),U_1741))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1740),U_1738))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1740),U_1741))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1737,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1737,U_1738,U_1739)),c_SetInterval_Oord__class_OatLeastAtMost(U_1737,U_1740,U_1741)))
| ~ class_Orderings_Oorder(U_1737) ),
inference(clausify,[status(thm)],[f_508_2]) ).
fof(f_509_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_509_2,plain,
! [U_1742] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,U_1742),
inference(variable_rename,[status(thm)],[f_509_1]) ).
cnf(f_509_3,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,U_1742),
inference(clausify,[status(thm)],[f_509_2]) ).
fof(f_510_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_510_2,plain,
! [U_1747,U_1746,U_1745,U_1744,U_1743] :
( c_Fun_Oinj__on(U_1743,U_1744,U_1745,U_1747)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1743,tc_HOL_Obool)),U_1747),U_1746))
| ~ c_Fun_Oinj__on(U_1743,U_1744,U_1745,U_1746) ),
inference(variable_rename,[status(thm)],[f_510_1]) ).
cnf(f_510_3,plain,
( c_Fun_Oinj__on(U_1743,U_1744,U_1745,U_1747)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1743,tc_HOL_Obool)),U_1747),U_1746))
| ~ c_Fun_Oinj__on(U_1743,U_1744,U_1745,U_1746) ),
inference(clausify,[status(thm)],[f_510_2]) ).
fof(f_511_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_511_2,plain,
! [U_1752,U_1751,U_1750,U_1749,U_1748] :
( U_1751 = U_1752
| hAPP(U_1750,U_1751) != hAPP(U_1750,U_1752)
| ~ c_Fun_Oinj__on(U_1748,U_1749,U_1750,c_Orderings_Otop__class_Otop(tc_fun(U_1748,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_511_1]) ).
fof(f_511_3,plain,
! [U_1752,U_1751,U_1750] :
( ! [U_1749,U_1748] : ~ c_Fun_Oinj__on(U_1748,U_1749,U_1750,c_Orderings_Otop__class_Otop(tc_fun(U_1748,tc_HOL_Obool)))
| U_1751 = U_1752
| hAPP(U_1750,U_1751) != hAPP(U_1750,U_1752) ),
inference(miniscope,[status(thm)],[f_511_2]) ).
cnf(f_511_4,plain,
( ~ c_Fun_Oinj__on(U_1748,U_1749,U_1750,c_Orderings_Otop__class_Otop(tc_fun(U_1748,tc_HOL_Obool)))
| U_1751 = U_1752
| hAPP(U_1750,U_1751) != hAPP(U_1750,U_1752) ),
inference(clausify,[status(thm)],[f_511_3]) ).
fof(f_512_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_512_2,plain,
! [U_1757,U_1756,U_1755,U_1754,U_1753] :
( ( ( hAPP(U_1755,U_1756) = hAPP(U_1755,U_1757)
| U_1756 != U_1757 )
& ( U_1756 = U_1757
| hAPP(U_1755,U_1756) != hAPP(U_1755,U_1757) ) )
| ~ c_Fun_Oinj__on(U_1753,U_1754,U_1755,c_Orderings_Otop__class_Otop(tc_fun(U_1753,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_512_1]) ).
fof(f_512_3,plain,
! [U_1757,U_1756,U_1755] :
( ! [U_1754,U_1753] : ~ c_Fun_Oinj__on(U_1753,U_1754,U_1755,c_Orderings_Otop__class_Otop(tc_fun(U_1753,tc_HOL_Obool)))
| ( ( hAPP(U_1755,U_1756) = hAPP(U_1755,U_1757)
| U_1756 != U_1757 )
& ( U_1756 = U_1757
| hAPP(U_1755,U_1756) != hAPP(U_1755,U_1757) ) ) ),
inference(miniscope,[status(thm)],[f_512_2]) ).
cnf(f_512_4,plain,
( U_1756 = U_1757
| hAPP(U_1755,U_1756) != hAPP(U_1755,U_1757)
| ~ c_Fun_Oinj__on(U_1753,U_1754,U_1755,c_Orderings_Otop__class_Otop(tc_fun(U_1753,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_512_3]) ).
cnf(f_512_5,plain,
( hAPP(U_1755,U_1756) = hAPP(U_1755,U_1757)
| U_1756 != U_1757
| ~ c_Fun_Oinj__on(U_1753,U_1754,U_1755,c_Orderings_Otop__class_Otop(tc_fun(U_1753,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_512_3]) ).
fof(f_513_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_513_2,plain,
! [U_1762,U_1761,U_1760,U_1759,U_1758] :
( c_Fun_Oinj__on(U_1758,U_1759,U_1760,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1758,tc_HOL_Obool)),U_1761),U_1762))
| ~ c_Fun_Oinj__on(U_1758,U_1759,U_1760,U_1762)
| ~ c_Fun_Oinj__on(U_1758,U_1759,U_1760,U_1761) ),
inference(variable_rename,[status(thm)],[f_513_1]) ).
cnf(f_513_3,plain,
( c_Fun_Oinj__on(U_1758,U_1759,U_1760,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1758,tc_HOL_Obool)),U_1761),U_1762))
| ~ c_Fun_Oinj__on(U_1758,U_1759,U_1760,U_1762)
| ~ c_Fun_Oinj__on(U_1758,U_1759,U_1760,U_1761) ),
inference(clausify,[status(thm)],[f_513_2]) ).
fof(f_514_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_514_2,plain,
! [U_1767,U_1766,U_1765,U_1764,U_1763] :
( c_Fun_Oinj__on(U_1763,U_1764,U_1765,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1763,tc_HOL_Obool)),U_1766),U_1767))
| ~ c_Fun_Oinj__on(U_1763,U_1764,U_1765,U_1766) ),
inference(variable_rename,[status(thm)],[f_514_1]) ).
cnf(f_514_3,plain,
( c_Fun_Oinj__on(U_1763,U_1764,U_1765,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1763,tc_HOL_Obool)),U_1766),U_1767))
| ~ c_Fun_Oinj__on(U_1763,U_1764,U_1765,U_1766) ),
inference(clausify,[status(thm)],[f_514_2]) ).
fof(f_515_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_515_2,plain,
! [U_1771,U_1770,U_1769,U_1768] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1769,U_1768)),U_1770),U_1771))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1769,U_1768)),U_1771),U_1770))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1769,U_1768)),U_1770),U_1771)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1769,U_1768)),U_1771),U_1770))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1769,U_1768)),U_1770),U_1771)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1769,U_1768)),U_1770),U_1771)) ) )
| ~ class_Orderings_Oord(U_1768) ),
inference(variable_rename,[status(thm)],[f_515_1]) ).
cnf(f_515_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1769,U_1768)),U_1770),U_1771))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1769,U_1768)),U_1770),U_1771))
| ~ class_Orderings_Oord(U_1768) ),
inference(clausify,[status(thm)],[f_515_2]) ).
cnf(f_515_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1769,U_1768)),U_1771),U_1770))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1769,U_1768)),U_1770),U_1771))
| ~ class_Orderings_Oord(U_1768) ),
inference(clausify,[status(thm)],[f_515_2]) ).
cnf(f_515_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1769,U_1768)),U_1770),U_1771))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1769,U_1768)),U_1771),U_1770))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1769,U_1768)),U_1770),U_1771))
| ~ class_Orderings_Oord(U_1768) ),
inference(clausify,[status(thm)],[f_515_2]) ).
fof(f_516_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_516_2,plain,
! [U_1773,U_1772] :
( U_1772 = U_1773
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1773),U_1772) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1772),U_1773) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_516_1]) ).
cnf(f_516_3,plain,
( U_1772 = U_1773
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1773),U_1772) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1772),U_1773) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_516_2]) ).
fof(f_517_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_517_2,plain,
! [U_1774] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1774),U_1774) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_517_1]) ).
cnf(f_517_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1774),U_1774) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_517_2]) ).
fof(f_518_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_518_2,plain,
! [U_1775] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1775),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1775,
inference(variable_rename,[status(thm)],[f_518_1]) ).
cnf(f_518_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1775),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1775,
inference(clausify,[status(thm)],[f_518_2]) ).
fof(f_519_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_519_2,plain,
! [U_1776] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1776) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_519_1]) ).
cnf(f_519_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1776) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_519_2]) ).
fof(f_520_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_520_2,plain,
! [U_1780,U_1779,U_1778,U_1777] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1777),U_1780),U_1779))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1777),U_1780),U_1778))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1777),U_1778),U_1779))
| ~ class_Orderings_Oorder(U_1777) ),
inference(variable_rename,[status(thm)],[f_520_1]) ).
cnf(f_520_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1777),U_1780),U_1779))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1777),U_1780),U_1778))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1777),U_1778),U_1779))
| ~ class_Orderings_Oorder(U_1777) ),
inference(clausify,[status(thm)],[f_520_2]) ).
fof(f_521_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_521_2,plain,
! [U_1784,U_1783,U_1782,U_1781] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1781),U_1782),U_1784))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1781),U_1783),U_1784))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1781),U_1782),U_1783))
| ~ class_Orderings_Opreorder(U_1781) ),
inference(variable_rename,[status(thm)],[f_521_1]) ).
cnf(f_521_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1781),U_1782),U_1784))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1781),U_1783),U_1784))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1781),U_1782),U_1783))
| ~ class_Orderings_Opreorder(U_1781) ),
inference(clausify,[status(thm)],[f_521_2]) ).
fof(f_522_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_522_2,plain,
! [U_1788,U_1787,U_1786,U_1785] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1785),U_1788),U_1787))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1785),U_1788),U_1786))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1785),U_1786),U_1787))
| ~ class_Orderings_Oorder(U_1785) ),
inference(variable_rename,[status(thm)],[f_522_1]) ).
cnf(f_522_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1785),U_1788),U_1787))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1785),U_1788),U_1786))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1785),U_1786),U_1787))
| ~ class_Orderings_Oorder(U_1785) ),
inference(clausify,[status(thm)],[f_522_2]) ).
fof(f_523_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_523_2,plain,
! [U_1792,U_1791,U_1790,U_1789] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1789),U_1790),U_1792))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1789),U_1791),U_1792))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1789),U_1790),U_1791))
| ~ class_Orderings_Opreorder(U_1789) ),
inference(variable_rename,[status(thm)],[f_523_1]) ).
cnf(f_523_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1789),U_1790),U_1792))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1789),U_1791),U_1792))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1789),U_1790),U_1791))
| ~ class_Orderings_Opreorder(U_1789) ),
inference(clausify,[status(thm)],[f_523_2]) ).
fof(f_524_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_524_2,plain,
! [U_1795,U_1794,U_1793] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1793),U_1794),U_1795))
| U_1795 = U_1794
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1793),U_1794),U_1795))
| ~ class_Orderings_Oorder(U_1793) ),
inference(variable_rename,[status(thm)],[f_524_1]) ).
cnf(f_524_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1793),U_1794),U_1795))
| U_1795 = U_1794
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1793),U_1794),U_1795))
| ~ class_Orderings_Oorder(U_1793) ),
inference(clausify,[status(thm)],[f_524_2]) ).
fof(f_525_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_525_2,plain,
! [U_1798,U_1797,U_1796] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1796),U_1797),U_1798))
| U_1797 = U_1798
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1796),U_1797),U_1798))
| ~ class_Orderings_Oorder(U_1796) ),
inference(variable_rename,[status(thm)],[f_525_1]) ).
cnf(f_525_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1796),U_1797),U_1798))
| U_1797 = U_1798
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1796),U_1797),U_1798))
| ~ class_Orderings_Oorder(U_1796) ),
inference(clausify,[status(thm)],[f_525_2]) ).
fof(f_526_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_526_2,plain,
! [U_1801,U_1800,U_1799] :
( U_1800 = U_1801
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1799),U_1800),U_1801))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1799),U_1800),U_1801))
| ~ class_Orderings_Oorder(U_1799) ),
inference(variable_rename,[status(thm)],[f_526_1]) ).
cnf(f_526_3,plain,
( U_1800 = U_1801
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1799),U_1800),U_1801))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1799),U_1800),U_1801))
| ~ class_Orderings_Oorder(U_1799) ),
inference(clausify,[status(thm)],[f_526_2]) ).
fof(f_527_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_527_2,plain,
! [U_1804,U_1803,U_1802] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1802),U_1803),U_1804))
| U_1803 != U_1804 )
& ( U_1803 = U_1804
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1802),U_1803),U_1804)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1802),U_1803),U_1804))
| ~ class_Orderings_Olinorder(U_1802) ),
inference(variable_rename,[status(thm)],[f_527_1]) ).
cnf(f_527_3,plain,
( U_1803 = U_1804
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1802),U_1803),U_1804))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1802),U_1803),U_1804))
| ~ class_Orderings_Olinorder(U_1802) ),
inference(clausify,[status(thm)],[f_527_2]) ).
cnf(f_527_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1802),U_1803),U_1804))
| U_1803 != U_1804
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1802),U_1803),U_1804))
| ~ class_Orderings_Olinorder(U_1802) ),
inference(clausify,[status(thm)],[f_527_2]) ).
fof(f_528_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_528_2,plain,
! [U_1807,U_1806,U_1805] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1805),U_1806),U_1807))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1805),U_1806),U_1807))
| ~ class_Orderings_Opreorder(U_1805) ),
inference(variable_rename,[status(thm)],[f_528_1]) ).
cnf(f_528_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1805),U_1806),U_1807))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1805),U_1806),U_1807))
| ~ class_Orderings_Opreorder(U_1805) ),
inference(clausify,[status(thm)],[f_528_2]) ).
fof(f_529_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_529_2,plain,
! [U_1810,U_1809,U_1808] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1808),U_1810),U_1809))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1808),U_1809),U_1810))
| ~ class_Orderings_Olinorder(U_1808) ),
inference(variable_rename,[status(thm)],[f_529_1]) ).
cnf(f_529_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1808),U_1810),U_1809))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1808),U_1809),U_1810))
| ~ class_Orderings_Olinorder(U_1808) ),
inference(clausify,[status(thm)],[f_529_2]) ).
fof(f_530_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_530_2,plain,
! [U_1813,U_1812,U_1811] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1811),U_1813),U_1812))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1811),U_1813),U_1812))
| U_1812 = U_1813
| ~ class_Orderings_Oorder(U_1811) ),
inference(variable_rename,[status(thm)],[f_530_1]) ).
cnf(f_530_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1811),U_1813),U_1812))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1811),U_1813),U_1812))
| U_1812 = U_1813
| ~ class_Orderings_Oorder(U_1811) ),
inference(clausify,[status(thm)],[f_530_2]) ).
fof(f_531_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_531_2,plain,
! [U_1816,U_1815,U_1814] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1814),U_1815),U_1816))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1814),U_1815),U_1816))
| U_1815 = U_1816
| ~ class_Orderings_Oorder(U_1814) ),
inference(variable_rename,[status(thm)],[f_531_1]) ).
cnf(f_531_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1814),U_1815),U_1816))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1814),U_1815),U_1816))
| U_1815 = U_1816
| ~ class_Orderings_Oorder(U_1814) ),
inference(clausify,[status(thm)],[f_531_2]) ).
fof(f_532_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_532_2,plain,
! [U_1819,U_1818,U_1817] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1817),U_1818),U_1819))
| U_1818 != U_1819 )
& ( U_1818 = U_1819
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1817),U_1818),U_1819)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1817),U_1818),U_1819))
| ~ class_Orderings_Olinorder(U_1817) ),
inference(variable_rename,[status(thm)],[f_532_1]) ).
cnf(f_532_3,plain,
( U_1818 = U_1819
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1817),U_1818),U_1819))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1817),U_1818),U_1819))
| ~ class_Orderings_Olinorder(U_1817) ),
inference(clausify,[status(thm)],[f_532_2]) ).
cnf(f_532_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1817),U_1818),U_1819))
| U_1818 != U_1819
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1817),U_1818),U_1819))
| ~ class_Orderings_Olinorder(U_1817) ),
inference(clausify,[status(thm)],[f_532_2]) ).
fof(f_533_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_533_2,plain,
! [U_1822,U_1821,U_1820] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1820),U_1822),U_1821))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1820),U_1821),U_1822))
| ~ class_Orderings_Olinorder(U_1820) ),
inference(variable_rename,[status(thm)],[f_533_1]) ).
cnf(f_533_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1820),U_1822),U_1821))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1820),U_1821),U_1822))
| ~ class_Orderings_Olinorder(U_1820) ),
inference(clausify,[status(thm)],[f_533_2]) ).
fof(f_534_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_534_2,plain,
! [U_1825,U_1824,U_1823] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1823),U_1825),U_1824))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1823),U_1824),U_1825))
| ~ class_Orderings_Olinorder(U_1823) ),
inference(variable_rename,[status(thm)],[f_534_1]) ).
cnf(f_534_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1823),U_1825),U_1824))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1823),U_1824),U_1825))
| ~ class_Orderings_Olinorder(U_1823) ),
inference(clausify,[status(thm)],[f_534_2]) ).
fof(f_535_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_535_2,plain,
! [U_1828,U_1827,U_1826] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1826),U_1827),U_1828))
| ( U_1827 != U_1828
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1826),U_1827),U_1828)) ) )
& ( U_1827 = U_1828
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1826),U_1827),U_1828))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1826),U_1827),U_1828)) ) )
| ~ class_Orderings_Oorder(U_1826) ),
inference(variable_rename,[status(thm)],[f_535_1]) ).
cnf(f_535_3,plain,
( U_1827 = U_1828
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1826),U_1827),U_1828))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1826),U_1827),U_1828))
| ~ class_Orderings_Oorder(U_1826) ),
inference(clausify,[status(thm)],[f_535_2]) ).
cnf(f_535_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1826),U_1827),U_1828))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1826),U_1827),U_1828))
| ~ class_Orderings_Oorder(U_1826) ),
inference(clausify,[status(thm)],[f_535_2]) ).
cnf(f_535_5,plain,
( U_1827 != U_1828
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1826),U_1827),U_1828))
| ~ class_Orderings_Oorder(U_1826) ),
inference(clausify,[status(thm)],[f_535_2]) ).
fof(f_536_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_536_2,plain,
! [U_1831,U_1830,U_1829] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1829),U_1830),U_1831))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1829),U_1831),U_1830))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1829),U_1830),U_1831)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1829),U_1831),U_1830))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1829),U_1830),U_1831)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1829),U_1830),U_1831)) ) )
| ~ class_Orderings_Opreorder(U_1829) ),
inference(variable_rename,[status(thm)],[f_536_1]) ).
cnf(f_536_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1829),U_1830),U_1831))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1829),U_1830),U_1831))
| ~ class_Orderings_Opreorder(U_1829) ),
inference(clausify,[status(thm)],[f_536_2]) ).
cnf(f_536_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1829),U_1831),U_1830))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1829),U_1830),U_1831))
| ~ class_Orderings_Opreorder(U_1829) ),
inference(clausify,[status(thm)],[f_536_2]) ).
cnf(f_536_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1829),U_1830),U_1831))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1829),U_1831),U_1830))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1829),U_1830),U_1831))
| ~ class_Orderings_Opreorder(U_1829) ),
inference(clausify,[status(thm)],[f_536_2]) ).
fof(f_537_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_537_2,plain,
! [U_1834,U_1833,U_1832] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1832),U_1833),U_1834))
| U_1833 = U_1834
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1832),U_1833),U_1834)) )
& ( ( U_1833 != U_1834
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1832),U_1833),U_1834)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1832),U_1833),U_1834)) ) )
| ~ class_Orderings_Oorder(U_1832) ),
inference(variable_rename,[status(thm)],[f_537_1]) ).
cnf(f_537_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1832),U_1833),U_1834))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1832),U_1833),U_1834))
| ~ class_Orderings_Oorder(U_1832) ),
inference(clausify,[status(thm)],[f_537_2]) ).
cnf(f_537_4,plain,
( U_1833 != U_1834
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1832),U_1833),U_1834))
| ~ class_Orderings_Oorder(U_1832) ),
inference(clausify,[status(thm)],[f_537_2]) ).
cnf(f_537_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1832),U_1833),U_1834))
| U_1833 = U_1834
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1832),U_1833),U_1834))
| ~ class_Orderings_Oorder(U_1832) ),
inference(clausify,[status(thm)],[f_537_2]) ).
fof(f_538_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_538_2,plain,
! [U_1837,U_1836,U_1835] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1835),U_1837),U_1836))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1835),U_1836),U_1837))
| ~ class_Orderings_Olinorder(U_1835) ),
inference(variable_rename,[status(thm)],[f_538_1]) ).
cnf(f_538_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1835),U_1837),U_1836))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1835),U_1836),U_1837))
| ~ class_Orderings_Olinorder(U_1835) ),
inference(clausify,[status(thm)],[f_538_2]) ).
fof(f_539_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_539_2,plain,
! [U_1840,U_1839,U_1838] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1838),U_1839),U_1840))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1838),U_1840),U_1839)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1838),U_1840),U_1839))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1838),U_1839),U_1840)) ) )
| ~ class_Orderings_Olinorder(U_1838) ),
inference(variable_rename,[status(thm)],[f_539_1]) ).
cnf(f_539_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1838),U_1840),U_1839))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1838),U_1839),U_1840))
| ~ class_Orderings_Olinorder(U_1838) ),
inference(clausify,[status(thm)],[f_539_2]) ).
cnf(f_539_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1838),U_1839),U_1840))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1838),U_1840),U_1839))
| ~ class_Orderings_Olinorder(U_1838) ),
inference(clausify,[status(thm)],[f_539_2]) ).
fof(f_540_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_540_2,plain,
! [U_1843,U_1842,U_1841] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1841),U_1842),U_1843))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1841),U_1843),U_1842)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1841),U_1843),U_1842))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1841),U_1842),U_1843)) ) )
| ~ class_Orderings_Olinorder(U_1841) ),
inference(variable_rename,[status(thm)],[f_540_1]) ).
cnf(f_540_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1841),U_1843),U_1842))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1841),U_1842),U_1843))
| ~ class_Orderings_Olinorder(U_1841) ),
inference(clausify,[status(thm)],[f_540_2]) ).
cnf(f_540_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1841),U_1842),U_1843))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1841),U_1843),U_1842))
| ~ class_Orderings_Olinorder(U_1841) ),
inference(clausify,[status(thm)],[f_540_2]) ).
fof(f_541_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_541_2,plain,
! [U_1845,U_1844] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1844)),hAPP(c_Nat_OSuc,U_1845)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1844),U_1845),
inference(variable_rename,[status(thm)],[f_541_1]) ).
cnf(f_541_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1844)),hAPP(c_Nat_OSuc,U_1845)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1844),U_1845),
inference(clausify,[status(thm)],[f_541_2]) ).
fof(f_542_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_542_2,plain,
! [U_1848,U_1847,U_1846] : 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_1846)),U_1847)),hAPP(c_Nat_OSuc,U_1848)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1846),U_1847)),U_1848),
inference(variable_rename,[status(thm)],[f_542_1]) ).
cnf(f_542_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_1846)),U_1847)),hAPP(c_Nat_OSuc,U_1848)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1846),U_1847)),U_1848),
inference(clausify,[status(thm)],[f_542_2]) ).
fof(f_543_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_543_2,plain,
! [U_1850,U_1849] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1849),U_1850)),U_1849)),
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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1849),U_1850)),U_1849)),
inference(clausify,[status(thm)],[f_543_2]) ).
fof(f_544_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_544_2,plain,
! [U_1853,U_1852,U_1851] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1853),U_1852)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1853),U_1851)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1851),U_1852)) ),
inference(variable_rename,[status(thm)],[f_544_1]) ).
cnf(f_544_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_1853),U_1852)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1853),U_1851)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1851),U_1852)) ),
inference(clausify,[status(thm)],[f_544_2]) ).
fof(f_545_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_545_2,plain,
! [U_1856,U_1855,U_1854] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1854),U_1856)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1855),U_1856)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1854),U_1855)) ),
inference(variable_rename,[status(thm)],[f_545_1]) ).
cnf(f_545_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_1854),U_1856)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1855),U_1856)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1854),U_1855)) ),
inference(clausify,[status(thm)],[f_545_2]) ).
fof(f_546_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_546_2,plain,
! [U_1858,U_1857] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1858),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1858),U_1857)) = U_1857
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1857),U_1858)) ),
inference(variable_rename,[status(thm)],[f_546_1]) ).
cnf(f_546_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1858),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1858),U_1857)) = U_1857
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1857),U_1858)) ),
inference(clausify,[status(thm)],[f_546_2]) ).
fof(f_547_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_547_2,plain,
! [U_1861,U_1860,U_1859] :
( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1860),U_1859) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1861),U_1859)
| U_1860 != U_1861 )
& ( U_1860 = U_1861
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1860),U_1859) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1861),U_1859) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1859),U_1861))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1859),U_1860)) ),
inference(variable_rename,[status(thm)],[f_547_1]) ).
cnf(f_547_3,plain,
( U_1860 = U_1861
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1860),U_1859) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1861),U_1859)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1859),U_1861))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1859),U_1860)) ),
inference(clausify,[status(thm)],[f_547_2]) ).
cnf(f_547_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1860),U_1859) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1861),U_1859)
| U_1860 != U_1861
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1859),U_1861))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1859),U_1860)) ),
inference(clausify,[status(thm)],[f_547_2]) ).
fof(f_548_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_548_2,plain,
! [U_1864,U_1863,U_1862] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1863),U_1862)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1864),U_1862)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1863),U_1864)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1862),U_1864))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1862),U_1863)) ),
inference(variable_rename,[status(thm)],[f_548_1]) ).
cnf(f_548_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1863),U_1862)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1864),U_1862)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1863),U_1864)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1862),U_1864))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1862),U_1863)) ),
inference(clausify,[status(thm)],[f_548_2]) ).
fof(f_549_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_549_2,plain,
! [U_1867,U_1866,U_1865] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1866),U_1865)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1867),U_1865)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1866),U_1867)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1866),U_1867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1866),U_1865)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1867),U_1865))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1865),U_1867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1865),U_1866)) ),
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),U_1866),U_1867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1866),U_1865)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1867),U_1865)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1865),U_1867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1865),U_1866)) ),
inference(clausify,[status(thm)],[f_549_2]) ).
cnf(f_549_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_1866),U_1865)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1867),U_1865)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1866),U_1867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1865),U_1867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1865),U_1866)) ),
inference(clausify,[status(thm)],[f_549_2]) ).
fof(f_550_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_550_2,plain,
! [U_1869,U_1868] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1868,tc_HOL_Obool)),U_1869),c_Orderings_Obot__class_Obot(tc_fun(U_1868,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_550_1]) ).
cnf(f_550_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1868,tc_HOL_Obool)),U_1869),c_Orderings_Obot__class_Obot(tc_fun(U_1868,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_550_2]) ).
fof(f_551_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) )
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less]) ).
fof(f_551_2,plain,
! [U_1874,U_1873,U_1872,U_1871,U_1870] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1870),U_1871),U_1872))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1870),U_1873),U_1874)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1870),U_1873),U_1874))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1870),U_1871),U_1872)) ) )
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1870),U_1871),U_1872) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1870),U_1873),U_1874)
| ~ class_Groups_Oordered__ab__group__add(U_1870) ),
inference(variable_rename,[status(thm)],[f_551_1]) ).
cnf(f_551_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1870),U_1873),U_1874))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1870),U_1871),U_1872))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1870),U_1871),U_1872) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1870),U_1873),U_1874)
| ~ class_Groups_Oordered__ab__group__add(U_1870) ),
inference(clausify,[status(thm)],[f_551_2]) ).
cnf(f_551_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1870),U_1871),U_1872))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1870),U_1873),U_1874))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1870),U_1871),U_1872) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1870),U_1873),U_1874)
| ~ class_Groups_Oordered__ab__group__add(U_1870) ),
inference(clausify,[status(thm)],[f_551_2]) ).
fof(f_552_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_552_2,plain,
! [U_1878,U_1877,U_1876,U_1875] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),U_1876),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1875),U_1877),U_1878)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),U_1876),U_1877))
| ~ class_Lattices_Osemilattice__sup(U_1875) ),
inference(variable_rename,[status(thm)],[f_552_1]) ).
cnf(f_552_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),U_1876),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1875),U_1877),U_1878)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),U_1876),U_1877))
| ~ class_Lattices_Osemilattice__sup(U_1875) ),
inference(clausify,[status(thm)],[f_552_2]) ).
fof(f_553_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_553_2,plain,
! [U_1882,U_1881,U_1880,U_1879] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1879),U_1880),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1879),U_1882),U_1881)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1879),U_1880),U_1881))
| ~ class_Lattices_Osemilattice__sup(U_1879) ),
inference(variable_rename,[status(thm)],[f_553_1]) ).
cnf(f_553_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1879),U_1880),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1879),U_1882),U_1881)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1879),U_1880),U_1881))
| ~ class_Lattices_Osemilattice__sup(U_1879) ),
inference(clausify,[status(thm)],[f_553_2]) ).
fof(f_554_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_554_2,plain,
! [U_1886,U_1885,U_1884,U_1883] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1883),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1883),U_1886),U_1884)),U_1885))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1883),U_1884),U_1885))
| ~ class_Lattices_Osemilattice__inf(U_1883) ),
inference(variable_rename,[status(thm)],[f_554_1]) ).
cnf(f_554_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1883),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1883),U_1886),U_1884)),U_1885))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1883),U_1884),U_1885))
| ~ class_Lattices_Osemilattice__inf(U_1883) ),
inference(clausify,[status(thm)],[f_554_2]) ).
fof(f_555_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_555_2,plain,
! [U_1890,U_1889,U_1888,U_1887] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1887),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1887),U_1888),U_1890)),U_1889))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1887),U_1888),U_1889))
| ~ class_Lattices_Osemilattice__inf(U_1887) ),
inference(variable_rename,[status(thm)],[f_555_1]) ).
cnf(f_555_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1887),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1887),U_1888),U_1890)),U_1889))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1887),U_1888),U_1889))
| ~ class_Lattices_Osemilattice__inf(U_1887) ),
inference(clausify,[status(thm)],[f_555_2]) ).
fof(f_556_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_556_2,plain,
! [U_1893,U_1892,U_1891] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1891),U_1892),hAPP(c_Groups_Ouminus__class_Ouminus(U_1891),U_1893)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1891),U_1893),hAPP(c_Groups_Ouminus__class_Ouminus(U_1891),U_1892))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1891),U_1893),hAPP(c_Groups_Ouminus__class_Ouminus(U_1891),U_1892)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1891),U_1892),hAPP(c_Groups_Ouminus__class_Ouminus(U_1891),U_1893))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1891) ),
inference(variable_rename,[status(thm)],[f_556_1]) ).
cnf(f_556_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1891),U_1893),hAPP(c_Groups_Ouminus__class_Ouminus(U_1891),U_1892)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1891),U_1892),hAPP(c_Groups_Ouminus__class_Ouminus(U_1891),U_1893)))
| ~ class_Groups_Oordered__ab__group__add(U_1891) ),
inference(clausify,[status(thm)],[f_556_2]) ).
cnf(f_556_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1891),U_1892),hAPP(c_Groups_Ouminus__class_Ouminus(U_1891),U_1893)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1891),U_1893),hAPP(c_Groups_Ouminus__class_Ouminus(U_1891),U_1892)))
| ~ class_Groups_Oordered__ab__group__add(U_1891) ),
inference(clausify,[status(thm)],[f_556_2]) ).
fof(f_557_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_557_2,plain,
! [U_1896,U_1895,U_1894] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1894),hAPP(c_Groups_Ouminus__class_Ouminus(U_1894),U_1895)),U_1896))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1894),hAPP(c_Groups_Ouminus__class_Ouminus(U_1894),U_1896)),U_1895)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1894),hAPP(c_Groups_Ouminus__class_Ouminus(U_1894),U_1896)),U_1895))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1894),hAPP(c_Groups_Ouminus__class_Ouminus(U_1894),U_1895)),U_1896)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1894) ),
inference(variable_rename,[status(thm)],[f_557_1]) ).
cnf(f_557_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1894),hAPP(c_Groups_Ouminus__class_Ouminus(U_1894),U_1896)),U_1895))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1894),hAPP(c_Groups_Ouminus__class_Ouminus(U_1894),U_1895)),U_1896))
| ~ class_Groups_Oordered__ab__group__add(U_1894) ),
inference(clausify,[status(thm)],[f_557_2]) ).
cnf(f_557_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1894),hAPP(c_Groups_Ouminus__class_Ouminus(U_1894),U_1895)),U_1896))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1894),hAPP(c_Groups_Ouminus__class_Ouminus(U_1894),U_1896)),U_1895))
| ~ class_Groups_Oordered__ab__group__add(U_1894) ),
inference(clausify,[status(thm)],[f_557_2]) ).
fof(f_558_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_558_2,plain,
! [U_1899,U_1898,U_1897] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1897),hAPP(c_Groups_Ouminus__class_Ouminus(U_1897),U_1898)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1897),U_1899)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1897),U_1899),U_1898)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1897),U_1899),U_1898))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1897),hAPP(c_Groups_Ouminus__class_Ouminus(U_1897),U_1898)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1897),U_1899))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1897) ),
inference(variable_rename,[status(thm)],[f_558_1]) ).
cnf(f_558_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1897),U_1899),U_1898))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1897),hAPP(c_Groups_Ouminus__class_Ouminus(U_1897),U_1898)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1897),U_1899)))
| ~ class_Groups_Oordered__ab__group__add(U_1897) ),
inference(clausify,[status(thm)],[f_558_2]) ).
cnf(f_558_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1897),hAPP(c_Groups_Ouminus__class_Ouminus(U_1897),U_1898)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1897),U_1899)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1897),U_1899),U_1898))
| ~ class_Groups_Oordered__ab__group__add(U_1897) ),
inference(clausify,[status(thm)],[f_558_2]) ).
fof(f_559_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_559_2,plain,
! [U_1903,U_1902,U_1901,U_1900] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1900,tc_HOL_Obool)),U_1901),U_1903))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1900,tc_HOL_Obool)),U_1902),U_1903))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1900,tc_HOL_Obool)),U_1901),U_1902)) ),
inference(variable_rename,[status(thm)],[f_559_1]) ).
cnf(f_559_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1900,tc_HOL_Obool)),U_1901),U_1903))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1900,tc_HOL_Obool)),U_1902),U_1903))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1900,tc_HOL_Obool)),U_1901),U_1902)) ),
inference(clausify,[status(thm)],[f_559_2]) ).
fof(f_560_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_560_2,plain,
! [U_1907,U_1906,U_1905,U_1904] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1904,tc_HOL_Obool)),U_1905),U_1907))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1904,tc_HOL_Obool)),U_1906),U_1907))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1904,tc_HOL_Obool)),U_1905),U_1906)) ),
inference(variable_rename,[status(thm)],[f_560_1]) ).
cnf(f_560_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1904,tc_HOL_Obool)),U_1905),U_1907))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1904,tc_HOL_Obool)),U_1906),U_1907))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1904,tc_HOL_Obool)),U_1905),U_1906)) ),
inference(clausify,[status(thm)],[f_560_2]) ).
fof(f_561_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_561_2,plain,
! [U_1910,U_1909,U_1908] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1908,tc_HOL_Obool)),U_1909),U_1910))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1908,tc_HOL_Obool)),U_1909),U_1910)) ),
inference(variable_rename,[status(thm)],[f_561_1]) ).
cnf(f_561_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1908,tc_HOL_Obool)),U_1909),U_1910))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1908,tc_HOL_Obool)),U_1909),U_1910)) ),
inference(clausify,[status(thm)],[f_561_2]) ).
fof(f_562_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_562_2,plain,
! [U_1913,U_1912,U_1911] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1911,tc_HOL_Obool)),U_1912),U_1913))
| ( U_1912 != U_1913
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1911,tc_HOL_Obool)),U_1912),U_1913)) ) )
& ( U_1912 = U_1913
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1911,tc_HOL_Obool)),U_1912),U_1913))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1911,tc_HOL_Obool)),U_1912),U_1913)) ) ),
inference(variable_rename,[status(thm)],[f_562_1]) ).
fof(f_562_3,plain,
( ! [U_1919,U_1917,U_1915] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1915,tc_HOL_Obool)),U_1917),U_1919))
| ( U_1917 != U_1919
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1915,tc_HOL_Obool)),U_1917),U_1919)) ) )
& ! [U_1918,U_1916,U_1914] :
( U_1916 = U_1918
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1914,tc_HOL_Obool)),U_1916),U_1918))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1914,tc_HOL_Obool)),U_1916),U_1918)) ) ),
inference(miniscope,[status(thm)],[f_562_2]) ).
cnf(f_562_4,plain,
( U_1916 = U_1918
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1914,tc_HOL_Obool)),U_1916),U_1918))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1914,tc_HOL_Obool)),U_1916),U_1918)) ),
inference(clausify,[status(thm)],[f_562_3]) ).
cnf(f_562_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1915,tc_HOL_Obool)),U_1917),U_1919))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1915,tc_HOL_Obool)),U_1917),U_1919)) ),
inference(clausify,[status(thm)],[f_562_3]) ).
cnf(f_562_6,plain,
( U_1917 != U_1919
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1915,tc_HOL_Obool)),U_1917),U_1919)) ),
inference(clausify,[status(thm)],[f_562_3]) ).
fof(f_563_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_563_2,plain,
! [U_1922,U_1921,U_1920] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1920,tc_HOL_Obool)),U_1921),U_1922))
| U_1921 = U_1922
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1920,tc_HOL_Obool)),U_1921),U_1922)) )
& ( ( U_1921 != U_1922
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1920,tc_HOL_Obool)),U_1921),U_1922)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1920,tc_HOL_Obool)),U_1921),U_1922)) ) ),
inference(variable_rename,[status(thm)],[f_563_1]) ).
fof(f_563_3,plain,
( ! [U_1928,U_1926,U_1924] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1924,tc_HOL_Obool)),U_1926),U_1928))
| U_1926 = U_1928
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1924,tc_HOL_Obool)),U_1926),U_1928)) )
& ! [U_1927,U_1925,U_1923] :
( ( U_1925 != U_1927
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1923,tc_HOL_Obool)),U_1925),U_1927)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1923,tc_HOL_Obool)),U_1925),U_1927)) ) ),
inference(miniscope,[status(thm)],[f_563_2]) ).
cnf(f_563_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1923,tc_HOL_Obool)),U_1925),U_1927))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1923,tc_HOL_Obool)),U_1925),U_1927)) ),
inference(clausify,[status(thm)],[f_563_3]) ).
cnf(f_563_5,plain,
( U_1925 != U_1927
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1923,tc_HOL_Obool)),U_1925),U_1927)) ),
inference(clausify,[status(thm)],[f_563_3]) ).
cnf(f_563_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1924,tc_HOL_Obool)),U_1926),U_1928))
| U_1926 = U_1928
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1924,tc_HOL_Obool)),U_1926),U_1928)) ),
inference(clausify,[status(thm)],[f_563_3]) ).
fof(f_564_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_564_2,plain,
! [U_1929] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1929))
| U_1929 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_564_1]) ).
cnf(f_564_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1929))
| U_1929 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_564_2]) ).
fof(f_565_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_565_2,plain,
! [U_1931,U_1930] :
( U_1931 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1930),U_1931)) ),
inference(variable_rename,[status(thm)],[f_565_1]) ).
fof(f_565_3,plain,
! [U_1931] :
( ! [U_1930] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1930),U_1931))
| U_1931 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(miniscope,[status(thm)],[f_565_2]) ).
cnf(f_565_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1930),U_1931))
| U_1931 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_565_3]) ).
fof(f_566_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_566_2,plain,
! [U_1932] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1932),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_566_1]) ).
cnf(f_566_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1932),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_566_2]) ).
fof(f_567_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_567_2,plain,
! [U_1933] :
( ( U_1933 != 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_1933)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1933))
| U_1933 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_567_1]) ).
fof(f_567_3,plain,
( ! [U_1935] :
( U_1935 != 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_1935)) )
& ! [U_1934] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1934))
| U_1934 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_567_2]) ).
cnf(f_567_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1934))
| U_1934 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_567_3]) ).
cnf(f_567_5,plain,
( U_1935 != 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_1935)) ),
inference(clausify,[status(thm)],[f_567_3]) ).
fof(f_568_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_568_2,plain,
! [U_1936] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1936),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
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_1936),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_568_2]) ).
fof(f_569_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_569_2,plain,
! [U_1938,U_1937] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1937),U_1938))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1938),hAPP(c_Nat_OSuc,U_1937))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1938),hAPP(c_Nat_OSuc,U_1937)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1937),U_1938)) ) ),
inference(variable_rename,[status(thm)],[f_569_1]) ).
fof(f_569_3,plain,
( ! [U_1942,U_1940] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1940),U_1942))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1942),hAPP(c_Nat_OSuc,U_1940))) )
& ! [U_1941,U_1939] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1941),hAPP(c_Nat_OSuc,U_1939)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1939),U_1941)) ) ),
inference(miniscope,[status(thm)],[f_569_2]) ).
cnf(f_569_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1941),hAPP(c_Nat_OSuc,U_1939)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1939),U_1941)) ),
inference(clausify,[status(thm)],[f_569_3]) ).
cnf(f_569_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1940),U_1942))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1942),hAPP(c_Nat_OSuc,U_1940))) ),
inference(clausify,[status(thm)],[f_569_3]) ).
fof(f_570_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_570_2,plain,
! [U_1944,U_1943] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1943),hAPP(c_Nat_OSuc,U_1944)))
| ( U_1943 != U_1944
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1943),U_1944)) ) )
& ( U_1943 = U_1944
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1943),U_1944))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1943),hAPP(c_Nat_OSuc,U_1944))) ) ),
inference(variable_rename,[status(thm)],[f_570_1]) ).
fof(f_570_3,plain,
( ! [U_1948,U_1946] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1946),hAPP(c_Nat_OSuc,U_1948)))
| ( U_1946 != U_1948
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1946),U_1948)) ) )
& ! [U_1947,U_1945] :
( U_1945 = U_1947
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1945),U_1947))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1945),hAPP(c_Nat_OSuc,U_1947))) ) ),
inference(miniscope,[status(thm)],[f_570_2]) ).
cnf(f_570_4,plain,
( U_1945 = U_1947
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1945),U_1947))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1945),hAPP(c_Nat_OSuc,U_1947))) ),
inference(clausify,[status(thm)],[f_570_3]) ).
cnf(f_570_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1946),U_1948))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1946),hAPP(c_Nat_OSuc,U_1948))) ),
inference(clausify,[status(thm)],[f_570_3]) ).
cnf(f_570_6,plain,
( U_1946 != U_1948
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1946),hAPP(c_Nat_OSuc,U_1948))) ),
inference(clausify,[status(thm)],[f_570_3]) ).
fof(f_571_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_571_2,plain,
! [U_1950,U_1949] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1949)),hAPP(c_Nat_OSuc,U_1950)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1949),U_1950)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1949),U_1950))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1949)),hAPP(c_Nat_OSuc,U_1950))) ) ),
inference(variable_rename,[status(thm)],[f_571_1]) ).
fof(f_571_3,plain,
( ! [U_1954,U_1952] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1952)),hAPP(c_Nat_OSuc,U_1954)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1952),U_1954)) )
& ! [U_1953,U_1951] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1951),U_1953))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1951)),hAPP(c_Nat_OSuc,U_1953))) ) ),
inference(miniscope,[status(thm)],[f_571_2]) ).
cnf(f_571_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1951),U_1953))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1951)),hAPP(c_Nat_OSuc,U_1953))) ),
inference(clausify,[status(thm)],[f_571_3]) ).
cnf(f_571_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1952)),hAPP(c_Nat_OSuc,U_1954)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1952),U_1954)) ),
inference(clausify,[status(thm)],[f_571_3]) ).
fof(f_572_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_572_2,plain,
! [U_1956,U_1955] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1955),hAPP(c_Nat_OSuc,U_1956)))
| U_1955 != U_1956 )
& ( U_1955 = U_1956
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1955),hAPP(c_Nat_OSuc,U_1956))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1955),U_1956)) ),
inference(variable_rename,[status(thm)],[f_572_1]) ).
cnf(f_572_3,plain,
( U_1955 = U_1956
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1955),hAPP(c_Nat_OSuc,U_1956)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1955),U_1956)) ),
inference(clausify,[status(thm)],[f_572_2]) ).
cnf(f_572_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1955),hAPP(c_Nat_OSuc,U_1956)))
| U_1955 != U_1956
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1955),U_1956)) ),
inference(clausify,[status(thm)],[f_572_2]) ).
fof(f_573_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_573_2,plain,
! [U_1958,U_1957] :
( U_1958 = U_1957
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1957),hAPP(c_Nat_OSuc,U_1958)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1957),U_1958)) ),
inference(variable_rename,[status(thm)],[f_573_1]) ).
cnf(f_573_3,plain,
( U_1958 = U_1957
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1957),hAPP(c_Nat_OSuc,U_1958)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1957),U_1958)) ),
inference(clausify,[status(thm)],[f_573_2]) ).
fof(f_574_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_574_2,plain,
! [U_1960,U_1959] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1959),hAPP(c_Nat_OSuc,U_1960)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1959),U_1960)) ),
inference(variable_rename,[status(thm)],[f_574_1]) ).
cnf(f_574_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1959),hAPP(c_Nat_OSuc,U_1960)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1959),U_1960)) ),
inference(clausify,[status(thm)],[f_574_2]) ).
fof(f_575_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_575_2,plain,
! [U_1962,U_1961] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1961)),U_1962))
| hAPP(c_Nat_OSuc,U_1961) = U_1962
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1961),U_1962)) ),
inference(variable_rename,[status(thm)],[f_575_1]) ).
cnf(f_575_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1961)),U_1962))
| hAPP(c_Nat_OSuc,U_1961) = U_1962
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1961),U_1962)) ),
inference(clausify,[status(thm)],[f_575_2]) ).
fof(f_576_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_576_2,plain,
! [U_1965,U_1964,U_1963] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1963)),U_1965))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1964),U_1965))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1963),U_1964)) ),
inference(variable_rename,[status(thm)],[f_576_1]) ).
cnf(f_576_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1963)),U_1965))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1964),U_1965))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1963),U_1964)) ),
inference(clausify,[status(thm)],[f_576_2]) ).
fof(f_577_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_577_2,plain,
! [U_1967,U_1966] :
( U_1966 = U_1967
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1966),U_1967))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1966),hAPP(c_Nat_OSuc,U_1967))) ),
inference(variable_rename,[status(thm)],[f_577_1]) ).
cnf(f_577_3,plain,
( U_1966 = U_1967
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1966),U_1967))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1966),hAPP(c_Nat_OSuc,U_1967))) ),
inference(clausify,[status(thm)],[f_577_2]) ).
fof(f_578_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_578_2,plain,
! [U_1969,U_1968] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1968),U_1969))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1968)),U_1969)) ),
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_1968),U_1969))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1968)),U_1969)) ),
inference(clausify,[status(thm)],[f_578_2]) ).
fof(f_579_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_579_2,plain,
! [U_1971,U_1970] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1970),U_1971))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1970)),hAPP(c_Nat_OSuc,U_1971))) ),
inference(variable_rename,[status(thm)],[f_579_1]) ).
cnf(f_579_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1970),U_1971))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1970)),hAPP(c_Nat_OSuc,U_1971))) ),
inference(clausify,[status(thm)],[f_579_2]) ).
fof(f_580_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_580_2,plain,
! [U_1973,U_1972] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1972),U_1973))
| U_1972 = U_1973
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1972),U_1973)) )
& ( ( U_1972 != U_1973
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1972),U_1973)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1972),U_1973)) ) ),
inference(variable_rename,[status(thm)],[f_580_1]) ).
fof(f_580_3,plain,
( ! [U_1977,U_1975] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1975),U_1977))
| U_1975 = U_1977
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1975),U_1977)) )
& ! [U_1976,U_1974] :
( ( U_1974 != U_1976
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1974),U_1976)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1974),U_1976)) ) ),
inference(miniscope,[status(thm)],[f_580_2]) ).
cnf(f_580_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1974),U_1976))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1974),U_1976)) ),
inference(clausify,[status(thm)],[f_580_3]) ).
cnf(f_580_5,plain,
( U_1974 != U_1976
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1974),U_1976)) ),
inference(clausify,[status(thm)],[f_580_3]) ).
cnf(f_580_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1975),U_1977))
| U_1975 = U_1977
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1975),U_1977)) ),
inference(clausify,[status(thm)],[f_580_3]) ).
fof(f_581_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_581_2,plain,
! [U_1979,U_1978] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1978),U_1979))
| ( U_1978 != U_1979
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1978),U_1979)) ) )
& ( U_1978 = U_1979
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1978),U_1979))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1978),U_1979)) ) ),
inference(variable_rename,[status(thm)],[f_581_1]) ).
fof(f_581_3,plain,
( ! [U_1983,U_1981] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1981),U_1983))
| ( U_1981 != U_1983
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1981),U_1983)) ) )
& ! [U_1982,U_1980] :
( U_1980 = U_1982
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1980),U_1982))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1980),U_1982)) ) ),
inference(miniscope,[status(thm)],[f_581_2]) ).
cnf(f_581_4,plain,
( U_1980 = U_1982
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1980),U_1982))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1980),U_1982)) ),
inference(clausify,[status(thm)],[f_581_3]) ).
cnf(f_581_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1981),U_1983))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1981),U_1983)) ),
inference(clausify,[status(thm)],[f_581_3]) ).
cnf(f_581_6,plain,
( U_1981 != U_1983
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1981),U_1983)) ),
inference(clausify,[status(thm)],[f_581_3]) ).
fof(f_582_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_582_2,plain,
! [U_1985,U_1984] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1984),U_1985))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1984),U_1985)) ),
inference(variable_rename,[status(thm)],[f_582_1]) ).
cnf(f_582_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1984),U_1985))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1984),U_1985)) ),
inference(clausify,[status(thm)],[f_582_2]) ).
fof(f_583_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_583_2,plain,
! [U_1987,U_1986] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1986),U_1987))
| U_1986 = U_1987
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1986),U_1987)) ),
inference(variable_rename,[status(thm)],[f_583_1]) ).
cnf(f_583_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1986),U_1987))
| U_1986 = U_1987
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1986),U_1987)) ),
inference(clausify,[status(thm)],[f_583_2]) ).
fof(f_584_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_584_2,plain,
! [U_1989,U_1988] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1988),U_1989))
| ( U_1988 != U_1989
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1988),U_1989)) ) ),
inference(variable_rename,[status(thm)],[f_584_1]) ).
cnf(f_584_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1988),U_1989))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1988),U_1989)) ),
inference(clausify,[status(thm)],[f_584_2]) ).
cnf(f_584_4,plain,
( U_1988 != U_1989
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1988),U_1989)) ),
inference(clausify,[status(thm)],[f_584_2]) ).
fof(f_585_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( V_b_2 = V_d_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I2_J]) ).
fof(f_585_2,plain,
! [U_1994,U_1993,U_1992,U_1991,U_1990] :
( U_1992 = U_1994
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1990),U_1993),U_1994))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1990),U_1991),U_1992))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1990,U_1991),U_1992) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1990,U_1993),U_1994)
| ~ class_Orderings_Olinorder(U_1990) ),
inference(variable_rename,[status(thm)],[f_585_1]) ).
cnf(f_585_3,plain,
( U_1992 = U_1994
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1990),U_1993),U_1994))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1990),U_1991),U_1992))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1990,U_1991),U_1992) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1990,U_1993),U_1994)
| ~ class_Orderings_Olinorder(U_1990) ),
inference(clausify,[status(thm)],[f_585_2]) ).
fof(f_586_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( V_a_2 = V_c_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I1_J]) ).
fof(f_586_2,plain,
! [U_1999,U_1998,U_1997,U_1996,U_1995] :
( U_1996 = U_1998
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),U_1998),U_1999))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),U_1996),U_1997))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1995,U_1996),U_1997) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1995,U_1998),U_1999)
| ~ class_Orderings_Olinorder(U_1995) ),
inference(variable_rename,[status(thm)],[f_586_1]) ).
cnf(f_586_3,plain,
( U_1996 = U_1998
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),U_1998),U_1999))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),U_1996),U_1997))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1995,U_1996),U_1997) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1995,U_1998),U_1999)
| ~ class_Orderings_Olinorder(U_1995) ),
inference(clausify,[status(thm)],[f_586_2]) ).
fof(f_587_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
| V_b_2 != V_d_2
| V_a_2 != V_c_2 )
& ( ( V_b_2 = V_d_2
& V_a_2 = V_c_2 )
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__eq__iff]) ).
fof(f_587_2,plain,
! [U_2004,U_2003,U_2002,U_2001,U_2000] :
( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2000,U_2001),U_2002) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2000,U_2003),U_2004)
| U_2002 != U_2004
| U_2001 != U_2003 )
& ( ( U_2002 = U_2004
& U_2001 = U_2003 )
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2000,U_2001),U_2002) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2000,U_2003),U_2004) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2000),U_2003),U_2004))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2000),U_2001),U_2002))
| ~ class_Orderings_Olinorder(U_2000) ),
inference(variable_rename,[status(thm)],[f_587_1]) ).
cnf(f_587_3,plain,
( U_2001 = U_2003
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2000,U_2001),U_2002) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2000,U_2003),U_2004)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2000),U_2003),U_2004))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2000),U_2001),U_2002))
| ~ class_Orderings_Olinorder(U_2000) ),
inference(clausify,[status(thm)],[f_587_2]) ).
cnf(f_587_4,plain,
( U_2002 = U_2004
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2000,U_2001),U_2002) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2000,U_2003),U_2004)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2000),U_2003),U_2004))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2000),U_2001),U_2002))
| ~ class_Orderings_Olinorder(U_2000) ),
inference(clausify,[status(thm)],[f_587_2]) ).
cnf(f_587_5,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2000,U_2001),U_2002) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2000,U_2003),U_2004)
| U_2002 != U_2004
| U_2001 != U_2003
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2000),U_2003),U_2004))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2000),U_2001),U_2002))
| ~ class_Orderings_Olinorder(U_2000) ),
inference(clausify,[status(thm)],[f_587_2]) ).
fof(f_588_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_588_2,plain,
! [U_2009,U_2008,U_2007] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2007),U_2008),c_Complete__Lattice_OSup__class_OSup(U_2007,U_2009)))
| ! [U_2006] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2007),U_2008),U_2006))
| ~ hBOOL(hAPP(hAPP(c_member(U_2007),U_2006),U_2009)) ) )
& ( ? [U_2005] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2007),U_2008),U_2005))
& hBOOL(hAPP(hAPP(c_member(U_2007),U_2005),U_2009)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2007),U_2008),c_Complete__Lattice_OSup__class_OSup(U_2007,U_2009))) ) )
| ~ class_Orderings_Olinorder(U_2007)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_2007) ),
inference(variable_rename,[status(thm)],[f_588_1]) ).
fof(f_588_3,plain,
! [U_2009,U_2008,U_2007] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2007),U_2008),c_Complete__Lattice_OSup__class_OSup(U_2007,U_2009)))
| ! [U_2006] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2007),U_2008),U_2006))
| ~ hBOOL(hAPP(hAPP(c_member(U_2007),U_2006),U_2009)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2007),U_2008),sK30(U_2009,U_2008,U_2007)))
& hBOOL(hAPP(hAPP(c_member(U_2007),sK30(U_2009,U_2008,U_2007)),U_2009)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2007),U_2008),c_Complete__Lattice_OSup__class_OSup(U_2007,U_2009))) ) )
| ~ class_Orderings_Olinorder(U_2007)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_2007) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_2005,sK30(U_2009,U_2008,U_2007))],[f_588_2]) ).
cnf(f_588_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2007),sK30(U_2009,U_2008,U_2007)),U_2009))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2007),U_2008),c_Complete__Lattice_OSup__class_OSup(U_2007,U_2009)))
| ~ class_Orderings_Olinorder(U_2007)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_2007) ),
inference(clausify,[status(thm)],[f_588_3]) ).
cnf(f_588_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2007),U_2008),sK30(U_2009,U_2008,U_2007)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2007),U_2008),c_Complete__Lattice_OSup__class_OSup(U_2007,U_2009)))
| ~ class_Orderings_Olinorder(U_2007)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_2007) ),
inference(clausify,[status(thm)],[f_588_3]) ).
cnf(f_588_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2007),U_2008),c_Complete__Lattice_OSup__class_OSup(U_2007,U_2009)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2007),U_2008),U_2006))
| ~ hBOOL(hAPP(hAPP(c_member(U_2007),U_2006),U_2009))
| ~ class_Orderings_Olinorder(U_2007)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_2007) ),
inference(clausify,[status(thm)],[f_588_3]) ).
fof(f_589_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_589_2,plain,
! [U_2014,U_2013,U_2012] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2012),c_Complete__Lattice_OInf__class_OInf(U_2012,U_2013)),U_2014))
| ! [U_2011] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2012),U_2011),U_2014))
| ~ hBOOL(hAPP(hAPP(c_member(U_2012),U_2011),U_2013)) ) )
& ( ? [U_2010] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2012),U_2010),U_2014))
& hBOOL(hAPP(hAPP(c_member(U_2012),U_2010),U_2013)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2012),c_Complete__Lattice_OInf__class_OInf(U_2012,U_2013)),U_2014)) ) )
| ~ class_Orderings_Olinorder(U_2012)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_2012) ),
inference(variable_rename,[status(thm)],[f_589_1]) ).
fof(f_589_3,plain,
! [U_2014,U_2013,U_2012] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2012),c_Complete__Lattice_OInf__class_OInf(U_2012,U_2013)),U_2014))
| ! [U_2011] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2012),U_2011),U_2014))
| ~ hBOOL(hAPP(hAPP(c_member(U_2012),U_2011),U_2013)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2012),sK31(U_2014,U_2013,U_2012)),U_2014))
& hBOOL(hAPP(hAPP(c_member(U_2012),sK31(U_2014,U_2013,U_2012)),U_2013)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2012),c_Complete__Lattice_OInf__class_OInf(U_2012,U_2013)),U_2014)) ) )
| ~ class_Orderings_Olinorder(U_2012)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_2012) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_2010,sK31(U_2014,U_2013,U_2012))],[f_589_2]) ).
cnf(f_589_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2012),sK31(U_2014,U_2013,U_2012)),U_2013))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2012),c_Complete__Lattice_OInf__class_OInf(U_2012,U_2013)),U_2014))
| ~ class_Orderings_Olinorder(U_2012)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_2012) ),
inference(clausify,[status(thm)],[f_589_3]) ).
cnf(f_589_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2012),sK31(U_2014,U_2013,U_2012)),U_2014))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2012),c_Complete__Lattice_OInf__class_OInf(U_2012,U_2013)),U_2014))
| ~ class_Orderings_Olinorder(U_2012)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_2012) ),
inference(clausify,[status(thm)],[f_589_3]) ).
cnf(f_589_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2012),c_Complete__Lattice_OInf__class_OInf(U_2012,U_2013)),U_2014))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2012),U_2011),U_2014))
| ~ hBOOL(hAPP(hAPP(c_member(U_2012),U_2011),U_2013))
| ~ class_Orderings_Olinorder(U_2012)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_2012) ),
inference(clausify,[status(thm)],[f_589_3]) ).
fof(f_590_1,plain,
! [V_A_2,V_f_2,T_b,T_c] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
| ~ c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_strict__mono__imp__inj__on]) ).
fof(f_590_2,plain,
! [U_2018,U_2017,U_2016,U_2015] :
( c_Fun_Oinj__on(U_2016,U_2015,U_2017,U_2018)
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_2016,U_2015,U_2017)
| ~ class_Orderings_Olinorder(U_2016)
| ~ class_Orderings_Oorder(U_2015) ),
inference(variable_rename,[status(thm)],[f_590_1]) ).
cnf(f_590_3,plain,
( c_Fun_Oinj__on(U_2016,U_2015,U_2017,U_2018)
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_2016,U_2015,U_2017)
| ~ class_Orderings_Olinorder(U_2016)
| ~ class_Orderings_Oorder(U_2015) ),
inference(clausify,[status(thm)],[f_590_2]) ).
fof(f_591_1,plain,
! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
| ~ c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
| ~ class_Orderings_Oorder(T_b)
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_strict__monoD]) ).
fof(f_591_2,plain,
! [U_2023,U_2022,U_2021,U_2020,U_2019] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2019),hAPP(U_2021,U_2022)),hAPP(U_2021,U_2023)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2020),U_2022),U_2023))
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_2020,U_2019,U_2021)
| ~ class_Orderings_Oorder(U_2020)
| ~ class_Orderings_Oorder(U_2019) ),
inference(variable_rename,[status(thm)],[f_591_1]) ).
cnf(f_591_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2019),hAPP(U_2021,U_2022)),hAPP(U_2021,U_2023)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2020),U_2022),U_2023))
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_2020,U_2019,U_2021)
| ~ class_Orderings_Oorder(U_2020)
| ~ class_Orderings_Oorder(U_2019) ),
inference(clausify,[status(thm)],[f_591_2]) ).
fof(f_592_1,plain,
! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) )
| ~ c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_strict__mono__less]) ).
fof(f_592_2,plain,
! [U_2028,U_2027,U_2026,U_2025,U_2024] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2024),hAPP(U_2026,U_2027)),hAPP(U_2026,U_2028)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2025),U_2027),U_2028)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2025),U_2027),U_2028))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2024),hAPP(U_2026,U_2027)),hAPP(U_2026,U_2028))) ) )
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_2025,U_2024,U_2026)
| ~ class_Orderings_Olinorder(U_2025)
| ~ class_Orderings_Oorder(U_2024) ),
inference(variable_rename,[status(thm)],[f_592_1]) ).
cnf(f_592_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2025),U_2027),U_2028))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2024),hAPP(U_2026,U_2027)),hAPP(U_2026,U_2028)))
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_2025,U_2024,U_2026)
| ~ class_Orderings_Olinorder(U_2025)
| ~ class_Orderings_Oorder(U_2024) ),
inference(clausify,[status(thm)],[f_592_2]) ).
cnf(f_592_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2024),hAPP(U_2026,U_2027)),hAPP(U_2026,U_2028)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2025),U_2027),U_2028))
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_2025,U_2024,U_2026)
| ~ class_Orderings_Olinorder(U_2025)
| ~ class_Orderings_Oorder(U_2024) ),
inference(clausify,[status(thm)],[f_592_2]) ).
fof(f_593_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_593_2,plain,
! [U_2033,U_2032,U_2031,U_2030,U_2029] :
( ( ( hAPP(c_Set_Oimage(U_2029,U_2030,U_2031),U_2032) = hAPP(c_Set_Oimage(U_2029,U_2030,U_2031),U_2033)
| U_2032 != U_2033 )
& ( U_2032 = U_2033
| hAPP(c_Set_Oimage(U_2029,U_2030,U_2031),U_2032) != hAPP(c_Set_Oimage(U_2029,U_2030,U_2031),U_2033) ) )
| ~ c_Fun_Oinj__on(U_2029,U_2030,U_2031,c_Orderings_Otop__class_Otop(tc_fun(U_2029,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_593_1]) ).
cnf(f_593_3,plain,
( U_2032 = U_2033
| hAPP(c_Set_Oimage(U_2029,U_2030,U_2031),U_2032) != hAPP(c_Set_Oimage(U_2029,U_2030,U_2031),U_2033)
| ~ c_Fun_Oinj__on(U_2029,U_2030,U_2031,c_Orderings_Otop__class_Otop(tc_fun(U_2029,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_593_2]) ).
cnf(f_593_4,plain,
( hAPP(c_Set_Oimage(U_2029,U_2030,U_2031),U_2032) = hAPP(c_Set_Oimage(U_2029,U_2030,U_2031),U_2033)
| U_2032 != U_2033
| ~ c_Fun_Oinj__on(U_2029,U_2030,U_2031,c_Orderings_Otop__class_Otop(tc_fun(U_2029,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_593_2]) ).
fof(f_594_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_594_2,plain,
! [U_2038,U_2037,U_2036,U_2035,U_2034] :
( ( ( hAPP(c_Set_Oimage(U_2034,U_2035,U_2036),U_2037) = hAPP(c_Set_Oimage(U_2034,U_2035,U_2036),U_2038)
| U_2037 != U_2038 )
& ( U_2037 = U_2038
| hAPP(c_Set_Oimage(U_2034,U_2035,U_2036),U_2037) != hAPP(c_Set_Oimage(U_2034,U_2035,U_2036),U_2038) ) )
| ~ c_Fun_Oinj__on(U_2034,U_2035,U_2036,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2034,tc_HOL_Obool)),U_2037),U_2038)) ),
inference(variable_rename,[status(thm)],[f_594_1]) ).
cnf(f_594_3,plain,
( U_2037 = U_2038
| hAPP(c_Set_Oimage(U_2034,U_2035,U_2036),U_2037) != hAPP(c_Set_Oimage(U_2034,U_2035,U_2036),U_2038)
| ~ c_Fun_Oinj__on(U_2034,U_2035,U_2036,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2034,tc_HOL_Obool)),U_2037),U_2038)) ),
inference(clausify,[status(thm)],[f_594_2]) ).
cnf(f_594_4,plain,
( hAPP(c_Set_Oimage(U_2034,U_2035,U_2036),U_2037) = hAPP(c_Set_Oimage(U_2034,U_2035,U_2036),U_2038)
| U_2037 != U_2038
| ~ c_Fun_Oinj__on(U_2034,U_2035,U_2036,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2034,tc_HOL_Obool)),U_2037),U_2038)) ),
inference(clausify,[status(thm)],[f_594_2]) ).
fof(f_595_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_595_2,plain,
! [U_2041,U_2040,U_2039] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2039),U_2040),U_2041))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2039),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2039),U_2040),U_2041)),c_Groups_Ozero__class_Ozero(U_2039))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2039),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2039),U_2040),U_2041)),c_Groups_Ozero__class_Ozero(U_2039)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2039),U_2040),U_2041)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2039) ),
inference(variable_rename,[status(thm)],[f_595_1]) ).
cnf(f_595_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2039),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2039),U_2040),U_2041)),c_Groups_Ozero__class_Ozero(U_2039)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2039),U_2040),U_2041))
| ~ class_Groups_Oordered__ab__group__add(U_2039) ),
inference(clausify,[status(thm)],[f_595_2]) ).
cnf(f_595_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2039),U_2040),U_2041))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2039),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2039),U_2040),U_2041)),c_Groups_Ozero__class_Ozero(U_2039)))
| ~ class_Groups_Oordered__ab__group__add(U_2039) ),
inference(clausify,[status(thm)],[f_595_2]) ).
fof(f_596_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_596_2,plain,
! [U_2043,U_2042] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2042),U_2043) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2042),U_2043)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2042),U_2043))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2042),U_2043) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_596_1]) ).
fof(f_596_3,plain,
( ! [U_2047,U_2045] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2045),U_2047) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2045),U_2047)) )
& ! [U_2046,U_2044] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2044),U_2046))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2044),U_2046) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_596_2]) ).
cnf(f_596_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2044),U_2046))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2044),U_2046) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_596_3]) ).
cnf(f_596_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2045),U_2047) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2045),U_2047)) ),
inference(clausify,[status(thm)],[f_596_3]) ).
fof(f_597_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_597_2,plain,
! [U_2049,U_2048] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2048),U_2049) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2048),U_2049)) ),
inference(variable_rename,[status(thm)],[f_597_1]) ).
cnf(f_597_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2048),U_2049) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2048),U_2049)) ),
inference(clausify,[status(thm)],[f_597_2]) ).
fof(f_598_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_598_2,plain,
! [U_2051,U_2050] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2051)),U_2050) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2051),U_2050))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2050),U_2051)) ),
inference(variable_rename,[status(thm)],[f_598_1]) ).
cnf(f_598_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2051)),U_2050) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2051),U_2050))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2050),U_2051)) ),
inference(clausify,[status(thm)],[f_598_2]) ).
fof(f_599_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_599_2,plain,
! [U_2053,U_2052] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2052),hAPP(c_Groups_Ouminus__class_Ouminus(U_2052),U_2053)),U_2053))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2052),c_Groups_Ozero__class_Ozero(U_2052)),U_2053)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2052),c_Groups_Ozero__class_Ozero(U_2052)),U_2053))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2052),hAPP(c_Groups_Ouminus__class_Ouminus(U_2052),U_2053)),U_2053)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_2052) ),
inference(variable_rename,[status(thm)],[f_599_1]) ).
cnf(f_599_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2052),c_Groups_Ozero__class_Ozero(U_2052)),U_2053))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2052),hAPP(c_Groups_Ouminus__class_Ouminus(U_2052),U_2053)),U_2053))
| ~ class_Groups_Olinordered__ab__group__add(U_2052) ),
inference(clausify,[status(thm)],[f_599_2]) ).
cnf(f_599_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2052),hAPP(c_Groups_Ouminus__class_Ouminus(U_2052),U_2053)),U_2053))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2052),c_Groups_Ozero__class_Ozero(U_2052)),U_2053))
| ~ class_Groups_Olinordered__ab__group__add(U_2052) ),
inference(clausify,[status(thm)],[f_599_2]) ).
fof(f_600_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_600_2,plain,
! [U_2055,U_2054] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2054),hAPP(c_Groups_Ouminus__class_Ouminus(U_2054),U_2055)),c_Groups_Ozero__class_Ozero(U_2054)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2054),c_Groups_Ozero__class_Ozero(U_2054)),U_2055)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2054),c_Groups_Ozero__class_Ozero(U_2054)),U_2055))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2054),hAPP(c_Groups_Ouminus__class_Ouminus(U_2054),U_2055)),c_Groups_Ozero__class_Ozero(U_2054))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2054) ),
inference(variable_rename,[status(thm)],[f_600_1]) ).
cnf(f_600_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2054),c_Groups_Ozero__class_Ozero(U_2054)),U_2055))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2054),hAPP(c_Groups_Ouminus__class_Ouminus(U_2054),U_2055)),c_Groups_Ozero__class_Ozero(U_2054)))
| ~ class_Groups_Oordered__ab__group__add(U_2054) ),
inference(clausify,[status(thm)],[f_600_2]) ).
cnf(f_600_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2054),hAPP(c_Groups_Ouminus__class_Ouminus(U_2054),U_2055)),c_Groups_Ozero__class_Ozero(U_2054)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2054),c_Groups_Ozero__class_Ozero(U_2054)),U_2055))
| ~ class_Groups_Oordered__ab__group__add(U_2054) ),
inference(clausify,[status(thm)],[f_600_2]) ).
fof(f_601_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_601_2,plain,
! [U_2057,U_2056] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2056),c_Groups_Ozero__class_Ozero(U_2056)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2056),U_2057)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2056),U_2057),c_Groups_Ozero__class_Ozero(U_2056))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2056),U_2057),c_Groups_Ozero__class_Ozero(U_2056)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2056),c_Groups_Ozero__class_Ozero(U_2056)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2056),U_2057))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2056) ),
inference(variable_rename,[status(thm)],[f_601_1]) ).
cnf(f_601_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2056),U_2057),c_Groups_Ozero__class_Ozero(U_2056)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2056),c_Groups_Ozero__class_Ozero(U_2056)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2056),U_2057)))
| ~ class_Groups_Oordered__ab__group__add(U_2056) ),
inference(clausify,[status(thm)],[f_601_2]) ).
cnf(f_601_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2056),c_Groups_Ozero__class_Ozero(U_2056)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2056),U_2057)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2056),U_2057),c_Groups_Ozero__class_Ozero(U_2056)))
| ~ class_Groups_Oordered__ab__group__add(U_2056) ),
inference(clausify,[status(thm)],[f_601_2]) ).
fof(f_602_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_602_2,plain,
! [U_2061,U_2060] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2060),hAPP(c_Nat_OSuc,U_2061)))
| ( ! [U_2059] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2059),U_2061))
| U_2060 != hAPP(c_Nat_OSuc,U_2059) )
& U_2060 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ? [U_2058] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2058),U_2061))
& U_2060 = hAPP(c_Nat_OSuc,U_2058) )
| U_2060 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2060),hAPP(c_Nat_OSuc,U_2061))) ) ),
inference(variable_rename,[status(thm)],[f_602_1]) ).
fof(f_602_3,plain,
( ! [U_2065,U_2063] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2063),hAPP(c_Nat_OSuc,U_2065)))
| ( ! [U_2059] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2059),U_2065))
| U_2063 != hAPP(c_Nat_OSuc,U_2059) )
& U_2063 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_2064,U_2062] :
( ? [U_2058] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2058),U_2064))
& U_2062 = hAPP(c_Nat_OSuc,U_2058) )
| U_2062 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2062),hAPP(c_Nat_OSuc,U_2064))) ) ),
inference(miniscope,[status(thm)],[f_602_2]) ).
fof(f_602_4,plain,
( ! [U_2065,U_2063] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2063),hAPP(c_Nat_OSuc,U_2065)))
| ( ! [U_2059] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2059),U_2065))
| U_2063 != hAPP(c_Nat_OSuc,U_2059) )
& U_2063 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_2064,U_2062] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK32(U_2064,U_2062)),U_2064))
& U_2062 = hAPP(c_Nat_OSuc,sK32(U_2064,U_2062)) )
| U_2062 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2062),hAPP(c_Nat_OSuc,U_2064))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_2058,sK32(U_2064,U_2062))],[f_602_3]) ).
cnf(f_602_5,plain,
( U_2062 = hAPP(c_Nat_OSuc,sK32(U_2064,U_2062))
| U_2062 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2062),hAPP(c_Nat_OSuc,U_2064))) ),
inference(clausify,[status(thm)],[f_602_4]) ).
cnf(f_602_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK32(U_2064,U_2062)),U_2064))
| U_2062 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2062),hAPP(c_Nat_OSuc,U_2064))) ),
inference(clausify,[status(thm)],[f_602_4]) ).
cnf(f_602_7,plain,
( U_2063 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2063),hAPP(c_Nat_OSuc,U_2065))) ),
inference(clausify,[status(thm)],[f_602_4]) ).
cnf(f_602_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2059),U_2065))
| U_2063 != hAPP(c_Nat_OSuc,U_2059)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2063),hAPP(c_Nat_OSuc,U_2065))) ),
inference(clausify,[status(thm)],[f_602_4]) ).
fof(f_603_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_603_2,plain,
! [U_2066] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2066),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| U_2066 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2066 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2066),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(variable_rename,[status(thm)],[f_603_1]) ).
fof(f_603_3,plain,
( ! [U_2068] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2068),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| U_2068 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2067] :
( U_2067 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2067),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(miniscope,[status(thm)],[f_603_2]) ).
cnf(f_603_4,plain,
( U_2067 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2067),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(clausify,[status(thm)],[f_603_3]) ).
cnf(f_603_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2068),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| U_2068 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_603_3]) ).
fof(f_604_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_604_2,plain,
! [U_2071] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2071))
| ! [U_2070] : U_2071 != hAPP(c_Nat_OSuc,U_2070) )
& ( ? [U_2069] : U_2071 = hAPP(c_Nat_OSuc,U_2069)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2071)) ) ),
inference(variable_rename,[status(thm)],[f_604_1]) ).
fof(f_604_3,plain,
( ! [U_2073] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2073))
| ! [U_2070] : U_2073 != hAPP(c_Nat_OSuc,U_2070) )
& ! [U_2072] :
( ? [U_2069] : U_2072 = hAPP(c_Nat_OSuc,U_2069)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2072)) ) ),
inference(miniscope,[status(thm)],[f_604_2]) ).
fof(f_604_4,plain,
( ! [U_2073] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2073))
| ! [U_2070] : U_2073 != hAPP(c_Nat_OSuc,U_2070) )
& ! [U_2072] :
( U_2072 = hAPP(c_Nat_OSuc,sK33(U_2072))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2072)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_2069,sK33(U_2072))],[f_604_3]) ).
cnf(f_604_5,plain,
( U_2072 = hAPP(c_Nat_OSuc,sK33(U_2072))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2072)) ),
inference(clausify,[status(thm)],[f_604_4]) ).
cnf(f_604_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2073))
| U_2073 != hAPP(c_Nat_OSuc,U_2070) ),
inference(clausify,[status(thm)],[f_604_4]) ).
fof(f_605_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_605_2,plain,
! [U_2076,U_2075,U_2074] :
( c_SetInterval_Oord__class_OatLeastAtMost(U_2074,U_2076,U_2075) = c_Orderings_Obot__class_Obot(tc_fun(U_2074,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2074),U_2075),U_2076))
| ~ class_Orderings_Oorder(U_2074) ),
inference(variable_rename,[status(thm)],[f_605_1]) ).
cnf(f_605_3,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(U_2074,U_2076,U_2075) = c_Orderings_Obot__class_Obot(tc_fun(U_2074,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2074),U_2075),U_2076))
| ~ class_Orderings_Oorder(U_2074) ),
inference(clausify,[status(thm)],[f_605_2]) ).
fof(f_606_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_606_2,plain,
! [U_2078,U_2077] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2077),U_2078))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2077)),U_2078)) ),
inference(variable_rename,[status(thm)],[f_606_1]) ).
cnf(f_606_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2077),U_2078))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2077)),U_2078)) ),
inference(clausify,[status(thm)],[f_606_2]) ).
fof(f_607_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_607_2,plain,
! [U_2080,U_2079] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2080),hAPP(c_Nat_OSuc,U_2079)))
| U_2080 != U_2079 )
& ( U_2080 = U_2079
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2080),hAPP(c_Nat_OSuc,U_2079))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2079),U_2080)) ),
inference(variable_rename,[status(thm)],[f_607_1]) ).
cnf(f_607_3,plain,
( U_2080 = U_2079
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2080),hAPP(c_Nat_OSuc,U_2079)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2079),U_2080)) ),
inference(clausify,[status(thm)],[f_607_2]) ).
cnf(f_607_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2080),hAPP(c_Nat_OSuc,U_2079)))
| U_2080 != U_2079
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2079),U_2080)) ),
inference(clausify,[status(thm)],[f_607_2]) ).
fof(f_608_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_608_2,plain,
! [U_2082,U_2081] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2081)),U_2082))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2081),U_2082)) ),
inference(variable_rename,[status(thm)],[f_608_1]) ).
cnf(f_608_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2081)),U_2082))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2081),U_2082)) ),
inference(clausify,[status(thm)],[f_608_2]) ).
fof(f_609_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_609_2,plain,
! [U_2084,U_2083] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2083),hAPP(c_Nat_OSuc,U_2084)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2083),U_2084)) ),
inference(variable_rename,[status(thm)],[f_609_1]) ).
cnf(f_609_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2083),hAPP(c_Nat_OSuc,U_2084)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2083),U_2084)) ),
inference(clausify,[status(thm)],[f_609_2]) ).
fof(f_610_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_610_2,plain,
! [U_2086,U_2085] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2085)),U_2086))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2085),U_2086)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2085),U_2086))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2085)),U_2086)) ) ),
inference(variable_rename,[status(thm)],[f_610_1]) ).
fof(f_610_3,plain,
( ! [U_2090,U_2088] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2088)),U_2090))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2088),U_2090)) )
& ! [U_2089,U_2087] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2087),U_2089))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2087)),U_2089)) ) ),
inference(miniscope,[status(thm)],[f_610_2]) ).
cnf(f_610_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2087),U_2089))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2087)),U_2089)) ),
inference(clausify,[status(thm)],[f_610_3]) ).
cnf(f_610_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2088)),U_2090))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2088),U_2090)) ),
inference(clausify,[status(thm)],[f_610_3]) ).
fof(f_611_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_611_2,plain,
! [U_2092,U_2091] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2091),hAPP(c_Nat_OSuc,U_2092)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2091),U_2092)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2091),U_2092))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2091),hAPP(c_Nat_OSuc,U_2092))) ) ),
inference(variable_rename,[status(thm)],[f_611_1]) ).
fof(f_611_3,plain,
( ! [U_2096,U_2094] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2094),hAPP(c_Nat_OSuc,U_2096)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2094),U_2096)) )
& ! [U_2095,U_2093] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2093),U_2095))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2093),hAPP(c_Nat_OSuc,U_2095))) ) ),
inference(miniscope,[status(thm)],[f_611_2]) ).
cnf(f_611_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2093),U_2095))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2093),hAPP(c_Nat_OSuc,U_2095))) ),
inference(clausify,[status(thm)],[f_611_3]) ).
cnf(f_611_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2094),hAPP(c_Nat_OSuc,U_2096)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2094),U_2096)) ),
inference(clausify,[status(thm)],[f_611_3]) ).
fof(f_612_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_612_2,plain,
! [U_2098,U_2097] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2097),U_2098))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2097)),U_2098)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2097)),U_2098))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2097),U_2098)) ) ),
inference(variable_rename,[status(thm)],[f_612_1]) ).
fof(f_612_3,plain,
( ! [U_2102,U_2100] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2100),U_2102))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2100)),U_2102)) )
& ! [U_2101,U_2099] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2099)),U_2101))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2099),U_2101)) ) ),
inference(miniscope,[status(thm)],[f_612_2]) ).
cnf(f_612_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2099)),U_2101))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2099),U_2101)) ),
inference(clausify,[status(thm)],[f_612_3]) ).
cnf(f_612_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2100),U_2102))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2100)),U_2102)) ),
inference(clausify,[status(thm)],[f_612_3]) ).
fof(f_613_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_613_2,plain,
! [U_2105,U_2104,U_2103] :
( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2103,U_2104),U_2105) = c_Orderings_Obot__class_Obot(tc_fun(U_2103,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2103),U_2104),U_2105)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2103),U_2104),U_2105))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2103,U_2104),U_2105) != c_Orderings_Obot__class_Obot(tc_fun(U_2103,tc_HOL_Obool)) ) )
| ~ class_Orderings_Oorder(U_2103) ),
inference(variable_rename,[status(thm)],[f_613_1]) ).
cnf(f_613_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2103),U_2104),U_2105))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2103,U_2104),U_2105) != c_Orderings_Obot__class_Obot(tc_fun(U_2103,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_2103) ),
inference(clausify,[status(thm)],[f_613_2]) ).
cnf(f_613_4,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2103,U_2104),U_2105) = c_Orderings_Obot__class_Obot(tc_fun(U_2103,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2103),U_2104),U_2105))
| ~ class_Orderings_Oorder(U_2103) ),
inference(clausify,[status(thm)],[f_613_2]) ).
fof(f_614_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_614_2,plain,
! [U_2108,U_2107,U_2106] :
( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_2106,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2106,U_2107),U_2108)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2106),U_2107),U_2108)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2106),U_2107),U_2108))
| c_Orderings_Obot__class_Obot(tc_fun(U_2106,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2106,U_2107),U_2108) ) )
| ~ class_Orderings_Oorder(U_2106) ),
inference(variable_rename,[status(thm)],[f_614_1]) ).
cnf(f_614_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2106),U_2107),U_2108))
| c_Orderings_Obot__class_Obot(tc_fun(U_2106,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2106,U_2107),U_2108)
| ~ class_Orderings_Oorder(U_2106) ),
inference(clausify,[status(thm)],[f_614_2]) ).
cnf(f_614_4,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_2106,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2106,U_2107),U_2108)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2106),U_2107),U_2108))
| ~ class_Orderings_Oorder(U_2106) ),
inference(clausify,[status(thm)],[f_614_2]) ).
fof(f_615_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_615_2,plain,
! [U_2111,U_2110,U_2109] :
( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_2109,U_2110,U_2111) = c_Orderings_Obot__class_Obot(tc_fun(U_2109,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2109),U_2110),U_2111)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2109),U_2110),U_2111))
| c_SetInterval_Oord__class_OgreaterThanAtMost(U_2109,U_2110,U_2111) != c_Orderings_Obot__class_Obot(tc_fun(U_2109,tc_HOL_Obool)) ) )
| ~ class_Orderings_Oorder(U_2109) ),
inference(variable_rename,[status(thm)],[f_615_1]) ).
cnf(f_615_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2109),U_2110),U_2111))
| c_SetInterval_Oord__class_OgreaterThanAtMost(U_2109,U_2110,U_2111) != c_Orderings_Obot__class_Obot(tc_fun(U_2109,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_2109) ),
inference(clausify,[status(thm)],[f_615_2]) ).
cnf(f_615_4,plain,
( c_SetInterval_Oord__class_OgreaterThanAtMost(U_2109,U_2110,U_2111) = c_Orderings_Obot__class_Obot(tc_fun(U_2109,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2109),U_2110),U_2111))
| ~ class_Orderings_Oorder(U_2109) ),
inference(clausify,[status(thm)],[f_615_2]) ).
fof(f_616_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_616_2,plain,
! [U_2114,U_2113,U_2112] :
( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_2112,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_2112,U_2113,U_2114)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2112),U_2113),U_2114)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2112),U_2113),U_2114))
| c_Orderings_Obot__class_Obot(tc_fun(U_2112,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_2112,U_2113,U_2114) ) )
| ~ class_Orderings_Oorder(U_2112) ),
inference(variable_rename,[status(thm)],[f_616_1]) ).
cnf(f_616_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2112),U_2113),U_2114))
| c_Orderings_Obot__class_Obot(tc_fun(U_2112,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_2112,U_2113,U_2114)
| ~ class_Orderings_Oorder(U_2112) ),
inference(clausify,[status(thm)],[f_616_2]) ).
cnf(f_616_4,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_2112,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_2112,U_2113,U_2114)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2112),U_2113),U_2114))
| ~ class_Orderings_Oorder(U_2112) ),
inference(clausify,[status(thm)],[f_616_2]) ).
fof(f_617_1,plain,
! [V_P_2,V_n_2] :
( ( ? [B_m] :
( hBOOL(hAPP(V_P_2,B_m))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) )
| ! [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) ) )
& ( ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) )
| ! [B_m] :
( ~ hBOOL(hAPP(V_P_2,B_m))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_ex__nat__less__eq]) ).
fof(f_617_2,plain,
! [U_2120,U_2119] :
( ( ? [U_2118] :
( hBOOL(hAPP(U_2120,U_2118))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2118),U_2119)) )
| ! [U_2117] :
( ~ hBOOL(hAPP(U_2120,U_2117))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_2117),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2119))) ) )
& ( ? [U_2116] :
( hBOOL(hAPP(U_2120,U_2116))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_2116),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2119))) )
| ! [U_2115] :
( ~ hBOOL(hAPP(U_2120,U_2115))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2115),U_2119)) ) ) ),
inference(variable_rename,[status(thm)],[f_617_1]) ).
fof(f_617_3,plain,
( ! [U_2124,U_2122] :
( ? [U_2118] :
( hBOOL(hAPP(U_2124,U_2118))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2118),U_2122)) )
| ! [U_2117] :
( ~ hBOOL(hAPP(U_2124,U_2117))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_2117),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2122))) ) )
& ! [U_2123,U_2121] :
( ? [U_2116] :
( hBOOL(hAPP(U_2123,U_2116))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_2116),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2121))) )
| ! [U_2115] :
( ~ hBOOL(hAPP(U_2123,U_2115))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2115),U_2121)) ) ) ),
inference(miniscope,[status(thm)],[f_617_2]) ).
fof(f_617_4,plain,
( ! [U_2124,U_2122] :
( ? [U_2118] :
( hBOOL(hAPP(U_2124,U_2118))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2118),U_2122)) )
| ! [U_2117] :
( ~ hBOOL(hAPP(U_2124,U_2117))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_2117),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2122))) ) )
& ! [U_2123,U_2121] :
( ( hBOOL(hAPP(U_2123,sK34(U_2123,U_2121)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK34(U_2123,U_2121)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2121))) )
| ! [U_2115] :
( ~ hBOOL(hAPP(U_2123,U_2115))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2115),U_2121)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_2116,sK34(U_2123,U_2121))],[f_617_3]) ).
fof(f_617_5,plain,
( ! [U_2124,U_2122] :
( ( hBOOL(hAPP(U_2124,sK35(U_2124,U_2122)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK35(U_2124,U_2122)),U_2122)) )
| ! [U_2117] :
( ~ hBOOL(hAPP(U_2124,U_2117))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_2117),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2122))) ) )
& ! [U_2123,U_2121] :
( ( hBOOL(hAPP(U_2123,sK34(U_2123,U_2121)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK34(U_2123,U_2121)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2121))) )
| ! [U_2115] :
( ~ hBOOL(hAPP(U_2123,U_2115))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2115),U_2121)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_2118,sK35(U_2124,U_2122))],[f_617_4]) ).
cnf(f_617_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK34(U_2123,U_2121)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2121)))
| ~ hBOOL(hAPP(U_2123,U_2115))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2115),U_2121)) ),
inference(clausify,[status(thm)],[f_617_5]) ).
cnf(f_617_7,plain,
( hBOOL(hAPP(U_2123,sK34(U_2123,U_2121)))
| ~ hBOOL(hAPP(U_2123,U_2115))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2115),U_2121)) ),
inference(clausify,[status(thm)],[f_617_5]) ).
cnf(f_617_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK35(U_2124,U_2122)),U_2122))
| ~ hBOOL(hAPP(U_2124,U_2117))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_2117),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2122))) ),
inference(clausify,[status(thm)],[f_617_5]) ).
cnf(f_617_9,plain,
( hBOOL(hAPP(U_2124,sK35(U_2124,U_2122)))
| ~ hBOOL(hAPP(U_2124,U_2117))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_2117),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2122))) ),
inference(clausify,[status(thm)],[f_617_5]) ).
fof(f_618_1,plain,
! [V_P_2,V_n_2] :
( ( ! [B_m] :
( hBOOL(hAPP(V_P_2,B_m))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) )
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) ) )
& ( ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) )
| ? [B_m] :
( ~ hBOOL(hAPP(V_P_2,B_m))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_all__nat__less__eq]) ).
fof(f_618_2,plain,
! [U_2130,U_2129] :
( ( ! [U_2128] :
( hBOOL(hAPP(U_2130,U_2128))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2128),U_2129)) )
| ? [U_2127] :
( ~ hBOOL(hAPP(U_2130,U_2127))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_2127),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2129))) ) )
& ( ! [U_2126] :
( hBOOL(hAPP(U_2130,U_2126))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_2126),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2129))) )
| ? [U_2125] :
( ~ hBOOL(hAPP(U_2130,U_2125))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2125),U_2129)) ) ) ),
inference(variable_rename,[status(thm)],[f_618_1]) ).
fof(f_618_3,plain,
( ! [U_2134,U_2132] :
( ! [U_2128] :
( hBOOL(hAPP(U_2134,U_2128))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2128),U_2132)) )
| ? [U_2127] :
( ~ hBOOL(hAPP(U_2134,U_2127))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_2127),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2132))) ) )
& ! [U_2133,U_2131] :
( ! [U_2126] :
( hBOOL(hAPP(U_2133,U_2126))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_2126),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2131))) )
| ? [U_2125] :
( ~ hBOOL(hAPP(U_2133,U_2125))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2125),U_2131)) ) ) ),
inference(miniscope,[status(thm)],[f_618_2]) ).
fof(f_618_4,plain,
( ! [U_2134,U_2132] :
( ! [U_2128] :
( hBOOL(hAPP(U_2134,U_2128))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2128),U_2132)) )
| ? [U_2127] :
( ~ hBOOL(hAPP(U_2134,U_2127))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_2127),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2132))) ) )
& ! [U_2133,U_2131] :
( ! [U_2126] :
( hBOOL(hAPP(U_2133,U_2126))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_2126),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2131))) )
| ( ~ hBOOL(hAPP(U_2133,sK36(U_2133,U_2131)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK36(U_2133,U_2131)),U_2131)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_2125,sK36(U_2133,U_2131))],[f_618_3]) ).
fof(f_618_5,plain,
( ! [U_2134,U_2132] :
( ! [U_2128] :
( hBOOL(hAPP(U_2134,U_2128))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2128),U_2132)) )
| ( ~ hBOOL(hAPP(U_2134,sK37(U_2134,U_2132)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK37(U_2134,U_2132)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2132))) ) )
& ! [U_2133,U_2131] :
( ! [U_2126] :
( hBOOL(hAPP(U_2133,U_2126))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_2126),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2131))) )
| ( ~ hBOOL(hAPP(U_2133,sK36(U_2133,U_2131)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK36(U_2133,U_2131)),U_2131)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_2127,sK37(U_2134,U_2132))],[f_618_4]) ).
cnf(f_618_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK36(U_2133,U_2131)),U_2131))
| hBOOL(hAPP(U_2133,U_2126))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_2126),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2131))) ),
inference(clausify,[status(thm)],[f_618_5]) ).
cnf(f_618_7,plain,
( ~ hBOOL(hAPP(U_2133,sK36(U_2133,U_2131)))
| hBOOL(hAPP(U_2133,U_2126))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_2126),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2131))) ),
inference(clausify,[status(thm)],[f_618_5]) ).
cnf(f_618_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK37(U_2134,U_2132)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2132)))
| hBOOL(hAPP(U_2134,U_2128))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2128),U_2132)) ),
inference(clausify,[status(thm)],[f_618_5]) ).
cnf(f_618_9,plain,
( ~ hBOOL(hAPP(U_2134,sK37(U_2134,U_2132)))
| hBOOL(hAPP(U_2134,U_2128))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2128),U_2132)) ),
inference(clausify,[status(thm)],[f_618_5]) ).
fof(f_619_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_619_2,plain,
! [U_2139,U_2138,U_2137,U_2136,U_2135] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2136,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2135,U_2136,U_2137),U_2138)),hAPP(c_Set_Oimage(U_2135,U_2136,U_2137),U_2139)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2135,tc_HOL_Obool)),U_2138),U_2139)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2135,tc_HOL_Obool)),U_2138),U_2139))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2136,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2135,U_2136,U_2137),U_2138)),hAPP(c_Set_Oimage(U_2135,U_2136,U_2137),U_2139))) ) )
| ~ c_Fun_Oinj__on(U_2135,U_2136,U_2137,c_Orderings_Otop__class_Otop(tc_fun(U_2135,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_619_1]) ).
cnf(f_619_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2135,tc_HOL_Obool)),U_2138),U_2139))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2136,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2135,U_2136,U_2137),U_2138)),hAPP(c_Set_Oimage(U_2135,U_2136,U_2137),U_2139)))
| ~ c_Fun_Oinj__on(U_2135,U_2136,U_2137,c_Orderings_Otop__class_Otop(tc_fun(U_2135,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_619_2]) ).
cnf(f_619_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2136,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2135,U_2136,U_2137),U_2138)),hAPP(c_Set_Oimage(U_2135,U_2136,U_2137),U_2139)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2135,tc_HOL_Obool)),U_2138),U_2139))
| ~ c_Fun_Oinj__on(U_2135,U_2136,U_2137,c_Orderings_Otop__class_Otop(tc_fun(U_2135,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_619_2]) ).
fof(f_620_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_620_2,plain,
! [U_2145,U_2144,U_2143,U_2142,U_2141,U_2140] :
( hAPP(c_Set_Oimage(U_2140,U_2141,U_2142),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2140,tc_HOL_Obool)),U_2144),U_2145)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2141,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2140,U_2141,U_2142),U_2144)),hAPP(c_Set_Oimage(U_2140,U_2141,U_2142),U_2145))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2140,tc_HOL_Obool)),U_2145),U_2143))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2140,tc_HOL_Obool)),U_2144),U_2143))
| ~ c_Fun_Oinj__on(U_2140,U_2141,U_2142,U_2143) ),
inference(variable_rename,[status(thm)],[f_620_1]) ).
cnf(f_620_3,plain,
( hAPP(c_Set_Oimage(U_2140,U_2141,U_2142),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2140,tc_HOL_Obool)),U_2144),U_2145)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2141,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2140,U_2141,U_2142),U_2144)),hAPP(c_Set_Oimage(U_2140,U_2141,U_2142),U_2145))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2140,tc_HOL_Obool)),U_2145),U_2143))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2140,tc_HOL_Obool)),U_2144),U_2143))
| ~ c_Fun_Oinj__on(U_2140,U_2141,U_2142,U_2143) ),
inference(clausify,[status(thm)],[f_620_2]) ).
fof(f_621_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_621_2,plain,
! [U_2150,U_2149,U_2148,U_2147,U_2146] :
( hAPP(c_Set_Oimage(U_2146,U_2147,U_2148),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2146,tc_HOL_Obool)),U_2149),U_2150)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2147,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2146,U_2147,U_2148),U_2149)),hAPP(c_Set_Oimage(U_2146,U_2147,U_2148),U_2150))
| ~ c_Fun_Oinj__on(U_2146,U_2147,U_2148,c_Orderings_Otop__class_Otop(tc_fun(U_2146,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_621_1]) ).
cnf(f_621_3,plain,
( hAPP(c_Set_Oimage(U_2146,U_2147,U_2148),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2146,tc_HOL_Obool)),U_2149),U_2150)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2147,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2146,U_2147,U_2148),U_2149)),hAPP(c_Set_Oimage(U_2146,U_2147,U_2148),U_2150))
| ~ c_Fun_Oinj__on(U_2146,U_2147,U_2148,c_Orderings_Otop__class_Otop(tc_fun(U_2146,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_621_2]) ).
fof(f_622_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_622_2,plain,
! [U_2156,U_2155,U_2154,U_2153,U_2152,U_2151] :
( hAPP(c_Set_Oimage(U_2151,U_2152,U_2153),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2151,tc_HOL_Obool)),U_2155),U_2156)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2152,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2151,U_2152,U_2153),U_2155)),hAPP(c_Set_Oimage(U_2151,U_2152,U_2153),U_2156))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2151,tc_HOL_Obool)),U_2156),U_2154))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2151,tc_HOL_Obool)),U_2155),U_2154))
| ~ c_Fun_Oinj__on(U_2151,U_2152,U_2153,U_2154) ),
inference(variable_rename,[status(thm)],[f_622_1]) ).
cnf(f_622_3,plain,
( hAPP(c_Set_Oimage(U_2151,U_2152,U_2153),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2151,tc_HOL_Obool)),U_2155),U_2156)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2152,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2151,U_2152,U_2153),U_2155)),hAPP(c_Set_Oimage(U_2151,U_2152,U_2153),U_2156))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2151,tc_HOL_Obool)),U_2156),U_2154))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2151,tc_HOL_Obool)),U_2155),U_2154))
| ~ c_Fun_Oinj__on(U_2151,U_2152,U_2153,U_2154) ),
inference(clausify,[status(thm)],[f_622_2]) ).
fof(f_623_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_623_2,plain,
! [U_2161,U_2160,U_2159,U_2158,U_2157] :
( hAPP(c_Set_Oimage(U_2157,U_2158,U_2159),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2157,tc_HOL_Obool)),U_2160),U_2161)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2158,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2157,U_2158,U_2159),U_2160)),hAPP(c_Set_Oimage(U_2157,U_2158,U_2159),U_2161))
| ~ c_Fun_Oinj__on(U_2157,U_2158,U_2159,c_Orderings_Otop__class_Otop(tc_fun(U_2157,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_623_1]) ).
cnf(f_623_3,plain,
( hAPP(c_Set_Oimage(U_2157,U_2158,U_2159),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2157,tc_HOL_Obool)),U_2160),U_2161)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2158,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2157,U_2158,U_2159),U_2160)),hAPP(c_Set_Oimage(U_2157,U_2158,U_2159),U_2161))
| ~ c_Fun_Oinj__on(U_2157,U_2158,U_2159,c_Orderings_Otop__class_Otop(tc_fun(U_2157,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_623_2]) ).
fof(f_624_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_624_2,plain,
! [U_2165,U_2164,U_2163,U_2162] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2163,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2162,U_2163,U_2164),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2162,tc_HOL_Obool)),U_2165))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2163,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2162,U_2163,U_2164),U_2165))))
| ~ c_Fun_Oinj__on(U_2162,U_2163,U_2164,c_Orderings_Otop__class_Otop(tc_fun(U_2162,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_624_1]) ).
cnf(f_624_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2163,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2162,U_2163,U_2164),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2162,tc_HOL_Obool)),U_2165))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2163,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2162,U_2163,U_2164),U_2165))))
| ~ c_Fun_Oinj__on(U_2162,U_2163,U_2164,c_Orderings_Otop__class_Otop(tc_fun(U_2162,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_624_2]) ).
fof(f_625_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_625_2,plain,
! [U_2173,U_2172,U_2171,U_2170] :
( ( ( ? [U_2169] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2172,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2171,U_2172,U_2169),U_2170)),U_2173))
& c_Fun_Oinj__on(U_2171,U_2172,U_2169,U_2170) )
| ! [U_2168] : hAPP(c_Set_Oimage(U_2172,U_2171,U_2168),U_2173) != U_2170 )
& ( ? [U_2167] : hAPP(c_Set_Oimage(U_2172,U_2171,U_2167),U_2173) = U_2170
| ! [U_2166] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2172,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2171,U_2172,U_2166),U_2170)),U_2173))
| ~ c_Fun_Oinj__on(U_2171,U_2172,U_2166,U_2170) ) ) )
| U_2170 = c_Orderings_Obot__class_Obot(tc_fun(U_2171,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_625_1]) ).
fof(f_625_3,plain,
! [U_2173,U_2172,U_2171,U_2170] :
( ( ( ? [U_2169] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2172,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2171,U_2172,U_2169),U_2170)),U_2173))
& c_Fun_Oinj__on(U_2171,U_2172,U_2169,U_2170) )
| ! [U_2168] : hAPP(c_Set_Oimage(U_2172,U_2171,U_2168),U_2173) != U_2170 )
& ( hAPP(c_Set_Oimage(U_2172,U_2171,sK38(U_2173,U_2172,U_2171,U_2170)),U_2173) = U_2170
| ! [U_2166] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2172,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2171,U_2172,U_2166),U_2170)),U_2173))
| ~ c_Fun_Oinj__on(U_2171,U_2172,U_2166,U_2170) ) ) )
| U_2170 = c_Orderings_Obot__class_Obot(tc_fun(U_2171,tc_HOL_Obool)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_2167,sK38(U_2173,U_2172,U_2171,U_2170))],[f_625_2]) ).
fof(f_625_4,plain,
! [U_2173,U_2172,U_2171,U_2170] :
( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2172,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2171,U_2172,sK39(U_2173,U_2172,U_2171,U_2170)),U_2170)),U_2173))
& c_Fun_Oinj__on(U_2171,U_2172,sK39(U_2173,U_2172,U_2171,U_2170),U_2170) )
| ! [U_2168] : hAPP(c_Set_Oimage(U_2172,U_2171,U_2168),U_2173) != U_2170 )
& ( hAPP(c_Set_Oimage(U_2172,U_2171,sK38(U_2173,U_2172,U_2171,U_2170)),U_2173) = U_2170
| ! [U_2166] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2172,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2171,U_2172,U_2166),U_2170)),U_2173))
| ~ c_Fun_Oinj__on(U_2171,U_2172,U_2166,U_2170) ) ) )
| U_2170 = c_Orderings_Obot__class_Obot(tc_fun(U_2171,tc_HOL_Obool)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_2169,sK39(U_2173,U_2172,U_2171,U_2170))],[f_625_3]) ).
cnf(f_625_5,plain,
( hAPP(c_Set_Oimage(U_2172,U_2171,sK38(U_2173,U_2172,U_2171,U_2170)),U_2173) = U_2170
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2172,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2171,U_2172,U_2166),U_2170)),U_2173))
| ~ c_Fun_Oinj__on(U_2171,U_2172,U_2166,U_2170)
| U_2170 = c_Orderings_Obot__class_Obot(tc_fun(U_2171,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_625_4]) ).
cnf(f_625_6,plain,
( c_Fun_Oinj__on(U_2171,U_2172,sK39(U_2173,U_2172,U_2171,U_2170),U_2170)
| hAPP(c_Set_Oimage(U_2172,U_2171,U_2168),U_2173) != U_2170
| U_2170 = c_Orderings_Obot__class_Obot(tc_fun(U_2171,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_625_4]) ).
cnf(f_625_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2172,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2171,U_2172,sK39(U_2173,U_2172,U_2171,U_2170)),U_2170)),U_2173))
| hAPP(c_Set_Oimage(U_2172,U_2171,U_2168),U_2173) != U_2170
| U_2170 = c_Orderings_Obot__class_Obot(tc_fun(U_2171,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_625_4]) ).
fof(f_626_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_626_2,plain,
! [U_2175,U_2174] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2174),U_2175),hAPP(c_Groups_Ouminus__class_Ouminus(U_2174),U_2175)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2174),U_2175),c_Groups_Ozero__class_Ozero(U_2174))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2174),U_2175),c_Groups_Ozero__class_Ozero(U_2174)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2174),U_2175),hAPP(c_Groups_Ouminus__class_Ouminus(U_2174),U_2175))) ) )
| ~ class_Rings_Olinordered__idom(U_2174) ),
inference(variable_rename,[status(thm)],[f_626_1]) ).
cnf(f_626_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2174),U_2175),c_Groups_Ozero__class_Ozero(U_2174)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2174),U_2175),hAPP(c_Groups_Ouminus__class_Ouminus(U_2174),U_2175)))
| ~ class_Rings_Olinordered__idom(U_2174) ),
inference(clausify,[status(thm)],[f_626_2]) ).
cnf(f_626_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2174),U_2175),hAPP(c_Groups_Ouminus__class_Ouminus(U_2174),U_2175)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2174),U_2175),c_Groups_Ozero__class_Ozero(U_2174)))
| ~ class_Rings_Olinordered__idom(U_2174) ),
inference(clausify,[status(thm)],[f_626_2]) ).
fof(f_627_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_627_2,plain,
! [U_2180,U_2179,U_2178,U_2177,U_2176] :
( ( c_Fun_Oinj__on(U_2176,U_2177,U_2178,hAPP(hAPP(c_Set_Oinsert(U_2176),U_2179),U_2180))
| hBOOL(hAPP(hAPP(c_member(U_2177),hAPP(U_2178,U_2179)),hAPP(c_Set_Oimage(U_2176,U_2177,U_2178),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2176,tc_HOL_Obool)),U_2180),hAPP(hAPP(c_Set_Oinsert(U_2176),U_2179),c_Orderings_Obot__class_Obot(tc_fun(U_2176,tc_HOL_Obool)))))))
| ~ c_Fun_Oinj__on(U_2176,U_2177,U_2178,U_2180) )
& ( ( ~ hBOOL(hAPP(hAPP(c_member(U_2177),hAPP(U_2178,U_2179)),hAPP(c_Set_Oimage(U_2176,U_2177,U_2178),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2176,tc_HOL_Obool)),U_2180),hAPP(hAPP(c_Set_Oinsert(U_2176),U_2179),c_Orderings_Obot__class_Obot(tc_fun(U_2176,tc_HOL_Obool)))))))
& c_Fun_Oinj__on(U_2176,U_2177,U_2178,U_2180) )
| ~ c_Fun_Oinj__on(U_2176,U_2177,U_2178,hAPP(hAPP(c_Set_Oinsert(U_2176),U_2179),U_2180)) ) ),
inference(variable_rename,[status(thm)],[f_627_1]) ).
fof(f_627_3,plain,
( ! [U_2190,U_2188,U_2186,U_2184,U_2182] :
( c_Fun_Oinj__on(U_2182,U_2184,U_2186,hAPP(hAPP(c_Set_Oinsert(U_2182),U_2188),U_2190))
| hBOOL(hAPP(hAPP(c_member(U_2184),hAPP(U_2186,U_2188)),hAPP(c_Set_Oimage(U_2182,U_2184,U_2186),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2182,tc_HOL_Obool)),U_2190),hAPP(hAPP(c_Set_Oinsert(U_2182),U_2188),c_Orderings_Obot__class_Obot(tc_fun(U_2182,tc_HOL_Obool)))))))
| ~ c_Fun_Oinj__on(U_2182,U_2184,U_2186,U_2190) )
& ! [U_2189,U_2187,U_2185,U_2183,U_2181] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_2183),hAPP(U_2185,U_2187)),hAPP(c_Set_Oimage(U_2181,U_2183,U_2185),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2181,tc_HOL_Obool)),U_2189),hAPP(hAPP(c_Set_Oinsert(U_2181),U_2187),c_Orderings_Obot__class_Obot(tc_fun(U_2181,tc_HOL_Obool)))))))
& c_Fun_Oinj__on(U_2181,U_2183,U_2185,U_2189) )
| ~ c_Fun_Oinj__on(U_2181,U_2183,U_2185,hAPP(hAPP(c_Set_Oinsert(U_2181),U_2187),U_2189)) ) ),
inference(miniscope,[status(thm)],[f_627_2]) ).
cnf(f_627_4,plain,
( c_Fun_Oinj__on(U_2181,U_2183,U_2185,U_2189)
| ~ c_Fun_Oinj__on(U_2181,U_2183,U_2185,hAPP(hAPP(c_Set_Oinsert(U_2181),U_2187),U_2189)) ),
inference(clausify,[status(thm)],[f_627_3]) ).
cnf(f_627_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2183),hAPP(U_2185,U_2187)),hAPP(c_Set_Oimage(U_2181,U_2183,U_2185),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2181,tc_HOL_Obool)),U_2189),hAPP(hAPP(c_Set_Oinsert(U_2181),U_2187),c_Orderings_Obot__class_Obot(tc_fun(U_2181,tc_HOL_Obool)))))))
| ~ c_Fun_Oinj__on(U_2181,U_2183,U_2185,hAPP(hAPP(c_Set_Oinsert(U_2181),U_2187),U_2189)) ),
inference(clausify,[status(thm)],[f_627_3]) ).
cnf(f_627_6,plain,
( c_Fun_Oinj__on(U_2182,U_2184,U_2186,hAPP(hAPP(c_Set_Oinsert(U_2182),U_2188),U_2190))
| hBOOL(hAPP(hAPP(c_member(U_2184),hAPP(U_2186,U_2188)),hAPP(c_Set_Oimage(U_2182,U_2184,U_2186),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2182,tc_HOL_Obool)),U_2190),hAPP(hAPP(c_Set_Oinsert(U_2182),U_2188),c_Orderings_Obot__class_Obot(tc_fun(U_2182,tc_HOL_Obool)))))))
| ~ c_Fun_Oinj__on(U_2182,U_2184,U_2186,U_2190) ),
inference(clausify,[status(thm)],[f_627_3]) ).
fof(f_628_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_628_2,plain,
! [U_2194,U_2193,U_2192,U_2191] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2191,tc_HOL_Obool)),U_2192),hAPP(hAPP(c_Set_Oinsert(U_2191),U_2193),U_2194)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2191,tc_HOL_Obool)),U_2192),U_2194))
& ~ hBOOL(hAPP(hAPP(c_member(U_2191),U_2193),U_2192)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2191,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2191,tc_HOL_Obool)),U_2192),hAPP(hAPP(c_Set_Oinsert(U_2191),U_2193),c_Orderings_Obot__class_Obot(tc_fun(U_2191,tc_HOL_Obool))))),U_2194))
& hBOOL(hAPP(hAPP(c_member(U_2191),U_2193),U_2192)) ) )
& ~ hBOOL(hAPP(hAPP(c_member(U_2191),U_2193),U_2194)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2191,tc_HOL_Obool)),U_2192),U_2194))
& hBOOL(hAPP(hAPP(c_member(U_2191),U_2193),U_2194)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2191,tc_HOL_Obool)),U_2192),U_2194))
| hBOOL(hAPP(hAPP(c_member(U_2191),U_2193),U_2192)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2191,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2191,tc_HOL_Obool)),U_2192),hAPP(hAPP(c_Set_Oinsert(U_2191),U_2193),c_Orderings_Obot__class_Obot(tc_fun(U_2191,tc_HOL_Obool))))),U_2194))
| ~ hBOOL(hAPP(hAPP(c_member(U_2191),U_2193),U_2192)) ) )
| hBOOL(hAPP(hAPP(c_member(U_2191),U_2193),U_2194)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2191,tc_HOL_Obool)),U_2192),U_2194))
| ~ hBOOL(hAPP(hAPP(c_member(U_2191),U_2193),U_2194)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2191,tc_HOL_Obool)),U_2192),hAPP(hAPP(c_Set_Oinsert(U_2191),U_2193),U_2194))) ) ),
inference(variable_rename,[status(thm)],[f_628_1]) ).
fof(f_628_3,plain,
( ! [U_2202,U_2200,U_2198,U_2196] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2196,tc_HOL_Obool)),U_2198),hAPP(hAPP(c_Set_Oinsert(U_2196),U_2200),U_2202)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2196,tc_HOL_Obool)),U_2198),U_2202))
& ~ hBOOL(hAPP(hAPP(c_member(U_2196),U_2200),U_2198)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2196,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2196,tc_HOL_Obool)),U_2198),hAPP(hAPP(c_Set_Oinsert(U_2196),U_2200),c_Orderings_Obot__class_Obot(tc_fun(U_2196,tc_HOL_Obool))))),U_2202))
& hBOOL(hAPP(hAPP(c_member(U_2196),U_2200),U_2198)) ) )
& ~ hBOOL(hAPP(hAPP(c_member(U_2196),U_2200),U_2202)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2196,tc_HOL_Obool)),U_2198),U_2202))
& hBOOL(hAPP(hAPP(c_member(U_2196),U_2200),U_2202)) ) )
& ! [U_2201,U_2199,U_2197,U_2195] :
( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2195,tc_HOL_Obool)),U_2197),U_2201))
| hBOOL(hAPP(hAPP(c_member(U_2195),U_2199),U_2197)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2195,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2195,tc_HOL_Obool)),U_2197),hAPP(hAPP(c_Set_Oinsert(U_2195),U_2199),c_Orderings_Obot__class_Obot(tc_fun(U_2195,tc_HOL_Obool))))),U_2201))
| ~ hBOOL(hAPP(hAPP(c_member(U_2195),U_2199),U_2197)) ) )
| hBOOL(hAPP(hAPP(c_member(U_2195),U_2199),U_2201)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2195,tc_HOL_Obool)),U_2197),U_2201))
| ~ hBOOL(hAPP(hAPP(c_member(U_2195),U_2199),U_2201)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2195,tc_HOL_Obool)),U_2197),hAPP(hAPP(c_Set_Oinsert(U_2195),U_2199),U_2201))) ) ),
inference(miniscope,[status(thm)],[f_628_2]) ).
cnf(f_628_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2195,tc_HOL_Obool)),U_2197),U_2201))
| ~ hBOOL(hAPP(hAPP(c_member(U_2195),U_2199),U_2201))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2195,tc_HOL_Obool)),U_2197),hAPP(hAPP(c_Set_Oinsert(U_2195),U_2199),U_2201))) ),
inference(clausify,[status(thm)],[f_628_3]) ).
cnf(f_628_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2195,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2195,tc_HOL_Obool)),U_2197),hAPP(hAPP(c_Set_Oinsert(U_2195),U_2199),c_Orderings_Obot__class_Obot(tc_fun(U_2195,tc_HOL_Obool))))),U_2201))
| ~ hBOOL(hAPP(hAPP(c_member(U_2195),U_2199),U_2197))
| hBOOL(hAPP(hAPP(c_member(U_2195),U_2199),U_2201))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2195,tc_HOL_Obool)),U_2197),hAPP(hAPP(c_Set_Oinsert(U_2195),U_2199),U_2201))) ),
inference(clausify,[status(thm)],[f_628_3]) ).
cnf(f_628_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2195,tc_HOL_Obool)),U_2197),U_2201))
| hBOOL(hAPP(hAPP(c_member(U_2195),U_2199),U_2197))
| hBOOL(hAPP(hAPP(c_member(U_2195),U_2199),U_2201))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2195,tc_HOL_Obool)),U_2197),hAPP(hAPP(c_Set_Oinsert(U_2195),U_2199),U_2201))) ),
inference(clausify,[status(thm)],[f_628_3]) ).
cnf(f_628_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2196),U_2200),U_2202))
| hBOOL(hAPP(hAPP(c_member(U_2196),U_2200),U_2202))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2196,tc_HOL_Obool)),U_2198),hAPP(hAPP(c_Set_Oinsert(U_2196),U_2200),U_2202))) ),
inference(clausify,[status(thm)],[f_628_3]) ).
cnf(f_628_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2196),U_2200),U_2198))
| hBOOL(hAPP(hAPP(c_member(U_2196),U_2200),U_2198))
| hBOOL(hAPP(hAPP(c_member(U_2196),U_2200),U_2202))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2196,tc_HOL_Obool)),U_2198),hAPP(hAPP(c_Set_Oinsert(U_2196),U_2200),U_2202))) ),
inference(clausify,[status(thm)],[f_628_3]) ).
cnf(f_628_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2196,tc_HOL_Obool)),U_2198),U_2202))
| hBOOL(hAPP(hAPP(c_member(U_2196),U_2200),U_2198))
| hBOOL(hAPP(hAPP(c_member(U_2196),U_2200),U_2202))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2196,tc_HOL_Obool)),U_2198),hAPP(hAPP(c_Set_Oinsert(U_2196),U_2200),U_2202))) ),
inference(clausify,[status(thm)],[f_628_3]) ).
cnf(f_628_10,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2196),U_2200),U_2198))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2196,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2196,tc_HOL_Obool)),U_2198),hAPP(hAPP(c_Set_Oinsert(U_2196),U_2200),c_Orderings_Obot__class_Obot(tc_fun(U_2196,tc_HOL_Obool))))),U_2202))
| hBOOL(hAPP(hAPP(c_member(U_2196),U_2200),U_2202))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2196,tc_HOL_Obool)),U_2198),hAPP(hAPP(c_Set_Oinsert(U_2196),U_2200),U_2202))) ),
inference(clausify,[status(thm)],[f_628_3]) ).
cnf(f_628_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2196,tc_HOL_Obool)),U_2198),U_2202))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2196,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2196,tc_HOL_Obool)),U_2198),hAPP(hAPP(c_Set_Oinsert(U_2196),U_2200),c_Orderings_Obot__class_Obot(tc_fun(U_2196,tc_HOL_Obool))))),U_2202))
| hBOOL(hAPP(hAPP(c_member(U_2196),U_2200),U_2202))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2196,tc_HOL_Obool)),U_2198),hAPP(hAPP(c_Set_Oinsert(U_2196),U_2200),U_2202))) ),
inference(clausify,[status(thm)],[f_628_3]) ).
cnf(f_628_12,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2196),U_2200),U_2202))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2196,tc_HOL_Obool)),U_2198),U_2202))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2196,tc_HOL_Obool)),U_2198),hAPP(hAPP(c_Set_Oinsert(U_2196),U_2200),U_2202))) ),
inference(clausify,[status(thm)],[f_628_3]) ).
cnf(f_628_13,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2196),U_2200),U_2198))
| hBOOL(hAPP(hAPP(c_member(U_2196),U_2200),U_2198))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2196,tc_HOL_Obool)),U_2198),U_2202))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2196,tc_HOL_Obool)),U_2198),hAPP(hAPP(c_Set_Oinsert(U_2196),U_2200),U_2202))) ),
inference(clausify,[status(thm)],[f_628_3]) ).
cnf(f_628_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2196,tc_HOL_Obool)),U_2198),U_2202))
| hBOOL(hAPP(hAPP(c_member(U_2196),U_2200),U_2198))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2196,tc_HOL_Obool)),U_2198),U_2202))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2196,tc_HOL_Obool)),U_2198),hAPP(hAPP(c_Set_Oinsert(U_2196),U_2200),U_2202))) ),
inference(clausify,[status(thm)],[f_628_3]) ).
cnf(f_628_15,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2196),U_2200),U_2198))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2196,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2196,tc_HOL_Obool)),U_2198),hAPP(hAPP(c_Set_Oinsert(U_2196),U_2200),c_Orderings_Obot__class_Obot(tc_fun(U_2196,tc_HOL_Obool))))),U_2202))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2196,tc_HOL_Obool)),U_2198),U_2202))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2196,tc_HOL_Obool)),U_2198),hAPP(hAPP(c_Set_Oinsert(U_2196),U_2200),U_2202))) ),
inference(clausify,[status(thm)],[f_628_3]) ).
cnf(f_628_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2196,tc_HOL_Obool)),U_2198),U_2202))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2196,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2196,tc_HOL_Obool)),U_2198),hAPP(hAPP(c_Set_Oinsert(U_2196),U_2200),c_Orderings_Obot__class_Obot(tc_fun(U_2196,tc_HOL_Obool))))),U_2202))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2196,tc_HOL_Obool)),U_2198),U_2202))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2196,tc_HOL_Obool)),U_2198),hAPP(hAPP(c_Set_Oinsert(U_2196),U_2200),U_2202))) ),
inference(clausify,[status(thm)],[f_628_3]) ).
fof(f_629_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_629_2,plain,
! [U_2206,U_2205,U_2204,U_2203] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2203,tc_HOL_Obool)),U_2204),hAPP(hAPP(c_Set_Oinsert(U_2203),U_2205),U_2206)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2203),U_2205),U_2204))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2203,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2203,tc_HOL_Obool)),U_2204),hAPP(hAPP(c_Set_Oinsert(U_2203),U_2205),c_Orderings_Obot__class_Obot(tc_fun(U_2203,tc_HOL_Obool))))),U_2206)) ),
inference(variable_rename,[status(thm)],[f_629_1]) ).
cnf(f_629_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2203,tc_HOL_Obool)),U_2204),hAPP(hAPP(c_Set_Oinsert(U_2203),U_2205),U_2206)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2203),U_2205),U_2204))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2203,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2203,tc_HOL_Obool)),U_2204),hAPP(hAPP(c_Set_Oinsert(U_2203),U_2205),c_Orderings_Obot__class_Obot(tc_fun(U_2203,tc_HOL_Obool))))),U_2206)) ),
inference(clausify,[status(thm)],[f_629_2]) ).
fof(f_630_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_630_2,plain,
! [U_2210,U_2209,U_2208,U_2207] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2207,tc_HOL_Obool)),U_2208),hAPP(hAPP(c_Set_Oinsert(U_2207),U_2209),U_2210)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2207,tc_HOL_Obool)),U_2208),U_2210))
& ~ hBOOL(hAPP(hAPP(c_member(U_2207),U_2209),U_2208)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2207,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2207,tc_HOL_Obool)),U_2208),hAPP(hAPP(c_Set_Oinsert(U_2207),U_2209),c_Orderings_Obot__class_Obot(tc_fun(U_2207,tc_HOL_Obool))))),U_2210))
& hBOOL(hAPP(hAPP(c_member(U_2207),U_2209),U_2208)) ) )
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2207,tc_HOL_Obool)),U_2208),U_2210))
| hBOOL(hAPP(hAPP(c_member(U_2207),U_2209),U_2208)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2207,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2207,tc_HOL_Obool)),U_2208),hAPP(hAPP(c_Set_Oinsert(U_2207),U_2209),c_Orderings_Obot__class_Obot(tc_fun(U_2207,tc_HOL_Obool))))),U_2210))
| ~ hBOOL(hAPP(hAPP(c_member(U_2207),U_2209),U_2208)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2207,tc_HOL_Obool)),U_2208),hAPP(hAPP(c_Set_Oinsert(U_2207),U_2209),U_2210))) ) ),
inference(variable_rename,[status(thm)],[f_630_1]) ).
fof(f_630_3,plain,
( ! [U_2218,U_2216,U_2214,U_2212] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2212,tc_HOL_Obool)),U_2214),hAPP(hAPP(c_Set_Oinsert(U_2212),U_2216),U_2218)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2212,tc_HOL_Obool)),U_2214),U_2218))
& ~ hBOOL(hAPP(hAPP(c_member(U_2212),U_2216),U_2214)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2212,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2212,tc_HOL_Obool)),U_2214),hAPP(hAPP(c_Set_Oinsert(U_2212),U_2216),c_Orderings_Obot__class_Obot(tc_fun(U_2212,tc_HOL_Obool))))),U_2218))
& hBOOL(hAPP(hAPP(c_member(U_2212),U_2216),U_2214)) ) )
& ! [U_2217,U_2215,U_2213,U_2211] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2211,tc_HOL_Obool)),U_2213),U_2217))
| hBOOL(hAPP(hAPP(c_member(U_2211),U_2215),U_2213)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2211,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2211,tc_HOL_Obool)),U_2213),hAPP(hAPP(c_Set_Oinsert(U_2211),U_2215),c_Orderings_Obot__class_Obot(tc_fun(U_2211,tc_HOL_Obool))))),U_2217))
| ~ hBOOL(hAPP(hAPP(c_member(U_2211),U_2215),U_2213)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2211,tc_HOL_Obool)),U_2213),hAPP(hAPP(c_Set_Oinsert(U_2211),U_2215),U_2217))) ) ),
inference(miniscope,[status(thm)],[f_630_2]) ).
cnf(f_630_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2211,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2211,tc_HOL_Obool)),U_2213),hAPP(hAPP(c_Set_Oinsert(U_2211),U_2215),c_Orderings_Obot__class_Obot(tc_fun(U_2211,tc_HOL_Obool))))),U_2217))
| ~ hBOOL(hAPP(hAPP(c_member(U_2211),U_2215),U_2213))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2211,tc_HOL_Obool)),U_2213),hAPP(hAPP(c_Set_Oinsert(U_2211),U_2215),U_2217))) ),
inference(clausify,[status(thm)],[f_630_3]) ).
cnf(f_630_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2211,tc_HOL_Obool)),U_2213),U_2217))
| hBOOL(hAPP(hAPP(c_member(U_2211),U_2215),U_2213))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2211,tc_HOL_Obool)),U_2213),hAPP(hAPP(c_Set_Oinsert(U_2211),U_2215),U_2217))) ),
inference(clausify,[status(thm)],[f_630_3]) ).
cnf(f_630_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2212),U_2216),U_2214))
| hBOOL(hAPP(hAPP(c_member(U_2212),U_2216),U_2214))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2212,tc_HOL_Obool)),U_2214),hAPP(hAPP(c_Set_Oinsert(U_2212),U_2216),U_2218))) ),
inference(clausify,[status(thm)],[f_630_3]) ).
cnf(f_630_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2212,tc_HOL_Obool)),U_2214),U_2218))
| hBOOL(hAPP(hAPP(c_member(U_2212),U_2216),U_2214))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2212,tc_HOL_Obool)),U_2214),hAPP(hAPP(c_Set_Oinsert(U_2212),U_2216),U_2218))) ),
inference(clausify,[status(thm)],[f_630_3]) ).
cnf(f_630_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2212),U_2216),U_2214))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2212,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2212,tc_HOL_Obool)),U_2214),hAPP(hAPP(c_Set_Oinsert(U_2212),U_2216),c_Orderings_Obot__class_Obot(tc_fun(U_2212,tc_HOL_Obool))))),U_2218))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2212,tc_HOL_Obool)),U_2214),hAPP(hAPP(c_Set_Oinsert(U_2212),U_2216),U_2218))) ),
inference(clausify,[status(thm)],[f_630_3]) ).
cnf(f_630_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2212,tc_HOL_Obool)),U_2214),U_2218))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2212,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2212,tc_HOL_Obool)),U_2214),hAPP(hAPP(c_Set_Oinsert(U_2212),U_2216),c_Orderings_Obot__class_Obot(tc_fun(U_2212,tc_HOL_Obool))))),U_2218))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2212,tc_HOL_Obool)),U_2214),hAPP(hAPP(c_Set_Oinsert(U_2212),U_2216),U_2218))) ),
inference(clausify,[status(thm)],[f_630_3]) ).
fof(f_631_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_631_2,plain,
! [U_2223,U_2222,U_2221,U_2220,U_2219] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2219,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_2219,U_2220,U_2221),U_2222)),U_2223))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2220,tc_HOL_Obool)),U_2222),hAPP(c_Set_Oimage(U_2219,U_2220,U_2221),U_2223)))
| ~ c_Fun_Oinj__on(U_2219,U_2220,U_2221,c_Orderings_Otop__class_Otop(tc_fun(U_2219,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_631_1]) ).
cnf(f_631_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2219,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_2219,U_2220,U_2221),U_2222)),U_2223))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2220,tc_HOL_Obool)),U_2222),hAPP(c_Set_Oimage(U_2219,U_2220,U_2221),U_2223)))
| ~ c_Fun_Oinj__on(U_2219,U_2220,U_2221,c_Orderings_Otop__class_Otop(tc_fun(U_2219,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_631_2]) ).
fof(f_632_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_632_2,plain,
! [U_2226,U_2225,U_2224] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_2224),U_2225),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2226)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_2224),U_2225),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2226))
| hAPP(U_2225,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_2224)
| ~ class_Groups_Ocomm__monoid__add(U_2224) ),
inference(variable_rename,[status(thm)],[f_632_1]) ).
cnf(f_632_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_2224),U_2225),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2226)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_2224),U_2225),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2226))
| hAPP(U_2225,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_2224)
| ~ class_Groups_Ocomm__monoid__add(U_2224) ),
inference(clausify,[status(thm)],[f_632_2]) ).
fof(f_633_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_633_2,plain,
! [U_2230,U_2229,U_2228,U_2227] :
( hAPP(c_Set_Oimage(U_2228,U_2227,c_Fun_Othe__inv__into(U_2227,U_2228,U_2230,U_2229)),hAPP(c_Set_Oimage(U_2227,U_2228,U_2229),U_2230)) = U_2230
| ~ c_Fun_Oinj__on(U_2227,U_2228,U_2229,U_2230) ),
inference(variable_rename,[status(thm)],[f_633_1]) ).
cnf(f_633_3,plain,
( hAPP(c_Set_Oimage(U_2228,U_2227,c_Fun_Othe__inv__into(U_2227,U_2228,U_2230,U_2229)),hAPP(c_Set_Oimage(U_2227,U_2228,U_2229),U_2230)) = U_2230
| ~ c_Fun_Oinj__on(U_2227,U_2228,U_2229,U_2230) ),
inference(clausify,[status(thm)],[f_633_2]) ).
fof(f_634_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_634_2,plain,
! [U_2234,U_2233,U_2232,U_2231] :
( c_Fun_Oinj__on(U_2232,U_2231,c_Fun_Othe__inv__into(U_2231,U_2232,U_2234,U_2233),hAPP(c_Set_Oimage(U_2231,U_2232,U_2233),U_2234))
| ~ c_Fun_Oinj__on(U_2231,U_2232,U_2233,U_2234) ),
inference(variable_rename,[status(thm)],[f_634_1]) ).
cnf(f_634_3,plain,
( c_Fun_Oinj__on(U_2232,U_2231,c_Fun_Othe__inv__into(U_2231,U_2232,U_2234,U_2233),hAPP(c_Set_Oimage(U_2231,U_2232,U_2233),U_2234))
| ~ c_Fun_Oinj__on(U_2231,U_2232,U_2233,U_2234) ),
inference(clausify,[status(thm)],[f_634_2]) ).
fof(f_635_1,plain,
! [V_c_2,T_b,V_B_2,V_A_2] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
| ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
| V_A_2 != V_B_2 ),
inference(fof_nnf,[status(thm)],[fact_equalityCE]) ).
fof(f_635_2,plain,
! [U_2238,U_2237,U_2236,U_2235] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_2237),U_2238),U_2236))
& ~ hBOOL(hAPP(hAPP(c_member(U_2237),U_2238),U_2235)) )
| ( hBOOL(hAPP(hAPP(c_member(U_2237),U_2238),U_2236))
& hBOOL(hAPP(hAPP(c_member(U_2237),U_2238),U_2235)) )
| U_2235 != U_2236 ),
inference(variable_rename,[status(thm)],[f_635_1]) ).
cnf(f_635_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2237),U_2238),U_2235))
| hBOOL(hAPP(hAPP(c_member(U_2237),U_2238),U_2235))
| U_2235 != U_2236 ),
inference(clausify,[status(thm)],[f_635_2]) ).
cnf(f_635_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2237),U_2238),U_2236))
| hBOOL(hAPP(hAPP(c_member(U_2237),U_2238),U_2235))
| U_2235 != U_2236 ),
inference(clausify,[status(thm)],[f_635_2]) ).
cnf(f_635_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2237),U_2238),U_2235))
| hBOOL(hAPP(hAPP(c_member(U_2237),U_2238),U_2236))
| U_2235 != U_2236 ),
inference(clausify,[status(thm)],[f_635_2]) ).
cnf(f_635_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2237),U_2238),U_2236))
| hBOOL(hAPP(hAPP(c_member(U_2237),U_2238),U_2236))
| U_2235 != U_2236 ),
inference(clausify,[status(thm)],[f_635_2]) ).
fof(f_636_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_636_2,plain,
! [U_2240,U_2239] : ~ hBOOL(hAPP(hAPP(c_member(U_2239),U_2240),c_Orderings_Obot__class_Obot(tc_fun(U_2239,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_636_1]) ).
cnf(f_636_3,plain,
~ hBOOL(hAPP(hAPP(c_member(U_2239),U_2240),c_Orderings_Obot__class_Obot(tc_fun(U_2239,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_636_2]) ).
fof(f_637_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_637_2,plain,
! [U_2244,U_2243,U_2242,U_2241] :
( hBOOL(hAPP(hAPP(c_member(U_2241),U_2242),U_2244))
| U_2242 = U_2243
| ~ hBOOL(hAPP(hAPP(c_member(U_2241),U_2242),hAPP(hAPP(c_Set_Oinsert(U_2241),U_2243),U_2244))) ),
inference(variable_rename,[status(thm)],[f_637_1]) ).
cnf(f_637_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2241),U_2242),U_2244))
| U_2242 = U_2243
| ~ hBOOL(hAPP(hAPP(c_member(U_2241),U_2242),hAPP(hAPP(c_Set_Oinsert(U_2241),U_2243),U_2244))) ),
inference(clausify,[status(thm)],[f_637_2]) ).
fof(f_638_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_638_2,plain,
! [U_2248,U_2247,U_2246,U_2245] :
( hBOOL(hAPP(hAPP(c_member(U_2245),U_2246),hAPP(hAPP(c_Set_Oinsert(U_2245),U_2248),U_2247)))
| ( U_2246 != U_2248
& ~ hBOOL(hAPP(hAPP(c_member(U_2245),U_2246),U_2247)) ) ),
inference(variable_rename,[status(thm)],[f_638_1]) ).
cnf(f_638_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2245),U_2246),U_2247))
| hBOOL(hAPP(hAPP(c_member(U_2245),U_2246),hAPP(hAPP(c_Set_Oinsert(U_2245),U_2248),U_2247))) ),
inference(clausify,[status(thm)],[f_638_2]) ).
cnf(f_638_4,plain,
( U_2246 != U_2248
| hBOOL(hAPP(hAPP(c_member(U_2245),U_2246),hAPP(hAPP(c_Set_Oinsert(U_2245),U_2248),U_2247))) ),
inference(clausify,[status(thm)],[f_638_2]) ).
fof(f_639_1,plain,
! [V_c_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_subsetD]) ).
fof(f_639_2,plain,
! [U_2252,U_2251,U_2250,U_2249] :
( hBOOL(hAPP(hAPP(c_member(U_2249),U_2252),U_2251))
| ~ hBOOL(hAPP(hAPP(c_member(U_2249),U_2252),U_2250))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2249,tc_HOL_Obool)),U_2250),U_2251)) ),
inference(variable_rename,[status(thm)],[f_639_1]) ).
cnf(f_639_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2249),U_2252),U_2251))
| ~ hBOOL(hAPP(hAPP(c_member(U_2249),U_2252),U_2250))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2249,tc_HOL_Obool)),U_2250),U_2251)) ),
inference(clausify,[status(thm)],[f_639_2]) ).
fof(f_640_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_640_2,plain,
! [U_2254,U_2253] : hBOOL(hAPP(hAPP(c_member(U_2253),U_2254),c_Orderings_Otop__class_Otop(tc_fun(U_2253,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_640_1]) ).
cnf(f_640_3,plain,
hBOOL(hAPP(hAPP(c_member(U_2253),U_2254),c_Orderings_Otop__class_Otop(tc_fun(U_2253,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_640_2]) ).
fof(f_641_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_641_2,plain,
! [U_2260,U_2259,U_2258,U_2257,U_2256,U_2255] :
( hBOOL(hAPP(hAPP(c_member(U_2260),U_2255),hAPP(c_Set_Oimage(U_2258,U_2260,U_2256),U_2259)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2258),U_2257),U_2259))
| U_2255 != hAPP(U_2256,U_2257) ),
inference(variable_rename,[status(thm)],[f_641_1]) ).
cnf(f_641_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2260),U_2255),hAPP(c_Set_Oimage(U_2258,U_2260,U_2256),U_2259)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2258),U_2257),U_2259))
| U_2255 != hAPP(U_2256,U_2257) ),
inference(clausify,[status(thm)],[f_641_2]) ).
fof(f_642_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_UnE]) ).
fof(f_642_2,plain,
! [U_2264,U_2263,U_2262,U_2261] :
( hBOOL(hAPP(hAPP(c_member(U_2261),U_2262),U_2264))
| hBOOL(hAPP(hAPP(c_member(U_2261),U_2262),U_2263))
| ~ hBOOL(hAPP(hAPP(c_member(U_2261),U_2262),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2261,tc_HOL_Obool)),U_2263),U_2264))) ),
inference(variable_rename,[status(thm)],[f_642_1]) ).
cnf(f_642_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2261),U_2262),U_2264))
| hBOOL(hAPP(hAPP(c_member(U_2261),U_2262),U_2263))
| ~ hBOOL(hAPP(hAPP(c_member(U_2261),U_2262),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2261,tc_HOL_Obool)),U_2263),U_2264))) ),
inference(clausify,[status(thm)],[f_642_2]) ).
fof(f_643_1,plain,
! [V_A_2,V_B_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_UnCI]) ).
fof(f_643_2,plain,
! [U_2268,U_2267,U_2266,U_2265] :
( hBOOL(hAPP(hAPP(c_member(U_2265),U_2266),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2265,tc_HOL_Obool)),U_2268),U_2267)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_2265),U_2266),U_2268))
& ~ hBOOL(hAPP(hAPP(c_member(U_2265),U_2266),U_2267)) ) ),
inference(variable_rename,[status(thm)],[f_643_1]) ).
cnf(f_643_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2265),U_2266),U_2267))
| hBOOL(hAPP(hAPP(c_member(U_2265),U_2266),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2265,tc_HOL_Obool)),U_2268),U_2267))) ),
inference(clausify,[status(thm)],[f_643_2]) ).
cnf(f_643_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2265),U_2266),U_2268))
| hBOOL(hAPP(hAPP(c_member(U_2265),U_2266),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2265,tc_HOL_Obool)),U_2268),U_2267))) ),
inference(clausify,[status(thm)],[f_643_2]) ).
fof(f_644_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_IntI]) ).
fof(f_644_2,plain,
! [U_2272,U_2271,U_2270,U_2269] :
( hBOOL(hAPP(hAPP(c_member(U_2269),U_2270),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2269,tc_HOL_Obool)),U_2271),U_2272)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2269),U_2270),U_2272))
| ~ hBOOL(hAPP(hAPP(c_member(U_2269),U_2270),U_2271)) ),
inference(variable_rename,[status(thm)],[f_644_1]) ).
cnf(f_644_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2269),U_2270),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2269,tc_HOL_Obool)),U_2271),U_2272)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2269),U_2270),U_2272))
| ~ hBOOL(hAPP(hAPP(c_member(U_2269),U_2270),U_2271)) ),
inference(clausify,[status(thm)],[f_644_2]) ).
fof(f_645_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_IntE]) ).
fof(f_645_2,plain,
! [U_2276,U_2275,U_2274,U_2273] :
( ( hBOOL(hAPP(hAPP(c_member(U_2273),U_2274),U_2276))
& hBOOL(hAPP(hAPP(c_member(U_2273),U_2274),U_2275)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2273),U_2274),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2273,tc_HOL_Obool)),U_2275),U_2276))) ),
inference(variable_rename,[status(thm)],[f_645_1]) ).
cnf(f_645_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2273),U_2274),U_2275))
| ~ hBOOL(hAPP(hAPP(c_member(U_2273),U_2274),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2273,tc_HOL_Obool)),U_2275),U_2276))) ),
inference(clausify,[status(thm)],[f_645_2]) ).
cnf(f_645_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2273),U_2274),U_2276))
| ~ hBOOL(hAPP(hAPP(c_member(U_2273),U_2274),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2273,tc_HOL_Obool)),U_2275),U_2276))) ),
inference(clausify,[status(thm)],[f_645_2]) ).
fof(f_646_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_DiffI]) ).
fof(f_646_2,plain,
! [U_2280,U_2279,U_2278,U_2277] :
( hBOOL(hAPP(hAPP(c_member(U_2277),U_2278),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2277,tc_HOL_Obool)),U_2279),U_2280)))
| hBOOL(hAPP(hAPP(c_member(U_2277),U_2278),U_2280))
| ~ hBOOL(hAPP(hAPP(c_member(U_2277),U_2278),U_2279)) ),
inference(variable_rename,[status(thm)],[f_646_1]) ).
cnf(f_646_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2277),U_2278),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2277,tc_HOL_Obool)),U_2279),U_2280)))
| hBOOL(hAPP(hAPP(c_member(U_2277),U_2278),U_2280))
| ~ hBOOL(hAPP(hAPP(c_member(U_2277),U_2278),U_2279)) ),
inference(clausify,[status(thm)],[f_646_2]) ).
fof(f_647_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_DiffE]) ).
fof(f_647_2,plain,
! [U_2284,U_2283,U_2282,U_2281] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_2281),U_2282),U_2284))
& hBOOL(hAPP(hAPP(c_member(U_2281),U_2282),U_2283)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2281),U_2282),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2281,tc_HOL_Obool)),U_2283),U_2284))) ),
inference(variable_rename,[status(thm)],[f_647_1]) ).
cnf(f_647_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2281),U_2282),U_2283))
| ~ hBOOL(hAPP(hAPP(c_member(U_2281),U_2282),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2281,tc_HOL_Obool)),U_2283),U_2284))) ),
inference(clausify,[status(thm)],[f_647_2]) ).
cnf(f_647_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2281),U_2282),U_2284))
| ~ hBOOL(hAPP(hAPP(c_member(U_2281),U_2282),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2281,tc_HOL_Obool)),U_2283),U_2284))) ),
inference(clausify,[status(thm)],[f_647_2]) ).
fof(f_648_1,plain,
! [V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
| hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_ComplI]) ).
fof(f_648_2,plain,
! [U_2287,U_2286,U_2285] :
( hBOOL(hAPP(hAPP(c_member(U_2285),U_2286),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2285,tc_HOL_Obool)),U_2287)))
| hBOOL(hAPP(hAPP(c_member(U_2285),U_2286),U_2287)) ),
inference(variable_rename,[status(thm)],[f_648_1]) ).
cnf(f_648_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2285),U_2286),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2285,tc_HOL_Obool)),U_2287)))
| hBOOL(hAPP(hAPP(c_member(U_2285),U_2286),U_2287)) ),
inference(clausify,[status(thm)],[f_648_2]) ).
fof(f_649_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_649_2,plain,
! [U_2293,U_2292,U_2291,U_2290,U_2289,U_2288] :
( hBOOL(hAPP(hAPP(c_member(U_2293),U_2289),hAPP(c_Set_Ovimage(U_2293,U_2291,U_2288),U_2292)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2291),U_2290),U_2292))
| hAPP(U_2288,U_2289) != U_2290 ),
inference(variable_rename,[status(thm)],[f_649_1]) ).
cnf(f_649_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2293),U_2289),hAPP(c_Set_Ovimage(U_2293,U_2291,U_2288),U_2292)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2291),U_2290),U_2292))
| hAPP(U_2288,U_2289) != U_2290 ),
inference(clausify,[status(thm)],[f_649_2]) ).
fof(f_650_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_650_2,plain,
! [U_2297,U_2296,U_2295,U_2294] :
( hBOOL(hAPP(hAPP(c_member(U_2294),U_2297),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2294,tc_HOL_Obool),U_2296)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2294),U_2297),U_2295))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2294,tc_HOL_Obool)),U_2295),U_2296)) ),
inference(variable_rename,[status(thm)],[f_650_1]) ).
cnf(f_650_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2294),U_2297),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2294,tc_HOL_Obool),U_2296)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2294),U_2297),U_2295))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2294,tc_HOL_Obool)),U_2295),U_2296)) ),
inference(clausify,[status(thm)],[f_650_2]) ).
fof(f_651_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_651_2,plain,
! [U_2301,U_2300,U_2299,U_2298] :
( hBOOL(hAPP(hAPP(c_member(U_2298),U_2299),U_2301))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2298,tc_HOL_Obool)),U_2301),U_2300))
| ~ hBOOL(hAPP(hAPP(c_member(U_2298),U_2299),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_2298,tc_HOL_Obool),U_2300))) ),
inference(variable_rename,[status(thm)],[f_651_1]) ).
cnf(f_651_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2298),U_2299),U_2301))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2298,tc_HOL_Obool)),U_2301),U_2300))
| ~ hBOOL(hAPP(hAPP(c_member(U_2298),U_2299),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_2298,tc_HOL_Obool),U_2300))) ),
inference(clausify,[status(thm)],[f_651_2]) ).
fof(f_652_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_652_2,plain,
! [U_2305,U_2304,U_2303,U_2302] :
( hBOOL(hAPP(hAPP(c_member(U_2302),U_2303),U_2305))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2302,tc_HOL_Obool)),U_2305),U_2304))
| ~ hBOOL(hAPP(hAPP(c_member(U_2302),U_2303),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_2302,tc_HOL_Obool),U_2304))) ),
inference(variable_rename,[status(thm)],[f_652_1]) ).
cnf(f_652_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2302),U_2303),U_2305))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2302,tc_HOL_Obool)),U_2305),U_2304))
| ~ hBOOL(hAPP(hAPP(c_member(U_2302),U_2303),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_2302,tc_HOL_Obool),U_2304))) ),
inference(clausify,[status(thm)],[f_652_2]) ).
fof(f_653_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_653_2,plain,
! [U_2308,U_2307,U_2306] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2306,tc_HOL_Obool)),U_2307),hAPP(c_Set_OPow(U_2306),U_2308)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2306,tc_HOL_Obool)),U_2307),U_2308)) ),
inference(variable_rename,[status(thm)],[f_653_1]) ).
cnf(f_653_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2306,tc_HOL_Obool)),U_2307),hAPP(c_Set_OPow(U_2306),U_2308)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2306,tc_HOL_Obool)),U_2307),U_2308)) ),
inference(clausify,[status(thm)],[f_653_2]) ).
fof(f_654_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_654_2,plain,
! [U_2311,U_2310,U_2309] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2309),U_2310)),U_2311) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2309),U_2311)),U_2310),
inference(variable_rename,[status(thm)],[f_654_1]) ).
cnf(f_654_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2309),U_2310)),U_2311) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2309),U_2311)),U_2310),
inference(clausify,[status(thm)],[f_654_2]) ).
fof(f_655_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_655_2,plain,
! [U_2314,U_2313,U_2312] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2312),U_2314)),U_2313))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2312),U_2313)) ),
inference(variable_rename,[status(thm)],[f_655_1]) ).
cnf(f_655_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2312),U_2314)),U_2313))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2312),U_2313)) ),
inference(clausify,[status(thm)],[f_655_2]) ).
fof(f_656_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_656_2,plain,
! [U_2317,U_2316,U_2315] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2317),U_2316)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2317),U_2315)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2315),U_2317))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2315),U_2316)) ),
inference(variable_rename,[status(thm)],[f_656_1]) ).
cnf(f_656_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2317),U_2316)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2317),U_2315)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2315),U_2317))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2315),U_2316)) ),
inference(clausify,[status(thm)],[f_656_2]) ).
fof(f_657_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_657_2,plain,
! [U_2321,U_2320,U_2319,U_2318] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2318,tc_HOL_Obool)),U_2319),U_2321))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2318,tc_HOL_Obool)),U_2320),U_2321))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2318,tc_HOL_Obool)),U_2319),U_2320)) ),
inference(variable_rename,[status(thm)],[f_657_1]) ).
cnf(f_657_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2318,tc_HOL_Obool)),U_2319),U_2321))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2318,tc_HOL_Obool)),U_2320),U_2321))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2318,tc_HOL_Obool)),U_2319),U_2320)) ),
inference(clausify,[status(thm)],[f_657_2]) ).
fof(f_658_1,plain,
! [V_c_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_psubsetD]) ).
fof(f_658_2,plain,
! [U_2325,U_2324,U_2323,U_2322] :
( hBOOL(hAPP(hAPP(c_member(U_2322),U_2325),U_2324))
| ~ hBOOL(hAPP(hAPP(c_member(U_2322),U_2325),U_2323))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2322,tc_HOL_Obool)),U_2323),U_2324)) ),
inference(variable_rename,[status(thm)],[f_658_1]) ).
cnf(f_658_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2322),U_2325),U_2324))
| ~ hBOOL(hAPP(hAPP(c_member(U_2322),U_2325),U_2323))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2322,tc_HOL_Obool)),U_2323),U_2324)) ),
inference(clausify,[status(thm)],[f_658_2]) ).
fof(f_659_1,plain,
! [V_P_2,V_n_2,V_m_2] :
( hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
| ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) )
| ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
& V_m_2 = V_n_2 )
| ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__cases]) ).
fof(f_659_2,plain,
! [U_2328,U_2327,U_2326] :
( hBOOL(hAPP(hAPP(U_2328,U_2327),U_2326))
| ( ~ hBOOL(hAPP(hAPP(U_2328,U_2327),U_2326))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2327),U_2326)) )
| ( ~ hBOOL(hAPP(hAPP(U_2328,U_2327),U_2326))
& U_2326 = U_2327 )
| ( ~ hBOOL(hAPP(hAPP(U_2328,U_2327),U_2326))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2326),U_2327)) ) ),
inference(variable_rename,[status(thm)],[f_659_1]) ).
cnf(f_659_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2327),U_2326))
| hBOOL(hAPP(hAPP(U_2328,U_2327),U_2326))
| U_2326 = U_2327
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2326),U_2327)) ),
inference(clausify,[status(thm)],[f_659_2]) ).
cnf(f_659_4,plain,
( ~ hBOOL(hAPP(hAPP(U_2328,U_2327),U_2326))
| hBOOL(hAPP(hAPP(U_2328,U_2327),U_2326))
| U_2326 = U_2327
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2326),U_2327)) ),
inference(clausify,[status(thm)],[f_659_2]) ).
cnf(f_659_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2327),U_2326))
| hBOOL(hAPP(hAPP(U_2328,U_2327),U_2326))
| ~ hBOOL(hAPP(hAPP(U_2328,U_2327),U_2326))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2326),U_2327)) ),
inference(clausify,[status(thm)],[f_659_2]) ).
cnf(f_659_6,plain,
( ~ hBOOL(hAPP(hAPP(U_2328,U_2327),U_2326))
| hBOOL(hAPP(hAPP(U_2328,U_2327),U_2326))
| ~ hBOOL(hAPP(hAPP(U_2328,U_2327),U_2326))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2326),U_2327)) ),
inference(clausify,[status(thm)],[f_659_2]) ).
cnf(f_659_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2327),U_2326))
| hBOOL(hAPP(hAPP(U_2328,U_2327),U_2326))
| U_2326 = U_2327
| ~ hBOOL(hAPP(hAPP(U_2328,U_2327),U_2326)) ),
inference(clausify,[status(thm)],[f_659_2]) ).
cnf(f_659_8,plain,
( ~ hBOOL(hAPP(hAPP(U_2328,U_2327),U_2326))
| hBOOL(hAPP(hAPP(U_2328,U_2327),U_2326))
| U_2326 = U_2327
| ~ hBOOL(hAPP(hAPP(U_2328,U_2327),U_2326)) ),
inference(clausify,[status(thm)],[f_659_2]) ).
cnf(f_659_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2327),U_2326))
| hBOOL(hAPP(hAPP(U_2328,U_2327),U_2326))
| ~ hBOOL(hAPP(hAPP(U_2328,U_2327),U_2326))
| ~ hBOOL(hAPP(hAPP(U_2328,U_2327),U_2326)) ),
inference(clausify,[status(thm)],[f_659_2]) ).
cnf(f_659_10,plain,
( ~ hBOOL(hAPP(hAPP(U_2328,U_2327),U_2326))
| hBOOL(hAPP(hAPP(U_2328,U_2327),U_2326))
| ~ hBOOL(hAPP(hAPP(U_2328,U_2327),U_2326))
| ~ hBOOL(hAPP(hAPP(U_2328,U_2327),U_2326)) ),
inference(clausify,[status(thm)],[f_659_2]) ).
fof(f_660_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_660_2,plain,
! [U_2330,U_2329] :
( U_2329 != U_2330
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2329),U_2330)) ),
inference(variable_rename,[status(thm)],[f_660_1]) ).
cnf(f_660_3,plain,
( U_2329 != U_2330
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2329),U_2330)) ),
inference(clausify,[status(thm)],[f_660_2]) ).
fof(f_661_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_661_2,plain,
! [U_2332,U_2331] :
( U_2332 != U_2331
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2331),U_2332)) ),
inference(variable_rename,[status(thm)],[f_661_1]) ).
cnf(f_661_3,plain,
( U_2332 != U_2331
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2331),U_2332)) ),
inference(clausify,[status(thm)],[f_661_2]) ).
fof(f_662_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_662_2,plain,
! [U_2333] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2333),U_2333)),
inference(variable_rename,[status(thm)],[f_662_1]) ).
cnf(f_662_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2333),U_2333)),
inference(clausify,[status(thm)],[f_662_2]) ).
fof(f_663_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_663_2,plain,
! [U_2335,U_2334] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2335),U_2334))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2334),U_2335))
| U_2334 = U_2335 ),
inference(variable_rename,[status(thm)],[f_663_1]) ).
cnf(f_663_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2335),U_2334))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2334),U_2335))
| U_2334 = U_2335 ),
inference(clausify,[status(thm)],[f_663_2]) ).
fof(f_664_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_664_2,plain,
! [U_2337,U_2336] :
( ( U_2336 != U_2337
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2337),U_2336))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2336),U_2337)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2337),U_2336))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2336),U_2337))
| U_2336 = U_2337 ) ),
inference(variable_rename,[status(thm)],[f_664_1]) ).
fof(f_664_3,plain,
( ! [U_2341,U_2339] :
( U_2339 != U_2341
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2341),U_2339))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2339),U_2341)) ) )
& ! [U_2340,U_2338] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2340),U_2338))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2338),U_2340))
| U_2338 = U_2340 ) ),
inference(miniscope,[status(thm)],[f_664_2]) ).
cnf(f_664_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2340),U_2338))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2338),U_2340))
| U_2338 = U_2340 ),
inference(clausify,[status(thm)],[f_664_3]) ).
cnf(f_664_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2339),U_2341))
| U_2339 != U_2341 ),
inference(clausify,[status(thm)],[f_664_3]) ).
cnf(f_664_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2341),U_2339))
| U_2339 != U_2341 ),
inference(clausify,[status(thm)],[f_664_3]) ).
fof(f_665_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_665_2,plain,
! [U_2342] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2342),U_2342)),
inference(variable_rename,[status(thm)],[f_665_1]) ).
cnf(f_665_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2342),U_2342)),
inference(clausify,[status(thm)],[f_665_2]) ).
fof(f_666_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_666_2,plain,
! [U_2345,U_2344,U_2343] :
( ( hBOOL(hAPP(hAPP(c_member(U_2343),U_2344),U_2345))
| ~ hBOOL(hAPP(U_2345,U_2344)) )
& ( hBOOL(hAPP(U_2345,U_2344))
| ~ hBOOL(hAPP(hAPP(c_member(U_2343),U_2344),U_2345)) ) ),
inference(variable_rename,[status(thm)],[f_666_1]) ).
fof(f_666_3,plain,
( ! [U_2351,U_2349] :
( ! [U_2347] : hBOOL(hAPP(hAPP(c_member(U_2347),U_2349),U_2351))
| ~ hBOOL(hAPP(U_2351,U_2349)) )
& ! [U_2350,U_2348] :
( ! [U_2346] : ~ hBOOL(hAPP(hAPP(c_member(U_2346),U_2348),U_2350))
| hBOOL(hAPP(U_2350,U_2348)) ) ),
inference(miniscope,[status(thm)],[f_666_2]) ).
cnf(f_666_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2346),U_2348),U_2350))
| hBOOL(hAPP(U_2350,U_2348)) ),
inference(clausify,[status(thm)],[f_666_3]) ).
cnf(f_666_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_2347),U_2349),U_2351))
| ~ hBOOL(hAPP(U_2351,U_2349)) ),
inference(clausify,[status(thm)],[f_666_3]) ).
fof(f_667_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_667_2,plain,
! [U_2354,U_2353,U_2352] :
( ( hBOOL(hAPP(hAPP(c_member(U_2352),U_2353),hAPP(c_fequal,U_2354)))
| U_2353 != U_2354 )
& ( U_2353 = U_2354
| ~ hBOOL(hAPP(hAPP(c_member(U_2352),U_2353),hAPP(c_fequal,U_2354))) ) ),
inference(variable_rename,[status(thm)],[f_667_1]) ).
fof(f_667_3,plain,
( ! [U_2360,U_2358] :
( ! [U_2356] : hBOOL(hAPP(hAPP(c_member(U_2356),U_2358),hAPP(c_fequal,U_2360)))
| U_2358 != U_2360 )
& ! [U_2359,U_2357] :
( ! [U_2355] : ~ hBOOL(hAPP(hAPP(c_member(U_2355),U_2357),hAPP(c_fequal,U_2359)))
| U_2357 = U_2359 ) ),
inference(miniscope,[status(thm)],[f_667_2]) ).
cnf(f_667_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2355),U_2357),hAPP(c_fequal,U_2359)))
| U_2357 = U_2359 ),
inference(clausify,[status(thm)],[f_667_3]) ).
cnf(f_667_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_2356),U_2358),hAPP(c_fequal,U_2360)))
| U_2358 != U_2360 ),
inference(clausify,[status(thm)],[f_667_3]) ).
fof(f_668_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_668_2,plain,
! [U_2365,U_2364,U_2363,U_2362,U_2361] :
( ( hBOOL(hAPP(hAPP(c_member(U_2361),U_2362),hAPP(c_Set_Ovimage(U_2361,U_2363,U_2364),U_2365)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2363),hAPP(U_2364,U_2362)),U_2365)) )
& ( hBOOL(hAPP(hAPP(c_member(U_2363),hAPP(U_2364,U_2362)),U_2365))
| ~ hBOOL(hAPP(hAPP(c_member(U_2361),U_2362),hAPP(c_Set_Ovimage(U_2361,U_2363,U_2364),U_2365))) ) ),
inference(variable_rename,[status(thm)],[f_668_1]) ).
fof(f_668_3,plain,
( ! [U_2375,U_2373,U_2371,U_2369] :
( ! [U_2367] : hBOOL(hAPP(hAPP(c_member(U_2367),U_2369),hAPP(c_Set_Ovimage(U_2367,U_2371,U_2373),U_2375)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2371),hAPP(U_2373,U_2369)),U_2375)) )
& ! [U_2374,U_2372,U_2370,U_2368] :
( ! [U_2366] : ~ hBOOL(hAPP(hAPP(c_member(U_2366),U_2368),hAPP(c_Set_Ovimage(U_2366,U_2370,U_2372),U_2374)))
| hBOOL(hAPP(hAPP(c_member(U_2370),hAPP(U_2372,U_2368)),U_2374)) ) ),
inference(miniscope,[status(thm)],[f_668_2]) ).
cnf(f_668_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2366),U_2368),hAPP(c_Set_Ovimage(U_2366,U_2370,U_2372),U_2374)))
| hBOOL(hAPP(hAPP(c_member(U_2370),hAPP(U_2372,U_2368)),U_2374)) ),
inference(clausify,[status(thm)],[f_668_3]) ).
cnf(f_668_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_2367),U_2369),hAPP(c_Set_Ovimage(U_2367,U_2371,U_2373),U_2375)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2371),hAPP(U_2373,U_2369)),U_2375)) ),
inference(clausify,[status(thm)],[f_668_3]) ).
fof(f_669_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_669_2,plain,
! [U_2380,U_2379,U_2378,U_2377,U_2376] :
( ( hBOOL(hAPP(hAPP(c_Set_Ovimage(U_2376,U_2377,U_2378),U_2379),U_2380))
| ~ hBOOL(hAPP(U_2379,hAPP(U_2378,U_2380))) )
& ( hBOOL(hAPP(U_2379,hAPP(U_2378,U_2380)))
| ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_2376,U_2377,U_2378),U_2379),U_2380)) ) ),
inference(variable_rename,[status(thm)],[f_669_1]) ).
fof(f_669_3,plain,
( ! [U_2390,U_2388,U_2386] :
( ! [U_2384,U_2382] : hBOOL(hAPP(hAPP(c_Set_Ovimage(U_2382,U_2384,U_2386),U_2388),U_2390))
| ~ hBOOL(hAPP(U_2388,hAPP(U_2386,U_2390))) )
& ! [U_2389,U_2387,U_2385] :
( ! [U_2383,U_2381] : ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_2381,U_2383,U_2385),U_2387),U_2389))
| hBOOL(hAPP(U_2387,hAPP(U_2385,U_2389))) ) ),
inference(miniscope,[status(thm)],[f_669_2]) ).
cnf(f_669_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_2381,U_2383,U_2385),U_2387),U_2389))
| hBOOL(hAPP(U_2387,hAPP(U_2385,U_2389))) ),
inference(clausify,[status(thm)],[f_669_3]) ).
cnf(f_669_5,plain,
( hBOOL(hAPP(hAPP(c_Set_Ovimage(U_2382,U_2384,U_2386),U_2388),U_2390))
| ~ hBOOL(hAPP(U_2388,hAPP(U_2386,U_2390))) ),
inference(clausify,[status(thm)],[f_669_3]) ).
fof(f_670_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_670_2,plain,
! [U_2394,U_2393,U_2392,U_2391] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_2393),U_2394),U_2391))
| ~ hBOOL(hAPP(hAPP(c_member(U_2393),U_2394),U_2392)) )
& ( hBOOL(hAPP(hAPP(c_member(U_2393),U_2394),U_2392))
| ~ hBOOL(hAPP(hAPP(c_member(U_2393),U_2394),U_2391)) ) )
| U_2391 != U_2392 ),
inference(variable_rename,[status(thm)],[f_670_1]) ).
cnf(f_670_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2393),U_2394),U_2392))
| ~ hBOOL(hAPP(hAPP(c_member(U_2393),U_2394),U_2391))
| U_2391 != U_2392 ),
inference(clausify,[status(thm)],[f_670_2]) ).
cnf(f_670_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2393),U_2394),U_2391))
| ~ hBOOL(hAPP(hAPP(c_member(U_2393),U_2394),U_2392))
| U_2391 != U_2392 ),
inference(clausify,[status(thm)],[f_670_2]) ).
fof(f_671_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_671_2,plain,
! [U_2398,U_2397,U_2396,U_2395] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_2397),U_2395),U_2398))
| ~ hBOOL(hAPP(hAPP(c_member(U_2397),U_2396),U_2398)) )
& ( hBOOL(hAPP(hAPP(c_member(U_2397),U_2396),U_2398))
| ~ hBOOL(hAPP(hAPP(c_member(U_2397),U_2395),U_2398)) ) )
| U_2395 != U_2396 ),
inference(variable_rename,[status(thm)],[f_671_1]) ).
cnf(f_671_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2397),U_2396),U_2398))
| ~ hBOOL(hAPP(hAPP(c_member(U_2397),U_2395),U_2398))
| U_2395 != U_2396 ),
inference(clausify,[status(thm)],[f_671_2]) ).
cnf(f_671_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2397),U_2395),U_2398))
| ~ hBOOL(hAPP(hAPP(c_member(U_2397),U_2396),U_2398))
| U_2395 != U_2396 ),
inference(clausify,[status(thm)],[f_671_2]) ).
fof(f_672_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_672_2,plain,
! [U_2402,U_2401,U_2400,U_2399] :
( hBOOL(hAPP(hAPP(c_member(U_2401),U_2399),U_2402))
| ~ hBOOL(hAPP(hAPP(c_member(U_2401),U_2400),U_2402))
| U_2399 != U_2400 ),
inference(variable_rename,[status(thm)],[f_672_1]) ).
cnf(f_672_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2401),U_2399),U_2402))
| ~ hBOOL(hAPP(hAPP(c_member(U_2401),U_2400),U_2402))
| U_2399 != U_2400 ),
inference(clausify,[status(thm)],[f_672_2]) ).
fof(f_673_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_673_2,plain,
! [U_2407,U_2406,U_2405,U_2404,U_2403] :
( hBOOL(hAPP(hAPP(c_member(U_2405),hAPP(U_2406,U_2404)),U_2407))
| ~ hBOOL(hAPP(hAPP(c_member(U_2403),U_2404),hAPP(c_Set_Ovimage(U_2403,U_2405,U_2406),U_2407))) ),
inference(variable_rename,[status(thm)],[f_673_1]) ).
fof(f_673_3,plain,
! [U_2407,U_2406,U_2405,U_2404] :
( ! [U_2403] : ~ hBOOL(hAPP(hAPP(c_member(U_2403),U_2404),hAPP(c_Set_Ovimage(U_2403,U_2405,U_2406),U_2407)))
| hBOOL(hAPP(hAPP(c_member(U_2405),hAPP(U_2406,U_2404)),U_2407)) ),
inference(miniscope,[status(thm)],[f_673_2]) ).
cnf(f_673_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2403),U_2404),hAPP(c_Set_Ovimage(U_2403,U_2405,U_2406),U_2407)))
| hBOOL(hAPP(hAPP(c_member(U_2405),hAPP(U_2406,U_2404)),U_2407)) ),
inference(clausify,[status(thm)],[f_673_3]) ).
fof(f_674_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_674_2,plain,
! [U_2412,U_2411,U_2410,U_2409,U_2408] :
( hBOOL(hAPP(hAPP(c_member(U_2412),U_2410),hAPP(c_Set_Ovimage(U_2412,U_2408,U_2409),U_2411)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2408),hAPP(U_2409,U_2410)),U_2411)) ),
inference(variable_rename,[status(thm)],[f_674_1]) ).
cnf(f_674_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2412),U_2410),hAPP(c_Set_Ovimage(U_2412,U_2408,U_2409),U_2411)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2408),hAPP(U_2409,U_2410)),U_2411)) ),
inference(clausify,[status(thm)],[f_674_2]) ).
fof(f_675_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_675_2,plain,
! [U_2417,U_2416,U_2415,U_2414,U_2413] :
( hAPP(c_Fun_Othe__inv__into(U_2413,U_2414,U_2416,U_2415),hAPP(U_2415,U_2417)) = U_2417
| ~ hBOOL(hAPP(hAPP(c_member(U_2413),U_2417),U_2416))
| ~ c_Fun_Oinj__on(U_2413,U_2414,U_2415,U_2416) ),
inference(variable_rename,[status(thm)],[f_675_1]) ).
cnf(f_675_3,plain,
( hAPP(c_Fun_Othe__inv__into(U_2413,U_2414,U_2416,U_2415),hAPP(U_2415,U_2417)) = U_2417
| ~ hBOOL(hAPP(hAPP(c_member(U_2413),U_2417),U_2416))
| ~ c_Fun_Oinj__on(U_2413,U_2414,U_2415,U_2416) ),
inference(clausify,[status(thm)],[f_675_2]) ).
fof(f_676_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_676_2,plain,
! [U_2423,U_2422,U_2421,U_2420,U_2419,U_2418] :
( hAPP(c_Fun_Othe__inv__into(U_2418,U_2419,U_2421,U_2420),U_2423) = U_2422
| ~ hBOOL(hAPP(hAPP(c_member(U_2418),U_2422),U_2421))
| hAPP(U_2420,U_2422) != U_2423
| ~ c_Fun_Oinj__on(U_2418,U_2419,U_2420,U_2421) ),
inference(variable_rename,[status(thm)],[f_676_1]) ).
cnf(f_676_3,plain,
( hAPP(c_Fun_Othe__inv__into(U_2418,U_2419,U_2421,U_2420),U_2423) = U_2422
| ~ hBOOL(hAPP(hAPP(c_member(U_2418),U_2422),U_2421))
| hAPP(U_2420,U_2422) != U_2423
| ~ c_Fun_Oinj__on(U_2418,U_2419,U_2420,U_2421) ),
inference(clausify,[status(thm)],[f_676_2]) ).
fof(f_677_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_677_2,plain,
! [U_2428,U_2427,U_2426,U_2425,U_2424] :
( ( hBOOL(hAPP(hAPP(c_member(U_2424),U_2425),hAPP(c_Set_Ovimage(U_2424,U_2426,U_2427),hAPP(hAPP(c_Set_Oinsert(U_2426),U_2428),c_Orderings_Obot__class_Obot(tc_fun(U_2426,tc_HOL_Obool))))))
| hAPP(U_2427,U_2425) != U_2428 )
& ( hAPP(U_2427,U_2425) = U_2428
| ~ hBOOL(hAPP(hAPP(c_member(U_2424),U_2425),hAPP(c_Set_Ovimage(U_2424,U_2426,U_2427),hAPP(hAPP(c_Set_Oinsert(U_2426),U_2428),c_Orderings_Obot__class_Obot(tc_fun(U_2426,tc_HOL_Obool)))))) ) ),
inference(variable_rename,[status(thm)],[f_677_1]) ).
fof(f_677_3,plain,
( ! [U_2438,U_2436,U_2434,U_2432] :
( ! [U_2430] : hBOOL(hAPP(hAPP(c_member(U_2430),U_2432),hAPP(c_Set_Ovimage(U_2430,U_2434,U_2436),hAPP(hAPP(c_Set_Oinsert(U_2434),U_2438),c_Orderings_Obot__class_Obot(tc_fun(U_2434,tc_HOL_Obool))))))
| hAPP(U_2436,U_2432) != U_2438 )
& ! [U_2437,U_2435,U_2433,U_2431] :
( ! [U_2429] : ~ hBOOL(hAPP(hAPP(c_member(U_2429),U_2431),hAPP(c_Set_Ovimage(U_2429,U_2433,U_2435),hAPP(hAPP(c_Set_Oinsert(U_2433),U_2437),c_Orderings_Obot__class_Obot(tc_fun(U_2433,tc_HOL_Obool))))))
| hAPP(U_2435,U_2431) = U_2437 ) ),
inference(miniscope,[status(thm)],[f_677_2]) ).
cnf(f_677_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2429),U_2431),hAPP(c_Set_Ovimage(U_2429,U_2433,U_2435),hAPP(hAPP(c_Set_Oinsert(U_2433),U_2437),c_Orderings_Obot__class_Obot(tc_fun(U_2433,tc_HOL_Obool))))))
| hAPP(U_2435,U_2431) = U_2437 ),
inference(clausify,[status(thm)],[f_677_3]) ).
cnf(f_677_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_2430),U_2432),hAPP(c_Set_Ovimage(U_2430,U_2434,U_2436),hAPP(hAPP(c_Set_Oinsert(U_2434),U_2438),c_Orderings_Obot__class_Obot(tc_fun(U_2434,tc_HOL_Obool))))))
| hAPP(U_2436,U_2432) != U_2438 ),
inference(clausify,[status(thm)],[f_677_3]) ).
fof(f_678_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_678_2,plain,
! [U_2441,U_2440,U_2439] : hAPP(c_Set_Ovimage(U_2439,U_2440,U_2441),c_Orderings_Obot__class_Obot(tc_fun(U_2440,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_2439,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_678_1]) ).
cnf(f_678_3,plain,
hAPP(c_Set_Ovimage(U_2439,U_2440,U_2441),c_Orderings_Obot__class_Obot(tc_fun(U_2440,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_2439,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_678_2]) ).
fof(f_679_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_679_2,plain,
! [U_2446,U_2445,U_2444,U_2443,U_2442] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2445,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_2445,U_2442,U_2446),U_2443)),hAPP(c_Set_Ovimage(U_2445,U_2442,U_2446),U_2444)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2442,tc_HOL_Obool)),U_2443),U_2444)) ),
inference(variable_rename,[status(thm)],[f_679_1]) ).
cnf(f_679_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2445,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_2445,U_2442,U_2446),U_2443)),hAPP(c_Set_Ovimage(U_2445,U_2442,U_2446),U_2444)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2442,tc_HOL_Obool)),U_2443),U_2444)) ),
inference(clausify,[status(thm)],[f_679_2]) ).
fof(f_680_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_680_2,plain,
! [U_2449,U_2448,U_2447] : hAPP(c_Set_Ovimage(U_2447,U_2448,U_2449),c_Orderings_Otop__class_Otop(tc_fun(U_2448,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_2447,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_680_1]) ).
cnf(f_680_3,plain,
hAPP(c_Set_Ovimage(U_2447,U_2448,U_2449),c_Orderings_Otop__class_Otop(tc_fun(U_2448,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_2447,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_680_2]) ).
fof(f_681_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_681_2,plain,
! [U_2454,U_2453,U_2452,U_2451,U_2450] : hAPP(c_Set_Ovimage(U_2450,U_2451,U_2452),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2451,tc_HOL_Obool)),U_2453),U_2454)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2450,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_2450,U_2451,U_2452),U_2453)),hAPP(c_Set_Ovimage(U_2450,U_2451,U_2452),U_2454)),
inference(variable_rename,[status(thm)],[f_681_1]) ).
cnf(f_681_3,plain,
hAPP(c_Set_Ovimage(U_2450,U_2451,U_2452),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2451,tc_HOL_Obool)),U_2453),U_2454)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2450,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_2450,U_2451,U_2452),U_2453)),hAPP(c_Set_Ovimage(U_2450,U_2451,U_2452),U_2454)),
inference(clausify,[status(thm)],[f_681_2]) ).
fof(f_682_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_682_2,plain,
! [U_2459,U_2458,U_2457,U_2456,U_2455] : hAPP(c_Set_Ovimage(U_2455,U_2456,U_2457),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2456,tc_HOL_Obool)),U_2458),U_2459)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2455,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_2455,U_2456,U_2457),U_2458)),hAPP(c_Set_Ovimage(U_2455,U_2456,U_2457),U_2459)),
inference(variable_rename,[status(thm)],[f_682_1]) ).
cnf(f_682_3,plain,
hAPP(c_Set_Ovimage(U_2455,U_2456,U_2457),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2456,tc_HOL_Obool)),U_2458),U_2459)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2455,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_2455,U_2456,U_2457),U_2458)),hAPP(c_Set_Ovimage(U_2455,U_2456,U_2457),U_2459)),
inference(clausify,[status(thm)],[f_682_2]) ).
fof(f_683_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_683_2,plain,
! [U_2464,U_2463,U_2462,U_2461,U_2460] : hAPP(c_Set_Ovimage(U_2460,U_2461,U_2462),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2461,tc_HOL_Obool)),U_2463),U_2464)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2460,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_2460,U_2461,U_2462),U_2463)),hAPP(c_Set_Ovimage(U_2460,U_2461,U_2462),U_2464)),
inference(variable_rename,[status(thm)],[f_683_1]) ).
cnf(f_683_3,plain,
hAPP(c_Set_Ovimage(U_2460,U_2461,U_2462),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2461,tc_HOL_Obool)),U_2463),U_2464)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2460,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_2460,U_2461,U_2462),U_2463)),hAPP(c_Set_Ovimage(U_2460,U_2461,U_2462),U_2464)),
inference(clausify,[status(thm)],[f_683_2]) ).
fof(f_684_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_684_2,plain,
! [U_2468,U_2467] :
( ( ! [U_2466] : ~ hBOOL(hAPP(hAPP(c_member(U_2467),U_2466),U_2468))
| U_2468 != c_Orderings_Obot__class_Obot(tc_fun(U_2467,tc_HOL_Obool)) )
& ( U_2468 = c_Orderings_Obot__class_Obot(tc_fun(U_2467,tc_HOL_Obool))
| ? [U_2465] : hBOOL(hAPP(hAPP(c_member(U_2467),U_2465),U_2468)) ) ),
inference(variable_rename,[status(thm)],[f_684_1]) ).
fof(f_684_3,plain,
( ! [U_2472,U_2470] :
( ! [U_2466] : ~ hBOOL(hAPP(hAPP(c_member(U_2470),U_2466),U_2472))
| U_2472 != c_Orderings_Obot__class_Obot(tc_fun(U_2470,tc_HOL_Obool)) )
& ! [U_2471,U_2469] :
( U_2471 = c_Orderings_Obot__class_Obot(tc_fun(U_2469,tc_HOL_Obool))
| ? [U_2465] : hBOOL(hAPP(hAPP(c_member(U_2469),U_2465),U_2471)) ) ),
inference(miniscope,[status(thm)],[f_684_2]) ).
fof(f_684_4,plain,
( ! [U_2472,U_2470] :
( ! [U_2466] : ~ hBOOL(hAPP(hAPP(c_member(U_2470),U_2466),U_2472))
| U_2472 != c_Orderings_Obot__class_Obot(tc_fun(U_2470,tc_HOL_Obool)) )
& ! [U_2471,U_2469] :
( U_2471 = c_Orderings_Obot__class_Obot(tc_fun(U_2469,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2469),sK40(U_2471,U_2469)),U_2471)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_2465,sK40(U_2471,U_2469))],[f_684_3]) ).
cnf(f_684_5,plain,
( U_2471 = c_Orderings_Obot__class_Obot(tc_fun(U_2469,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2469),sK40(U_2471,U_2469)),U_2471)) ),
inference(clausify,[status(thm)],[f_684_4]) ).
cnf(f_684_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2470),U_2466),U_2472))
| U_2472 != c_Orderings_Obot__class_Obot(tc_fun(U_2470,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_684_4]) ).
fof(f_685_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_685_2,plain,
! [U_2476,U_2475] :
( ( ? [U_2474] : hBOOL(hAPP(hAPP(c_member(U_2475),U_2474),U_2476))
| U_2476 = c_Orderings_Obot__class_Obot(tc_fun(U_2475,tc_HOL_Obool)) )
& ( U_2476 != c_Orderings_Obot__class_Obot(tc_fun(U_2475,tc_HOL_Obool))
| ! [U_2473] : ~ hBOOL(hAPP(hAPP(c_member(U_2475),U_2473),U_2476)) ) ),
inference(variable_rename,[status(thm)],[f_685_1]) ).
fof(f_685_3,plain,
( ! [U_2480,U_2478] :
( ? [U_2474] : hBOOL(hAPP(hAPP(c_member(U_2478),U_2474),U_2480))
| U_2480 = c_Orderings_Obot__class_Obot(tc_fun(U_2478,tc_HOL_Obool)) )
& ! [U_2479,U_2477] :
( U_2479 != c_Orderings_Obot__class_Obot(tc_fun(U_2477,tc_HOL_Obool))
| ! [U_2473] : ~ hBOOL(hAPP(hAPP(c_member(U_2477),U_2473),U_2479)) ) ),
inference(miniscope,[status(thm)],[f_685_2]) ).
fof(f_685_4,plain,
( ! [U_2480,U_2478] :
( hBOOL(hAPP(hAPP(c_member(U_2478),sK41(U_2480,U_2478)),U_2480))
| U_2480 = c_Orderings_Obot__class_Obot(tc_fun(U_2478,tc_HOL_Obool)) )
& ! [U_2479,U_2477] :
( U_2479 != c_Orderings_Obot__class_Obot(tc_fun(U_2477,tc_HOL_Obool))
| ! [U_2473] : ~ hBOOL(hAPP(hAPP(c_member(U_2477),U_2473),U_2479)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_2474,sK41(U_2480,U_2478))],[f_685_3]) ).
cnf(f_685_5,plain,
( U_2479 != c_Orderings_Obot__class_Obot(tc_fun(U_2477,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_2477),U_2473),U_2479)) ),
inference(clausify,[status(thm)],[f_685_4]) ).
cnf(f_685_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_2478),sK41(U_2480,U_2478)),U_2480))
| U_2480 = c_Orderings_Obot__class_Obot(tc_fun(U_2478,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_685_4]) ).
fof(f_686_1,plain,
! [V_c_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_empty__iff]) ).
fof(f_686_2,plain,
! [U_2482,U_2481] : ~ hBOOL(hAPP(hAPP(c_member(U_2481),U_2482),c_Orderings_Obot__class_Obot(tc_fun(U_2481,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_686_1]) ).
cnf(f_686_3,plain,
~ hBOOL(hAPP(hAPP(c_member(U_2481),U_2482),c_Orderings_Obot__class_Obot(tc_fun(U_2481,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_686_2]) ).
fof(f_687_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_687_2,plain,
! [U_2485,U_2484,U_2483] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2484),U_2485),U_2483))
| U_2483 != c_Orderings_Obot__class_Obot(tc_fun(U_2484,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_687_1]) ).
cnf(f_687_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2484),U_2485),U_2483))
| U_2483 != c_Orderings_Obot__class_Obot(tc_fun(U_2484,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_687_2]) ).
fof(f_688_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_688_2,plain,
! [U_2488,U_2487,U_2486] : hBOOL(hAPP(hAPP(c_member(U_2486),U_2487),hAPP(hAPP(c_Set_Oinsert(U_2486),U_2487),U_2488))),
inference(variable_rename,[status(thm)],[f_688_1]) ).
cnf(f_688_3,plain,
hBOOL(hAPP(hAPP(c_member(U_2486),U_2487),hAPP(hAPP(c_Set_Oinsert(U_2486),U_2487),U_2488))),
inference(clausify,[status(thm)],[f_688_2]) ).
fof(f_689_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_689_2,plain,
! [U_2492,U_2491,U_2490,U_2489] :
( ( hBOOL(hAPP(hAPP(c_member(U_2489),U_2490),hAPP(hAPP(c_Set_Oinsert(U_2489),U_2491),U_2492)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_2489),U_2490),U_2492))
& U_2490 != U_2491 ) )
& ( hBOOL(hAPP(hAPP(c_member(U_2489),U_2490),U_2492))
| U_2490 = U_2491
| ~ hBOOL(hAPP(hAPP(c_member(U_2489),U_2490),hAPP(hAPP(c_Set_Oinsert(U_2489),U_2491),U_2492))) ) ),
inference(variable_rename,[status(thm)],[f_689_1]) ).
fof(f_689_3,plain,
( ! [U_2500,U_2498,U_2496,U_2494] :
( hBOOL(hAPP(hAPP(c_member(U_2494),U_2496),hAPP(hAPP(c_Set_Oinsert(U_2494),U_2498),U_2500)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_2494),U_2496),U_2500))
& U_2496 != U_2498 ) )
& ! [U_2499,U_2497,U_2495,U_2493] :
( hBOOL(hAPP(hAPP(c_member(U_2493),U_2495),U_2499))
| U_2495 = U_2497
| ~ hBOOL(hAPP(hAPP(c_member(U_2493),U_2495),hAPP(hAPP(c_Set_Oinsert(U_2493),U_2497),U_2499))) ) ),
inference(miniscope,[status(thm)],[f_689_2]) ).
cnf(f_689_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2493),U_2495),U_2499))
| U_2495 = U_2497
| ~ hBOOL(hAPP(hAPP(c_member(U_2493),U_2495),hAPP(hAPP(c_Set_Oinsert(U_2493),U_2497),U_2499))) ),
inference(clausify,[status(thm)],[f_689_3]) ).
cnf(f_689_5,plain,
( U_2496 != U_2498
| hBOOL(hAPP(hAPP(c_member(U_2494),U_2496),hAPP(hAPP(c_Set_Oinsert(U_2494),U_2498),U_2500))) ),
inference(clausify,[status(thm)],[f_689_3]) ).
cnf(f_689_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2494),U_2496),U_2500))
| hBOOL(hAPP(hAPP(c_member(U_2494),U_2496),hAPP(hAPP(c_Set_Oinsert(U_2494),U_2498),U_2500))) ),
inference(clausify,[status(thm)],[f_689_3]) ).
fof(f_690_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_690_2,plain,
! [U_2504,U_2503,U_2502,U_2501] :
( ( ( hAPP(hAPP(c_Set_Oinsert(U_2501),U_2502),U_2503) = hAPP(hAPP(c_Set_Oinsert(U_2501),U_2502),U_2504)
| U_2503 != U_2504 )
& ( U_2503 = U_2504
| hAPP(hAPP(c_Set_Oinsert(U_2501),U_2502),U_2503) != hAPP(hAPP(c_Set_Oinsert(U_2501),U_2502),U_2504) ) )
| hBOOL(hAPP(hAPP(c_member(U_2501),U_2502),U_2504))
| hBOOL(hAPP(hAPP(c_member(U_2501),U_2502),U_2503)) ),
inference(variable_rename,[status(thm)],[f_690_1]) ).
cnf(f_690_3,plain,
( U_2503 = U_2504
| hAPP(hAPP(c_Set_Oinsert(U_2501),U_2502),U_2503) != hAPP(hAPP(c_Set_Oinsert(U_2501),U_2502),U_2504)
| hBOOL(hAPP(hAPP(c_member(U_2501),U_2502),U_2504))
| hBOOL(hAPP(hAPP(c_member(U_2501),U_2502),U_2503)) ),
inference(clausify,[status(thm)],[f_690_2]) ).
cnf(f_690_4,plain,
( hAPP(hAPP(c_Set_Oinsert(U_2501),U_2502),U_2503) = hAPP(hAPP(c_Set_Oinsert(U_2501),U_2502),U_2504)
| U_2503 != U_2504
| hBOOL(hAPP(hAPP(c_member(U_2501),U_2502),U_2504))
| hBOOL(hAPP(hAPP(c_member(U_2501),U_2502),U_2503)) ),
inference(clausify,[status(thm)],[f_690_2]) ).
fof(f_691_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_691_2,plain,
! [U_2508,U_2507,U_2506,U_2505] :
( hBOOL(hAPP(hAPP(c_member(U_2505),U_2506),hAPP(hAPP(c_Set_Oinsert(U_2505),U_2508),U_2507)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2505),U_2506),U_2507)) ),
inference(variable_rename,[status(thm)],[f_691_1]) ).
cnf(f_691_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2505),U_2506),hAPP(hAPP(c_Set_Oinsert(U_2505),U_2508),U_2507)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2505),U_2506),U_2507)) ),
inference(clausify,[status(thm)],[f_691_2]) ).
fof(f_692_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_692_2,plain,
! [U_2511,U_2510,U_2509] :
( hAPP(hAPP(c_Set_Oinsert(U_2509),U_2510),U_2511) = U_2511
| ~ hBOOL(hAPP(hAPP(c_member(U_2509),U_2510),U_2511)) ),
inference(variable_rename,[status(thm)],[f_692_1]) ).
cnf(f_692_3,plain,
( hAPP(hAPP(c_Set_Oinsert(U_2509),U_2510),U_2511) = U_2511
| ~ hBOOL(hAPP(hAPP(c_member(U_2509),U_2510),U_2511)) ),
inference(clausify,[status(thm)],[f_692_2]) ).
fof(f_693_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_693_2,plain,
! [U_2515,U_2514,U_2513,U_2512] :
( hBOOL(hAPP(hAPP(c_member(U_2512),U_2515),U_2514))
| ~ hBOOL(hAPP(hAPP(c_member(U_2512),U_2515),U_2513))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2512,tc_HOL_Obool)),U_2513),U_2514)) ),
inference(variable_rename,[status(thm)],[f_693_1]) ).
cnf(f_693_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2512),U_2515),U_2514))
| ~ hBOOL(hAPP(hAPP(c_member(U_2512),U_2515),U_2513))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2512,tc_HOL_Obool)),U_2513),U_2514)) ),
inference(clausify,[status(thm)],[f_693_2]) ).
fof(f_694_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_694_2,plain,
! [U_2519,U_2518,U_2517,U_2516] :
( hBOOL(hAPP(hAPP(c_member(U_2516),U_2517),U_2519))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2516,tc_HOL_Obool)),U_2518),U_2519))
| ~ hBOOL(hAPP(hAPP(c_member(U_2516),U_2517),U_2518)) ),
inference(variable_rename,[status(thm)],[f_694_1]) ).
cnf(f_694_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2516),U_2517),U_2519))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2516,tc_HOL_Obool)),U_2518),U_2519))
| ~ hBOOL(hAPP(hAPP(c_member(U_2516),U_2517),U_2518)) ),
inference(clausify,[status(thm)],[f_694_2]) ).
fof(f_695_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_695_2,plain,
! [U_2523,U_2522,U_2521,U_2520] :
( hBOOL(hAPP(hAPP(c_member(U_2520),U_2523),U_2522))
| ~ hBOOL(hAPP(hAPP(c_member(U_2520),U_2523),U_2521))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2520,tc_HOL_Obool)),U_2521),U_2522)) ),
inference(variable_rename,[status(thm)],[f_695_1]) ).
cnf(f_695_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2520),U_2523),U_2522))
| ~ hBOOL(hAPP(hAPP(c_member(U_2520),U_2523),U_2521))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2520,tc_HOL_Obool)),U_2521),U_2522)) ),
inference(clausify,[status(thm)],[f_695_2]) ).
fof(f_696_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_696_2,plain,
! [U_2530,U_2529,U_2528,U_2527,U_2526] :
( ( hBOOL(hAPP(hAPP(c_member(U_2526),U_2527),hAPP(c_Set_Oimage(U_2528,U_2526,U_2529),U_2530)))
| ! [U_2525] :
( U_2527 != hAPP(U_2529,U_2525)
| ~ hBOOL(hAPP(hAPP(c_member(U_2528),U_2525),U_2530)) ) )
& ( ? [U_2524] :
( U_2527 = hAPP(U_2529,U_2524)
& hBOOL(hAPP(hAPP(c_member(U_2528),U_2524),U_2530)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2526),U_2527),hAPP(c_Set_Oimage(U_2528,U_2526,U_2529),U_2530))) ) ),
inference(variable_rename,[status(thm)],[f_696_1]) ).
fof(f_696_3,plain,
( ! [U_2540,U_2538,U_2536,U_2534] :
( ! [U_2532] : hBOOL(hAPP(hAPP(c_member(U_2532),U_2534),hAPP(c_Set_Oimage(U_2536,U_2532,U_2538),U_2540)))
| ! [U_2525] :
( U_2534 != hAPP(U_2538,U_2525)
| ~ hBOOL(hAPP(hAPP(c_member(U_2536),U_2525),U_2540)) ) )
& ! [U_2539,U_2537,U_2535,U_2533] :
( ! [U_2531] : ~ hBOOL(hAPP(hAPP(c_member(U_2531),U_2533),hAPP(c_Set_Oimage(U_2535,U_2531,U_2537),U_2539)))
| ? [U_2524] :
( U_2533 = hAPP(U_2537,U_2524)
& hBOOL(hAPP(hAPP(c_member(U_2535),U_2524),U_2539)) ) ) ),
inference(miniscope,[status(thm)],[f_696_2]) ).
fof(f_696_4,plain,
( ! [U_2540,U_2538,U_2536,U_2534] :
( ! [U_2532] : hBOOL(hAPP(hAPP(c_member(U_2532),U_2534),hAPP(c_Set_Oimage(U_2536,U_2532,U_2538),U_2540)))
| ! [U_2525] :
( U_2534 != hAPP(U_2538,U_2525)
| ~ hBOOL(hAPP(hAPP(c_member(U_2536),U_2525),U_2540)) ) )
& ! [U_2539,U_2537,U_2535,U_2533] :
( ! [U_2531] : ~ hBOOL(hAPP(hAPP(c_member(U_2531),U_2533),hAPP(c_Set_Oimage(U_2535,U_2531,U_2537),U_2539)))
| ( U_2533 = hAPP(U_2537,sK42(U_2539,U_2537,U_2535,U_2533))
& hBOOL(hAPP(hAPP(c_member(U_2535),sK42(U_2539,U_2537,U_2535,U_2533)),U_2539)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_2524,sK42(U_2539,U_2537,U_2535,U_2533))],[f_696_3]) ).
cnf(f_696_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_2535),sK42(U_2539,U_2537,U_2535,U_2533)),U_2539))
| ~ hBOOL(hAPP(hAPP(c_member(U_2531),U_2533),hAPP(c_Set_Oimage(U_2535,U_2531,U_2537),U_2539))) ),
inference(clausify,[status(thm)],[f_696_4]) ).
cnf(f_696_6,plain,
( U_2533 = hAPP(U_2537,sK42(U_2539,U_2537,U_2535,U_2533))
| ~ hBOOL(hAPP(hAPP(c_member(U_2531),U_2533),hAPP(c_Set_Oimage(U_2535,U_2531,U_2537),U_2539))) ),
inference(clausify,[status(thm)],[f_696_4]) ).
cnf(f_696_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_2532),U_2534),hAPP(c_Set_Oimage(U_2536,U_2532,U_2538),U_2540)))
| U_2534 != hAPP(U_2538,U_2525)
| ~ hBOOL(hAPP(hAPP(c_member(U_2536),U_2525),U_2540)) ),
inference(clausify,[status(thm)],[f_696_4]) ).
fof(f_697_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_697_2,plain,
! [U_2545,U_2544,U_2543,U_2542,U_2541] :
( hBOOL(hAPP(hAPP(c_member(U_2544),hAPP(U_2545,U_2542)),hAPP(c_Set_Oimage(U_2541,U_2544,U_2545),U_2543)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2541),U_2542),U_2543)) ),
inference(variable_rename,[status(thm)],[f_697_1]) ).
cnf(f_697_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2544),hAPP(U_2545,U_2542)),hAPP(c_Set_Oimage(U_2541,U_2544,U_2545),U_2543)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2541),U_2542),U_2543)) ),
inference(clausify,[status(thm)],[f_697_2]) ).
fof(f_698_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_698_2,plain,
! [U_2551,U_2550,U_2549,U_2548,U_2547,U_2546] :
( hBOOL(hAPP(hAPP(c_member(U_2551),U_2549),hAPP(c_Set_Oimage(U_2546,U_2551,U_2550),U_2548)))
| U_2549 != hAPP(U_2550,U_2547)
| ~ hBOOL(hAPP(hAPP(c_member(U_2546),U_2547),U_2548)) ),
inference(variable_rename,[status(thm)],[f_698_1]) ).
cnf(f_698_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2551),U_2549),hAPP(c_Set_Oimage(U_2546,U_2551,U_2550),U_2548)))
| U_2549 != hAPP(U_2550,U_2547)
| ~ hBOOL(hAPP(hAPP(c_member(U_2546),U_2547),U_2548)) ),
inference(clausify,[status(thm)],[f_698_2]) ).
fof(f_699_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Un__iff]) ).
fof(f_699_2,plain,
! [U_2555,U_2554,U_2553,U_2552] :
( ( hBOOL(hAPP(hAPP(c_member(U_2552),U_2553),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2552,tc_HOL_Obool)),U_2554),U_2555)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_2552),U_2553),U_2555))
& ~ hBOOL(hAPP(hAPP(c_member(U_2552),U_2553),U_2554)) ) )
& ( hBOOL(hAPP(hAPP(c_member(U_2552),U_2553),U_2555))
| hBOOL(hAPP(hAPP(c_member(U_2552),U_2553),U_2554))
| ~ hBOOL(hAPP(hAPP(c_member(U_2552),U_2553),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2552,tc_HOL_Obool)),U_2554),U_2555))) ) ),
inference(variable_rename,[status(thm)],[f_699_1]) ).
fof(f_699_3,plain,
( ! [U_2563,U_2561,U_2559,U_2557] :
( hBOOL(hAPP(hAPP(c_member(U_2557),U_2559),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2557,tc_HOL_Obool)),U_2561),U_2563)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_2557),U_2559),U_2563))
& ~ hBOOL(hAPP(hAPP(c_member(U_2557),U_2559),U_2561)) ) )
& ! [U_2562,U_2560,U_2558,U_2556] :
( hBOOL(hAPP(hAPP(c_member(U_2556),U_2558),U_2562))
| hBOOL(hAPP(hAPP(c_member(U_2556),U_2558),U_2560))
| ~ hBOOL(hAPP(hAPP(c_member(U_2556),U_2558),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2556,tc_HOL_Obool)),U_2560),U_2562))) ) ),
inference(miniscope,[status(thm)],[f_699_2]) ).
cnf(f_699_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2556),U_2558),U_2562))
| hBOOL(hAPP(hAPP(c_member(U_2556),U_2558),U_2560))
| ~ hBOOL(hAPP(hAPP(c_member(U_2556),U_2558),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2556,tc_HOL_Obool)),U_2560),U_2562))) ),
inference(clausify,[status(thm)],[f_699_3]) ).
cnf(f_699_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2557),U_2559),U_2561))
| hBOOL(hAPP(hAPP(c_member(U_2557),U_2559),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2557,tc_HOL_Obool)),U_2561),U_2563))) ),
inference(clausify,[status(thm)],[f_699_3]) ).
cnf(f_699_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2557),U_2559),U_2563))
| hBOOL(hAPP(hAPP(c_member(U_2557),U_2559),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2557,tc_HOL_Obool)),U_2561),U_2563))) ),
inference(clausify,[status(thm)],[f_699_3]) ).
fof(f_700_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_UnI1]) ).
fof(f_700_2,plain,
! [U_2567,U_2566,U_2565,U_2564] :
( hBOOL(hAPP(hAPP(c_member(U_2564),U_2565),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2564,tc_HOL_Obool)),U_2566),U_2567)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2564),U_2565),U_2566)) ),
inference(variable_rename,[status(thm)],[f_700_1]) ).
cnf(f_700_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2564),U_2565),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2564,tc_HOL_Obool)),U_2566),U_2567)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2564),U_2565),U_2566)) ),
inference(clausify,[status(thm)],[f_700_2]) ).
fof(f_701_1,plain,
! [V_A_2,V_B_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_UnI2]) ).
fof(f_701_2,plain,
! [U_2571,U_2570,U_2569,U_2568] :
( hBOOL(hAPP(hAPP(c_member(U_2568),U_2569),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2568,tc_HOL_Obool)),U_2571),U_2570)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2568),U_2569),U_2570)) ),
inference(variable_rename,[status(thm)],[f_701_1]) ).
cnf(f_701_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2568),U_2569),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2568,tc_HOL_Obool)),U_2571),U_2570)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2568),U_2569),U_2570)) ),
inference(clausify,[status(thm)],[f_701_2]) ).
fof(f_702_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
& ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Int__iff]) ).
fof(f_702_2,plain,
! [U_2575,U_2574,U_2573,U_2572] :
( ( hBOOL(hAPP(hAPP(c_member(U_2572),U_2573),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2572,tc_HOL_Obool)),U_2574),U_2575)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2572),U_2573),U_2575))
| ~ hBOOL(hAPP(hAPP(c_member(U_2572),U_2573),U_2574)) )
& ( ( hBOOL(hAPP(hAPP(c_member(U_2572),U_2573),U_2575))
& hBOOL(hAPP(hAPP(c_member(U_2572),U_2573),U_2574)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2572),U_2573),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2572,tc_HOL_Obool)),U_2574),U_2575))) ) ),
inference(variable_rename,[status(thm)],[f_702_1]) ).
fof(f_702_3,plain,
( ! [U_2583,U_2581,U_2579,U_2577] :
( hBOOL(hAPP(hAPP(c_member(U_2577),U_2579),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2577,tc_HOL_Obool)),U_2581),U_2583)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2577),U_2579),U_2583))
| ~ hBOOL(hAPP(hAPP(c_member(U_2577),U_2579),U_2581)) )
& ! [U_2582,U_2580,U_2578,U_2576] :
( ( hBOOL(hAPP(hAPP(c_member(U_2576),U_2578),U_2582))
& hBOOL(hAPP(hAPP(c_member(U_2576),U_2578),U_2580)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2576),U_2578),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2576,tc_HOL_Obool)),U_2580),U_2582))) ) ),
inference(miniscope,[status(thm)],[f_702_2]) ).
cnf(f_702_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2576),U_2578),U_2580))
| ~ hBOOL(hAPP(hAPP(c_member(U_2576),U_2578),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2576,tc_HOL_Obool)),U_2580),U_2582))) ),
inference(clausify,[status(thm)],[f_702_3]) ).
cnf(f_702_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_2576),U_2578),U_2582))
| ~ hBOOL(hAPP(hAPP(c_member(U_2576),U_2578),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2576,tc_HOL_Obool)),U_2580),U_2582))) ),
inference(clausify,[status(thm)],[f_702_3]) ).
cnf(f_702_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_2577),U_2579),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2577,tc_HOL_Obool)),U_2581),U_2583)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2577),U_2579),U_2583))
| ~ hBOOL(hAPP(hAPP(c_member(U_2577),U_2579),U_2581)) ),
inference(clausify,[status(thm)],[f_702_3]) ).
fof(f_703_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_IntD1]) ).
fof(f_703_2,plain,
! [U_2587,U_2586,U_2585,U_2584] :
( hBOOL(hAPP(hAPP(c_member(U_2584),U_2585),U_2586))
| ~ hBOOL(hAPP(hAPP(c_member(U_2584),U_2585),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2584,tc_HOL_Obool)),U_2586),U_2587))) ),
inference(variable_rename,[status(thm)],[f_703_1]) ).
cnf(f_703_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2584),U_2585),U_2586))
| ~ hBOOL(hAPP(hAPP(c_member(U_2584),U_2585),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2584,tc_HOL_Obool)),U_2586),U_2587))) ),
inference(clausify,[status(thm)],[f_703_2]) ).
fof(f_704_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_IntD2]) ).
fof(f_704_2,plain,
! [U_2591,U_2590,U_2589,U_2588] :
( hBOOL(hAPP(hAPP(c_member(U_2588),U_2589),U_2591))
| ~ hBOOL(hAPP(hAPP(c_member(U_2588),U_2589),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2588,tc_HOL_Obool)),U_2590),U_2591))) ),
inference(variable_rename,[status(thm)],[f_704_1]) ).
cnf(f_704_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2588),U_2589),U_2591))
| ~ hBOOL(hAPP(hAPP(c_member(U_2588),U_2589),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2588,tc_HOL_Obool)),U_2590),U_2591))) ),
inference(clausify,[status(thm)],[f_704_2]) ).
fof(f_705_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Diff__iff]) ).
fof(f_705_2,plain,
! [U_2595,U_2594,U_2593,U_2592] :
( ( hBOOL(hAPP(hAPP(c_member(U_2592),U_2593),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2592,tc_HOL_Obool)),U_2594),U_2595)))
| hBOOL(hAPP(hAPP(c_member(U_2592),U_2593),U_2595))
| ~ hBOOL(hAPP(hAPP(c_member(U_2592),U_2593),U_2594)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_member(U_2592),U_2593),U_2595))
& hBOOL(hAPP(hAPP(c_member(U_2592),U_2593),U_2594)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2592),U_2593),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2592,tc_HOL_Obool)),U_2594),U_2595))) ) ),
inference(variable_rename,[status(thm)],[f_705_1]) ).
fof(f_705_3,plain,
( ! [U_2603,U_2601,U_2599,U_2597] :
( hBOOL(hAPP(hAPP(c_member(U_2597),U_2599),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2597,tc_HOL_Obool)),U_2601),U_2603)))
| hBOOL(hAPP(hAPP(c_member(U_2597),U_2599),U_2603))
| ~ hBOOL(hAPP(hAPP(c_member(U_2597),U_2599),U_2601)) )
& ! [U_2602,U_2600,U_2598,U_2596] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_2596),U_2598),U_2602))
& hBOOL(hAPP(hAPP(c_member(U_2596),U_2598),U_2600)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2596),U_2598),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2596,tc_HOL_Obool)),U_2600),U_2602))) ) ),
inference(miniscope,[status(thm)],[f_705_2]) ).
cnf(f_705_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2596),U_2598),U_2600))
| ~ hBOOL(hAPP(hAPP(c_member(U_2596),U_2598),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2596,tc_HOL_Obool)),U_2600),U_2602))) ),
inference(clausify,[status(thm)],[f_705_3]) ).
cnf(f_705_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2596),U_2598),U_2602))
| ~ hBOOL(hAPP(hAPP(c_member(U_2596),U_2598),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2596,tc_HOL_Obool)),U_2600),U_2602))) ),
inference(clausify,[status(thm)],[f_705_3]) ).
cnf(f_705_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_2597),U_2599),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2597,tc_HOL_Obool)),U_2601),U_2603)))
| hBOOL(hAPP(hAPP(c_member(U_2597),U_2599),U_2603))
| ~ hBOOL(hAPP(hAPP(c_member(U_2597),U_2599),U_2601)) ),
inference(clausify,[status(thm)],[f_705_3]) ).
fof(f_706_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_DiffD1]) ).
fof(f_706_2,plain,
! [U_2607,U_2606,U_2605,U_2604] :
( hBOOL(hAPP(hAPP(c_member(U_2604),U_2605),U_2606))
| ~ hBOOL(hAPP(hAPP(c_member(U_2604),U_2605),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2604,tc_HOL_Obool)),U_2606),U_2607))) ),
inference(variable_rename,[status(thm)],[f_706_1]) ).
cnf(f_706_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2604),U_2605),U_2606))
| ~ hBOOL(hAPP(hAPP(c_member(U_2604),U_2605),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2604,tc_HOL_Obool)),U_2606),U_2607))) ),
inference(clausify,[status(thm)],[f_706_2]) ).
fof(f_707_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_DiffD2]) ).
fof(f_707_2,plain,
! [U_2611,U_2610,U_2609,U_2608] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2608),U_2609),U_2611))
| ~ hBOOL(hAPP(hAPP(c_member(U_2608),U_2609),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2608,tc_HOL_Obool)),U_2610),U_2611))) ),
inference(variable_rename,[status(thm)],[f_707_1]) ).
cnf(f_707_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2608),U_2609),U_2611))
| ~ hBOOL(hAPP(hAPP(c_member(U_2608),U_2609),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2608,tc_HOL_Obool)),U_2610),U_2611))) ),
inference(clausify,[status(thm)],[f_707_2]) ).
fof(f_708_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_708_2,plain,
! [U_2617,U_2616,U_2615,U_2614,U_2613,U_2612] :
( hAPP(U_2614,U_2616) != hAPP(U_2614,U_2617)
| ~ hBOOL(hAPP(hAPP(c_member(U_2612),U_2617),U_2615))
| ~ hBOOL(hAPP(hAPP(c_member(U_2612),U_2616),U_2615))
| U_2616 = U_2617
| ~ c_Fun_Oinj__on(U_2612,U_2613,U_2614,U_2615) ),
inference(variable_rename,[status(thm)],[f_708_1]) ).
cnf(f_708_3,plain,
( hAPP(U_2614,U_2616) != hAPP(U_2614,U_2617)
| ~ hBOOL(hAPP(hAPP(c_member(U_2612),U_2617),U_2615))
| ~ hBOOL(hAPP(hAPP(c_member(U_2612),U_2616),U_2615))
| U_2616 = U_2617
| ~ c_Fun_Oinj__on(U_2612,U_2613,U_2614,U_2615) ),
inference(clausify,[status(thm)],[f_708_2]) ).
fof(f_709_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_709_2,plain,
! [U_2623,U_2622,U_2621,U_2620,U_2619,U_2618] :
( ( ( hAPP(U_2620,U_2622) = hAPP(U_2620,U_2623)
| U_2622 != U_2623 )
& ( U_2622 = U_2623
| hAPP(U_2620,U_2622) != hAPP(U_2620,U_2623) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2618),U_2623),U_2621))
| ~ hBOOL(hAPP(hAPP(c_member(U_2618),U_2622),U_2621))
| ~ c_Fun_Oinj__on(U_2618,U_2619,U_2620,U_2621) ),
inference(variable_rename,[status(thm)],[f_709_1]) ).
cnf(f_709_3,plain,
( U_2622 = U_2623
| hAPP(U_2620,U_2622) != hAPP(U_2620,U_2623)
| ~ hBOOL(hAPP(hAPP(c_member(U_2618),U_2623),U_2621))
| ~ hBOOL(hAPP(hAPP(c_member(U_2618),U_2622),U_2621))
| ~ c_Fun_Oinj__on(U_2618,U_2619,U_2620,U_2621) ),
inference(clausify,[status(thm)],[f_709_2]) ).
cnf(f_709_4,plain,
( hAPP(U_2620,U_2622) = hAPP(U_2620,U_2623)
| U_2622 != U_2623
| ~ hBOOL(hAPP(hAPP(c_member(U_2618),U_2623),U_2621))
| ~ hBOOL(hAPP(hAPP(c_member(U_2618),U_2622),U_2621))
| ~ c_Fun_Oinj__on(U_2618,U_2619,U_2620,U_2621) ),
inference(clausify,[status(thm)],[f_709_2]) ).
fof(f_710_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_710_2,plain,
! [U_2629,U_2628,U_2627,U_2626,U_2625,U_2624] :
( U_2628 = U_2629
| ~ hBOOL(hAPP(hAPP(c_member(U_2624),U_2629),U_2627))
| ~ hBOOL(hAPP(hAPP(c_member(U_2624),U_2628),U_2627))
| hAPP(U_2626,U_2628) != hAPP(U_2626,U_2629)
| ~ c_Fun_Oinj__on(U_2624,U_2625,U_2626,U_2627) ),
inference(variable_rename,[status(thm)],[f_710_1]) ).
cnf(f_710_3,plain,
( U_2628 = U_2629
| ~ hBOOL(hAPP(hAPP(c_member(U_2624),U_2629),U_2627))
| ~ hBOOL(hAPP(hAPP(c_member(U_2624),U_2628),U_2627))
| hAPP(U_2626,U_2628) != hAPP(U_2626,U_2629)
| ~ c_Fun_Oinj__on(U_2624,U_2625,U_2626,U_2627) ),
inference(clausify,[status(thm)],[f_710_2]) ).
fof(f_711_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_711_2,plain,
! [U_2633,U_2632,U_2631,U_2630] : hAPP(c_Set_Ovimage(U_2630,U_2631,U_2632),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2631,tc_HOL_Obool)),U_2633)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2630,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_2630,U_2631,U_2632),U_2633)),
inference(variable_rename,[status(thm)],[f_711_1]) ).
cnf(f_711_3,plain,
hAPP(c_Set_Ovimage(U_2630,U_2631,U_2632),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2631,tc_HOL_Obool)),U_2633)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2630,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_2630,U_2631,U_2632),U_2633)),
inference(clausify,[status(thm)],[f_711_2]) ).
fof(f_712_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_712_2,plain,
! [U_2638,U_2637,U_2636,U_2635,U_2634] :
( hAPP(U_2636,hAPP(c_Fun_Othe__inv__into(U_2634,U_2635,U_2637,U_2636),U_2638)) = U_2638
| ~ hBOOL(hAPP(hAPP(c_member(U_2635),U_2638),hAPP(c_Set_Oimage(U_2634,U_2635,U_2636),U_2637)))
| ~ c_Fun_Oinj__on(U_2634,U_2635,U_2636,U_2637) ),
inference(variable_rename,[status(thm)],[f_712_1]) ).
cnf(f_712_3,plain,
( hAPP(U_2636,hAPP(c_Fun_Othe__inv__into(U_2634,U_2635,U_2637,U_2636),U_2638)) = U_2638
| ~ hBOOL(hAPP(hAPP(c_member(U_2635),U_2638),hAPP(c_Set_Oimage(U_2634,U_2635,U_2636),U_2637)))
| ~ c_Fun_Oinj__on(U_2634,U_2635,U_2636,U_2637) ),
inference(clausify,[status(thm)],[f_712_2]) ).
fof(f_713_1,plain,
! [V_A_2,V_c_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
| hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Compl__iff]) ).
fof(f_713_2,plain,
! [U_2641,U_2640,U_2639] :
( ( hBOOL(hAPP(hAPP(c_member(U_2639),U_2640),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2639,tc_HOL_Obool)),U_2641)))
| hBOOL(hAPP(hAPP(c_member(U_2639),U_2640),U_2641)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(U_2639),U_2640),U_2641))
| ~ hBOOL(hAPP(hAPP(c_member(U_2639),U_2640),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2639,tc_HOL_Obool)),U_2641))) ) ),
inference(variable_rename,[status(thm)],[f_713_1]) ).
fof(f_713_3,plain,
( ! [U_2647,U_2645,U_2643] :
( hBOOL(hAPP(hAPP(c_member(U_2643),U_2645),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2643,tc_HOL_Obool)),U_2647)))
| hBOOL(hAPP(hAPP(c_member(U_2643),U_2645),U_2647)) )
& ! [U_2646,U_2644,U_2642] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2642),U_2644),U_2646))
| ~ hBOOL(hAPP(hAPP(c_member(U_2642),U_2644),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2642,tc_HOL_Obool)),U_2646))) ) ),
inference(miniscope,[status(thm)],[f_713_2]) ).
cnf(f_713_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2642),U_2644),U_2646))
| ~ hBOOL(hAPP(hAPP(c_member(U_2642),U_2644),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2642,tc_HOL_Obool)),U_2646))) ),
inference(clausify,[status(thm)],[f_713_3]) ).
cnf(f_713_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_2643),U_2645),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2643,tc_HOL_Obool)),U_2647)))
| hBOOL(hAPP(hAPP(c_member(U_2643),U_2645),U_2647)) ),
inference(clausify,[status(thm)],[f_713_3]) ).
fof(f_714_1,plain,
! [V_A_2,V_c_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_ComplD]) ).
fof(f_714_2,plain,
! [U_2650,U_2649,U_2648] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2648),U_2649),U_2650))
| ~ hBOOL(hAPP(hAPP(c_member(U_2648),U_2649),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2648,tc_HOL_Obool)),U_2650))) ),
inference(variable_rename,[status(thm)],[f_714_1]) ).
cnf(f_714_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2648),U_2649),U_2650))
| ~ hBOOL(hAPP(hAPP(c_member(U_2648),U_2649),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2648,tc_HOL_Obool)),U_2650))) ),
inference(clausify,[status(thm)],[f_714_2]) ).
fof(f_715_1,plain,
! [V_A_2,V_c_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_ComplE]) ).
fof(f_715_2,plain,
! [U_2653,U_2652,U_2651] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2651),U_2652),U_2653))
| ~ hBOOL(hAPP(hAPP(c_member(U_2651),U_2652),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2651,tc_HOL_Obool)),U_2653))) ),
inference(variable_rename,[status(thm)],[f_715_1]) ).
cnf(f_715_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2651),U_2652),U_2653))
| ~ hBOOL(hAPP(hAPP(c_member(U_2651),U_2652),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2651,tc_HOL_Obool)),U_2653))) ),
inference(clausify,[status(thm)],[f_715_2]) ).
fof(f_716_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_716_2,plain,
! [U_2655,U_2654] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_2654,tc_HOL_Obool)),U_2655),hAPP(c_Set_OPow(U_2654),U_2655))),
inference(variable_rename,[status(thm)],[f_716_1]) ).
cnf(f_716_3,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(U_2654,tc_HOL_Obool)),U_2655),hAPP(c_Set_OPow(U_2654),U_2655))),
inference(clausify,[status(thm)],[f_716_2]) ).
fof(f_717_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_717_2,plain,
! [U_2658,U_2657,U_2656] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2657,U_2656),U_2658),c_Orderings_Obot__class_Obot(tc_fun(U_2657,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_2656)
| ~ class_Groups_Ocomm__monoid__add(U_2656) ),
inference(variable_rename,[status(thm)],[f_717_1]) ).
cnf(f_717_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2657,U_2656),U_2658),c_Orderings_Obot__class_Obot(tc_fun(U_2657,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_2656)
| ~ class_Groups_Ocomm__monoid__add(U_2656) ),
inference(clausify,[status(thm)],[f_717_2]) ).
fof(f_718_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_718_2,plain,
! [U_2661,U_2660,U_2659] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2660,U_2659),U_2661),c_Orderings_Obot__class_Obot(tc_fun(U_2660,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_2659)
| ~ class_Groups_Ocomm__monoid__add(U_2659) ),
inference(variable_rename,[status(thm)],[f_718_1]) ).
cnf(f_718_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2660,U_2659),U_2661),c_Orderings_Obot__class_Obot(tc_fun(U_2660,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_2659)
| ~ class_Groups_Ocomm__monoid__add(U_2659) ),
inference(clausify,[status(thm)],[f_718_2]) ).
fof(f_719_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_719_2,plain,
! [U_2667,U_2666,U_2665,U_2664,U_2663,U_2662] :
( hBOOL(hAPP(hAPP(c_member(U_2662),hAPP(c_Fun_Othe__inv__into(U_2662,U_2663,U_2665,U_2664),U_2666)),U_2667))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2662,tc_HOL_Obool)),U_2665),U_2667))
| ~ hBOOL(hAPP(hAPP(c_member(U_2663),U_2666),hAPP(c_Set_Oimage(U_2662,U_2663,U_2664),U_2665)))
| ~ c_Fun_Oinj__on(U_2662,U_2663,U_2664,U_2665) ),
inference(variable_rename,[status(thm)],[f_719_1]) ).
cnf(f_719_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2662),hAPP(c_Fun_Othe__inv__into(U_2662,U_2663,U_2665,U_2664),U_2666)),U_2667))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2662,tc_HOL_Obool)),U_2665),U_2667))
| ~ hBOOL(hAPP(hAPP(c_member(U_2663),U_2666),hAPP(c_Set_Oimage(U_2662,U_2663,U_2664),U_2665)))
| ~ c_Fun_Oinj__on(U_2662,U_2663,U_2664,U_2665) ),
inference(clausify,[status(thm)],[f_719_2]) ).
fof(f_720_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_720_2,plain,
! [U_2671,U_2670,U_2669,U_2668] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2668,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2669,U_2668,U_2670),hAPP(c_Set_Ovimage(U_2669,U_2668,U_2670),U_2671))),U_2671)),
inference(variable_rename,[status(thm)],[f_720_1]) ).
cnf(f_720_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2668,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2669,U_2668,U_2670),hAPP(c_Set_Ovimage(U_2669,U_2668,U_2670),U_2671))),U_2671)),
inference(clausify,[status(thm)],[f_720_2]) ).
fof(f_721_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_721_2,plain,
! [U_2675,U_2674,U_2673,U_2672] :
( hAPP(c_Set_Oimage(U_2672,U_2673,U_2674),hAPP(c_Set_Ovimage(U_2672,U_2673,U_2674),U_2675)) = U_2675
| hAPP(c_Set_Oimage(U_2672,U_2673,U_2674),c_Orderings_Otop__class_Otop(tc_fun(U_2672,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_2673,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_721_1]) ).
cnf(f_721_3,plain,
( hAPP(c_Set_Oimage(U_2672,U_2673,U_2674),hAPP(c_Set_Ovimage(U_2672,U_2673,U_2674),U_2675)) = U_2675
| hAPP(c_Set_Oimage(U_2672,U_2673,U_2674),c_Orderings_Otop__class_Otop(tc_fun(U_2672,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_2673,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_721_2]) ).
fof(f_722_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_722_2,plain,
! [U_2678,U_2677,U_2676] :
( ( hBOOL(hAPP(hAPP(c_member(U_2676),U_2677),hAPP(hAPP(c_Set_Oinsert(U_2676),U_2678),c_Orderings_Obot__class_Obot(tc_fun(U_2676,tc_HOL_Obool)))))
| U_2677 != U_2678 )
& ( U_2677 = U_2678
| ~ hBOOL(hAPP(hAPP(c_member(U_2676),U_2677),hAPP(hAPP(c_Set_Oinsert(U_2676),U_2678),c_Orderings_Obot__class_Obot(tc_fun(U_2676,tc_HOL_Obool))))) ) ),
inference(variable_rename,[status(thm)],[f_722_1]) ).
fof(f_722_3,plain,
( ! [U_2684,U_2682] :
( ! [U_2680] : hBOOL(hAPP(hAPP(c_member(U_2680),U_2682),hAPP(hAPP(c_Set_Oinsert(U_2680),U_2684),c_Orderings_Obot__class_Obot(tc_fun(U_2680,tc_HOL_Obool)))))
| U_2682 != U_2684 )
& ! [U_2683,U_2681] :
( ! [U_2679] : ~ hBOOL(hAPP(hAPP(c_member(U_2679),U_2681),hAPP(hAPP(c_Set_Oinsert(U_2679),U_2683),c_Orderings_Obot__class_Obot(tc_fun(U_2679,tc_HOL_Obool)))))
| U_2681 = U_2683 ) ),
inference(miniscope,[status(thm)],[f_722_2]) ).
cnf(f_722_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2679),U_2681),hAPP(hAPP(c_Set_Oinsert(U_2679),U_2683),c_Orderings_Obot__class_Obot(tc_fun(U_2679,tc_HOL_Obool)))))
| U_2681 = U_2683 ),
inference(clausify,[status(thm)],[f_722_3]) ).
cnf(f_722_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_2680),U_2682),hAPP(hAPP(c_Set_Oinsert(U_2680),U_2684),c_Orderings_Obot__class_Obot(tc_fun(U_2680,tc_HOL_Obool)))))
| U_2682 != U_2684 ),
inference(clausify,[status(thm)],[f_722_3]) ).
fof(f_723_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_723_2,plain,
! [U_2687,U_2686,U_2685] :
( U_2686 = U_2687
| ~ hBOOL(hAPP(hAPP(c_member(U_2685),U_2686),hAPP(hAPP(c_Set_Oinsert(U_2685),U_2687),c_Orderings_Obot__class_Obot(tc_fun(U_2685,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[f_723_1]) ).
fof(f_723_3,plain,
! [U_2687,U_2686] :
( ! [U_2685] : ~ hBOOL(hAPP(hAPP(c_member(U_2685),U_2686),hAPP(hAPP(c_Set_Oinsert(U_2685),U_2687),c_Orderings_Obot__class_Obot(tc_fun(U_2685,tc_HOL_Obool)))))
| U_2686 = U_2687 ),
inference(miniscope,[status(thm)],[f_723_2]) ).
cnf(f_723_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2685),U_2686),hAPP(hAPP(c_Set_Oinsert(U_2685),U_2687),c_Orderings_Obot__class_Obot(tc_fun(U_2685,tc_HOL_Obool)))))
| U_2686 = U_2687 ),
inference(clausify,[status(thm)],[f_723_3]) ).
fof(f_724_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_724_2,plain,
! [U_2691,U_2690,U_2689,U_2688] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2688,tc_HOL_Obool)),U_2690),hAPP(hAPP(c_Set_Oinsert(U_2688),U_2689),U_2691)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2688,tc_HOL_Obool)),U_2690),U_2691)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2688,tc_HOL_Obool)),U_2690),U_2691))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2688,tc_HOL_Obool)),U_2690),hAPP(hAPP(c_Set_Oinsert(U_2688),U_2689),U_2691))) ) )
| hBOOL(hAPP(hAPP(c_member(U_2688),U_2689),U_2690)) ),
inference(variable_rename,[status(thm)],[f_724_1]) ).
cnf(f_724_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2688,tc_HOL_Obool)),U_2690),U_2691))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2688,tc_HOL_Obool)),U_2690),hAPP(hAPP(c_Set_Oinsert(U_2688),U_2689),U_2691)))
| hBOOL(hAPP(hAPP(c_member(U_2688),U_2689),U_2690)) ),
inference(clausify,[status(thm)],[f_724_2]) ).
cnf(f_724_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2688,tc_HOL_Obool)),U_2690),hAPP(hAPP(c_Set_Oinsert(U_2688),U_2689),U_2691)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2688,tc_HOL_Obool)),U_2690),U_2691))
| hBOOL(hAPP(hAPP(c_member(U_2688),U_2689),U_2690)) ),
inference(clausify,[status(thm)],[f_724_2]) ).
fof(f_725_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_725_2,plain,
! [U_2695,U_2694,U_2693,U_2692] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2692,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2692),U_2693),U_2694)),U_2695))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2692,tc_HOL_Obool)),U_2694),U_2695))
| ~ hBOOL(hAPP(hAPP(c_member(U_2692),U_2693),U_2695)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2692,tc_HOL_Obool)),U_2694),U_2695))
& hBOOL(hAPP(hAPP(c_member(U_2692),U_2693),U_2695)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2692,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2692),U_2693),U_2694)),U_2695)) ) ),
inference(variable_rename,[status(thm)],[f_725_1]) ).
fof(f_725_3,plain,
( ! [U_2703,U_2701,U_2699,U_2697] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2697,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2697),U_2699),U_2701)),U_2703))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2697,tc_HOL_Obool)),U_2701),U_2703))
| ~ hBOOL(hAPP(hAPP(c_member(U_2697),U_2699),U_2703)) )
& ! [U_2702,U_2700,U_2698,U_2696] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2696,tc_HOL_Obool)),U_2700),U_2702))
& hBOOL(hAPP(hAPP(c_member(U_2696),U_2698),U_2702)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2696,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2696),U_2698),U_2700)),U_2702)) ) ),
inference(miniscope,[status(thm)],[f_725_2]) ).
cnf(f_725_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2696),U_2698),U_2702))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2696,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2696),U_2698),U_2700)),U_2702)) ),
inference(clausify,[status(thm)],[f_725_3]) ).
cnf(f_725_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2696,tc_HOL_Obool)),U_2700),U_2702))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2696,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2696),U_2698),U_2700)),U_2702)) ),
inference(clausify,[status(thm)],[f_725_3]) ).
cnf(f_725_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2697,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2697),U_2699),U_2701)),U_2703))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2697,tc_HOL_Obool)),U_2701),U_2703))
| ~ hBOOL(hAPP(hAPP(c_member(U_2697),U_2699),U_2703)) ),
inference(clausify,[status(thm)],[f_725_3]) ).
fof(f_726_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_726_2,plain,
! [U_2708,U_2707,U_2706,U_2705,U_2704] :
( hAPP(hAPP(c_Set_Oinsert(U_2707),hAPP(U_2708,U_2705)),hAPP(c_Set_Oimage(U_2704,U_2707,U_2708),U_2706)) = hAPP(c_Set_Oimage(U_2704,U_2707,U_2708),U_2706)
| ~ hBOOL(hAPP(hAPP(c_member(U_2704),U_2705),U_2706)) ),
inference(variable_rename,[status(thm)],[f_726_1]) ).
cnf(f_726_3,plain,
( hAPP(hAPP(c_Set_Oinsert(U_2707),hAPP(U_2708,U_2705)),hAPP(c_Set_Oimage(U_2704,U_2707,U_2708),U_2706)) = hAPP(c_Set_Oimage(U_2704,U_2707,U_2708),U_2706)
| ~ hBOOL(hAPP(hAPP(c_member(U_2704),U_2705),U_2706)) ),
inference(clausify,[status(thm)],[f_726_2]) ).
fof(f_727_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_727_2,plain,
! [U_2712,U_2711,U_2710,U_2709] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2709,tc_HOL_Obool)),U_2711),hAPP(hAPP(c_Set_Oinsert(U_2709),U_2710),U_2712)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2709,tc_HOL_Obool)),U_2711),U_2712)
| hBOOL(hAPP(hAPP(c_member(U_2709),U_2710),U_2711)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2709,tc_HOL_Obool)),U_2711),hAPP(hAPP(c_Set_Oinsert(U_2709),U_2710),U_2712)) = hAPP(hAPP(c_Set_Oinsert(U_2709),U_2710),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2709,tc_HOL_Obool)),U_2711),U_2712))
| ~ hBOOL(hAPP(hAPP(c_member(U_2709),U_2710),U_2711)) ) ),
inference(variable_rename,[status(thm)],[f_727_1]) ).
fof(f_727_3,plain,
( ! [U_2720,U_2718,U_2716,U_2714] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2714,tc_HOL_Obool)),U_2718),hAPP(hAPP(c_Set_Oinsert(U_2714),U_2716),U_2720)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2714,tc_HOL_Obool)),U_2718),U_2720)
| hBOOL(hAPP(hAPP(c_member(U_2714),U_2716),U_2718)) )
& ! [U_2719,U_2717,U_2715,U_2713] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2713,tc_HOL_Obool)),U_2717),hAPP(hAPP(c_Set_Oinsert(U_2713),U_2715),U_2719)) = hAPP(hAPP(c_Set_Oinsert(U_2713),U_2715),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2713,tc_HOL_Obool)),U_2717),U_2719))
| ~ hBOOL(hAPP(hAPP(c_member(U_2713),U_2715),U_2717)) ) ),
inference(miniscope,[status(thm)],[f_727_2]) ).
cnf(f_727_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2713,tc_HOL_Obool)),U_2717),hAPP(hAPP(c_Set_Oinsert(U_2713),U_2715),U_2719)) = hAPP(hAPP(c_Set_Oinsert(U_2713),U_2715),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2713,tc_HOL_Obool)),U_2717),U_2719))
| ~ hBOOL(hAPP(hAPP(c_member(U_2713),U_2715),U_2717)) ),
inference(clausify,[status(thm)],[f_727_3]) ).
cnf(f_727_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2714,tc_HOL_Obool)),U_2718),hAPP(hAPP(c_Set_Oinsert(U_2714),U_2716),U_2720)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2714,tc_HOL_Obool)),U_2718),U_2720)
| hBOOL(hAPP(hAPP(c_member(U_2714),U_2716),U_2718)) ),
inference(clausify,[status(thm)],[f_727_3]) ).
fof(f_728_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_728_2,plain,
! [U_2724,U_2723,U_2722,U_2721] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2721,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2721),U_2722),U_2724)),U_2723) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2721,tc_HOL_Obool)),U_2724),U_2723)
| hBOOL(hAPP(hAPP(c_member(U_2721),U_2722),U_2723)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2721,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2721),U_2722),U_2724)),U_2723) = hAPP(hAPP(c_Set_Oinsert(U_2721),U_2722),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2721,tc_HOL_Obool)),U_2724),U_2723))
| ~ hBOOL(hAPP(hAPP(c_member(U_2721),U_2722),U_2723)) ) ),
inference(variable_rename,[status(thm)],[f_728_1]) ).
fof(f_728_3,plain,
( ! [U_2732,U_2730,U_2728,U_2726] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2726,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2726),U_2728),U_2732)),U_2730) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2726,tc_HOL_Obool)),U_2732),U_2730)
| hBOOL(hAPP(hAPP(c_member(U_2726),U_2728),U_2730)) )
& ! [U_2731,U_2729,U_2727,U_2725] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2725,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2725),U_2727),U_2731)),U_2729) = hAPP(hAPP(c_Set_Oinsert(U_2725),U_2727),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2725,tc_HOL_Obool)),U_2731),U_2729))
| ~ hBOOL(hAPP(hAPP(c_member(U_2725),U_2727),U_2729)) ) ),
inference(miniscope,[status(thm)],[f_728_2]) ).
cnf(f_728_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2725,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2725),U_2727),U_2731)),U_2729) = hAPP(hAPP(c_Set_Oinsert(U_2725),U_2727),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2725,tc_HOL_Obool)),U_2731),U_2729))
| ~ hBOOL(hAPP(hAPP(c_member(U_2725),U_2727),U_2729)) ),
inference(clausify,[status(thm)],[f_728_3]) ).
cnf(f_728_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2726,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2726),U_2728),U_2732)),U_2730) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2726,tc_HOL_Obool)),U_2732),U_2730)
| hBOOL(hAPP(hAPP(c_member(U_2726),U_2728),U_2730)) ),
inference(clausify,[status(thm)],[f_728_3]) ).
fof(f_729_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_729_2,plain,
! [U_2736,U_2735,U_2734,U_2733] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2733,tc_HOL_Obool)),U_2735),hAPP(hAPP(c_Set_Oinsert(U_2733),U_2734),U_2736)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2733,tc_HOL_Obool)),U_2735),U_2736)
| hBOOL(hAPP(hAPP(c_member(U_2733),U_2734),U_2735)) ),
inference(variable_rename,[status(thm)],[f_729_1]) ).
cnf(f_729_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2733,tc_HOL_Obool)),U_2735),hAPP(hAPP(c_Set_Oinsert(U_2733),U_2734),U_2736)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2733,tc_HOL_Obool)),U_2735),U_2736)
| hBOOL(hAPP(hAPP(c_member(U_2733),U_2734),U_2735)) ),
inference(clausify,[status(thm)],[f_729_2]) ).
fof(f_730_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_730_2,plain,
! [U_2740,U_2739,U_2738,U_2737] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2737,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2737),U_2738),U_2740)),U_2739) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2737,tc_HOL_Obool)),U_2740),U_2739)
| hBOOL(hAPP(hAPP(c_member(U_2737),U_2738),U_2739)) ),
inference(variable_rename,[status(thm)],[f_730_1]) ).
cnf(f_730_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2737,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2737),U_2738),U_2740)),U_2739) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2737,tc_HOL_Obool)),U_2740),U_2739)
| hBOOL(hAPP(hAPP(c_member(U_2737),U_2738),U_2739)) ),
inference(clausify,[status(thm)],[f_730_2]) ).
fof(f_731_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_731_2,plain,
! [U_2744,U_2743,U_2742,U_2741] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2741,tc_HOL_Obool)),U_2743),hAPP(hAPP(c_Set_Oinsert(U_2741),U_2742),U_2744)) = hAPP(hAPP(c_Set_Oinsert(U_2741),U_2742),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2741,tc_HOL_Obool)),U_2743),U_2744))
| ~ hBOOL(hAPP(hAPP(c_member(U_2741),U_2742),U_2743)) ),
inference(variable_rename,[status(thm)],[f_731_1]) ).
cnf(f_731_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2741,tc_HOL_Obool)),U_2743),hAPP(hAPP(c_Set_Oinsert(U_2741),U_2742),U_2744)) = hAPP(hAPP(c_Set_Oinsert(U_2741),U_2742),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2741,tc_HOL_Obool)),U_2743),U_2744))
| ~ hBOOL(hAPP(hAPP(c_member(U_2741),U_2742),U_2743)) ),
inference(clausify,[status(thm)],[f_731_2]) ).
fof(f_732_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_732_2,plain,
! [U_2748,U_2747,U_2746,U_2745] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2745,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2745),U_2746),U_2748)),U_2747) = hAPP(hAPP(c_Set_Oinsert(U_2745),U_2746),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2745,tc_HOL_Obool)),U_2748),U_2747))
| ~ hBOOL(hAPP(hAPP(c_member(U_2745),U_2746),U_2747)) ),
inference(variable_rename,[status(thm)],[f_732_1]) ).
cnf(f_732_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2745,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2745),U_2746),U_2748)),U_2747) = hAPP(hAPP(c_Set_Oinsert(U_2745),U_2746),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2745,tc_HOL_Obool)),U_2748),U_2747))
| ~ hBOOL(hAPP(hAPP(c_member(U_2745),U_2746),U_2747)) ),
inference(clausify,[status(thm)],[f_732_2]) ).
fof(f_733_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_733_2,plain,
! [U_2752,U_2751,U_2750,U_2749] : hBOOL(hAPP(hAPP(c_member(U_2749),hAPP(U_2750,U_2751)),hAPP(c_Set_Oimage(U_2752,U_2749,U_2750),c_Orderings_Otop__class_Otop(tc_fun(U_2752,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_733_1]) ).
cnf(f_733_3,plain,
hBOOL(hAPP(hAPP(c_member(U_2749),hAPP(U_2750,U_2751)),hAPP(c_Set_Oimage(U_2752,U_2749,U_2750),c_Orderings_Otop__class_Otop(tc_fun(U_2752,tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_733_2]) ).
fof(f_734_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_734_2,plain,
! [U_2757,U_2756,U_2755,U_2754,U_2753] :
( hBOOL(hAPP(hAPP(c_member(U_2756),U_2753),hAPP(c_Set_Oimage(U_2757,U_2756,U_2754),c_Orderings_Otop__class_Otop(tc_fun(U_2757,tc_HOL_Obool)))))
| U_2753 != hAPP(U_2754,U_2755) ),
inference(variable_rename,[status(thm)],[f_734_1]) ).
cnf(f_734_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2756),U_2753),hAPP(c_Set_Oimage(U_2757,U_2756,U_2754),c_Orderings_Otop__class_Otop(tc_fun(U_2757,tc_HOL_Obool)))))
| U_2753 != hAPP(U_2754,U_2755) ),
inference(clausify,[status(thm)],[f_734_2]) ).
fof(f_735_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_735_2,plain,
! [U_2761,U_2760,U_2759,U_2758] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2758,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2758),U_2759),U_2761)),U_2760) = hAPP(hAPP(c_Set_Oinsert(U_2758),U_2759),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2758,tc_HOL_Obool)),U_2761),U_2760))
| hBOOL(hAPP(hAPP(c_member(U_2758),U_2759),U_2760)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2758,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2758),U_2759),U_2761)),U_2760) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2758,tc_HOL_Obool)),U_2761),U_2760)
| ~ hBOOL(hAPP(hAPP(c_member(U_2758),U_2759),U_2760)) ) ),
inference(variable_rename,[status(thm)],[f_735_1]) ).
fof(f_735_3,plain,
( ! [U_2769,U_2767,U_2765,U_2763] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2763,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2763),U_2765),U_2769)),U_2767) = hAPP(hAPP(c_Set_Oinsert(U_2763),U_2765),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2763,tc_HOL_Obool)),U_2769),U_2767))
| hBOOL(hAPP(hAPP(c_member(U_2763),U_2765),U_2767)) )
& ! [U_2768,U_2766,U_2764,U_2762] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2762,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2762),U_2764),U_2768)),U_2766) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2762,tc_HOL_Obool)),U_2768),U_2766)
| ~ hBOOL(hAPP(hAPP(c_member(U_2762),U_2764),U_2766)) ) ),
inference(miniscope,[status(thm)],[f_735_2]) ).
cnf(f_735_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2762,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2762),U_2764),U_2768)),U_2766) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2762,tc_HOL_Obool)),U_2768),U_2766)
| ~ hBOOL(hAPP(hAPP(c_member(U_2762),U_2764),U_2766)) ),
inference(clausify,[status(thm)],[f_735_3]) ).
cnf(f_735_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2763,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2763),U_2765),U_2769)),U_2767) = hAPP(hAPP(c_Set_Oinsert(U_2763),U_2765),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2763,tc_HOL_Obool)),U_2769),U_2767))
| hBOOL(hAPP(hAPP(c_member(U_2763),U_2765),U_2767)) ),
inference(clausify,[status(thm)],[f_735_3]) ).
fof(f_736_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_736_2,plain,
! [U_2773,U_2772,U_2771,U_2770] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2770,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2770),U_2771),U_2773)),U_2772) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2770,tc_HOL_Obool)),U_2773),U_2772)
| ~ hBOOL(hAPP(hAPP(c_member(U_2770),U_2771),U_2772)) ),
inference(variable_rename,[status(thm)],[f_736_1]) ).
cnf(f_736_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2770,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2770),U_2771),U_2773)),U_2772) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2770,tc_HOL_Obool)),U_2773),U_2772)
| ~ hBOOL(hAPP(hAPP(c_member(U_2770),U_2771),U_2772)) ),
inference(clausify,[status(thm)],[f_736_2]) ).
fof(f_737_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_737_2,plain,
! [U_2776,U_2775,U_2774] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2774),U_2775),c_Complete__Lattice_OSup__class_OSup(U_2774,U_2776)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2774),U_2775),U_2776))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_2774) ),
inference(variable_rename,[status(thm)],[f_737_1]) ).
cnf(f_737_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2774),U_2775),c_Complete__Lattice_OSup__class_OSup(U_2774,U_2776)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2774),U_2775),U_2776))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_2774) ),
inference(clausify,[status(thm)],[f_737_2]) ).
fof(f_738_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_738_2,plain,
! [U_2779,U_2778,U_2777] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2777),c_Complete__Lattice_OInf__class_OInf(U_2777,U_2779)),U_2778))
| ~ hBOOL(hAPP(hAPP(c_member(U_2777),U_2778),U_2779))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_2777) ),
inference(variable_rename,[status(thm)],[f_738_1]) ).
cnf(f_738_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2777),c_Complete__Lattice_OInf__class_OInf(U_2777,U_2779)),U_2778))
| ~ hBOOL(hAPP(hAPP(c_member(U_2777),U_2778),U_2779))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_2777) ),
inference(clausify,[status(thm)],[f_738_2]) ).
fof(f_739_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_739_2,plain,
! [U_2782,U_2781,U_2780] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_2780),U_2781),hAPP(c_SetInterval_Oord__class_OlessThan(U_2780),U_2782)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2780),U_2781),U_2782)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2780),U_2781),U_2782))
| ~ hBOOL(hAPP(hAPP(c_member(U_2780),U_2781),hAPP(c_SetInterval_Oord__class_OlessThan(U_2780),U_2782))) ) )
| ~ class_Orderings_Oord(U_2780) ),
inference(variable_rename,[status(thm)],[f_739_1]) ).
cnf(f_739_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2780),U_2781),U_2782))
| ~ hBOOL(hAPP(hAPP(c_member(U_2780),U_2781),hAPP(c_SetInterval_Oord__class_OlessThan(U_2780),U_2782)))
| ~ class_Orderings_Oord(U_2780) ),
inference(clausify,[status(thm)],[f_739_2]) ).
cnf(f_739_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2780),U_2781),hAPP(c_SetInterval_Oord__class_OlessThan(U_2780),U_2782)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2780),U_2781),U_2782))
| ~ class_Orderings_Oord(U_2780) ),
inference(clausify,[status(thm)],[f_739_2]) ).
fof(f_740_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_740_2,plain,
! [U_2785,U_2784,U_2783] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_2783),U_2784),hAPP(c_SetInterval_Oord__class_OatMost(U_2783),U_2785)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2783),U_2784),U_2785)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2783),U_2784),U_2785))
| ~ hBOOL(hAPP(hAPP(c_member(U_2783),U_2784),hAPP(c_SetInterval_Oord__class_OatMost(U_2783),U_2785))) ) )
| ~ class_Orderings_Oord(U_2783) ),
inference(variable_rename,[status(thm)],[f_740_1]) ).
cnf(f_740_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2783),U_2784),U_2785))
| ~ hBOOL(hAPP(hAPP(c_member(U_2783),U_2784),hAPP(c_SetInterval_Oord__class_OatMost(U_2783),U_2785)))
| ~ class_Orderings_Oord(U_2783) ),
inference(clausify,[status(thm)],[f_740_2]) ).
cnf(f_740_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2783),U_2784),hAPP(c_SetInterval_Oord__class_OatMost(U_2783),U_2785)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2783),U_2784),U_2785))
| ~ class_Orderings_Oord(U_2783) ),
inference(clausify,[status(thm)],[f_740_2]) ).
fof(f_741_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_741_2,plain,
! [U_2788,U_2787,U_2786] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2786,tc_HOL_Obool)),U_2787),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2786,tc_HOL_Obool),U_2788)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2786,tc_HOL_Obool)),U_2787),U_2788)) ),
inference(variable_rename,[status(thm)],[f_741_1]) ).
cnf(f_741_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2786,tc_HOL_Obool)),U_2787),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2786,tc_HOL_Obool),U_2788)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2786,tc_HOL_Obool)),U_2787),U_2788)) ),
inference(clausify,[status(thm)],[f_741_2]) ).
fof(f_742_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_742_2,plain,
! [U_2790,U_2789] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_2789,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_2789,tc_HOL_Obool))),hAPP(c_Set_OPow(U_2789),U_2790))),
inference(variable_rename,[status(thm)],[f_742_1]) ).
cnf(f_742_3,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(U_2789,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_2789,tc_HOL_Obool))),hAPP(c_Set_OPow(U_2789),U_2790))),
inference(clausify,[status(thm)],[f_742_2]) ).
fof(f_743_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_743_2,plain,
! [U_2793,U_2792,U_2791] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_2791),U_2792),hAPP(c_SetInterval_Oord__class_OatLeast(U_2791),U_2793)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2791),U_2793),U_2792)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2791),U_2793),U_2792))
| ~ hBOOL(hAPP(hAPP(c_member(U_2791),U_2792),hAPP(c_SetInterval_Oord__class_OatLeast(U_2791),U_2793))) ) )
| ~ class_Orderings_Oord(U_2791) ),
inference(variable_rename,[status(thm)],[f_743_1]) ).
cnf(f_743_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2791),U_2793),U_2792))
| ~ hBOOL(hAPP(hAPP(c_member(U_2791),U_2792),hAPP(c_SetInterval_Oord__class_OatLeast(U_2791),U_2793)))
| ~ class_Orderings_Oord(U_2791) ),
inference(clausify,[status(thm)],[f_743_2]) ).
cnf(f_743_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2791),U_2792),hAPP(c_SetInterval_Oord__class_OatLeast(U_2791),U_2793)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2791),U_2793),U_2792))
| ~ class_Orderings_Oord(U_2791) ),
inference(clausify,[status(thm)],[f_743_2]) ).
fof(f_744_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_744_2,plain,
! [U_2796,U_2795,U_2794] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2794,tc_HOL_Obool)),U_2795),U_2796))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2794,tc_HOL_Obool)),U_2795),hAPP(c_Set_OPow(U_2794),U_2796))) ),
inference(variable_rename,[status(thm)],[f_744_1]) ).
cnf(f_744_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2794,tc_HOL_Obool)),U_2795),U_2796))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2794,tc_HOL_Obool)),U_2795),hAPP(c_Set_OPow(U_2794),U_2796))) ),
inference(clausify,[status(thm)],[f_744_2]) ).
fof(f_745_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_745_2,plain,
! [U_2799,U_2798,U_2797] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2797,tc_HOL_Obool)),U_2798),hAPP(c_Set_OPow(U_2797),U_2799)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2797,tc_HOL_Obool)),U_2798),U_2799)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2797,tc_HOL_Obool)),U_2798),U_2799))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2797,tc_HOL_Obool)),U_2798),hAPP(c_Set_OPow(U_2797),U_2799))) ) ),
inference(variable_rename,[status(thm)],[f_745_1]) ).
fof(f_745_3,plain,
( ! [U_2805,U_2803,U_2801] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2801,tc_HOL_Obool)),U_2803),hAPP(c_Set_OPow(U_2801),U_2805)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2801,tc_HOL_Obool)),U_2803),U_2805)) )
& ! [U_2804,U_2802,U_2800] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2800,tc_HOL_Obool)),U_2802),U_2804))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2800,tc_HOL_Obool)),U_2802),hAPP(c_Set_OPow(U_2800),U_2804))) ) ),
inference(miniscope,[status(thm)],[f_745_2]) ).
cnf(f_745_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2800,tc_HOL_Obool)),U_2802),U_2804))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2800,tc_HOL_Obool)),U_2802),hAPP(c_Set_OPow(U_2800),U_2804))) ),
inference(clausify,[status(thm)],[f_745_3]) ).
cnf(f_745_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2801,tc_HOL_Obool)),U_2803),hAPP(c_Set_OPow(U_2801),U_2805)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2801,tc_HOL_Obool)),U_2803),U_2805)) ),
inference(clausify,[status(thm)],[f_745_3]) ).
fof(f_746_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_746_2,plain,
! [U_2808,U_2807,U_2806] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_2806),U_2807),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_2806),U_2808)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2806),U_2808),U_2807)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2806),U_2808),U_2807))
| ~ hBOOL(hAPP(hAPP(c_member(U_2806),U_2807),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_2806),U_2808))) ) )
| ~ class_Orderings_Oord(U_2806) ),
inference(variable_rename,[status(thm)],[f_746_1]) ).
cnf(f_746_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2806),U_2808),U_2807))
| ~ hBOOL(hAPP(hAPP(c_member(U_2806),U_2807),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_2806),U_2808)))
| ~ class_Orderings_Oord(U_2806) ),
inference(clausify,[status(thm)],[f_746_2]) ).
cnf(f_746_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2806),U_2807),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_2806),U_2808)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2806),U_2808),U_2807))
| ~ class_Orderings_Oord(U_2806) ),
inference(clausify,[status(thm)],[f_746_2]) ).
fof(f_747_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_747_2,plain,
! [U_2811,U_2810,U_2809] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2809,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_2809,tc_HOL_Obool),U_2811)),U_2810))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2809,tc_HOL_Obool)),U_2810),U_2811)) ),
inference(variable_rename,[status(thm)],[f_747_1]) ).
cnf(f_747_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2809,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_2809,tc_HOL_Obool),U_2811)),U_2810))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2809,tc_HOL_Obool)),U_2810),U_2811)) ),
inference(clausify,[status(thm)],[f_747_2]) ).
fof(f_748_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_748_2,plain,
! [U_2816,U_2815,U_2814,U_2813,U_2812] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2812),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_2812),U_2816),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_2813),U_2815))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_2812),U_2816),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_2813),U_2814))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_2812),U_2816),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_2814),U_2815))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2814),U_2815))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2813),U_2814))
| ~ class_Groups_Oab__group__add(U_2812) ),
inference(variable_rename,[status(thm)],[f_748_1]) ).
cnf(f_748_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2812),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_2812),U_2816),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_2813),U_2815))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_2812),U_2816),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_2813),U_2814))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_2812),U_2816),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_2814),U_2815))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2814),U_2815))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2813),U_2814))
| ~ class_Groups_Oab__group__add(U_2812) ),
inference(clausify,[status(thm)],[f_748_2]) ).
fof(f_749_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_749_2,plain,
! [U_2818,U_2817] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_2817),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2818)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_2817),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2818))
| hAPP(U_2817,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_749_1]) ).
cnf(f_749_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_2817),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2818)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_2817),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2818))
| hAPP(U_2817,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_749_2]) ).
fof(f_750_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_750_2,plain,
! [U_2823,U_2822,U_2821,U_2820,U_2819] : hAPP(c_Set_Ovimage(U_2819,U_2820,U_2821),hAPP(hAPP(c_Set_Oinsert(U_2820),U_2822),U_2823)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2819,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_2819,U_2820,U_2821),hAPP(hAPP(c_Set_Oinsert(U_2820),U_2822),c_Orderings_Obot__class_Obot(tc_fun(U_2820,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(U_2819,U_2820,U_2821),U_2823)),
inference(variable_rename,[status(thm)],[f_750_1]) ).
cnf(f_750_3,plain,
hAPP(c_Set_Ovimage(U_2819,U_2820,U_2821),hAPP(hAPP(c_Set_Oinsert(U_2820),U_2822),U_2823)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2819,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_2819,U_2820,U_2821),hAPP(hAPP(c_Set_Oinsert(U_2820),U_2822),c_Orderings_Obot__class_Obot(tc_fun(U_2820,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(U_2819,U_2820,U_2821),U_2823)),
inference(clausify,[status(thm)],[f_750_2]) ).
fof(f_751_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_751_2,plain,
! [U_2828,U_2827,U_2826,U_2825,U_2824] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2825,tc_HOL_Obool)),U_2827),hAPP(c_Set_Oimage(U_2824,U_2825,U_2826),U_2828)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2824,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_2824,U_2825,U_2826),U_2827)),U_2828))
| hAPP(c_Set_Oimage(U_2824,U_2825,U_2826),c_Orderings_Otop__class_Otop(tc_fun(U_2824,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_2825,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_751_1]) ).
cnf(f_751_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2825,tc_HOL_Obool)),U_2827),hAPP(c_Set_Oimage(U_2824,U_2825,U_2826),U_2828)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2824,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_2824,U_2825,U_2826),U_2827)),U_2828))
| hAPP(c_Set_Oimage(U_2824,U_2825,U_2826),c_Orderings_Otop__class_Otop(tc_fun(U_2824,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_2825,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_751_2]) ).
fof(f_752_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_752_2,plain,
! [U_2832,U_2831,U_2830,U_2829] : hAPP(c_Set_Oimage(U_2829,U_2830,U_2831),hAPP(c_Set_Ovimage(U_2829,U_2830,U_2831),U_2832)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2830,tc_HOL_Obool)),U_2832),hAPP(c_Set_Oimage(U_2829,U_2830,U_2831),c_Orderings_Otop__class_Otop(tc_fun(U_2829,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_752_1]) ).
cnf(f_752_3,plain,
hAPP(c_Set_Oimage(U_2829,U_2830,U_2831),hAPP(c_Set_Ovimage(U_2829,U_2830,U_2831),U_2832)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2830,tc_HOL_Obool)),U_2832),hAPP(c_Set_Oimage(U_2829,U_2830,U_2831),c_Orderings_Otop__class_Otop(tc_fun(U_2829,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_752_2]) ).
fof(f_753_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_753_2,plain,
! [U_2836,U_2835,U_2834,U_2833] :
( hAPP(c_Set_Ovimage(U_2833,U_2834,U_2835),hAPP(c_Set_Oimage(U_2833,U_2834,U_2835),U_2836)) = U_2836
| ~ c_Fun_Oinj__on(U_2833,U_2834,U_2835,c_Orderings_Otop__class_Otop(tc_fun(U_2833,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_753_1]) ).
cnf(f_753_3,plain,
( hAPP(c_Set_Ovimage(U_2833,U_2834,U_2835),hAPP(c_Set_Oimage(U_2833,U_2834,U_2835),U_2836)) = U_2836
| ~ c_Fun_Oinj__on(U_2833,U_2834,U_2835,c_Orderings_Otop__class_Otop(tc_fun(U_2833,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_753_2]) ).
fof(f_754_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_754_2,plain,
! [U_2839,U_2838,U_2837] :
( hAPP(hAPP(c_Set_Oinsert(U_2837),U_2838),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2837,tc_HOL_Obool)),U_2839),hAPP(hAPP(c_Set_Oinsert(U_2837),U_2838),c_Orderings_Obot__class_Obot(tc_fun(U_2837,tc_HOL_Obool))))) = U_2839
| ~ hBOOL(hAPP(hAPP(c_member(U_2837),U_2838),U_2839)) ),
inference(variable_rename,[status(thm)],[f_754_1]) ).
cnf(f_754_3,plain,
( hAPP(hAPP(c_Set_Oinsert(U_2837),U_2838),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2837,tc_HOL_Obool)),U_2839),hAPP(hAPP(c_Set_Oinsert(U_2837),U_2838),c_Orderings_Obot__class_Obot(tc_fun(U_2837,tc_HOL_Obool))))) = U_2839
| ~ hBOOL(hAPP(hAPP(c_member(U_2837),U_2838),U_2839)) ),
inference(clausify,[status(thm)],[f_754_2]) ).
fof(f_755_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_755_2,plain,
! [U_2842,U_2841,U_2840] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2840,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2840),U_2841),U_2842)),hAPP(hAPP(c_Set_Oinsert(U_2840),U_2841),c_Orderings_Obot__class_Obot(tc_fun(U_2840,tc_HOL_Obool)))) = U_2842
| hBOOL(hAPP(hAPP(c_member(U_2840),U_2841),U_2842)) ),
inference(variable_rename,[status(thm)],[f_755_1]) ).
cnf(f_755_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2840,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2840),U_2841),U_2842)),hAPP(hAPP(c_Set_Oinsert(U_2840),U_2841),c_Orderings_Obot__class_Obot(tc_fun(U_2840,tc_HOL_Obool)))) = U_2842
| hBOOL(hAPP(hAPP(c_member(U_2840),U_2841),U_2842)) ),
inference(clausify,[status(thm)],[f_755_2]) ).
fof(f_756_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_756_2,plain,
! [U_2850,U_2849,U_2848,U_2847] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_2848),U_2850),hAPP(c_Set_Oimage(U_2847,U_2848,U_2849),c_Orderings_Otop__class_Otop(tc_fun(U_2847,tc_HOL_Obool)))))
| ! [U_2846] :
( ? [U_2845] :
( U_2845 != U_2846
& U_2850 = hAPP(U_2849,U_2845) )
| U_2850 != hAPP(U_2849,U_2846) ) )
& ( ? [U_2844] :
( ! [U_2843] :
( U_2843 = U_2844
| U_2850 != hAPP(U_2849,U_2843) )
& U_2850 = hAPP(U_2849,U_2844) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2848),U_2850),hAPP(c_Set_Oimage(U_2847,U_2848,U_2849),c_Orderings_Otop__class_Otop(tc_fun(U_2847,tc_HOL_Obool))))) ) )
| ~ c_Fun_Oinj__on(U_2847,U_2848,U_2849,c_Orderings_Otop__class_Otop(tc_fun(U_2847,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_756_1]) ).
fof(f_756_3,plain,
! [U_2850,U_2849,U_2848,U_2847] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_2848),U_2850),hAPP(c_Set_Oimage(U_2847,U_2848,U_2849),c_Orderings_Otop__class_Otop(tc_fun(U_2847,tc_HOL_Obool)))))
| ! [U_2846] :
( ? [U_2845] :
( U_2845 != U_2846
& U_2850 = hAPP(U_2849,U_2845) )
| U_2850 != hAPP(U_2849,U_2846) ) )
& ( ( ! [U_2843] :
( U_2843 = sK43(U_2850,U_2849,U_2848,U_2847)
| U_2850 != hAPP(U_2849,U_2843) )
& U_2850 = hAPP(U_2849,sK43(U_2850,U_2849,U_2848,U_2847)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2848),U_2850),hAPP(c_Set_Oimage(U_2847,U_2848,U_2849),c_Orderings_Otop__class_Otop(tc_fun(U_2847,tc_HOL_Obool))))) ) )
| ~ c_Fun_Oinj__on(U_2847,U_2848,U_2849,c_Orderings_Otop__class_Otop(tc_fun(U_2847,tc_HOL_Obool))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_2844,sK43(U_2850,U_2849,U_2848,U_2847))],[f_756_2]) ).
fof(f_756_4,plain,
! [U_2850,U_2849,U_2848,U_2847] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_2848),U_2850),hAPP(c_Set_Oimage(U_2847,U_2848,U_2849),c_Orderings_Otop__class_Otop(tc_fun(U_2847,tc_HOL_Obool)))))
| ! [U_2846] :
( ( sK44(U_2850,U_2849,U_2848,U_2847,U_2846) != U_2846
& U_2850 = hAPP(U_2849,sK44(U_2850,U_2849,U_2848,U_2847,U_2846)) )
| U_2850 != hAPP(U_2849,U_2846) ) )
& ( ( ! [U_2843] :
( U_2843 = sK43(U_2850,U_2849,U_2848,U_2847)
| U_2850 != hAPP(U_2849,U_2843) )
& U_2850 = hAPP(U_2849,sK43(U_2850,U_2849,U_2848,U_2847)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2848),U_2850),hAPP(c_Set_Oimage(U_2847,U_2848,U_2849),c_Orderings_Otop__class_Otop(tc_fun(U_2847,tc_HOL_Obool))))) ) )
| ~ c_Fun_Oinj__on(U_2847,U_2848,U_2849,c_Orderings_Otop__class_Otop(tc_fun(U_2847,tc_HOL_Obool))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_2845,sK44(U_2850,U_2849,U_2848,U_2847,U_2846))],[f_756_3]) ).
cnf(f_756_5,plain,
( U_2850 = hAPP(U_2849,sK43(U_2850,U_2849,U_2848,U_2847))
| ~ hBOOL(hAPP(hAPP(c_member(U_2848),U_2850),hAPP(c_Set_Oimage(U_2847,U_2848,U_2849),c_Orderings_Otop__class_Otop(tc_fun(U_2847,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(U_2847,U_2848,U_2849,c_Orderings_Otop__class_Otop(tc_fun(U_2847,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_756_4]) ).
cnf(f_756_6,plain,
( U_2843 = sK43(U_2850,U_2849,U_2848,U_2847)
| U_2850 != hAPP(U_2849,U_2843)
| ~ hBOOL(hAPP(hAPP(c_member(U_2848),U_2850),hAPP(c_Set_Oimage(U_2847,U_2848,U_2849),c_Orderings_Otop__class_Otop(tc_fun(U_2847,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(U_2847,U_2848,U_2849,c_Orderings_Otop__class_Otop(tc_fun(U_2847,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_756_4]) ).
cnf(f_756_7,plain,
( U_2850 = hAPP(U_2849,sK44(U_2850,U_2849,U_2848,U_2847,U_2846))
| U_2850 != hAPP(U_2849,U_2846)
| hBOOL(hAPP(hAPP(c_member(U_2848),U_2850),hAPP(c_Set_Oimage(U_2847,U_2848,U_2849),c_Orderings_Otop__class_Otop(tc_fun(U_2847,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(U_2847,U_2848,U_2849,c_Orderings_Otop__class_Otop(tc_fun(U_2847,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_756_4]) ).
cnf(f_756_8,plain,
( sK44(U_2850,U_2849,U_2848,U_2847,U_2846) != U_2846
| U_2850 != hAPP(U_2849,U_2846)
| hBOOL(hAPP(hAPP(c_member(U_2848),U_2850),hAPP(c_Set_Oimage(U_2847,U_2848,U_2849),c_Orderings_Otop__class_Otop(tc_fun(U_2847,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(U_2847,U_2848,U_2849,c_Orderings_Otop__class_Otop(tc_fun(U_2847,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_756_4]) ).
fof(f_757_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_757_2,plain,
! [U_2855,U_2854,U_2853,U_2852,U_2851] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_2852),hAPP(U_2853,U_2854)),hAPP(c_Set_Oimage(U_2851,U_2852,U_2853),U_2855)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2851),U_2854),U_2855)) )
& ( hBOOL(hAPP(hAPP(c_member(U_2851),U_2854),U_2855))
| ~ hBOOL(hAPP(hAPP(c_member(U_2852),hAPP(U_2853,U_2854)),hAPP(c_Set_Oimage(U_2851,U_2852,U_2853),U_2855))) ) )
| ~ c_Fun_Oinj__on(U_2851,U_2852,U_2853,c_Orderings_Otop__class_Otop(tc_fun(U_2851,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_757_1]) ).
cnf(f_757_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_2851),U_2854),U_2855))
| ~ hBOOL(hAPP(hAPP(c_member(U_2852),hAPP(U_2853,U_2854)),hAPP(c_Set_Oimage(U_2851,U_2852,U_2853),U_2855)))
| ~ c_Fun_Oinj__on(U_2851,U_2852,U_2853,c_Orderings_Otop__class_Otop(tc_fun(U_2851,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_757_2]) ).
cnf(f_757_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2852),hAPP(U_2853,U_2854)),hAPP(c_Set_Oimage(U_2851,U_2852,U_2853),U_2855)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2851),U_2854),U_2855))
| ~ c_Fun_Oinj__on(U_2851,U_2852,U_2853,c_Orderings_Otop__class_Otop(tc_fun(U_2851,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_757_2]) ).
fof(f_758_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_758_2,plain,
! [U_2858,U_2857,U_2856] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2856),U_2858),U_2857))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2856),U_2857),U_2858))
| U_2857 = U_2858
| ~ class_Rings_Olinordered__idom(U_2856) ),
inference(variable_rename,[status(thm)],[f_758_1]) ).
cnf(f_758_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2856),U_2858),U_2857))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2856),U_2857),U_2858))
| U_2857 = U_2858
| ~ class_Rings_Olinordered__idom(U_2856) ),
inference(clausify,[status(thm)],[f_758_2]) ).
fof(f_759_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_759_2,plain,
! [U_2862,U_2861,U_2860,U_2859] :
( hAPP(c_Fun_Othe__inv__into(U_2859,U_2860,c_Orderings_Otop__class_Otop(tc_fun(U_2859,tc_HOL_Obool)),U_2861),hAPP(U_2861,U_2862)) = U_2862
| ~ c_Fun_Oinj__on(U_2859,U_2860,U_2861,c_Orderings_Otop__class_Otop(tc_fun(U_2859,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_759_1]) ).
cnf(f_759_3,plain,
( hAPP(c_Fun_Othe__inv__into(U_2859,U_2860,c_Orderings_Otop__class_Otop(tc_fun(U_2859,tc_HOL_Obool)),U_2861),hAPP(U_2861,U_2862)) = U_2862
| ~ c_Fun_Oinj__on(U_2859,U_2860,U_2861,c_Orderings_Otop__class_Otop(tc_fun(U_2859,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_759_2]) ).
fof(f_760_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_760_2,plain,
! [U_2866,U_2865,U_2864,U_2863] :
( ( hBOOL(hAPP(hAPP(c_member(U_2863),U_2864),c_SetInterval_Oord_OatMost(U_2863,U_2865,U_2866)))
| ~ hBOOL(hAPP(hAPP(U_2865,U_2864),U_2866)) )
& ( hBOOL(hAPP(hAPP(U_2865,U_2864),U_2866))
| ~ hBOOL(hAPP(hAPP(c_member(U_2863),U_2864),c_SetInterval_Oord_OatMost(U_2863,U_2865,U_2866))) ) ),
inference(variable_rename,[status(thm)],[f_760_1]) ).
fof(f_760_3,plain,
( ! [U_2874,U_2872,U_2870] :
( ! [U_2868] : hBOOL(hAPP(hAPP(c_member(U_2868),U_2870),c_SetInterval_Oord_OatMost(U_2868,U_2872,U_2874)))
| ~ hBOOL(hAPP(hAPP(U_2872,U_2870),U_2874)) )
& ! [U_2873,U_2871,U_2869] :
( ! [U_2867] : ~ hBOOL(hAPP(hAPP(c_member(U_2867),U_2869),c_SetInterval_Oord_OatMost(U_2867,U_2871,U_2873)))
| hBOOL(hAPP(hAPP(U_2871,U_2869),U_2873)) ) ),
inference(miniscope,[status(thm)],[f_760_2]) ).
cnf(f_760_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2867),U_2869),c_SetInterval_Oord_OatMost(U_2867,U_2871,U_2873)))
| hBOOL(hAPP(hAPP(U_2871,U_2869),U_2873)) ),
inference(clausify,[status(thm)],[f_760_3]) ).
cnf(f_760_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_2868),U_2870),c_SetInterval_Oord_OatMost(U_2868,U_2872,U_2874)))
| ~ hBOOL(hAPP(hAPP(U_2872,U_2870),U_2874)) ),
inference(clausify,[status(thm)],[f_760_3]) ).
fof(f_761_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_761_2,plain,
! [U_2878,U_2877,U_2876,U_2875] :
( ( hBOOL(hAPP(hAPP(c_member(U_2875),U_2876),c_SetInterval_Oord_OatLeast(U_2875,U_2877,U_2878)))
| ~ hBOOL(hAPP(hAPP(U_2877,U_2878),U_2876)) )
& ( hBOOL(hAPP(hAPP(U_2877,U_2878),U_2876))
| ~ hBOOL(hAPP(hAPP(c_member(U_2875),U_2876),c_SetInterval_Oord_OatLeast(U_2875,U_2877,U_2878))) ) ),
inference(variable_rename,[status(thm)],[f_761_1]) ).
fof(f_761_3,plain,
( ! [U_2886,U_2884,U_2882] :
( ! [U_2880] : hBOOL(hAPP(hAPP(c_member(U_2880),U_2882),c_SetInterval_Oord_OatLeast(U_2880,U_2884,U_2886)))
| ~ hBOOL(hAPP(hAPP(U_2884,U_2886),U_2882)) )
& ! [U_2885,U_2883,U_2881] :
( ! [U_2879] : ~ hBOOL(hAPP(hAPP(c_member(U_2879),U_2881),c_SetInterval_Oord_OatLeast(U_2879,U_2883,U_2885)))
| hBOOL(hAPP(hAPP(U_2883,U_2885),U_2881)) ) ),
inference(miniscope,[status(thm)],[f_761_2]) ).
cnf(f_761_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2879),U_2881),c_SetInterval_Oord_OatLeast(U_2879,U_2883,U_2885)))
| hBOOL(hAPP(hAPP(U_2883,U_2885),U_2881)) ),
inference(clausify,[status(thm)],[f_761_3]) ).
cnf(f_761_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_2880),U_2882),c_SetInterval_Oord_OatLeast(U_2880,U_2884,U_2886)))
| ~ hBOOL(hAPP(hAPP(U_2884,U_2886),U_2882)) ),
inference(clausify,[status(thm)],[f_761_3]) ).
fof(f_762_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_762_2,plain,
! [U_2890,U_2889,U_2888,U_2887] :
( ( hBOOL(hAPP(hAPP(c_member(U_2887),U_2888),c_SetInterval_Oord_OlessThan(U_2887,U_2889,U_2890)))
| ~ hBOOL(hAPP(hAPP(U_2889,U_2888),U_2890)) )
& ( hBOOL(hAPP(hAPP(U_2889,U_2888),U_2890))
| ~ hBOOL(hAPP(hAPP(c_member(U_2887),U_2888),c_SetInterval_Oord_OlessThan(U_2887,U_2889,U_2890))) ) ),
inference(variable_rename,[status(thm)],[f_762_1]) ).
fof(f_762_3,plain,
( ! [U_2898,U_2896,U_2894] :
( ! [U_2892] : hBOOL(hAPP(hAPP(c_member(U_2892),U_2894),c_SetInterval_Oord_OlessThan(U_2892,U_2896,U_2898)))
| ~ hBOOL(hAPP(hAPP(U_2896,U_2894),U_2898)) )
& ! [U_2897,U_2895,U_2893] :
( ! [U_2891] : ~ hBOOL(hAPP(hAPP(c_member(U_2891),U_2893),c_SetInterval_Oord_OlessThan(U_2891,U_2895,U_2897)))
| hBOOL(hAPP(hAPP(U_2895,U_2893),U_2897)) ) ),
inference(miniscope,[status(thm)],[f_762_2]) ).
cnf(f_762_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2891),U_2893),c_SetInterval_Oord_OlessThan(U_2891,U_2895,U_2897)))
| hBOOL(hAPP(hAPP(U_2895,U_2893),U_2897)) ),
inference(clausify,[status(thm)],[f_762_3]) ).
cnf(f_762_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_2892),U_2894),c_SetInterval_Oord_OlessThan(U_2892,U_2896,U_2898)))
| ~ hBOOL(hAPP(hAPP(U_2896,U_2894),U_2898)) ),
inference(clausify,[status(thm)],[f_762_3]) ).
fof(f_763_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_763_2,plain,
! [U_2902,U_2901,U_2900,U_2899] :
( ( hBOOL(hAPP(hAPP(c_member(U_2899),U_2900),c_SetInterval_Oord_OgreaterThan(U_2899,U_2901,U_2902)))
| ~ hBOOL(hAPP(hAPP(U_2901,U_2902),U_2900)) )
& ( hBOOL(hAPP(hAPP(U_2901,U_2902),U_2900))
| ~ hBOOL(hAPP(hAPP(c_member(U_2899),U_2900),c_SetInterval_Oord_OgreaterThan(U_2899,U_2901,U_2902))) ) ),
inference(variable_rename,[status(thm)],[f_763_1]) ).
fof(f_763_3,plain,
( ! [U_2910,U_2908,U_2906] :
( ! [U_2904] : hBOOL(hAPP(hAPP(c_member(U_2904),U_2906),c_SetInterval_Oord_OgreaterThan(U_2904,U_2908,U_2910)))
| ~ hBOOL(hAPP(hAPP(U_2908,U_2910),U_2906)) )
& ! [U_2909,U_2907,U_2905] :
( ! [U_2903] : ~ hBOOL(hAPP(hAPP(c_member(U_2903),U_2905),c_SetInterval_Oord_OgreaterThan(U_2903,U_2907,U_2909)))
| hBOOL(hAPP(hAPP(U_2907,U_2909),U_2905)) ) ),
inference(miniscope,[status(thm)],[f_763_2]) ).
cnf(f_763_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2903),U_2905),c_SetInterval_Oord_OgreaterThan(U_2903,U_2907,U_2909)))
| hBOOL(hAPP(hAPP(U_2907,U_2909),U_2905)) ),
inference(clausify,[status(thm)],[f_763_3]) ).
cnf(f_763_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_2904),U_2906),c_SetInterval_Oord_OgreaterThan(U_2904,U_2908,U_2910)))
| ~ hBOOL(hAPP(hAPP(U_2908,U_2910),U_2906)) ),
inference(clausify,[status(thm)],[f_763_3]) ).
fof(f_764_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_764_2,plain,
! [U_2915,U_2914,U_2913,U_2912,U_2911] :
( ( hBOOL(hAPP(hAPP(c_member(U_2911),U_2912),c_SetInterval_Oord_OatLeastAtMost(U_2911,U_2913,U_2914,U_2915)))
| ~ hBOOL(hAPP(hAPP(U_2913,U_2912),U_2915))
| ~ hBOOL(hAPP(hAPP(U_2913,U_2914),U_2912)) )
& ( ( hBOOL(hAPP(hAPP(U_2913,U_2912),U_2915))
& hBOOL(hAPP(hAPP(U_2913,U_2914),U_2912)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2911),U_2912),c_SetInterval_Oord_OatLeastAtMost(U_2911,U_2913,U_2914,U_2915))) ) ),
inference(variable_rename,[status(thm)],[f_764_1]) ).
fof(f_764_3,plain,
( ! [U_2925,U_2923,U_2921,U_2919] :
( ! [U_2917] : hBOOL(hAPP(hAPP(c_member(U_2917),U_2919),c_SetInterval_Oord_OatLeastAtMost(U_2917,U_2921,U_2923,U_2925)))
| ~ hBOOL(hAPP(hAPP(U_2921,U_2919),U_2925))
| ~ hBOOL(hAPP(hAPP(U_2921,U_2923),U_2919)) )
& ! [U_2924,U_2922,U_2920,U_2918] :
( ! [U_2916] : ~ hBOOL(hAPP(hAPP(c_member(U_2916),U_2918),c_SetInterval_Oord_OatLeastAtMost(U_2916,U_2920,U_2922,U_2924)))
| ( hBOOL(hAPP(hAPP(U_2920,U_2918),U_2924))
& hBOOL(hAPP(hAPP(U_2920,U_2922),U_2918)) ) ) ),
inference(miniscope,[status(thm)],[f_764_2]) ).
cnf(f_764_4,plain,
( hBOOL(hAPP(hAPP(U_2920,U_2922),U_2918))
| ~ hBOOL(hAPP(hAPP(c_member(U_2916),U_2918),c_SetInterval_Oord_OatLeastAtMost(U_2916,U_2920,U_2922,U_2924))) ),
inference(clausify,[status(thm)],[f_764_3]) ).
cnf(f_764_5,plain,
( hBOOL(hAPP(hAPP(U_2920,U_2918),U_2924))
| ~ hBOOL(hAPP(hAPP(c_member(U_2916),U_2918),c_SetInterval_Oord_OatLeastAtMost(U_2916,U_2920,U_2922,U_2924))) ),
inference(clausify,[status(thm)],[f_764_3]) ).
cnf(f_764_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_2917),U_2919),c_SetInterval_Oord_OatLeastAtMost(U_2917,U_2921,U_2923,U_2925)))
| ~ hBOOL(hAPP(hAPP(U_2921,U_2919),U_2925))
| ~ hBOOL(hAPP(hAPP(U_2921,U_2923),U_2919)) ),
inference(clausify,[status(thm)],[f_764_3]) ).
fof(f_765_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_765_2,plain,
! [U_2930,U_2929,U_2928,U_2927,U_2926] :
( ( hBOOL(hAPP(hAPP(c_member(U_2926),U_2927),c_SetInterval_Oord_OgreaterThanLessThan(U_2926,U_2928,U_2929,U_2930)))
| ~ hBOOL(hAPP(hAPP(U_2928,U_2927),U_2930))
| ~ hBOOL(hAPP(hAPP(U_2928,U_2929),U_2927)) )
& ( ( hBOOL(hAPP(hAPP(U_2928,U_2927),U_2930))
& hBOOL(hAPP(hAPP(U_2928,U_2929),U_2927)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2926),U_2927),c_SetInterval_Oord_OgreaterThanLessThan(U_2926,U_2928,U_2929,U_2930))) ) ),
inference(variable_rename,[status(thm)],[f_765_1]) ).
fof(f_765_3,plain,
( ! [U_2940,U_2938,U_2936,U_2934] :
( ! [U_2932] : hBOOL(hAPP(hAPP(c_member(U_2932),U_2934),c_SetInterval_Oord_OgreaterThanLessThan(U_2932,U_2936,U_2938,U_2940)))
| ~ hBOOL(hAPP(hAPP(U_2936,U_2934),U_2940))
| ~ hBOOL(hAPP(hAPP(U_2936,U_2938),U_2934)) )
& ! [U_2939,U_2937,U_2935,U_2933] :
( ! [U_2931] : ~ hBOOL(hAPP(hAPP(c_member(U_2931),U_2933),c_SetInterval_Oord_OgreaterThanLessThan(U_2931,U_2935,U_2937,U_2939)))
| ( hBOOL(hAPP(hAPP(U_2935,U_2933),U_2939))
& hBOOL(hAPP(hAPP(U_2935,U_2937),U_2933)) ) ) ),
inference(miniscope,[status(thm)],[f_765_2]) ).
cnf(f_765_4,plain,
( hBOOL(hAPP(hAPP(U_2935,U_2937),U_2933))
| ~ hBOOL(hAPP(hAPP(c_member(U_2931),U_2933),c_SetInterval_Oord_OgreaterThanLessThan(U_2931,U_2935,U_2937,U_2939))) ),
inference(clausify,[status(thm)],[f_765_3]) ).
cnf(f_765_5,plain,
( hBOOL(hAPP(hAPP(U_2935,U_2933),U_2939))
| ~ hBOOL(hAPP(hAPP(c_member(U_2931),U_2933),c_SetInterval_Oord_OgreaterThanLessThan(U_2931,U_2935,U_2937,U_2939))) ),
inference(clausify,[status(thm)],[f_765_3]) ).
cnf(f_765_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_2932),U_2934),c_SetInterval_Oord_OgreaterThanLessThan(U_2932,U_2936,U_2938,U_2940)))
| ~ hBOOL(hAPP(hAPP(U_2936,U_2934),U_2940))
| ~ hBOOL(hAPP(hAPP(U_2936,U_2938),U_2934)) ),
inference(clausify,[status(thm)],[f_765_3]) ).
fof(f_766_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_766_2,plain,
! [U_2946,U_2945,U_2944,U_2943,U_2942,U_2941] :
( ( hBOOL(hAPP(hAPP(c_member(U_2941),U_2942),c_SetInterval_Oord_OatLeastLessThan(U_2941,U_2943,U_2944,U_2945,U_2946)))
| ~ hBOOL(hAPP(hAPP(U_2944,U_2942),U_2946))
| ~ hBOOL(hAPP(hAPP(U_2943,U_2945),U_2942)) )
& ( ( hBOOL(hAPP(hAPP(U_2944,U_2942),U_2946))
& hBOOL(hAPP(hAPP(U_2943,U_2945),U_2942)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2941),U_2942),c_SetInterval_Oord_OatLeastLessThan(U_2941,U_2943,U_2944,U_2945,U_2946))) ) ),
inference(variable_rename,[status(thm)],[f_766_1]) ).
fof(f_766_3,plain,
( ! [U_2958,U_2956,U_2954,U_2952,U_2950] :
( ! [U_2948] : hBOOL(hAPP(hAPP(c_member(U_2948),U_2950),c_SetInterval_Oord_OatLeastLessThan(U_2948,U_2952,U_2954,U_2956,U_2958)))
| ~ hBOOL(hAPP(hAPP(U_2954,U_2950),U_2958))
| ~ hBOOL(hAPP(hAPP(U_2952,U_2956),U_2950)) )
& ! [U_2957,U_2955,U_2953,U_2951,U_2949] :
( ! [U_2947] : ~ hBOOL(hAPP(hAPP(c_member(U_2947),U_2949),c_SetInterval_Oord_OatLeastLessThan(U_2947,U_2951,U_2953,U_2955,U_2957)))
| ( hBOOL(hAPP(hAPP(U_2953,U_2949),U_2957))
& hBOOL(hAPP(hAPP(U_2951,U_2955),U_2949)) ) ) ),
inference(miniscope,[status(thm)],[f_766_2]) ).
cnf(f_766_4,plain,
( hBOOL(hAPP(hAPP(U_2951,U_2955),U_2949))
| ~ hBOOL(hAPP(hAPP(c_member(U_2947),U_2949),c_SetInterval_Oord_OatLeastLessThan(U_2947,U_2951,U_2953,U_2955,U_2957))) ),
inference(clausify,[status(thm)],[f_766_3]) ).
cnf(f_766_5,plain,
( hBOOL(hAPP(hAPP(U_2953,U_2949),U_2957))
| ~ hBOOL(hAPP(hAPP(c_member(U_2947),U_2949),c_SetInterval_Oord_OatLeastLessThan(U_2947,U_2951,U_2953,U_2955,U_2957))) ),
inference(clausify,[status(thm)],[f_766_3]) ).
cnf(f_766_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_2948),U_2950),c_SetInterval_Oord_OatLeastLessThan(U_2948,U_2952,U_2954,U_2956,U_2958)))
| ~ hBOOL(hAPP(hAPP(U_2954,U_2950),U_2958))
| ~ hBOOL(hAPP(hAPP(U_2952,U_2956),U_2950)) ),
inference(clausify,[status(thm)],[f_766_3]) ).
fof(f_767_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_767_2,plain,
! [U_2964,U_2963,U_2962,U_2961,U_2960,U_2959] :
( ( hBOOL(hAPP(hAPP(c_member(U_2959),U_2960),c_SetInterval_Oord_OgreaterThanAtMost(U_2959,U_2961,U_2962,U_2963,U_2964)))
| ~ hBOOL(hAPP(hAPP(U_2961,U_2960),U_2964))
| ~ hBOOL(hAPP(hAPP(U_2962,U_2963),U_2960)) )
& ( ( hBOOL(hAPP(hAPP(U_2961,U_2960),U_2964))
& hBOOL(hAPP(hAPP(U_2962,U_2963),U_2960)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2959),U_2960),c_SetInterval_Oord_OgreaterThanAtMost(U_2959,U_2961,U_2962,U_2963,U_2964))) ) ),
inference(variable_rename,[status(thm)],[f_767_1]) ).
fof(f_767_3,plain,
( ! [U_2976,U_2974,U_2972,U_2970,U_2968] :
( ! [U_2966] : hBOOL(hAPP(hAPP(c_member(U_2966),U_2968),c_SetInterval_Oord_OgreaterThanAtMost(U_2966,U_2970,U_2972,U_2974,U_2976)))
| ~ hBOOL(hAPP(hAPP(U_2970,U_2968),U_2976))
| ~ hBOOL(hAPP(hAPP(U_2972,U_2974),U_2968)) )
& ! [U_2975,U_2973,U_2971,U_2969,U_2967] :
( ! [U_2965] : ~ hBOOL(hAPP(hAPP(c_member(U_2965),U_2967),c_SetInterval_Oord_OgreaterThanAtMost(U_2965,U_2969,U_2971,U_2973,U_2975)))
| ( hBOOL(hAPP(hAPP(U_2969,U_2967),U_2975))
& hBOOL(hAPP(hAPP(U_2971,U_2973),U_2967)) ) ) ),
inference(miniscope,[status(thm)],[f_767_2]) ).
cnf(f_767_4,plain,
( hBOOL(hAPP(hAPP(U_2971,U_2973),U_2967))
| ~ hBOOL(hAPP(hAPP(c_member(U_2965),U_2967),c_SetInterval_Oord_OgreaterThanAtMost(U_2965,U_2969,U_2971,U_2973,U_2975))) ),
inference(clausify,[status(thm)],[f_767_3]) ).
cnf(f_767_5,plain,
( hBOOL(hAPP(hAPP(U_2969,U_2967),U_2975))
| ~ hBOOL(hAPP(hAPP(c_member(U_2965),U_2967),c_SetInterval_Oord_OgreaterThanAtMost(U_2965,U_2969,U_2971,U_2973,U_2975))) ),
inference(clausify,[status(thm)],[f_767_3]) ).
cnf(f_767_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_2966),U_2968),c_SetInterval_Oord_OgreaterThanAtMost(U_2966,U_2970,U_2972,U_2974,U_2976)))
| ~ hBOOL(hAPP(hAPP(U_2970,U_2968),U_2976))
| ~ hBOOL(hAPP(hAPP(U_2972,U_2974),U_2968)) ),
inference(clausify,[status(thm)],[f_767_3]) ).
fof(f_768_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_768_2,plain,
! [U_2978,U_2977] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2977),U_2978))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2977),U_2978)) ),
inference(variable_rename,[status(thm)],[f_768_1]) ).
cnf(f_768_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2977),U_2978))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2977),U_2978)) ),
inference(clausify,[status(thm)],[f_768_2]) ).
fof(f_769_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_769_2,plain,
! [U_2982,U_2981,U_2980,U_2979] :
( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2979,tc_Nat_Onat),U_2982),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2979,tc_HOL_Obool)),U_2981),hAPP(hAPP(c_Set_Oinsert(U_2979),U_2980),c_Orderings_Obot__class_Obot(tc_fun(U_2979,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2979,tc_Nat_Onat),U_2982),U_2981)
| hBOOL(hAPP(hAPP(c_member(U_2979),U_2980),U_2981)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2979,tc_Nat_Onat),U_2982),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2979,tc_HOL_Obool)),U_2981),hAPP(hAPP(c_Set_Oinsert(U_2979),U_2980),c_Orderings_Obot__class_Obot(tc_fun(U_2979,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2979,tc_Nat_Onat),U_2982),U_2981)),hAPP(U_2982,U_2980))
| ~ hBOOL(hAPP(hAPP(c_member(U_2979),U_2980),U_2981)) ) ),
inference(variable_rename,[status(thm)],[f_769_1]) ).
fof(f_769_3,plain,
( ! [U_2990,U_2988,U_2986,U_2984] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2984,tc_Nat_Onat),U_2990),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2984,tc_HOL_Obool)),U_2988),hAPP(hAPP(c_Set_Oinsert(U_2984),U_2986),c_Orderings_Obot__class_Obot(tc_fun(U_2984,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2984,tc_Nat_Onat),U_2990),U_2988)
| hBOOL(hAPP(hAPP(c_member(U_2984),U_2986),U_2988)) )
& ! [U_2989,U_2987,U_2985,U_2983] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2983,tc_Nat_Onat),U_2989),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2983,tc_HOL_Obool)),U_2987),hAPP(hAPP(c_Set_Oinsert(U_2983),U_2985),c_Orderings_Obot__class_Obot(tc_fun(U_2983,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2983,tc_Nat_Onat),U_2989),U_2987)),hAPP(U_2989,U_2985))
| ~ hBOOL(hAPP(hAPP(c_member(U_2983),U_2985),U_2987)) ) ),
inference(miniscope,[status(thm)],[f_769_2]) ).
cnf(f_769_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2983,tc_Nat_Onat),U_2989),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2983,tc_HOL_Obool)),U_2987),hAPP(hAPP(c_Set_Oinsert(U_2983),U_2985),c_Orderings_Obot__class_Obot(tc_fun(U_2983,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2983,tc_Nat_Onat),U_2989),U_2987)),hAPP(U_2989,U_2985))
| ~ hBOOL(hAPP(hAPP(c_member(U_2983),U_2985),U_2987)) ),
inference(clausify,[status(thm)],[f_769_3]) ).
cnf(f_769_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2984,tc_Nat_Onat),U_2990),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2984,tc_HOL_Obool)),U_2988),hAPP(hAPP(c_Set_Oinsert(U_2984),U_2986),c_Orderings_Obot__class_Obot(tc_fun(U_2984,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2984,tc_Nat_Onat),U_2990),U_2988)
| hBOOL(hAPP(hAPP(c_member(U_2984),U_2986),U_2988)) ),
inference(clausify,[status(thm)],[f_769_3]) ).
fof(f_770_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_770_2,plain,
! [U_2992,U_2991] : hBOOL(hAPP(hAPP(c_member(U_2991),U_2992),c_Orderings_Otop__class_Otop(tc_fun(U_2991,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_770_1]) ).
cnf(f_770_3,plain,
hBOOL(hAPP(hAPP(c_member(U_2991),U_2992),c_Orderings_Otop__class_Otop(tc_fun(U_2991,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_770_2]) ).
fof(f_771_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_771_2,plain,
! [U_2998,U_2997,U_2996,U_2995,U_2994,U_2993] :
( ( hAPP(c_Set_Oimage(U_2993,U_2996,c_Fun_Ofun__upd(U_2993,U_2996,U_2997,U_2994,U_2998)),U_2995) = hAPP(c_Set_Oimage(U_2993,U_2996,U_2997),U_2995)
| hBOOL(hAPP(hAPP(c_member(U_2993),U_2994),U_2995)) )
& ( hAPP(c_Set_Oimage(U_2993,U_2996,c_Fun_Ofun__upd(U_2993,U_2996,U_2997,U_2994,U_2998)),U_2995) = hAPP(hAPP(c_Set_Oinsert(U_2996),U_2998),hAPP(c_Set_Oimage(U_2993,U_2996,U_2997),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2993,tc_HOL_Obool)),U_2995),hAPP(hAPP(c_Set_Oinsert(U_2993),U_2994),c_Orderings_Obot__class_Obot(tc_fun(U_2993,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_2993),U_2994),U_2995)) ) ),
inference(variable_rename,[status(thm)],[f_771_1]) ).
fof(f_771_3,plain,
( ! [U_3010,U_3008,U_3006,U_3004,U_3002,U_3000] :
( hAPP(c_Set_Oimage(U_3000,U_3006,c_Fun_Ofun__upd(U_3000,U_3006,U_3008,U_3002,U_3010)),U_3004) = hAPP(c_Set_Oimage(U_3000,U_3006,U_3008),U_3004)
| hBOOL(hAPP(hAPP(c_member(U_3000),U_3002),U_3004)) )
& ! [U_3009,U_3007,U_3005,U_3003,U_3001,U_2999] :
( hAPP(c_Set_Oimage(U_2999,U_3005,c_Fun_Ofun__upd(U_2999,U_3005,U_3007,U_3001,U_3009)),U_3003) = hAPP(hAPP(c_Set_Oinsert(U_3005),U_3009),hAPP(c_Set_Oimage(U_2999,U_3005,U_3007),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2999,tc_HOL_Obool)),U_3003),hAPP(hAPP(c_Set_Oinsert(U_2999),U_3001),c_Orderings_Obot__class_Obot(tc_fun(U_2999,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_2999),U_3001),U_3003)) ) ),
inference(miniscope,[status(thm)],[f_771_2]) ).
cnf(f_771_4,plain,
( hAPP(c_Set_Oimage(U_2999,U_3005,c_Fun_Ofun__upd(U_2999,U_3005,U_3007,U_3001,U_3009)),U_3003) = hAPP(hAPP(c_Set_Oinsert(U_3005),U_3009),hAPP(c_Set_Oimage(U_2999,U_3005,U_3007),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2999,tc_HOL_Obool)),U_3003),hAPP(hAPP(c_Set_Oinsert(U_2999),U_3001),c_Orderings_Obot__class_Obot(tc_fun(U_2999,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_2999),U_3001),U_3003)) ),
inference(clausify,[status(thm)],[f_771_3]) ).
cnf(f_771_5,plain,
( hAPP(c_Set_Oimage(U_3000,U_3006,c_Fun_Ofun__upd(U_3000,U_3006,U_3008,U_3002,U_3010)),U_3004) = hAPP(c_Set_Oimage(U_3000,U_3006,U_3008),U_3004)
| hBOOL(hAPP(hAPP(c_member(U_3000),U_3002),U_3004)) ),
inference(clausify,[status(thm)],[f_771_3]) ).
fof(f_772_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_772_2,plain,
! [U_3015,U_3014,U_3013,U_3012,U_3011] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3012,U_3011),U_3015),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3012,tc_HOL_Obool)),U_3013),hAPP(hAPP(c_Set_Oinsert(U_3012),U_3014),c_Orderings_Obot__class_Obot(tc_fun(U_3012,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3012,U_3011),U_3015),U_3013)
| hBOOL(hAPP(hAPP(c_member(U_3012),U_3014),U_3013)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3012,U_3011),U_3015),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3012,tc_HOL_Obool)),U_3013),hAPP(hAPP(c_Set_Oinsert(U_3012),U_3014),c_Orderings_Obot__class_Obot(tc_fun(U_3012,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3011),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3012,U_3011),U_3015),U_3013)),hAPP(U_3015,U_3014))
| ~ hBOOL(hAPP(hAPP(c_member(U_3012),U_3014),U_3013)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3012),U_3013))
| ~ class_Groups_Oab__group__add(U_3011) ),
inference(variable_rename,[status(thm)],[f_772_1]) ).
cnf(f_772_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3012,U_3011),U_3015),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3012,tc_HOL_Obool)),U_3013),hAPP(hAPP(c_Set_Oinsert(U_3012),U_3014),c_Orderings_Obot__class_Obot(tc_fun(U_3012,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3011),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3012,U_3011),U_3015),U_3013)),hAPP(U_3015,U_3014))
| ~ hBOOL(hAPP(hAPP(c_member(U_3012),U_3014),U_3013))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3012),U_3013))
| ~ class_Groups_Oab__group__add(U_3011) ),
inference(clausify,[status(thm)],[f_772_2]) ).
cnf(f_772_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3012,U_3011),U_3015),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3012,tc_HOL_Obool)),U_3013),hAPP(hAPP(c_Set_Oinsert(U_3012),U_3014),c_Orderings_Obot__class_Obot(tc_fun(U_3012,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3012,U_3011),U_3015),U_3013)
| hBOOL(hAPP(hAPP(c_member(U_3012),U_3014),U_3013))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3012),U_3013))
| ~ class_Groups_Oab__group__add(U_3011) ),
inference(clausify,[status(thm)],[f_772_2]) ).
fof(f_773_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_773_2,plain,
! [U_3020,U_3019,U_3018,U_3017,U_3016] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3017,U_3016),U_3020),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3017,tc_HOL_Obool)),U_3018),hAPP(hAPP(c_Set_Oinsert(U_3017),U_3019),c_Orderings_Obot__class_Obot(tc_fun(U_3017,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3016),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3017,U_3016),U_3020),U_3018)),hAPP(U_3020,U_3019))
| ~ hBOOL(hAPP(hAPP(c_member(U_3017),U_3019),U_3018))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3017),U_3018))
| ~ class_Rings_Oring(U_3016) ),
inference(variable_rename,[status(thm)],[f_773_1]) ).
cnf(f_773_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3017,U_3016),U_3020),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3017,tc_HOL_Obool)),U_3018),hAPP(hAPP(c_Set_Oinsert(U_3017),U_3019),c_Orderings_Obot__class_Obot(tc_fun(U_3017,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3016),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3017,U_3016),U_3020),U_3018)),hAPP(U_3020,U_3019))
| ~ hBOOL(hAPP(hAPP(c_member(U_3017),U_3019),U_3018))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3017),U_3018))
| ~ class_Rings_Oring(U_3016) ),
inference(clausify,[status(thm)],[f_773_2]) ).
fof(f_774_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_774_2,plain,
! [U_3025,U_3024,U_3023,U_3022] :
( c_Fun_Oinj__on(U_3023,U_3024,U_3025,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3023,tc_HOL_Obool),U_3022))
| ? [U_3021] :
( ~ c_Fun_Oinj__on(U_3023,U_3024,U_3025,U_3021)
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_3023,tc_HOL_Obool)),U_3021),U_3022)) )
| U_3022 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_3023,tc_HOL_Obool),tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_774_1]) ).
fof(f_774_3,plain,
! [U_3025,U_3024,U_3023,U_3022] :
( c_Fun_Oinj__on(U_3023,U_3024,U_3025,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3023,tc_HOL_Obool),U_3022))
| ( ~ c_Fun_Oinj__on(U_3023,U_3024,U_3025,sK45(U_3025,U_3024,U_3023,U_3022))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_3023,tc_HOL_Obool)),sK45(U_3025,U_3024,U_3023,U_3022)),U_3022)) )
| U_3022 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_3023,tc_HOL_Obool),tc_HOL_Obool)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_3021,sK45(U_3025,U_3024,U_3023,U_3022))],[f_774_2]) ).
cnf(f_774_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_3023,tc_HOL_Obool)),sK45(U_3025,U_3024,U_3023,U_3022)),U_3022))
| c_Fun_Oinj__on(U_3023,U_3024,U_3025,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3023,tc_HOL_Obool),U_3022))
| U_3022 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_3023,tc_HOL_Obool),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_774_3]) ).
cnf(f_774_5,plain,
( ~ c_Fun_Oinj__on(U_3023,U_3024,U_3025,sK45(U_3025,U_3024,U_3023,U_3022))
| c_Fun_Oinj__on(U_3023,U_3024,U_3025,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3023,tc_HOL_Obool),U_3022))
| U_3022 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_3023,tc_HOL_Obool),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_774_3]) ).
fof(f_775_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_775_2,plain,
! [U_3029,U_3028,U_3027] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3027,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3027,tc_HOL_Obool),U_3028)),U_3029))
| U_3028 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_3027,tc_HOL_Obool),tc_HOL_Obool))
| ? [U_3026] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3027,tc_HOL_Obool)),U_3026),U_3029))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_3027,tc_HOL_Obool)),U_3026),U_3028)) ) ),
inference(variable_rename,[status(thm)],[f_775_1]) ).
fof(f_775_3,plain,
! [U_3029,U_3028,U_3027] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3027,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3027,tc_HOL_Obool),U_3028)),U_3029))
| U_3028 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_3027,tc_HOL_Obool),tc_HOL_Obool))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3027,tc_HOL_Obool)),sK46(U_3029,U_3028,U_3027)),U_3029))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_3027,tc_HOL_Obool)),sK46(U_3029,U_3028,U_3027)),U_3028)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_3026,sK46(U_3029,U_3028,U_3027))],[f_775_2]) ).
cnf(f_775_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_3027,tc_HOL_Obool)),sK46(U_3029,U_3028,U_3027)),U_3028))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3027,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3027,tc_HOL_Obool),U_3028)),U_3029))
| U_3028 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_3027,tc_HOL_Obool),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_775_3]) ).
cnf(f_775_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3027,tc_HOL_Obool)),sK46(U_3029,U_3028,U_3027)),U_3029))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3027,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3027,tc_HOL_Obool),U_3028)),U_3029))
| U_3028 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_3027,tc_HOL_Obool),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_775_3]) ).
fof(f_776_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_776_2,plain,
! [U_3034,U_3033,U_3032,U_3031] :
( ? [U_3030] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_3032,U_3030)))
& hBOOL(hAPP(hAPP(c_member(U_3031),U_3030),U_3033)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3031,tc_Nat_Onat),U_3032),U_3033) != hAPP(c_Nat_OSuc,U_3034) ),
inference(variable_rename,[status(thm)],[f_776_1]) ).
fof(f_776_3,plain,
! [U_3034,U_3033,U_3032,U_3031] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_3032,sK47(U_3034,U_3033,U_3032,U_3031))))
& hBOOL(hAPP(hAPP(c_member(U_3031),sK47(U_3034,U_3033,U_3032,U_3031)),U_3033)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3031,tc_Nat_Onat),U_3032),U_3033) != hAPP(c_Nat_OSuc,U_3034) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_3030,sK47(U_3034,U_3033,U_3032,U_3031))],[f_776_2]) ).
cnf(f_776_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_3031),sK47(U_3034,U_3033,U_3032,U_3031)),U_3033))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3031,tc_Nat_Onat),U_3032),U_3033) != hAPP(c_Nat_OSuc,U_3034) ),
inference(clausify,[status(thm)],[f_776_3]) ).
cnf(f_776_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_3032,sK47(U_3034,U_3033,U_3032,U_3031))))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3031,tc_Nat_Onat),U_3032),U_3033) != hAPP(c_Nat_OSuc,U_3034) ),
inference(clausify,[status(thm)],[f_776_3]) ).
fof(f_777_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_777_2,plain,
! [U_3038,U_3037,U_3036,U_3035] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3035),U_3038),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_3037,hAPP(c_Nat_OSuc,U_3036))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3035),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3035),U_3038),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_3037,U_3036))),hAPP(U_3038,hAPP(c_Nat_OSuc,U_3036)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3036)),U_3037)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3035),U_3038),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_3037,hAPP(c_Nat_OSuc,U_3036))) = c_Groups_Ozero__class_Ozero(U_3035)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3036)),U_3037)) ) )
| ~ class_Groups_Ocomm__monoid__add(U_3035) ),
inference(variable_rename,[status(thm)],[f_777_1]) ).
cnf(f_777_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3035),U_3038),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_3037,hAPP(c_Nat_OSuc,U_3036))) = c_Groups_Ozero__class_Ozero(U_3035)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3036)),U_3037))
| ~ class_Groups_Ocomm__monoid__add(U_3035) ),
inference(clausify,[status(thm)],[f_777_2]) ).
cnf(f_777_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3035),U_3038),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_3037,hAPP(c_Nat_OSuc,U_3036))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3035),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3035),U_3038),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_3037,U_3036))),hAPP(U_3038,hAPP(c_Nat_OSuc,U_3036)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3036)),U_3037))
| ~ class_Groups_Ocomm__monoid__add(U_3035) ),
inference(clausify,[status(thm)],[f_777_2]) ).
fof(f_778_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_778_2,plain,
! [U_3042,U_3041,U_3040,U_3039] : c_Fun_Ofun__upd(U_3039,U_3040,U_3041,U_3042,hAPP(U_3041,U_3042)) = U_3041,
inference(variable_rename,[status(thm)],[f_778_1]) ).
cnf(f_778_3,plain,
c_Fun_Ofun__upd(U_3039,U_3040,U_3041,U_3042,hAPP(U_3041,U_3042)) = U_3041,
inference(clausify,[status(thm)],[f_778_2]) ).
fof(f_779_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_779_2,plain,
! [U_3044,U_3043] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3043),U_3044))),
inference(variable_rename,[status(thm)],[f_779_1]) ).
cnf(f_779_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3043),U_3044))),
inference(clausify,[status(thm)],[f_779_2]) ).
fof(f_780_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_780_2,plain,
! [U_3046,U_3045] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_3045,U_3046))),
inference(variable_rename,[status(thm)],[f_780_1]) ).
cnf(f_780_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_3045,U_3046))),
inference(clausify,[status(thm)],[f_780_2]) ).
fof(f_781_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_781_2,plain,
! [U_3047] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_3047))),
inference(variable_rename,[status(thm)],[f_781_1]) ).
cnf(f_781_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_3047))),
inference(clausify,[status(thm)],[f_781_2]) ).
fof(f_782_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_782_2,plain,
! [U_3048] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_3048))),
inference(variable_rename,[status(thm)],[f_782_1]) ).
cnf(f_782_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_3048))),
inference(clausify,[status(thm)],[f_782_2]) ).
fof(f_783_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_783_2,plain,
! [U_3050,U_3049] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_3049,U_3050))),
inference(variable_rename,[status(thm)],[f_783_1]) ).
cnf(f_783_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_3049,U_3050))),
inference(clausify,[status(thm)],[f_783_2]) ).
fof(f_784_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_784_2,plain,
! [U_3052,U_3051] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_3051,U_3052))),
inference(variable_rename,[status(thm)],[f_784_1]) ).
cnf(f_784_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_3051,U_3052))),
inference(clausify,[status(thm)],[f_784_2]) ).
fof(f_785_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_785_2,plain,
! [U_3057,U_3056,U_3055,U_3054,U_3053] :
( ( c_Fun_Ofun__upd(U_3053,U_3054,U_3055,U_3056,U_3057) = U_3055
| hAPP(U_3055,U_3056) != U_3057 )
& ( hAPP(U_3055,U_3056) = U_3057
| c_Fun_Ofun__upd(U_3053,U_3054,U_3055,U_3056,U_3057) != U_3055 ) ),
inference(variable_rename,[status(thm)],[f_785_1]) ).
fof(f_785_3,plain,
( ! [U_3067,U_3065,U_3063] :
( ! [U_3061,U_3059] : c_Fun_Ofun__upd(U_3059,U_3061,U_3063,U_3065,U_3067) = U_3063
| hAPP(U_3063,U_3065) != U_3067 )
& ! [U_3066,U_3064,U_3062] :
( ! [U_3060,U_3058] : c_Fun_Ofun__upd(U_3058,U_3060,U_3062,U_3064,U_3066) != U_3062
| hAPP(U_3062,U_3064) = U_3066 ) ),
inference(miniscope,[status(thm)],[f_785_2]) ).
cnf(f_785_4,plain,
( c_Fun_Ofun__upd(U_3058,U_3060,U_3062,U_3064,U_3066) != U_3062
| hAPP(U_3062,U_3064) = U_3066 ),
inference(clausify,[status(thm)],[f_785_3]) ).
cnf(f_785_5,plain,
( c_Fun_Ofun__upd(U_3059,U_3061,U_3063,U_3065,U_3067) = U_3063
| hAPP(U_3063,U_3065) != U_3067 ),
inference(clausify,[status(thm)],[f_785_3]) ).
fof(f_786_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_786_2,plain,
! [U_3073,U_3072,U_3071,U_3070,U_3069,U_3068] : c_Fun_Ofun__upd(U_3068,U_3069,c_Fun_Ofun__upd(U_3068,U_3069,U_3070,U_3071,U_3072),U_3071,U_3073) = c_Fun_Ofun__upd(U_3068,U_3069,U_3070,U_3071,U_3073),
inference(variable_rename,[status(thm)],[f_786_1]) ).
cnf(f_786_3,plain,
c_Fun_Ofun__upd(U_3068,U_3069,c_Fun_Ofun__upd(U_3068,U_3069,U_3070,U_3071,U_3072),U_3071,U_3073) = c_Fun_Ofun__upd(U_3068,U_3069,U_3070,U_3071,U_3073),
inference(clausify,[status(thm)],[f_786_2]) ).
fof(f_787_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_787_2,plain,
! [U_3078,U_3077,U_3076,U_3075,U_3074] : hAPP(c_Fun_Ofun__upd(U_3074,U_3075,U_3076,U_3077,U_3078),U_3077) = U_3078,
inference(variable_rename,[status(thm)],[f_787_1]) ).
cnf(f_787_3,plain,
hAPP(c_Fun_Ofun__upd(U_3074,U_3075,U_3076,U_3077,U_3078),U_3077) = U_3078,
inference(clausify,[status(thm)],[f_787_2]) ).
fof(f_788_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_788_2,plain,
! [U_3084,U_3083,U_3082,U_3081,U_3080,U_3079] :
( ( hAPP(c_Fun_Ofun__upd(U_3081,U_3082,U_3083,U_3080,U_3084),U_3079) = hAPP(U_3083,U_3079)
| U_3079 = U_3080 )
& ( hAPP(c_Fun_Ofun__upd(U_3081,U_3082,U_3083,U_3080,U_3084),U_3079) = U_3084
| U_3079 != U_3080 ) ),
inference(variable_rename,[status(thm)],[f_788_1]) ).
fof(f_788_3,plain,
( ! [U_3096,U_3094,U_3092,U_3090,U_3088,U_3086] :
( hAPP(c_Fun_Ofun__upd(U_3090,U_3092,U_3094,U_3088,U_3096),U_3086) = hAPP(U_3094,U_3086)
| U_3086 = U_3088 )
& ! [U_3095,U_3093,U_3091,U_3089,U_3087,U_3085] :
( hAPP(c_Fun_Ofun__upd(U_3089,U_3091,U_3093,U_3087,U_3095),U_3085) = U_3095
| U_3085 != U_3087 ) ),
inference(miniscope,[status(thm)],[f_788_2]) ).
cnf(f_788_4,plain,
( hAPP(c_Fun_Ofun__upd(U_3089,U_3091,U_3093,U_3087,U_3095),U_3085) = U_3095
| U_3085 != U_3087 ),
inference(clausify,[status(thm)],[f_788_3]) ).
cnf(f_788_5,plain,
( hAPP(c_Fun_Ofun__upd(U_3090,U_3092,U_3094,U_3088,U_3096),U_3086) = hAPP(U_3094,U_3086)
| U_3086 = U_3088 ),
inference(clausify,[status(thm)],[f_788_3]) ).
fof(f_789_1,plain,
! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_c_2,V_a_2] :
( c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_a_2,V_b_2),V_c_2,V_d_2) = c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_c_2,V_d_2),V_a_2,V_b_2)
| V_a_2 = V_c_2 ),
inference(fof_nnf,[status(thm)],[fact_fun__upd__twist]) ).
fof(f_789_2,plain,
! [U_3103,U_3102,U_3101,U_3100,U_3099,U_3098,U_3097] :
( c_Fun_Ofun__upd(U_3099,U_3100,c_Fun_Ofun__upd(U_3099,U_3100,U_3101,U_3097,U_3102),U_3098,U_3103) = c_Fun_Ofun__upd(U_3099,U_3100,c_Fun_Ofun__upd(U_3099,U_3100,U_3101,U_3098,U_3103),U_3097,U_3102)
| U_3097 = U_3098 ),
inference(variable_rename,[status(thm)],[f_789_1]) ).
cnf(f_789_3,plain,
( c_Fun_Ofun__upd(U_3099,U_3100,c_Fun_Ofun__upd(U_3099,U_3100,U_3101,U_3097,U_3102),U_3098,U_3103) = c_Fun_Ofun__upd(U_3099,U_3100,c_Fun_Ofun__upd(U_3099,U_3100,U_3101,U_3098,U_3103),U_3097,U_3102)
| U_3097 = U_3098 ),
inference(clausify,[status(thm)],[f_789_2]) ).
fof(f_790_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_790_2,plain,
! [U_3109,U_3108,U_3107,U_3106,U_3105,U_3104] :
( hAPP(c_Fun_Ofun__upd(U_3106,U_3107,U_3108,U_3105,U_3109),U_3104) = hAPP(U_3108,U_3104)
| U_3104 = U_3105 ),
inference(variable_rename,[status(thm)],[f_790_1]) ).
cnf(f_790_3,plain,
( hAPP(c_Fun_Ofun__upd(U_3106,U_3107,U_3108,U_3105,U_3109),U_3104) = hAPP(U_3108,U_3104)
| U_3104 = U_3105 ),
inference(clausify,[status(thm)],[f_790_2]) ).
fof(f_791_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_791_2,plain,
! [U_3114,U_3113,U_3112,U_3111,U_3110] :
( c_Fun_Ofun__upd(U_3113,U_3114,U_3110,U_3111,U_3112) = U_3110
| hAPP(U_3110,U_3111) != U_3112 ),
inference(variable_rename,[status(thm)],[f_791_1]) ).
cnf(f_791_3,plain,
( c_Fun_Ofun__upd(U_3113,U_3114,U_3110,U_3111,U_3112) = U_3110
| hAPP(U_3110,U_3111) != U_3112 ),
inference(clausify,[status(thm)],[f_791_2]) ).
fof(f_792_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_792_2,plain,
! [U_3118,U_3117,U_3116,U_3115] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3115),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3115),U_3116),U_3117)),U_3118) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3115),U_3116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3115),U_3117),U_3118))
| ~ class_Groups_Oab__semigroup__add(U_3115) ),
inference(variable_rename,[status(thm)],[f_792_1]) ).
cnf(f_792_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3115),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3115),U_3116),U_3117)),U_3118) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3115),U_3116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3115),U_3117),U_3118))
| ~ class_Groups_Oab__semigroup__add(U_3115) ),
inference(clausify,[status(thm)],[f_792_2]) ).
fof(f_793_1,plain,
! [V_c_2,V_b_2,V_a_2,T_b] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)
| V_b_2 != V_c_2 )
& ( V_b_2 = V_c_2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2) ) )
| ~ class_Groups_Ocancel__semigroup__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__left__cancel]) ).
fof(f_793_2,plain,
! [U_3122,U_3121,U_3120,U_3119] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3119),U_3120),U_3121) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3119),U_3120),U_3122)
| U_3121 != U_3122 )
& ( U_3121 = U_3122
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3119),U_3120),U_3121) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3119),U_3120),U_3122) ) )
| ~ class_Groups_Ocancel__semigroup__add(U_3119) ),
inference(variable_rename,[status(thm)],[f_793_1]) ).
cnf(f_793_3,plain,
( U_3121 = U_3122
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3119),U_3120),U_3121) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3119),U_3120),U_3122)
| ~ class_Groups_Ocancel__semigroup__add(U_3119) ),
inference(clausify,[status(thm)],[f_793_2]) ).
cnf(f_793_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3119),U_3120),U_3121) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3119),U_3120),U_3122)
| U_3121 != U_3122
| ~ class_Groups_Ocancel__semigroup__add(U_3119) ),
inference(clausify,[status(thm)],[f_793_2]) ).
fof(f_794_1,plain,
! [V_c_2,V_a_2,V_b_2,T_b] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)
| V_b_2 != V_c_2 )
& ( V_b_2 = V_c_2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2) ) )
| ~ class_Groups_Ocancel__semigroup__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__right__cancel]) ).
fof(f_794_2,plain,
! [U_3126,U_3125,U_3124,U_3123] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3123),U_3124),U_3125) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3123),U_3126),U_3125)
| U_3124 != U_3126 )
& ( U_3124 = U_3126
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3123),U_3124),U_3125) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3123),U_3126),U_3125) ) )
| ~ class_Groups_Ocancel__semigroup__add(U_3123) ),
inference(variable_rename,[status(thm)],[f_794_1]) ).
cnf(f_794_3,plain,
( U_3124 = U_3126
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3123),U_3124),U_3125) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3123),U_3126),U_3125)
| ~ class_Groups_Ocancel__semigroup__add(U_3123) ),
inference(clausify,[status(thm)],[f_794_2]) ).
cnf(f_794_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3123),U_3124),U_3125) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3123),U_3126),U_3125)
| U_3124 != U_3126
| ~ class_Groups_Ocancel__semigroup__add(U_3123) ),
inference(clausify,[status(thm)],[f_794_2]) ).
fof(f_795_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_795_2,plain,
! [U_3130,U_3129,U_3128,U_3127] :
( U_3129 = U_3130
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3127),U_3128),U_3129) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3127),U_3128),U_3130)
| ~ class_Groups_Ocancel__semigroup__add(U_3127) ),
inference(variable_rename,[status(thm)],[f_795_1]) ).
cnf(f_795_3,plain,
( U_3129 = U_3130
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3127),U_3128),U_3129) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3127),U_3128),U_3130)
| ~ class_Groups_Ocancel__semigroup__add(U_3127) ),
inference(clausify,[status(thm)],[f_795_2]) ).
fof(f_796_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_796_2,plain,
! [U_3134,U_3133,U_3132,U_3131] :
( U_3133 = U_3134
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3131),U_3132),U_3133) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3131),U_3132),U_3134)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_3131) ),
inference(variable_rename,[status(thm)],[f_796_1]) ).
cnf(f_796_3,plain,
( U_3133 = U_3134
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3131),U_3132),U_3133) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3131),U_3132),U_3134)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_3131) ),
inference(clausify,[status(thm)],[f_796_2]) ).
fof(f_797_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_797_2,plain,
! [U_3138,U_3137,U_3136,U_3135] :
( U_3136 = U_3138
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3135),U_3136),U_3137) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3135),U_3138),U_3137)
| ~ class_Groups_Ocancel__semigroup__add(U_3135) ),
inference(variable_rename,[status(thm)],[f_797_1]) ).
cnf(f_797_3,plain,
( U_3136 = U_3138
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3135),U_3136),U_3137) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3135),U_3138),U_3137)
| ~ class_Groups_Ocancel__semigroup__add(U_3135) ),
inference(clausify,[status(thm)],[f_797_2]) ).
fof(f_798_1,plain,
! [V_b_2,V_c_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right]) ).
fof(f_798_2,plain,
! [U_3142,U_3141,U_3140,U_3139] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3139),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3139),U_3140),U_3141)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3139),U_3142),U_3141)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3139),U_3140),U_3142)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3139),U_3140),U_3142))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3139),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3139),U_3140),U_3141)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3139),U_3142),U_3141))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3139) ),
inference(variable_rename,[status(thm)],[f_798_1]) ).
cnf(f_798_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3139),U_3140),U_3142))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3139),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3139),U_3140),U_3141)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3139),U_3142),U_3141)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3139) ),
inference(clausify,[status(thm)],[f_798_2]) ).
cnf(f_798_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3139),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3139),U_3140),U_3141)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3139),U_3142),U_3141)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3139),U_3140),U_3142))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3139) ),
inference(clausify,[status(thm)],[f_798_2]) ).
fof(f_799_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left]) ).
fof(f_799_2,plain,
! [U_3146,U_3145,U_3144,U_3143] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3143),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3143),U_3144),U_3145)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3143),U_3144),U_3146)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3143),U_3145),U_3146)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3143),U_3145),U_3146))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3143),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3143),U_3144),U_3145)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3143),U_3144),U_3146))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3143) ),
inference(variable_rename,[status(thm)],[f_799_1]) ).
cnf(f_799_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3143),U_3145),U_3146))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3143),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3143),U_3144),U_3145)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3143),U_3144),U_3146)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3143) ),
inference(clausify,[status(thm)],[f_799_2]) ).
cnf(f_799_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3143),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3143),U_3144),U_3145)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3143),U_3144),U_3146)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3143),U_3145),U_3146))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3143) ),
inference(clausify,[status(thm)],[f_799_2]) ).
fof(f_800_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_800_2,plain,
! [U_3150,U_3149,U_3148,U_3147] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3147),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3147),U_3148),U_3150)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3147),U_3149),U_3150)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3147),U_3148),U_3149))
| ~ class_Groups_Oordered__ab__semigroup__add(U_3147) ),
inference(variable_rename,[status(thm)],[f_800_1]) ).
cnf(f_800_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3147),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3147),U_3148),U_3150)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3147),U_3149),U_3150)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3147),U_3148),U_3149))
| ~ class_Groups_Oordered__ab__semigroup__add(U_3147) ),
inference(clausify,[status(thm)],[f_800_2]) ).
fof(f_801_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_801_2,plain,
! [U_3154,U_3153,U_3152,U_3151] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3151),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3151),U_3154),U_3152)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3151),U_3154),U_3153)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3151),U_3152),U_3153))
| ~ class_Groups_Oordered__ab__semigroup__add(U_3151) ),
inference(variable_rename,[status(thm)],[f_801_1]) ).
cnf(f_801_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3151),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3151),U_3154),U_3152)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3151),U_3154),U_3153)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3151),U_3152),U_3153))
| ~ class_Groups_Oordered__ab__semigroup__add(U_3151) ),
inference(clausify,[status(thm)],[f_801_2]) ).
fof(f_802_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_802_2,plain,
! [U_3159,U_3158,U_3157,U_3156,U_3155] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3155),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3155),U_3156),U_3158)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3155),U_3157),U_3159)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3155),U_3158),U_3159))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3155),U_3156),U_3157))
| ~ class_Groups_Oordered__ab__semigroup__add(U_3155) ),
inference(variable_rename,[status(thm)],[f_802_1]) ).
cnf(f_802_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3155),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3155),U_3156),U_3158)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3155),U_3157),U_3159)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3155),U_3158),U_3159))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3155),U_3156),U_3157))
| ~ class_Groups_Oordered__ab__semigroup__add(U_3155) ),
inference(clausify,[status(thm)],[f_802_2]) ).
fof(f_803_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_803_2,plain,
! [U_3163,U_3162,U_3161,U_3160] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3160),U_3161),U_3163))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3160),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3160),U_3161),U_3162)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3160),U_3163),U_3162)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3160) ),
inference(variable_rename,[status(thm)],[f_803_1]) ).
cnf(f_803_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3160),U_3161),U_3163))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3160),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3160),U_3161),U_3162)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3160),U_3163),U_3162)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3160) ),
inference(clausify,[status(thm)],[f_803_2]) ).
fof(f_804_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_804_2,plain,
! [U_3167,U_3166,U_3165,U_3164] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3164),U_3166),U_3167))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3164),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3164),U_3165),U_3166)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3164),U_3165),U_3167)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3164) ),
inference(variable_rename,[status(thm)],[f_804_1]) ).
cnf(f_804_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3164),U_3166),U_3167))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3164),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3164),U_3165),U_3166)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3164),U_3165),U_3167)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3164) ),
inference(clausify,[status(thm)],[f_804_2]) ).
fof(f_805_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_805_2,plain,
! [U_3169,U_3168] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3168),c_Groups_Ozero__class_Ozero(U_3168)),U_3169) = U_3169
| ~ class_Groups_Omonoid__add(U_3168) ),
inference(variable_rename,[status(thm)],[f_805_1]) ).
cnf(f_805_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3168),c_Groups_Ozero__class_Ozero(U_3168)),U_3169) = U_3169
| ~ class_Groups_Omonoid__add(U_3168) ),
inference(clausify,[status(thm)],[f_805_2]) ).
fof(f_806_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_806_2,plain,
! [U_3171,U_3170] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3170),c_Groups_Ozero__class_Ozero(U_3170)),U_3171) = U_3171
| ~ class_Groups_Ocomm__monoid__add(U_3170) ),
inference(variable_rename,[status(thm)],[f_806_1]) ).
cnf(f_806_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3170),c_Groups_Ozero__class_Ozero(U_3170)),U_3171) = U_3171
| ~ class_Groups_Ocomm__monoid__add(U_3170) ),
inference(clausify,[status(thm)],[f_806_2]) ).
fof(f_807_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_807_2,plain,
! [U_3173,U_3172] :
( ( ( c_Groups_Ozero__class_Ozero(U_3172) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3172),U_3173),U_3173)
| U_3173 != c_Groups_Ozero__class_Ozero(U_3172) )
& ( U_3173 = c_Groups_Ozero__class_Ozero(U_3172)
| c_Groups_Ozero__class_Ozero(U_3172) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3172),U_3173),U_3173) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_3172) ),
inference(variable_rename,[status(thm)],[f_807_1]) ).
cnf(f_807_3,plain,
( U_3173 = c_Groups_Ozero__class_Ozero(U_3172)
| c_Groups_Ozero__class_Ozero(U_3172) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3172),U_3173),U_3173)
| ~ class_Groups_Olinordered__ab__group__add(U_3172) ),
inference(clausify,[status(thm)],[f_807_2]) ).
cnf(f_807_4,plain,
( c_Groups_Ozero__class_Ozero(U_3172) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3172),U_3173),U_3173)
| U_3173 != c_Groups_Ozero__class_Ozero(U_3172)
| ~ class_Groups_Olinordered__ab__group__add(U_3172) ),
inference(clausify,[status(thm)],[f_807_2]) ).
fof(f_808_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_808_2,plain,
! [U_3175,U_3174] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3174),U_3175),c_Groups_Ozero__class_Ozero(U_3174)) = U_3175
| ~ class_Groups_Omonoid__add(U_3174) ),
inference(variable_rename,[status(thm)],[f_808_1]) ).
cnf(f_808_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3174),U_3175),c_Groups_Ozero__class_Ozero(U_3174)) = U_3175
| ~ class_Groups_Omonoid__add(U_3174) ),
inference(clausify,[status(thm)],[f_808_2]) ).
fof(f_809_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_809_2,plain,
! [U_3177,U_3176] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3176),U_3177),c_Groups_Ozero__class_Ozero(U_3176)) = U_3177
| ~ class_Groups_Ocomm__monoid__add(U_3176) ),
inference(variable_rename,[status(thm)],[f_809_1]) ).
cnf(f_809_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3176),U_3177),c_Groups_Ozero__class_Ozero(U_3176)) = U_3177
| ~ class_Groups_Ocomm__monoid__add(U_3176) ),
inference(clausify,[status(thm)],[f_809_2]) ).
fof(f_810_1,plain,
! [V_b_2,V_c_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right]) ).
fof(f_810_2,plain,
! [U_3181,U_3180,U_3179,U_3178] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3178),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3178),U_3179),U_3180)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3178),U_3181),U_3180)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3178),U_3179),U_3181)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3178),U_3179),U_3181))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3178),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3178),U_3179),U_3180)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3178),U_3181),U_3180))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3178) ),
inference(variable_rename,[status(thm)],[f_810_1]) ).
cnf(f_810_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3178),U_3179),U_3181))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3178),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3178),U_3179),U_3180)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3178),U_3181),U_3180)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3178) ),
inference(clausify,[status(thm)],[f_810_2]) ).
cnf(f_810_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3178),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3178),U_3179),U_3180)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3178),U_3181),U_3180)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3178),U_3179),U_3181))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3178) ),
inference(clausify,[status(thm)],[f_810_2]) ).
fof(f_811_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left]) ).
fof(f_811_2,plain,
! [U_3185,U_3184,U_3183,U_3182] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3182),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3182),U_3183),U_3184)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3182),U_3183),U_3185)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3182),U_3184),U_3185)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3182),U_3184),U_3185))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3182),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3182),U_3183),U_3184)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3182),U_3183),U_3185))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3182) ),
inference(variable_rename,[status(thm)],[f_811_1]) ).
cnf(f_811_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3182),U_3184),U_3185))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3182),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3182),U_3183),U_3184)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3182),U_3183),U_3185)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3182) ),
inference(clausify,[status(thm)],[f_811_2]) ).
cnf(f_811_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3182),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3182),U_3183),U_3184)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3182),U_3183),U_3185)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3182),U_3184),U_3185))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3182) ),
inference(clausify,[status(thm)],[f_811_2]) ).
fof(f_812_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_812_2,plain,
! [U_3189,U_3188,U_3187,U_3186] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3186),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3186),U_3187),U_3189)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3186),U_3188),U_3189)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3186),U_3187),U_3188))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3186) ),
inference(variable_rename,[status(thm)],[f_812_1]) ).
cnf(f_812_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3186),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3186),U_3187),U_3189)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3186),U_3188),U_3189)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3186),U_3187),U_3188))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3186) ),
inference(clausify,[status(thm)],[f_812_2]) ).
fof(f_813_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_813_2,plain,
! [U_3193,U_3192,U_3191,U_3190] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3190),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3190),U_3193),U_3191)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3190),U_3193),U_3192)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3190),U_3191),U_3192))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3190) ),
inference(variable_rename,[status(thm)],[f_813_1]) ).
cnf(f_813_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3190),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3190),U_3193),U_3191)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3190),U_3193),U_3192)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3190),U_3191),U_3192))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3190) ),
inference(clausify,[status(thm)],[f_813_2]) ).
fof(f_814_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_814_2,plain,
! [U_3198,U_3197,U_3196,U_3195,U_3194] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3194),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3194),U_3195),U_3197)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3194),U_3196),U_3198)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3194),U_3197),U_3198))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3194),U_3195),U_3196))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3194) ),
inference(variable_rename,[status(thm)],[f_814_1]) ).
cnf(f_814_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3194),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3194),U_3195),U_3197)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3194),U_3196),U_3198)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3194),U_3197),U_3198))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3194),U_3195),U_3196))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3194) ),
inference(clausify,[status(thm)],[f_814_2]) ).
fof(f_815_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_815_2,plain,
! [U_3202,U_3201,U_3200,U_3199] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3199),U_3200),U_3202))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3199),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3199),U_3200),U_3201)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3199),U_3202),U_3201)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3199) ),
inference(variable_rename,[status(thm)],[f_815_1]) ).
cnf(f_815_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3199),U_3200),U_3202))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3199),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3199),U_3200),U_3201)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3199),U_3202),U_3201)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3199) ),
inference(clausify,[status(thm)],[f_815_2]) ).
fof(f_816_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_816_2,plain,
! [U_3206,U_3205,U_3204,U_3203] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3203),U_3205),U_3206))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3203),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3203),U_3204),U_3205)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3203),U_3204),U_3206)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3203) ),
inference(variable_rename,[status(thm)],[f_816_1]) ).
cnf(f_816_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3203),U_3205),U_3206))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3203),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3203),U_3204),U_3205)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3203),U_3204),U_3206)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3203) ),
inference(clausify,[status(thm)],[f_816_2]) ).
fof(f_817_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_817_2,plain,
! [U_3209,U_3208,U_3207] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3207),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3207),U_3208),U_3209)),U_3209) = U_3208
| ~ class_Groups_Ogroup__add(U_3207) ),
inference(variable_rename,[status(thm)],[f_817_1]) ).
cnf(f_817_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3207),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3207),U_3208),U_3209)),U_3209) = U_3208
| ~ class_Groups_Ogroup__add(U_3207) ),
inference(clausify,[status(thm)],[f_817_2]) ).
fof(f_818_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_818_2,plain,
! [U_3212,U_3211,U_3210] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3210),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3210),U_3211),U_3212)),U_3212) = U_3211
| ~ class_Groups_Ogroup__add(U_3210) ),
inference(variable_rename,[status(thm)],[f_818_1]) ).
cnf(f_818_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3210),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3210),U_3211),U_3212)),U_3212) = U_3211
| ~ class_Groups_Ogroup__add(U_3210) ),
inference(clausify,[status(thm)],[f_818_2]) ).
fof(f_819_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_819_2,plain,
! [U_3215,U_3214,U_3213] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3213),hAPP(c_Groups_Ouminus__class_Ouminus(U_3213),U_3214)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3213),U_3214),U_3215)) = U_3215
| ~ class_Groups_Ogroup__add(U_3213) ),
inference(variable_rename,[status(thm)],[f_819_1]) ).
cnf(f_819_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3213),hAPP(c_Groups_Ouminus__class_Ouminus(U_3213),U_3214)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3213),U_3214),U_3215)) = U_3215
| ~ class_Groups_Ogroup__add(U_3213) ),
inference(clausify,[status(thm)],[f_819_2]) ).
fof(f_820_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_820_2,plain,
! [U_3218,U_3217,U_3216] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3216),U_3217),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3216),hAPP(c_Groups_Ouminus__class_Ouminus(U_3216),U_3217)),U_3218)) = U_3218
| ~ class_Groups_Ogroup__add(U_3216) ),
inference(variable_rename,[status(thm)],[f_820_1]) ).
cnf(f_820_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3216),U_3217),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3216),hAPP(c_Groups_Ouminus__class_Ouminus(U_3216),U_3217)),U_3218)) = U_3218
| ~ class_Groups_Ogroup__add(U_3216) ),
inference(clausify,[status(thm)],[f_820_2]) ).
fof(f_821_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_821_2,plain,
! [U_3221,U_3220,U_3219] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_3219),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3219),U_3220),U_3221)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3219),hAPP(c_Groups_Ouminus__class_Ouminus(U_3219),U_3221)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3219),U_3220))
| ~ class_Groups_Ogroup__add(U_3219) ),
inference(variable_rename,[status(thm)],[f_821_1]) ).
cnf(f_821_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_3219),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3219),U_3220),U_3221)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3219),hAPP(c_Groups_Ouminus__class_Ouminus(U_3219),U_3221)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3219),U_3220))
| ~ class_Groups_Ogroup__add(U_3219) ),
inference(clausify,[status(thm)],[f_821_2]) ).
fof(f_822_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_822_2,plain,
! [U_3224,U_3223,U_3222] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_3222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3222),U_3223),U_3224)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3222),hAPP(c_Groups_Ouminus__class_Ouminus(U_3222),U_3223)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3222),U_3224))
| ~ class_Groups_Oab__group__add(U_3222) ),
inference(variable_rename,[status(thm)],[f_822_1]) ).
cnf(f_822_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_3222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3222),U_3223),U_3224)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3222),hAPP(c_Groups_Ouminus__class_Ouminus(U_3222),U_3223)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3222),U_3224))
| ~ class_Groups_Oab__group__add(U_3222) ),
inference(clausify,[status(thm)],[f_822_2]) ).
fof(f_823_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_823_2,plain,
! [U_3225] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3225) = U_3225,
inference(variable_rename,[status(thm)],[f_823_1]) ).
cnf(f_823_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3225) = U_3225,
inference(clausify,[status(thm)],[f_823_2]) ).
fof(f_824_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_824_2,plain,
! [U_3226] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3226),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_3226,
inference(variable_rename,[status(thm)],[f_824_1]) ).
cnf(f_824_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3226),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_3226,
inference(clausify,[status(thm)],[f_824_2]) ).
fof(f_825_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_825_2,plain,
! [U_3228,U_3227] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3227),U_3228) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3228 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3227 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( U_3228 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_3227 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3227),U_3228) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_825_1]) ).
fof(f_825_3,plain,
( ! [U_3232,U_3230] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3230),U_3232) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3232 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3230 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_3231,U_3229] :
( ( U_3231 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_3229 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3229),U_3231) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_825_2]) ).
cnf(f_825_4,plain,
( U_3229 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3229),U_3231) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_825_3]) ).
cnf(f_825_5,plain,
( U_3231 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3229),U_3231) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_825_3]) ).
cnf(f_825_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3230),U_3232) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3232 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3230 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_825_3]) ).
fof(f_826_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_826_2,plain,
! [U_3234,U_3233] :
( U_3234 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3233),U_3234) != U_3233 ),
inference(variable_rename,[status(thm)],[f_826_1]) ).
fof(f_826_3,plain,
! [U_3234] :
( ! [U_3233] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3233),U_3234) != U_3233
| U_3234 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(miniscope,[status(thm)],[f_826_2]) ).
cnf(f_826_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3233),U_3234) != U_3233
| U_3234 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_826_3]) ).
fof(f_827_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_827_2,plain,
! [U_3236,U_3235] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3235)),U_3236) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3235),hAPP(c_Nat_OSuc,U_3236)),
inference(variable_rename,[status(thm)],[f_827_1]) ).
cnf(f_827_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3235)),U_3236) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3235),hAPP(c_Nat_OSuc,U_3236)),
inference(clausify,[status(thm)],[f_827_2]) ).
fof(f_828_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_828_2,plain,
! [U_3238,U_3237] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3237)),U_3238) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3237),U_3238)),
inference(variable_rename,[status(thm)],[f_828_1]) ).
cnf(f_828_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3237)),U_3238) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3237),U_3238)),
inference(clausify,[status(thm)],[f_828_2]) ).
fof(f_829_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_829_2,plain,
! [U_3240,U_3239] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3239),hAPP(c_Nat_OSuc,U_3240)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3239),U_3240)),
inference(variable_rename,[status(thm)],[f_829_1]) ).
cnf(f_829_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3239),hAPP(c_Nat_OSuc,U_3240)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3239),U_3240)),
inference(clausify,[status(thm)],[f_829_2]) ).
fof(f_830_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_830_2,plain,
! [U_3243,U_3242,U_3241] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3241),U_3243))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3241),U_3242)),U_3243)) ),
inference(variable_rename,[status(thm)],[f_830_1]) ).
cnf(f_830_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3241),U_3243))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3241),U_3242)),U_3243)) ),
inference(clausify,[status(thm)],[f_830_2]) ).
fof(f_831_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_831_2,plain,
! [U_3247,U_3246,U_3245,U_3244] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3246),U_3247))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3246),U_3245) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3244),U_3247)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3244),U_3245)) ),
inference(variable_rename,[status(thm)],[f_831_1]) ).
cnf(f_831_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3246),U_3247))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3246),U_3245) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3244),U_3247)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3244),U_3245)) ),
inference(clausify,[status(thm)],[f_831_2]) ).
fof(f_832_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_832_2,plain,
! [U_3251,U_3250,U_3249,U_3248] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3248),U_3250)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3249),U_3251)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3250),U_3251))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3248),U_3249)) ),
inference(variable_rename,[status(thm)],[f_832_1]) ).
cnf(f_832_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3248),U_3250)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3249),U_3251)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3250),U_3251))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3248),U_3249)) ),
inference(clausify,[status(thm)],[f_832_2]) ).
fof(f_833_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_833_2,plain,
! [U_3254,U_3253,U_3252] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3252),U_3254)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3253),U_3254)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3252),U_3253)) ),
inference(variable_rename,[status(thm)],[f_833_1]) ).
cnf(f_833_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3252),U_3254)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3253),U_3254)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3252),U_3253)) ),
inference(clausify,[status(thm)],[f_833_2]) ).
fof(f_834_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_834_2,plain,
! [U_3257,U_3256,U_3255] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3255),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3257),U_3256)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3255),U_3256)) ),
inference(variable_rename,[status(thm)],[f_834_1]) ).
cnf(f_834_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3255),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3257),U_3256)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3255),U_3256)) ),
inference(clausify,[status(thm)],[f_834_2]) ).
fof(f_835_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_835_2,plain,
! [U_3260,U_3259,U_3258] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3258),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3259),U_3260)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3258),U_3259)) ),
inference(variable_rename,[status(thm)],[f_835_1]) ).
cnf(f_835_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3258),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3259),U_3260)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3258),U_3259)) ),
inference(clausify,[status(thm)],[f_835_2]) ).
fof(f_836_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_836_2,plain,
! [U_3263,U_3262,U_3261] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3261),U_3262)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3261),U_3263)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3262),U_3263)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3262),U_3263))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3261),U_3262)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3261),U_3263))) ) ),
inference(variable_rename,[status(thm)],[f_836_1]) ).
fof(f_836_3,plain,
( ! [U_3269,U_3267] :
( ! [U_3265] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3265),U_3267)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3265),U_3269)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3267),U_3269)) )
& ! [U_3268,U_3266] :
( ! [U_3264] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3264),U_3266)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3264),U_3268)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3266),U_3268)) ) ),
inference(miniscope,[status(thm)],[f_836_2]) ).
cnf(f_836_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3264),U_3266)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3264),U_3268)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3266),U_3268)) ),
inference(clausify,[status(thm)],[f_836_3]) ).
cnf(f_836_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3265),U_3267)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3265),U_3269)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3267),U_3269)) ),
inference(clausify,[status(thm)],[f_836_3]) ).
fof(f_837_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_837_2,plain,
! [U_3271,U_3270] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3270),U_3271)),U_3271)),
inference(variable_rename,[status(thm)],[f_837_1]) ).
cnf(f_837_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3270),U_3271)),U_3271)),
inference(clausify,[status(thm)],[f_837_2]) ).
fof(f_838_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_838_2,plain,
! [U_3273,U_3272] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3272),U_3273)),U_3272)),
inference(variable_rename,[status(thm)],[f_838_1]) ).
cnf(f_838_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3272),U_3273)),U_3272)),
inference(clausify,[status(thm)],[f_838_2]) ).
fof(f_839_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_839_2,plain,
! [U_3276,U_3275,U_3274] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3274),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3275),U_3276)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3274),U_3275)) ),
inference(variable_rename,[status(thm)],[f_839_1]) ).
cnf(f_839_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3274),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3275),U_3276)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3274),U_3275)) ),
inference(clausify,[status(thm)],[f_839_2]) ).
fof(f_840_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_840_2,plain,
! [U_3279,U_3278,U_3277] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3277),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3279),U_3278)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3277),U_3278)) ),
inference(variable_rename,[status(thm)],[f_840_1]) ).
cnf(f_840_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3277),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3279),U_3278)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3277),U_3278)) ),
inference(clausify,[status(thm)],[f_840_2]) ).
fof(f_841_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_841_2,plain,
! [U_3282,U_3281,U_3280] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3281),U_3282))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3280),U_3282)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3280),U_3281)),U_3282)) ),
inference(variable_rename,[status(thm)],[f_841_1]) ).
cnf(f_841_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3280),U_3282))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3280),U_3281)),U_3282)) ),
inference(clausify,[status(thm)],[f_841_2]) ).
cnf(f_841_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3281),U_3282))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3280),U_3281)),U_3282)) ),
inference(clausify,[status(thm)],[f_841_2]) ).
fof(f_842_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_842_2,plain,
! [U_3285,U_3284,U_3283] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3283),U_3285))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3283),U_3284)),U_3285)) ),
inference(variable_rename,[status(thm)],[f_842_1]) ).
cnf(f_842_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3283),U_3285))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3283),U_3284)),U_3285)) ),
inference(clausify,[status(thm)],[f_842_2]) ).
fof(f_843_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_843_2,plain,
! [U_3288,U_3287,U_3286] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3287),U_3288))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3286),U_3287)),U_3288)) ),
inference(variable_rename,[status(thm)],[f_843_1]) ).
fof(f_843_3,plain,
! [U_3288,U_3287] :
( ! [U_3286] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3286),U_3287)),U_3288))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3287),U_3288)) ),
inference(miniscope,[status(thm)],[f_843_2]) ).
cnf(f_843_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_3286),U_3287)),U_3288))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3287),U_3288)) ),
inference(clausify,[status(thm)],[f_843_3]) ).
fof(f_844_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_844_2,plain,
! [U_3292,U_3291,U_3290,U_3289] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3289),U_3291)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3290),U_3292)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3291),U_3292))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3289),U_3290)) ),
inference(variable_rename,[status(thm)],[f_844_1]) ).
cnf(f_844_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_3289),U_3291)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3290),U_3292)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3291),U_3292))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3289),U_3290)) ),
inference(clausify,[status(thm)],[f_844_2]) ).
fof(f_845_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_845_2,plain,
! [U_3295,U_3294,U_3293] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3293),U_3295)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3294),U_3295)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3293),U_3294)) ),
inference(variable_rename,[status(thm)],[f_845_1]) ).
cnf(f_845_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_3293),U_3295)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3294),U_3295)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3293),U_3294)) ),
inference(clausify,[status(thm)],[f_845_2]) ).
fof(f_846_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_846_2,plain,
! [U_3298,U_3297,U_3296] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3296),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3298),U_3297)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3296),U_3297)) ),
inference(variable_rename,[status(thm)],[f_846_1]) ).
cnf(f_846_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3296),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3298),U_3297)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3296),U_3297)) ),
inference(clausify,[status(thm)],[f_846_2]) ).
fof(f_847_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_847_2,plain,
! [U_3301,U_3300,U_3299] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3299),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3300),U_3301)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3299),U_3300)) ),
inference(variable_rename,[status(thm)],[f_847_1]) ).
cnf(f_847_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3299),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3300),U_3301)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3299),U_3300)) ),
inference(clausify,[status(thm)],[f_847_2]) ).
fof(f_848_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_848_2,plain,
! [U_3304,U_3303,U_3302] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3302),U_3303)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3302),U_3304)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3303),U_3304)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3303),U_3304))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3302),U_3303)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3302),U_3304))) ) ),
inference(variable_rename,[status(thm)],[f_848_1]) ).
fof(f_848_3,plain,
( ! [U_3310,U_3308] :
( ! [U_3306] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3306),U_3308)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3306),U_3310)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3308),U_3310)) )
& ! [U_3309,U_3307] :
( ! [U_3305] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3305),U_3307)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3305),U_3309)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3307),U_3309)) ) ),
inference(miniscope,[status(thm)],[f_848_2]) ).
cnf(f_848_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_3305),U_3307)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3305),U_3309)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3307),U_3309)) ),
inference(clausify,[status(thm)],[f_848_3]) ).
cnf(f_848_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_3306),U_3308)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3306),U_3310)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3308),U_3310)) ),
inference(clausify,[status(thm)],[f_848_3]) ).
fof(f_849_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_849_2,plain,
! [U_3314,U_3313] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3313),U_3314))
| ! [U_3312] : U_3314 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3313),U_3312) )
& ( ? [U_3311] : U_3314 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3313),U_3311)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3313),U_3314)) ) ),
inference(variable_rename,[status(thm)],[f_849_1]) ).
fof(f_849_3,plain,
( ! [U_3318,U_3316] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3316),U_3318))
| ! [U_3312] : U_3318 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3316),U_3312) )
& ! [U_3317,U_3315] :
( ? [U_3311] : U_3317 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3315),U_3311)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3315),U_3317)) ) ),
inference(miniscope,[status(thm)],[f_849_2]) ).
fof(f_849_4,plain,
( ! [U_3318,U_3316] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3316),U_3318))
| ! [U_3312] : U_3318 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3316),U_3312) )
& ! [U_3317,U_3315] :
( U_3317 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3315),sK48(U_3317,U_3315))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3315),U_3317)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_3311,sK48(U_3317,U_3315))],[f_849_3]) ).
cnf(f_849_5,plain,
( U_3317 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3315),sK48(U_3317,U_3315))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3315),U_3317)) ),
inference(clausify,[status(thm)],[f_849_4]) ).
cnf(f_849_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3316),U_3318))
| U_3318 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3316),U_3312) ),
inference(clausify,[status(thm)],[f_849_4]) ).
fof(f_850_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_850_2,plain,
! [U_3320,U_3319] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3319),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3319),U_3320))),
inference(variable_rename,[status(thm)],[f_850_1]) ).
cnf(f_850_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3319),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3319),U_3320))),
inference(clausify,[status(thm)],[f_850_2]) ).
fof(f_851_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_851_2,plain,
! [U_3322,U_3321] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3321),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3322),U_3321))),
inference(variable_rename,[status(thm)],[f_851_1]) ).
cnf(f_851_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3321),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3322),U_3321))),
inference(clausify,[status(thm)],[f_851_2]) ).
fof(f_852_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_852_2,plain,
! [U_3325,U_3324,U_3323] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3323),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3325),U_3324)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3323),U_3324)) ),
inference(variable_rename,[status(thm)],[f_852_1]) ).
cnf(f_852_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3323),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3325),U_3324)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3323),U_3324)) ),
inference(clausify,[status(thm)],[f_852_2]) ).
fof(f_853_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_853_2,plain,
! [U_3328,U_3327,U_3326] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3326),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3327),U_3328)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3326),U_3327)) ),
inference(variable_rename,[status(thm)],[f_853_1]) ).
cnf(f_853_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3326),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3327),U_3328)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3326),U_3327)) ),
inference(clausify,[status(thm)],[f_853_2]) ).
fof(f_854_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_854_2,plain,
! [U_3330,U_3329] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3329),U_3330)),U_3330) = U_3329,
inference(variable_rename,[status(thm)],[f_854_1]) ).
cnf(f_854_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3329),U_3330)),U_3330) = U_3329,
inference(clausify,[status(thm)],[f_854_2]) ).
fof(f_855_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_855_2,plain,
! [U_3332,U_3331] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3331),U_3332)),U_3331) = U_3332,
inference(variable_rename,[status(thm)],[f_855_1]) ).
cnf(f_855_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3331),U_3332)),U_3331) = U_3332,
inference(clausify,[status(thm)],[f_855_2]) ).
fof(f_856_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_856_2,plain,
! [U_3335,U_3334,U_3333] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3333),U_3334)),U_3335) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3333),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3334),U_3335)),
inference(variable_rename,[status(thm)],[f_856_1]) ).
cnf(f_856_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3333),U_3334)),U_3335) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3333),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3334),U_3335)),
inference(clausify,[status(thm)],[f_856_2]) ).
fof(f_857_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_857_2,plain,
! [U_3338,U_3337,U_3336] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3336),U_3337)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3336),U_3338)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3337),U_3338),
inference(variable_rename,[status(thm)],[f_857_1]) ).
cnf(f_857_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3336),U_3337)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3336),U_3338)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3337),U_3338),
inference(clausify,[status(thm)],[f_857_2]) ).
fof(f_858_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_858_2,plain,
! [U_3341,U_3340,U_3339] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3339),U_3340)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3341),U_3340)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3339),U_3341),
inference(variable_rename,[status(thm)],[f_858_1]) ).
cnf(f_858_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3339),U_3340)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3341),U_3340)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3339),U_3341),
inference(clausify,[status(thm)],[f_858_2]) ).
fof(f_859_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_859_2,plain,
! [U_3346] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3346))
| ! [U_3345] :
? [U_3344] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3344),U_3345))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3344),U_3346)) ) )
& ( ? [U_3343] :
! [U_3342] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3342),U_3343))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3342),U_3346)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3346)) ) ),
inference(variable_rename,[status(thm)],[f_859_1]) ).
fof(f_859_3,plain,
( ! [U_3348] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3348))
| ! [U_3345] :
? [U_3344] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3344),U_3345))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3344),U_3348)) ) )
& ! [U_3347] :
( ? [U_3343] :
! [U_3342] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3342),U_3343))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3342),U_3347)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3347)) ) ),
inference(miniscope,[status(thm)],[f_859_2]) ).
fof(f_859_4,plain,
( ! [U_3348] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3348))
| ! [U_3345] :
? [U_3344] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3344),U_3345))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3344),U_3348)) ) )
& ! [U_3347] :
( ! [U_3342] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3342),sK49(U_3347)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3342),U_3347)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3347)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_3343,sK49(U_3347))],[f_859_3]) ).
fof(f_859_5,plain,
( ! [U_3348] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3348))
| ! [U_3345] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK50(U_3348,U_3345)),U_3345))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK50(U_3348,U_3345)),U_3348)) ) )
& ! [U_3347] :
( ! [U_3342] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3342),sK49(U_3347)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3342),U_3347)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3347)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_3344,sK50(U_3348,U_3345))],[f_859_4]) ).
cnf(f_859_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3342),sK49(U_3347)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3342),U_3347))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3347)) ),
inference(clausify,[status(thm)],[f_859_5]) ).
cnf(f_859_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK50(U_3348,U_3345)),U_3348))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3348)) ),
inference(clausify,[status(thm)],[f_859_5]) ).
cnf(f_859_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK50(U_3348,U_3345)),U_3345))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3348)) ),
inference(clausify,[status(thm)],[f_859_5]) ).
fof(f_860_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_860_2,plain,
! [U_3353] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3353))
| ! [U_3352] :
? [U_3351] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3351),U_3352))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3351),U_3353)) ) )
& ( ? [U_3350] :
! [U_3349] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3349),U_3350))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3349),U_3353)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3353)) ) ),
inference(variable_rename,[status(thm)],[f_860_1]) ).
fof(f_860_3,plain,
( ! [U_3355] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3355))
| ! [U_3352] :
? [U_3351] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3351),U_3352))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3351),U_3355)) ) )
& ! [U_3354] :
( ? [U_3350] :
! [U_3349] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3349),U_3350))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3349),U_3354)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3354)) ) ),
inference(miniscope,[status(thm)],[f_860_2]) ).
fof(f_860_4,plain,
( ! [U_3355] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3355))
| ! [U_3352] :
? [U_3351] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3351),U_3352))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3351),U_3355)) ) )
& ! [U_3354] :
( ! [U_3349] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3349),sK51(U_3354)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3349),U_3354)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3354)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_3350,sK51(U_3354))],[f_860_3]) ).
fof(f_860_5,plain,
( ! [U_3355] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3355))
| ! [U_3352] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK52(U_3355,U_3352)),U_3352))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK52(U_3355,U_3352)),U_3355)) ) )
& ! [U_3354] :
( ! [U_3349] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3349),sK51(U_3354)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3349),U_3354)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3354)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_3351,sK52(U_3355,U_3352))],[f_860_4]) ).
cnf(f_860_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3349),sK51(U_3354)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3349),U_3354))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3354)) ),
inference(clausify,[status(thm)],[f_860_5]) ).
cnf(f_860_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK52(U_3355,U_3352)),U_3355))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3355)) ),
inference(clausify,[status(thm)],[f_860_5]) ).
cnf(f_860_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK52(U_3355,U_3352)),U_3352))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3355)) ),
inference(clausify,[status(thm)],[f_860_5]) ).
fof(f_861_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_861_2,plain,
! [U_3360,U_3359,U_3358,U_3357,U_3356] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3357,U_3356),U_3360),hAPP(hAPP(c_Set_Oinsert(U_3357),U_3359),U_3358)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3356),hAPP(U_3360,U_3359)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3357,U_3356),U_3360),U_3358))
| hBOOL(hAPP(hAPP(c_member(U_3357),U_3359),U_3358))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3357),U_3358))
| ~ class_Groups_Ocomm__monoid__add(U_3356) ),
inference(variable_rename,[status(thm)],[f_861_1]) ).
cnf(f_861_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3357,U_3356),U_3360),hAPP(hAPP(c_Set_Oinsert(U_3357),U_3359),U_3358)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3356),hAPP(U_3360,U_3359)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3357,U_3356),U_3360),U_3358))
| hBOOL(hAPP(hAPP(c_member(U_3357),U_3359),U_3358))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3357),U_3358))
| ~ class_Groups_Ocomm__monoid__add(U_3356) ),
inference(clausify,[status(thm)],[f_861_2]) ).
fof(f_862_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_862_2,plain,
! [U_3365,U_3364,U_3363,U_3362,U_3361] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3362,U_3361),U_3365),hAPP(hAPP(c_Set_Oinsert(U_3362),U_3364),U_3363)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3361),hAPP(U_3365,U_3364)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3362,U_3361),U_3365),U_3363))
| hBOOL(hAPP(hAPP(c_member(U_3362),U_3364),U_3363))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3362),U_3363))
| ~ class_Groups_Ocomm__monoid__add(U_3361) ),
inference(variable_rename,[status(thm)],[f_862_1]) ).
cnf(f_862_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3362,U_3361),U_3365),hAPP(hAPP(c_Set_Oinsert(U_3362),U_3364),U_3363)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3361),hAPP(U_3365,U_3364)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3362,U_3361),U_3365),U_3363))
| hBOOL(hAPP(hAPP(c_member(U_3362),U_3364),U_3363))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3362),U_3363))
| ~ class_Groups_Ocomm__monoid__add(U_3361) ),
inference(clausify,[status(thm)],[f_862_2]) ).
fof(f_863_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_863_2,plain,
! [U_3370,U_3369,U_3368,U_3367,U_3366] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3366),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3367,U_3366),U_3370),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3367,tc_HOL_Obool)),U_3368),U_3369))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3367,U_3366),U_3370),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3367,tc_HOL_Obool)),U_3368),U_3369))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3366),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3367,U_3366),U_3370),U_3368)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3367,U_3366),U_3370),U_3369))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3367),U_3369))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3367),U_3368))
| ~ class_Groups_Ocomm__monoid__add(U_3366) ),
inference(variable_rename,[status(thm)],[f_863_1]) ).
cnf(f_863_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3366),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3367,U_3366),U_3370),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3367,tc_HOL_Obool)),U_3368),U_3369))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3367,U_3366),U_3370),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3367,tc_HOL_Obool)),U_3368),U_3369))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3366),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3367,U_3366),U_3370),U_3368)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3367,U_3366),U_3370),U_3369))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3367),U_3369))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3367),U_3368))
| ~ class_Groups_Ocomm__monoid__add(U_3366) ),
inference(clausify,[status(thm)],[f_863_2]) ).
fof(f_864_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_864_2,plain,
! [U_3375,U_3374,U_3373,U_3372,U_3371] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3372,U_3371),U_3374),hAPP(hAPP(c_Set_Oinsert(U_3372),U_3375),U_3373)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3371),hAPP(U_3374,U_3375)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3372,U_3371),U_3374),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3372,tc_HOL_Obool)),U_3373),hAPP(hAPP(c_Set_Oinsert(U_3372),U_3375),c_Orderings_Obot__class_Obot(tc_fun(U_3372,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3372),U_3373))
| ~ class_Groups_Ocomm__monoid__add(U_3371) ),
inference(variable_rename,[status(thm)],[f_864_1]) ).
cnf(f_864_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3372,U_3371),U_3374),hAPP(hAPP(c_Set_Oinsert(U_3372),U_3375),U_3373)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3371),hAPP(U_3374,U_3375)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3372,U_3371),U_3374),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3372,tc_HOL_Obool)),U_3373),hAPP(hAPP(c_Set_Oinsert(U_3372),U_3375),c_Orderings_Obot__class_Obot(tc_fun(U_3372,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3372),U_3373))
| ~ class_Groups_Ocomm__monoid__add(U_3371) ),
inference(clausify,[status(thm)],[f_864_2]) ).
fof(f_865_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_865_2,plain,
! [U_3380,U_3379,U_3378,U_3377,U_3376] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3377,U_3376),U_3380),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3377,tc_HOL_Obool)),U_3378),U_3379)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3376),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3377,U_3376),U_3380),U_3378)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3377,U_3376),U_3380),U_3379))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3377,tc_HOL_Obool)),U_3378),U_3379) != c_Orderings_Obot__class_Obot(tc_fun(U_3377,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3377),U_3379))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3377),U_3378))
| ~ class_Groups_Ocomm__monoid__add(U_3376) ),
inference(variable_rename,[status(thm)],[f_865_1]) ).
cnf(f_865_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3377,U_3376),U_3380),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3377,tc_HOL_Obool)),U_3378),U_3379)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3376),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3377,U_3376),U_3380),U_3378)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3377,U_3376),U_3380),U_3379))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3377,tc_HOL_Obool)),U_3378),U_3379) != c_Orderings_Obot__class_Obot(tc_fun(U_3377,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3377),U_3379))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3377),U_3378))
| ~ class_Groups_Ocomm__monoid__add(U_3376) ),
inference(clausify,[status(thm)],[f_865_2]) ).
fof(f_866_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_866_2,plain,
! [U_3382,U_3381] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3381),c_Groups_Ozero__class_Ozero(U_3381)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3381),U_3382),U_3382)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3381),c_Groups_Ozero__class_Ozero(U_3381)),U_3382)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3381),c_Groups_Ozero__class_Ozero(U_3381)),U_3382))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3381),c_Groups_Ozero__class_Ozero(U_3381)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3381),U_3382),U_3382))) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_3381) ),
inference(variable_rename,[status(thm)],[f_866_1]) ).
cnf(f_866_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3381),c_Groups_Ozero__class_Ozero(U_3381)),U_3382))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3381),c_Groups_Ozero__class_Ozero(U_3381)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3381),U_3382),U_3382)))
| ~ class_Groups_Olinordered__ab__group__add(U_3381) ),
inference(clausify,[status(thm)],[f_866_2]) ).
cnf(f_866_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3381),c_Groups_Ozero__class_Ozero(U_3381)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3381),U_3382),U_3382)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3381),c_Groups_Ozero__class_Ozero(U_3381)),U_3382))
| ~ class_Groups_Olinordered__ab__group__add(U_3381) ),
inference(clausify,[status(thm)],[f_866_2]) ).
fof(f_867_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_867_2,plain,
! [U_3384,U_3383] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3383),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3383),U_3384),U_3384)),c_Groups_Ozero__class_Ozero(U_3383)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3383),U_3384),c_Groups_Ozero__class_Ozero(U_3383))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3383),U_3384),c_Groups_Ozero__class_Ozero(U_3383)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3383),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3383),U_3384),U_3384)),c_Groups_Ozero__class_Ozero(U_3383))) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_3383) ),
inference(variable_rename,[status(thm)],[f_867_1]) ).
cnf(f_867_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3383),U_3384),c_Groups_Ozero__class_Ozero(U_3383)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3383),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3383),U_3384),U_3384)),c_Groups_Ozero__class_Ozero(U_3383)))
| ~ class_Groups_Olinordered__ab__group__add(U_3383) ),
inference(clausify,[status(thm)],[f_867_2]) ).
cnf(f_867_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3383),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3383),U_3384),U_3384)),c_Groups_Ozero__class_Ozero(U_3383)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3383),U_3384),c_Groups_Ozero__class_Ozero(U_3383)))
| ~ class_Groups_Olinordered__ab__group__add(U_3383) ),
inference(clausify,[status(thm)],[f_867_2]) ).
fof(f_868_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_868_2,plain,
! [U_3387,U_3386,U_3385] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3385),c_Groups_Ozero__class_Ozero(U_3385)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3385),U_3386),U_3387)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3385),c_Groups_Ozero__class_Ozero(U_3385)),U_3387))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3385),c_Groups_Ozero__class_Ozero(U_3385)),U_3386))
| ~ class_Groups_Oordered__comm__monoid__add(U_3385) ),
inference(variable_rename,[status(thm)],[f_868_1]) ).
cnf(f_868_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3385),c_Groups_Ozero__class_Ozero(U_3385)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3385),U_3386),U_3387)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3385),c_Groups_Ozero__class_Ozero(U_3385)),U_3387))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3385),c_Groups_Ozero__class_Ozero(U_3385)),U_3386))
| ~ class_Groups_Oordered__comm__monoid__add(U_3385) ),
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),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_869_2,plain,
! [U_3390,U_3389,U_3388] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3388),U_3389),U_3390) = c_Groups_Ozero__class_Ozero(U_3388)
| U_3390 != c_Groups_Ozero__class_Ozero(U_3388)
| U_3389 != c_Groups_Ozero__class_Ozero(U_3388) )
& ( ( U_3390 = c_Groups_Ozero__class_Ozero(U_3388)
& U_3389 = c_Groups_Ozero__class_Ozero(U_3388) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3388),U_3389),U_3390) != c_Groups_Ozero__class_Ozero(U_3388) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3388),c_Groups_Ozero__class_Ozero(U_3388)),U_3390))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3388),c_Groups_Ozero__class_Ozero(U_3388)),U_3389))
| ~ class_Groups_Oordered__comm__monoid__add(U_3388) ),
inference(variable_rename,[status(thm)],[f_869_1]) ).
cnf(f_869_3,plain,
( U_3389 = c_Groups_Ozero__class_Ozero(U_3388)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3388),U_3389),U_3390) != c_Groups_Ozero__class_Ozero(U_3388)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3388),c_Groups_Ozero__class_Ozero(U_3388)),U_3390))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3388),c_Groups_Ozero__class_Ozero(U_3388)),U_3389))
| ~ class_Groups_Oordered__comm__monoid__add(U_3388) ),
inference(clausify,[status(thm)],[f_869_2]) ).
cnf(f_869_4,plain,
( U_3390 = c_Groups_Ozero__class_Ozero(U_3388)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3388),U_3389),U_3390) != c_Groups_Ozero__class_Ozero(U_3388)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3388),c_Groups_Ozero__class_Ozero(U_3388)),U_3390))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3388),c_Groups_Ozero__class_Ozero(U_3388)),U_3389))
| ~ class_Groups_Oordered__comm__monoid__add(U_3388) ),
inference(clausify,[status(thm)],[f_869_2]) ).
cnf(f_869_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3388),U_3389),U_3390) = c_Groups_Ozero__class_Ozero(U_3388)
| U_3390 != c_Groups_Ozero__class_Ozero(U_3388)
| U_3389 != c_Groups_Ozero__class_Ozero(U_3388)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3388),c_Groups_Ozero__class_Ozero(U_3388)),U_3390))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3388),c_Groups_Ozero__class_Ozero(U_3388)),U_3389))
| ~ class_Groups_Oordered__comm__monoid__add(U_3388) ),
inference(clausify,[status(thm)],[f_869_2]) ).
fof(f_870_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_870_2,plain,
! [U_3394,U_3393,U_3392,U_3391] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3391),U_3393),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3391),U_3392),U_3394)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3391),U_3393),U_3394))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3391),c_Groups_Ozero__class_Ozero(U_3391)),U_3392))
| ~ class_Groups_Oordered__comm__monoid__add(U_3391) ),
inference(variable_rename,[status(thm)],[f_870_1]) ).
cnf(f_870_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3391),U_3393),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3391),U_3392),U_3394)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3391),U_3393),U_3394))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3391),c_Groups_Ozero__class_Ozero(U_3391)),U_3392))
| ~ class_Groups_Oordered__comm__monoid__add(U_3391) ),
inference(clausify,[status(thm)],[f_870_2]) ).
fof(f_871_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_871_2,plain,
! [U_3398,U_3397,U_3396,U_3395] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3395),U_3397),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3395),U_3398),U_3396)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3395),U_3397),U_3398))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3395),c_Groups_Ozero__class_Ozero(U_3395)),U_3396))
| ~ class_Groups_Oordered__comm__monoid__add(U_3395) ),
inference(variable_rename,[status(thm)],[f_871_1]) ).
cnf(f_871_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3395),U_3397),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3395),U_3398),U_3396)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3395),U_3397),U_3398))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3395),c_Groups_Ozero__class_Ozero(U_3395)),U_3396))
| ~ class_Groups_Oordered__comm__monoid__add(U_3395) ),
inference(clausify,[status(thm)],[f_871_2]) ).
fof(f_872_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_872_2,plain,
! [U_3401,U_3400,U_3399] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3399),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3399),U_3400),U_3401)),c_Groups_Ozero__class_Ozero(U_3399)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3399),U_3401),c_Groups_Ozero__class_Ozero(U_3399)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3399),U_3400),c_Groups_Ozero__class_Ozero(U_3399)))
| ~ class_Groups_Oordered__comm__monoid__add(U_3399) ),
inference(variable_rename,[status(thm)],[f_872_1]) ).
cnf(f_872_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3399),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3399),U_3400),U_3401)),c_Groups_Ozero__class_Ozero(U_3399)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3399),U_3401),c_Groups_Ozero__class_Ozero(U_3399)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3399),U_3400),c_Groups_Ozero__class_Ozero(U_3399)))
| ~ class_Groups_Oordered__comm__monoid__add(U_3399) ),
inference(clausify,[status(thm)],[f_872_2]) ).
fof(f_873_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_873_2,plain,
! [U_3406,U_3405,U_3404,U_3403,U_3402] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3403,U_3402),U_3406),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3403,tc_HOL_Obool)),U_3404),U_3405)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3402),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3402),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3403,U_3402),U_3406),U_3404)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3403,U_3402),U_3406),U_3405))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3403,U_3402),U_3406),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3403,tc_HOL_Obool)),U_3404),U_3405)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3403),U_3405))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3403),U_3404))
| ~ class_Groups_Oab__group__add(U_3402) ),
inference(variable_rename,[status(thm)],[f_873_1]) ).
cnf(f_873_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3403,U_3402),U_3406),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3403,tc_HOL_Obool)),U_3404),U_3405)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3402),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3402),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3403,U_3402),U_3406),U_3404)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3403,U_3402),U_3406),U_3405))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3403,U_3402),U_3406),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3403,tc_HOL_Obool)),U_3404),U_3405)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3403),U_3405))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3403),U_3404))
| ~ class_Groups_Oab__group__add(U_3402) ),
inference(clausify,[status(thm)],[f_873_2]) ).
fof(f_874_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_874_2,plain,
! [U_3411,U_3410,U_3409,U_3408,U_3407] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3407),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3407),U_3408),U_3410)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3407),U_3409),U_3411)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3407),U_3410),U_3411))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3407),U_3408),U_3409))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3407) ),
inference(variable_rename,[status(thm)],[f_874_1]) ).
cnf(f_874_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3407),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3407),U_3408),U_3410)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3407),U_3409),U_3411)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3407),U_3410),U_3411))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3407),U_3408),U_3409))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3407) ),
inference(clausify,[status(thm)],[f_874_2]) ).
fof(f_875_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_875_2,plain,
! [U_3416,U_3415,U_3414,U_3413,U_3412] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3412),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3412),U_3413),U_3415)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3412),U_3414),U_3416)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3412),U_3415),U_3416))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3412),U_3413),U_3414))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3412) ),
inference(variable_rename,[status(thm)],[f_875_1]) ).
cnf(f_875_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3412),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3412),U_3413),U_3415)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3412),U_3414),U_3416)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3412),U_3415),U_3416))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3412),U_3413),U_3414))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3412) ),
inference(clausify,[status(thm)],[f_875_2]) ).
fof(f_876_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_876_2,plain,
! [U_3420,U_3419,U_3418,U_3417] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3417),U_3419),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3417),U_3418),U_3420)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3417),U_3419),U_3420))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3417),c_Groups_Ozero__class_Ozero(U_3417)),U_3418))
| ~ class_Rings_Olinordered__semidom(U_3417) ),
inference(variable_rename,[status(thm)],[f_876_1]) ).
cnf(f_876_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3417),U_3419),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3417),U_3418),U_3420)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3417),U_3419),U_3420))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3417),c_Groups_Ozero__class_Ozero(U_3417)),U_3418))
| ~ class_Rings_Olinordered__semidom(U_3417) ),
inference(clausify,[status(thm)],[f_876_2]) ).
fof(f_877_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_877_2,plain,
! [U_3422,U_3421] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3421),c_Groups_Ozero__class_Ozero(U_3421)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3421),U_3422),U_3422)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3421),c_Groups_Ozero__class_Ozero(U_3421)),U_3422)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3421),c_Groups_Ozero__class_Ozero(U_3421)),U_3422))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3421),c_Groups_Ozero__class_Ozero(U_3421)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3421),U_3422),U_3422))) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_3421) ),
inference(variable_rename,[status(thm)],[f_877_1]) ).
cnf(f_877_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3421),c_Groups_Ozero__class_Ozero(U_3421)),U_3422))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3421),c_Groups_Ozero__class_Ozero(U_3421)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3421),U_3422),U_3422)))
| ~ class_Groups_Olinordered__ab__group__add(U_3421) ),
inference(clausify,[status(thm)],[f_877_2]) ).
cnf(f_877_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3421),c_Groups_Ozero__class_Ozero(U_3421)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3421),U_3422),U_3422)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3421),c_Groups_Ozero__class_Ozero(U_3421)),U_3422))
| ~ class_Groups_Olinordered__ab__group__add(U_3421) ),
inference(clausify,[status(thm)],[f_877_2]) ).
fof(f_878_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_878_2,plain,
! [U_3424,U_3423] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3423),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3423),U_3424),U_3424)),c_Groups_Ozero__class_Ozero(U_3423)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3423),U_3424),c_Groups_Ozero__class_Ozero(U_3423))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3423),U_3424),c_Groups_Ozero__class_Ozero(U_3423)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3423),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3423),U_3424),U_3424)),c_Groups_Ozero__class_Ozero(U_3423))) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_3423) ),
inference(variable_rename,[status(thm)],[f_878_1]) ).
cnf(f_878_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3423),U_3424),c_Groups_Ozero__class_Ozero(U_3423)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3423),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3423),U_3424),U_3424)),c_Groups_Ozero__class_Ozero(U_3423)))
| ~ class_Groups_Olinordered__ab__group__add(U_3423) ),
inference(clausify,[status(thm)],[f_878_2]) ).
cnf(f_878_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3423),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3423),U_3424),U_3424)),c_Groups_Ozero__class_Ozero(U_3423)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3423),U_3424),c_Groups_Ozero__class_Ozero(U_3423)))
| ~ class_Groups_Olinordered__ab__group__add(U_3423) ),
inference(clausify,[status(thm)],[f_878_2]) ).
fof(f_879_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_879_2,plain,
! [U_3427,U_3426,U_3425] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3425),c_Groups_Ozero__class_Ozero(U_3425)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3425),U_3426),U_3427)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3425),c_Groups_Ozero__class_Ozero(U_3425)),U_3427))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3425),c_Groups_Ozero__class_Ozero(U_3425)),U_3426))
| ~ class_Groups_Oordered__comm__monoid__add(U_3425) ),
inference(variable_rename,[status(thm)],[f_879_1]) ).
cnf(f_879_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3425),c_Groups_Ozero__class_Ozero(U_3425)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3425),U_3426),U_3427)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3425),c_Groups_Ozero__class_Ozero(U_3425)),U_3427))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3425),c_Groups_Ozero__class_Ozero(U_3425)),U_3426))
| ~ class_Groups_Oordered__comm__monoid__add(U_3425) ),
inference(clausify,[status(thm)],[f_879_2]) ).
fof(f_880_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_880_2,plain,
! [U_3430,U_3429,U_3428] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3428),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3428),U_3429),U_3430)),c_Groups_Ozero__class_Ozero(U_3428)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3428),U_3430),c_Groups_Ozero__class_Ozero(U_3428)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3428),U_3429),c_Groups_Ozero__class_Ozero(U_3428)))
| ~ class_Groups_Oordered__comm__monoid__add(U_3428) ),
inference(variable_rename,[status(thm)],[f_880_1]) ).
cnf(f_880_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3428),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3428),U_3429),U_3430)),c_Groups_Ozero__class_Ozero(U_3428)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3428),U_3430),c_Groups_Ozero__class_Ozero(U_3428)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3428),U_3429),c_Groups_Ozero__class_Ozero(U_3428)))
| ~ class_Groups_Oordered__comm__monoid__add(U_3428) ),
inference(clausify,[status(thm)],[f_880_2]) ).
fof(f_881_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_881_2,plain,
! [U_3432,U_3431] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3431),U_3432),hAPP(c_Groups_Ouminus__class_Ouminus(U_3431),U_3432)) = c_Groups_Ozero__class_Ozero(U_3431)
| ~ class_Groups_Ogroup__add(U_3431) ),
inference(variable_rename,[status(thm)],[f_881_1]) ).
cnf(f_881_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3431),U_3432),hAPP(c_Groups_Ouminus__class_Ouminus(U_3431),U_3432)) = c_Groups_Ozero__class_Ozero(U_3431)
| ~ class_Groups_Ogroup__add(U_3431) ),
inference(clausify,[status(thm)],[f_881_2]) ).
fof(f_882_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_882_2,plain,
! [U_3435,U_3434,U_3433] :
( ( ( U_3434 = hAPP(c_Groups_Ouminus__class_Ouminus(U_3433),U_3435)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3433),U_3434),U_3435) != c_Groups_Ozero__class_Ozero(U_3433) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3433),U_3434),U_3435) = c_Groups_Ozero__class_Ozero(U_3433)
| U_3434 != hAPP(c_Groups_Ouminus__class_Ouminus(U_3433),U_3435) ) )
| ~ class_Groups_Ogroup__add(U_3433) ),
inference(variable_rename,[status(thm)],[f_882_1]) ).
cnf(f_882_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3433),U_3434),U_3435) = c_Groups_Ozero__class_Ozero(U_3433)
| U_3434 != hAPP(c_Groups_Ouminus__class_Ouminus(U_3433),U_3435)
| ~ class_Groups_Ogroup__add(U_3433) ),
inference(clausify,[status(thm)],[f_882_2]) ).
cnf(f_882_4,plain,
( U_3434 = hAPP(c_Groups_Ouminus__class_Ouminus(U_3433),U_3435)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3433),U_3434),U_3435) != c_Groups_Ozero__class_Ozero(U_3433)
| ~ class_Groups_Ogroup__add(U_3433) ),
inference(clausify,[status(thm)],[f_882_2]) ).
fof(f_883_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_883_2,plain,
! [U_3437,U_3436] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3436),hAPP(c_Groups_Ouminus__class_Ouminus(U_3436),U_3437)),U_3437) = c_Groups_Ozero__class_Ozero(U_3436)
| ~ class_Groups_Ogroup__add(U_3436) ),
inference(variable_rename,[status(thm)],[f_883_1]) ).
cnf(f_883_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3436),hAPP(c_Groups_Ouminus__class_Ouminus(U_3436),U_3437)),U_3437) = c_Groups_Ozero__class_Ozero(U_3436)
| ~ class_Groups_Ogroup__add(U_3436) ),
inference(clausify,[status(thm)],[f_883_2]) ).
fof(f_884_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_884_2,plain,
! [U_3439,U_3438] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3438),hAPP(c_Groups_Ouminus__class_Ouminus(U_3438),U_3439)),U_3439) = c_Groups_Ozero__class_Ozero(U_3438)
| ~ class_Groups_Oab__group__add(U_3438) ),
inference(variable_rename,[status(thm)],[f_884_1]) ).
cnf(f_884_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3438),hAPP(c_Groups_Ouminus__class_Ouminus(U_3438),U_3439)),U_3439) = c_Groups_Ozero__class_Ozero(U_3438)
| ~ class_Groups_Oab__group__add(U_3438) ),
inference(clausify,[status(thm)],[f_884_2]) ).
fof(f_885_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_885_2,plain,
! [U_3442,U_3441,U_3440] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_3440),U_3441) = U_3442
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3440),U_3441),U_3442) != c_Groups_Ozero__class_Ozero(U_3440)
| ~ class_Groups_Ogroup__add(U_3440) ),
inference(variable_rename,[status(thm)],[f_885_1]) ).
cnf(f_885_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_3440),U_3441) = U_3442
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3440),U_3441),U_3442) != c_Groups_Ozero__class_Ozero(U_3440)
| ~ class_Groups_Ogroup__add(U_3440) ),
inference(clausify,[status(thm)],[f_885_2]) ).
fof(f_886_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_886_2,plain,
! [U_3445,U_3444,U_3443] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3443),U_3444),hAPP(c_Groups_Ouminus__class_Ouminus(U_3443),U_3445)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3443),U_3444),U_3445)
| ~ class_Groups_Ogroup__add(U_3443) ),
inference(variable_rename,[status(thm)],[f_886_1]) ).
cnf(f_886_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3443),U_3444),hAPP(c_Groups_Ouminus__class_Ouminus(U_3443),U_3445)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3443),U_3444),U_3445)
| ~ class_Groups_Ogroup__add(U_3443) ),
inference(clausify,[status(thm)],[f_886_2]) ).
fof(f_887_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_887_2,plain,
! [U_3448,U_3447,U_3446] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3446),U_3447),U_3448) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3446),U_3447),hAPP(c_Groups_Ouminus__class_Ouminus(U_3446),U_3448))
| ~ class_Groups_Oab__group__add(U_3446) ),
inference(variable_rename,[status(thm)],[f_887_1]) ).
cnf(f_887_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3446),U_3447),U_3448) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3446),U_3447),hAPP(c_Groups_Ouminus__class_Ouminus(U_3446),U_3448))
| ~ class_Groups_Oab__group__add(U_3446) ),
inference(clausify,[status(thm)],[f_887_2]) ).
fof(f_888_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_888_2,plain,
! [U_3451,U_3450,U_3449] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3449),U_3450),U_3451) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3449),U_3450),hAPP(c_Groups_Ouminus__class_Ouminus(U_3449),U_3451))
| ~ class_Groups_Ogroup__add(U_3449) ),
inference(variable_rename,[status(thm)],[f_888_1]) ).
cnf(f_888_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3449),U_3450),U_3451) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3449),U_3450),hAPP(c_Groups_Ouminus__class_Ouminus(U_3449),U_3451))
| ~ class_Groups_Ogroup__add(U_3449) ),
inference(clausify,[status(thm)],[f_888_2]) ).
fof(f_889_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_889_2,plain,
! [U_3453,U_3452] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3452),U_3453)
| ( ( U_3453 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_3452 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_3453 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3452 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( U_3453 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_3452 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_3453 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_3452 = 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_3452),U_3453) ) ),
inference(variable_rename,[status(thm)],[f_889_1]) ).
fof(f_889_3,plain,
( ! [U_3457,U_3455] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3455),U_3457)
| ( ( U_3457 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_3455 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_3457 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3455 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ! [U_3456,U_3454] :
( ( U_3456 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_3454 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_3456 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_3454 = 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_3454),U_3456) ) ),
inference(miniscope,[status(thm)],[f_889_2]) ).
cnf(f_889_4,plain,
( U_3454 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3454 = 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_3454),U_3456) ),
inference(clausify,[status(thm)],[f_889_3]) ).
cnf(f_889_5,plain,
( U_3456 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_3454 = 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_3454),U_3456) ),
inference(clausify,[status(thm)],[f_889_3]) ).
cnf(f_889_6,plain,
( U_3454 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3456 = 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_3454),U_3456) ),
inference(clausify,[status(thm)],[f_889_3]) ).
cnf(f_889_7,plain,
( U_3456 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_3456 = 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_3454),U_3456) ),
inference(clausify,[status(thm)],[f_889_3]) ).
cnf(f_889_8,plain,
( U_3457 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3455 != 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_3455),U_3457) ),
inference(clausify,[status(thm)],[f_889_3]) ).
cnf(f_889_9,plain,
( U_3457 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_3455 != 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_3455),U_3457) ),
inference(clausify,[status(thm)],[f_889_3]) ).
fof(f_890_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_890_2,plain,
! [U_3459,U_3458] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3458),U_3459) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( ( U_3459 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_3458 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_3459 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3458 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( U_3459 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_3458 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_3459 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_3458 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3458),U_3459) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_890_1]) ).
fof(f_890_3,plain,
( ! [U_3463,U_3461] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3461),U_3463) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( ( U_3463 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_3461 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_3463 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3461 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ! [U_3462,U_3460] :
( ( U_3462 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_3460 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_3462 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_3460 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3460),U_3462) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_890_2]) ).
cnf(f_890_4,plain,
( U_3460 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3460 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3460),U_3462) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_890_3]) ).
cnf(f_890_5,plain,
( U_3462 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_3460 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3460),U_3462) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_890_3]) ).
cnf(f_890_6,plain,
( U_3460 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3462 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3460),U_3462) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_890_3]) ).
cnf(f_890_7,plain,
( U_3462 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_3462 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3460),U_3462) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_890_3]) ).
cnf(f_890_8,plain,
( U_3463 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3461 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3461),U_3463) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_890_3]) ).
cnf(f_890_9,plain,
( U_3463 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_3461 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3461),U_3463) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_890_3]) ).
fof(f_891_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_891_2,plain,
! [U_3467,U_3466,U_3465,U_3464] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3464,tc_Nat_Onat),U_3467),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3464,tc_HOL_Obool)),U_3465),U_3466)) = 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_3464,tc_Nat_Onat),U_3467),U_3465)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3464,tc_Nat_Onat),U_3467),U_3466))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3464,tc_Nat_Onat),U_3467),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3464,tc_HOL_Obool)),U_3465),U_3466)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3464),U_3466))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3464),U_3465)) ),
inference(variable_rename,[status(thm)],[f_891_1]) ).
cnf(f_891_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3464,tc_Nat_Onat),U_3467),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3464,tc_HOL_Obool)),U_3465),U_3466)) = 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_3464,tc_Nat_Onat),U_3467),U_3465)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3464,tc_Nat_Onat),U_3467),U_3466))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3464,tc_Nat_Onat),U_3467),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3464,tc_HOL_Obool)),U_3465),U_3466)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3464),U_3466))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3464),U_3465)) ),
inference(clausify,[status(thm)],[f_891_2]) ).
fof(f_892_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_892_2,plain,
! [U_3469,U_3468] :
( ( 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_3468),U_3469)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3469))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3468)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3469))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3468))
| ~ 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_3468),U_3469))) ) ),
inference(variable_rename,[status(thm)],[f_892_1]) ).
fof(f_892_3,plain,
( ! [U_3473,U_3471] :
( 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_3471),U_3473)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3473))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3471)) ) )
& ! [U_3472,U_3470] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3472))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3470))
| ~ 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_3470),U_3472))) ) ),
inference(miniscope,[status(thm)],[f_892_2]) ).
cnf(f_892_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3472))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3470))
| ~ 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_3470),U_3472))) ),
inference(clausify,[status(thm)],[f_892_3]) ).
cnf(f_892_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3471))
| 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_3471),U_3473))) ),
inference(clausify,[status(thm)],[f_892_3]) ).
cnf(f_892_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3473))
| 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_3471),U_3473))) ),
inference(clausify,[status(thm)],[f_892_3]) ).
fof(f_893_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_893_2,plain,
! [U_3477,U_3476] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3476),U_3477))
| ! [U_3475] : U_3477 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3476),U_3475)) )
& ( ? [U_3474] : U_3477 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3476),U_3474))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3476),U_3477)) ) ),
inference(variable_rename,[status(thm)],[f_893_1]) ).
fof(f_893_3,plain,
( ! [U_3481,U_3479] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3479),U_3481))
| ! [U_3475] : U_3481 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3479),U_3475)) )
& ! [U_3480,U_3478] :
( ? [U_3474] : U_3480 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3478),U_3474))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3478),U_3480)) ) ),
inference(miniscope,[status(thm)],[f_893_2]) ).
fof(f_893_4,plain,
( ! [U_3481,U_3479] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3479),U_3481))
| ! [U_3475] : U_3481 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3479),U_3475)) )
& ! [U_3480,U_3478] :
( U_3480 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3478),sK53(U_3480,U_3478)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3478),U_3480)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_3474,sK53(U_3480,U_3478))],[f_893_3]) ).
cnf(f_893_5,plain,
( U_3480 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3478),sK53(U_3480,U_3478)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3478),U_3480)) ),
inference(clausify,[status(thm)],[f_893_4]) ).
cnf(f_893_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3479),U_3481))
| U_3481 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3479),U_3475)) ),
inference(clausify,[status(thm)],[f_893_4]) ).
fof(f_894_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_894_2,plain,
! [U_3483,U_3482] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3482),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3483),U_3482)))),
inference(variable_rename,[status(thm)],[f_894_1]) ).
cnf(f_894_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3482),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3483),U_3482)))),
inference(clausify,[status(thm)],[f_894_2]) ).
fof(f_895_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_895_2,plain,
! [U_3485,U_3484] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3484),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3484),U_3485)))),
inference(variable_rename,[status(thm)],[f_895_1]) ).
cnf(f_895_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3484),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3484),U_3485)))),
inference(clausify,[status(thm)],[f_895_2]) ).
fof(f_896_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_896_2,plain,
! [U_3487,U_3486] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3486),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3486),U_3487)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_896_1]) ).
cnf(f_896_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3486),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3486),U_3487)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_896_2]) ).
fof(f_897_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_897_2,plain,
! [U_3490,U_3489,U_3488] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3488),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3489),U_3490)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3488),U_3490)),U_3489)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3488),U_3490)),U_3489))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3488),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3489),U_3490))) ) ),
inference(variable_rename,[status(thm)],[f_897_1]) ).
fof(f_897_3,plain,
( ! [U_3496,U_3494,U_3492] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3492),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3494),U_3496)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3492),U_3496)),U_3494)) )
& ! [U_3495,U_3493,U_3491] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3491),U_3495)),U_3493))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3491),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3493),U_3495))) ) ),
inference(miniscope,[status(thm)],[f_897_2]) ).
cnf(f_897_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3491),U_3495)),U_3493))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3491),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3493),U_3495))) ),
inference(clausify,[status(thm)],[f_897_3]) ).
cnf(f_897_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3492),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3494),U_3496)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3492),U_3496)),U_3494)) ),
inference(clausify,[status(thm)],[f_897_3]) ).
fof(f_898_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_898_2,plain,
! [U_3498,U_3497] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3498),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3497),U_3498)) = U_3497
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3497),U_3498)) ),
inference(variable_rename,[status(thm)],[f_898_1]) ).
cnf(f_898_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3498),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3497),U_3498)) = U_3497
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3497),U_3498)) ),
inference(clausify,[status(thm)],[f_898_2]) ).
fof(f_899_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_899_2,plain,
! [U_3501,U_3500,U_3499] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3501),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3500),U_3499)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3501),U_3499)),U_3500)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3499),U_3500)) ),
inference(variable_rename,[status(thm)],[f_899_1]) ).
cnf(f_899_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3501),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3500),U_3499)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3501),U_3499)),U_3500)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3499),U_3500)) ),
inference(clausify,[status(thm)],[f_899_2]) ).
fof(f_900_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_900_2,plain,
! [U_3504,U_3503,U_3502] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3502),U_3503)),U_3504))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3502),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3504),U_3503))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3502),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3504),U_3503)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3502),U_3503)),U_3504)) ) ),
inference(variable_rename,[status(thm)],[f_900_1]) ).
fof(f_900_3,plain,
( ! [U_3510,U_3508,U_3506] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3506),U_3508)),U_3510))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3506),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3510),U_3508))) )
& ! [U_3509,U_3507,U_3505] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3505),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3509),U_3507)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3505),U_3507)),U_3509)) ) ),
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_3505),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3509),U_3507)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3505),U_3507)),U_3509)) ),
inference(clausify,[status(thm)],[f_900_3]) ).
cnf(f_900_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_3506),U_3508)),U_3510))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3506),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3510),U_3508))) ),
inference(clausify,[status(thm)],[f_900_3]) ).
fof(f_901_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_901_2,plain,
! [U_3513,U_3512,U_3511] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3513),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3512),U_3513)),U_3511)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3511),U_3512)) ),
inference(variable_rename,[status(thm)],[f_901_1]) ).
cnf(f_901_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3513),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3512),U_3513)),U_3511)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3511),U_3512)) ),
inference(clausify,[status(thm)],[f_901_2]) ).
fof(f_902_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_902_2,plain,
! [U_3515,U_3514] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3514),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3515),U_3514)) = U_3515
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3514),U_3515)) ),
inference(variable_rename,[status(thm)],[f_902_1]) ).
cnf(f_902_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3514),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3515),U_3514)) = U_3515
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3514),U_3515)) ),
inference(clausify,[status(thm)],[f_902_2]) ).
fof(f_903_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_903_2,plain,
! [U_3518,U_3517,U_3516] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3518),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3517),U_3516)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3518),U_3517)),U_3516)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3516),U_3517)) ),
inference(variable_rename,[status(thm)],[f_903_1]) ).
cnf(f_903_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3518),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3517),U_3516)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3518),U_3517)),U_3516)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3516),U_3517)) ),
inference(clausify,[status(thm)],[f_903_2]) ).
fof(f_904_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_904_2,plain,
! [U_3521,U_3520,U_3519] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3521),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3520),U_3519)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3521),U_3519)),U_3520)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3521),U_3519)),U_3520))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3521),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3520),U_3519))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3519),U_3520)) ),
inference(variable_rename,[status(thm)],[f_904_1]) ).
cnf(f_904_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_3521),U_3519)),U_3520))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3521),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3520),U_3519)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3519),U_3520)) ),
inference(clausify,[status(thm)],[f_904_2]) ).
cnf(f_904_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3521),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3520),U_3519)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3521),U_3519)),U_3520))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3519),U_3520)) ),
inference(clausify,[status(thm)],[f_904_2]) ).
fof(f_905_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_905_2,plain,
! [U_3523,U_3522] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3523),U_3522)),U_3522) = U_3523
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3522),U_3523)) ),
inference(variable_rename,[status(thm)],[f_905_1]) ).
cnf(f_905_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3523),U_3522)),U_3522) = U_3523
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3522),U_3523)) ),
inference(clausify,[status(thm)],[f_905_2]) ).
fof(f_906_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_906_2,plain,
! [U_3526,U_3525,U_3524] :
( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3525),U_3524) = U_3526
| U_3525 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3526),U_3524) )
& ( U_3525 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3526),U_3524)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3525),U_3524) != U_3526 ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3524),U_3525)) ),
inference(variable_rename,[status(thm)],[f_906_1]) ).
cnf(f_906_3,plain,
( U_3525 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3526),U_3524)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3525),U_3524) != U_3526
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3524),U_3525)) ),
inference(clausify,[status(thm)],[f_906_2]) ).
cnf(f_906_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3525),U_3524) = U_3526
| U_3525 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3526),U_3524)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3524),U_3525)) ),
inference(clausify,[status(thm)],[f_906_2]) ).
fof(f_907_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_907_2,plain,
! [U_3529,U_3528,U_3527] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3529),U_3528)),U_3527) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3529),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3528),U_3527))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3527),U_3528)) ),
inference(variable_rename,[status(thm)],[f_907_1]) ).
cnf(f_907_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3529),U_3528)),U_3527) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3529),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3528),U_3527))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3527),U_3528)) ),
inference(clausify,[status(thm)],[f_907_2]) ).
fof(f_908_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_908_2,plain,
! [U_3532,U_3531,U_3530] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3531),U_3530)),U_3532) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3531),U_3532)),U_3530)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3530),U_3531)) ),
inference(variable_rename,[status(thm)],[f_908_1]) ).
cnf(f_908_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3531),U_3530)),U_3532) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3531),U_3532)),U_3530)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3530),U_3531)) ),
inference(clausify,[status(thm)],[f_908_2]) ).
fof(f_909_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_909_2,plain,
! [U_3535,U_3534,U_3533] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3534),U_3535)),U_3533) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3534),U_3533)),U_3535)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3533),U_3534)) ),
inference(variable_rename,[status(thm)],[f_909_1]) ).
cnf(f_909_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3534),U_3535)),U_3533) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3534),U_3533)),U_3535)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3533),U_3534)) ),
inference(clausify,[status(thm)],[f_909_2]) ).
fof(f_910_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_910_2,plain,
! [U_3539,U_3538,U_3537,U_3536] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3537,U_3536),U_3539),U_3538) = c_Groups_Ozero__class_Ozero(U_3536)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3537),U_3538))
| ~ class_Groups_Ocomm__monoid__add(U_3536) ),
inference(variable_rename,[status(thm)],[f_910_1]) ).
cnf(f_910_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3537,U_3536),U_3539),U_3538) = c_Groups_Ozero__class_Ozero(U_3536)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3537),U_3538))
| ~ class_Groups_Ocomm__monoid__add(U_3536) ),
inference(clausify,[status(thm)],[f_910_2]) ).
fof(f_911_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_911_2,plain,
! [U_3543,U_3542,U_3541,U_3540] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3541,U_3540),U_3543),U_3542) = c_Groups_Ozero__class_Ozero(U_3540)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3541),U_3542))
| ~ class_Groups_Ocomm__monoid__add(U_3540) ),
inference(variable_rename,[status(thm)],[f_911_1]) ).
cnf(f_911_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3541,U_3540),U_3543),U_3542) = c_Groups_Ozero__class_Ozero(U_3540)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3541),U_3542))
| ~ class_Groups_Ocomm__monoid__add(U_3540) ),
inference(clausify,[status(thm)],[f_911_2]) ).
fof(f_912_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_912_2,plain,
! [U_3546,U_3545,U_3544] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3544),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3545),U_3546)) = 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_3544),U_3545)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3545),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3545),U_3546)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3544),U_3545)) ),
inference(variable_rename,[status(thm)],[f_912_1]) ).
cnf(f_912_3,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3544),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3545),U_3546)) = 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_3544),U_3545)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3545),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3545),U_3546)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3544),U_3545)) ),
inference(clausify,[status(thm)],[f_912_2]) ).
fof(f_913_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_913_2,plain,
! [U_3551,U_3550,U_3549] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3549,tc_Nat_Onat),U_3551),U_3550) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [U_3548] :
( hAPP(U_3551,U_3548) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_3549),U_3548),U_3550)) ) )
& ( ! [U_3547] :
( hAPP(U_3551,U_3547) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_3549),U_3547),U_3550)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3549,tc_Nat_Onat),U_3551),U_3550) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3549),U_3550)) ),
inference(variable_rename,[status(thm)],[f_913_1]) ).
fof(f_913_3,plain,
! [U_3551,U_3550,U_3549] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3549,tc_Nat_Onat),U_3551),U_3550) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hAPP(U_3551,sK54(U_3551,U_3550,U_3549)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_3549),sK54(U_3551,U_3550,U_3549)),U_3550)) ) )
& ( ! [U_3547] :
( hAPP(U_3551,U_3547) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_3549),U_3547),U_3550)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3549,tc_Nat_Onat),U_3551),U_3550) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3549),U_3550)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_3548,sK54(U_3551,U_3550,U_3549))],[f_913_2]) ).
cnf(f_913_4,plain,
( hAPP(U_3551,U_3547) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_3549),U_3547),U_3550))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3549,tc_Nat_Onat),U_3551),U_3550) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3549),U_3550)) ),
inference(clausify,[status(thm)],[f_913_3]) ).
cnf(f_913_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_3549),sK54(U_3551,U_3550,U_3549)),U_3550))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3549,tc_Nat_Onat),U_3551),U_3550) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3549),U_3550)) ),
inference(clausify,[status(thm)],[f_913_3]) ).
cnf(f_913_6,plain,
( hAPP(U_3551,sK54(U_3551,U_3550,U_3549)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3549,tc_Nat_Onat),U_3551),U_3550) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3549),U_3550)) ),
inference(clausify,[status(thm)],[f_913_3]) ).
fof(f_914_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_914_2,plain,
! [U_3556,U_3555,U_3554,U_3553,U_3552] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3553,U_3552),U_3556),U_3554) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3552),hAPP(U_3556,U_3555)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3553,U_3552),U_3556),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3553,tc_HOL_Obool)),U_3554),hAPP(hAPP(c_Set_Oinsert(U_3553),U_3555),c_Orderings_Obot__class_Obot(tc_fun(U_3553,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_3553),U_3555),U_3554))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3553),U_3554))
| ~ class_Groups_Ocomm__monoid__add(U_3552) ),
inference(variable_rename,[status(thm)],[f_914_1]) ).
cnf(f_914_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3553,U_3552),U_3556),U_3554) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3552),hAPP(U_3556,U_3555)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3553,U_3552),U_3556),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3553,tc_HOL_Obool)),U_3554),hAPP(hAPP(c_Set_Oinsert(U_3553),U_3555),c_Orderings_Obot__class_Obot(tc_fun(U_3553,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_3553),U_3555),U_3554))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3553),U_3554))
| ~ class_Groups_Ocomm__monoid__add(U_3552) ),
inference(clausify,[status(thm)],[f_914_2]) ).
fof(f_915_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_915_2,plain,
! [U_3561,U_3560,U_3559,U_3558,U_3557] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3558,U_3557),U_3561),U_3559) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3557),hAPP(U_3561,U_3560)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3558,U_3557),U_3561),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3558,tc_HOL_Obool)),U_3559),hAPP(hAPP(c_Set_Oinsert(U_3558),U_3560),c_Orderings_Obot__class_Obot(tc_fun(U_3558,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_3558),U_3560),U_3559))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3558),U_3559))
| ~ class_Groups_Ocomm__monoid__add(U_3557) ),
inference(variable_rename,[status(thm)],[f_915_1]) ).
cnf(f_915_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3558,U_3557),U_3561),U_3559) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3557),hAPP(U_3561,U_3560)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3558,U_3557),U_3561),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3558,tc_HOL_Obool)),U_3559),hAPP(hAPP(c_Set_Oinsert(U_3558),U_3560),c_Orderings_Obot__class_Obot(tc_fun(U_3558,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_3558),U_3560),U_3559))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3558),U_3559))
| ~ class_Groups_Ocomm__monoid__add(U_3557) ),
inference(clausify,[status(thm)],[f_915_2]) ).
fof(f_916_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_916_2,plain,
! [U_3564,U_3563,U_3562] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3562),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3562),U_3563),U_3564)),c_Groups_Ozero__class_Ozero(U_3562)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3562),U_3564),c_Groups_Ozero__class_Ozero(U_3562)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3562),U_3563),c_Groups_Ozero__class_Ozero(U_3562)))
| ~ class_Groups_Oordered__comm__monoid__add(U_3562) ),
inference(variable_rename,[status(thm)],[f_916_1]) ).
cnf(f_916_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3562),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3562),U_3563),U_3564)),c_Groups_Ozero__class_Ozero(U_3562)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3562),U_3564),c_Groups_Ozero__class_Ozero(U_3562)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3562),U_3563),c_Groups_Ozero__class_Ozero(U_3562)))
| ~ class_Groups_Oordered__comm__monoid__add(U_3562) ),
inference(clausify,[status(thm)],[f_916_2]) ).
fof(f_917_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_917_2,plain,
! [U_3567,U_3566,U_3565] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3565),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3565),U_3566),U_3567)),c_Groups_Ozero__class_Ozero(U_3565)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3565),U_3567),c_Groups_Ozero__class_Ozero(U_3565)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3565),U_3566),c_Groups_Ozero__class_Ozero(U_3565)))
| ~ class_Groups_Oordered__comm__monoid__add(U_3565) ),
inference(variable_rename,[status(thm)],[f_917_1]) ).
cnf(f_917_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3565),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3565),U_3566),U_3567)),c_Groups_Ozero__class_Ozero(U_3565)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3565),U_3567),c_Groups_Ozero__class_Ozero(U_3565)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3565),U_3566),c_Groups_Ozero__class_Ozero(U_3565)))
| ~ class_Groups_Oordered__comm__monoid__add(U_3565) ),
inference(clausify,[status(thm)],[f_917_2]) ).
fof(f_918_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_918_2,plain,
! [U_3571,U_3570,U_3569,U_3568] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3568),U_3570),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3568),U_3569),U_3571)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3568),U_3570),U_3571))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3568),c_Groups_Ozero__class_Ozero(U_3568)),U_3569))
| ~ class_Groups_Oordered__comm__monoid__add(U_3568) ),
inference(variable_rename,[status(thm)],[f_918_1]) ).
cnf(f_918_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3568),U_3570),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3568),U_3569),U_3571)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3568),U_3570),U_3571))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3568),c_Groups_Ozero__class_Ozero(U_3568)),U_3569))
| ~ class_Groups_Oordered__comm__monoid__add(U_3568) ),
inference(clausify,[status(thm)],[f_918_2]) ).
fof(f_919_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_919_2,plain,
! [U_3575,U_3574,U_3573,U_3572] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3572),U_3574),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3572),U_3573),U_3575)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3572),U_3574),U_3575))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3572),c_Groups_Ozero__class_Ozero(U_3572)),U_3573))
| ~ class_Groups_Oordered__comm__monoid__add(U_3572) ),
inference(variable_rename,[status(thm)],[f_919_1]) ).
cnf(f_919_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3572),U_3574),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3572),U_3573),U_3575)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3572),U_3574),U_3575))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3572),c_Groups_Ozero__class_Ozero(U_3572)),U_3573))
| ~ class_Groups_Oordered__comm__monoid__add(U_3572) ),
inference(clausify,[status(thm)],[f_919_2]) ).
fof(f_920_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_920_2,plain,
! [U_3578,U_3577,U_3576] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3576),c_Groups_Ozero__class_Ozero(U_3576)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3576),U_3577),U_3578)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3576),c_Groups_Ozero__class_Ozero(U_3576)),U_3578))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3576),c_Groups_Ozero__class_Ozero(U_3576)),U_3577))
| ~ class_Groups_Oordered__comm__monoid__add(U_3576) ),
inference(variable_rename,[status(thm)],[f_920_1]) ).
cnf(f_920_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3576),c_Groups_Ozero__class_Ozero(U_3576)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3576),U_3577),U_3578)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3576),c_Groups_Ozero__class_Ozero(U_3576)),U_3578))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3576),c_Groups_Ozero__class_Ozero(U_3576)),U_3577))
| ~ class_Groups_Oordered__comm__monoid__add(U_3576) ),
inference(clausify,[status(thm)],[f_920_2]) ).
fof(f_921_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_921_2,plain,
! [U_3581,U_3580,U_3579] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3579),c_Groups_Ozero__class_Ozero(U_3579)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3579),U_3580),U_3581)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3579),c_Groups_Ozero__class_Ozero(U_3579)),U_3581))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3579),c_Groups_Ozero__class_Ozero(U_3579)),U_3580))
| ~ class_Groups_Oordered__comm__monoid__add(U_3579) ),
inference(variable_rename,[status(thm)],[f_921_1]) ).
cnf(f_921_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3579),c_Groups_Ozero__class_Ozero(U_3579)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3579),U_3580),U_3581)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3579),c_Groups_Ozero__class_Ozero(U_3579)),U_3581))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3579),c_Groups_Ozero__class_Ozero(U_3579)),U_3580))
| ~ class_Groups_Oordered__comm__monoid__add(U_3579) ),
inference(clausify,[status(thm)],[f_921_2]) ).
fof(f_922_1,plain,
! [V_b_2,V_a_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
| ? [B_d] :
( ~ hBOOL(hAPP(V_P_2,B_d))
& V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
| ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) )
& ( ( ! [B_d] :
( hBOOL(hAPP(V_P_2,B_d))
| V_a_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
& ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) )
| ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__diff__split__asm]) ).
fof(f_922_2,plain,
! [U_3586,U_3585,U_3584] :
( ( hBOOL(hAPP(U_3584,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3585),U_3586)))
| ? [U_3583] :
( ~ hBOOL(hAPP(U_3584,U_3583))
& U_3585 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3586),U_3583) )
| ( ~ hBOOL(hAPP(U_3584,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3585),U_3586)) ) )
& ( ( ! [U_3582] :
( hBOOL(hAPP(U_3584,U_3582))
| U_3585 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3586),U_3582) )
& ( hBOOL(hAPP(U_3584,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3585),U_3586)) ) )
| ~ hBOOL(hAPP(U_3584,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3585),U_3586))) ) ),
inference(variable_rename,[status(thm)],[f_922_1]) ).
fof(f_922_3,plain,
( ! [U_3592,U_3590,U_3588] :
( hBOOL(hAPP(U_3588,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3590),U_3592)))
| ? [U_3583] :
( ~ hBOOL(hAPP(U_3588,U_3583))
& U_3590 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3592),U_3583) )
| ( ~ hBOOL(hAPP(U_3588,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3590),U_3592)) ) )
& ! [U_3591,U_3589,U_3587] :
( ( ! [U_3582] :
( hBOOL(hAPP(U_3587,U_3582))
| U_3589 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3591),U_3582) )
& ( hBOOL(hAPP(U_3587,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3589),U_3591)) ) )
| ~ hBOOL(hAPP(U_3587,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3589),U_3591))) ) ),
inference(miniscope,[status(thm)],[f_922_2]) ).
fof(f_922_4,plain,
( ! [U_3592,U_3590,U_3588] :
( hBOOL(hAPP(U_3588,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3590),U_3592)))
| ( ~ hBOOL(hAPP(U_3588,sK55(U_3592,U_3590,U_3588)))
& U_3590 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3592),sK55(U_3592,U_3590,U_3588)) )
| ( ~ hBOOL(hAPP(U_3588,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3590),U_3592)) ) )
& ! [U_3591,U_3589,U_3587] :
( ( ! [U_3582] :
( hBOOL(hAPP(U_3587,U_3582))
| U_3589 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3591),U_3582) )
& ( hBOOL(hAPP(U_3587,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3589),U_3591)) ) )
| ~ hBOOL(hAPP(U_3587,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3589),U_3591))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_3583,sK55(U_3592,U_3590,U_3588))],[f_922_3]) ).
cnf(f_922_5,plain,
( hBOOL(hAPP(U_3587,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3589),U_3591))
| ~ hBOOL(hAPP(U_3587,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3589),U_3591))) ),
inference(clausify,[status(thm)],[f_922_4]) ).
cnf(f_922_6,plain,
( hBOOL(hAPP(U_3587,U_3582))
| U_3589 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3591),U_3582)
| ~ hBOOL(hAPP(U_3587,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3589),U_3591))) ),
inference(clausify,[status(thm)],[f_922_4]) ).
cnf(f_922_7,plain,
( U_3590 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3592),sK55(U_3592,U_3590,U_3588))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3590),U_3592))
| hBOOL(hAPP(U_3588,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3590),U_3592))) ),
inference(clausify,[status(thm)],[f_922_4]) ).
cnf(f_922_8,plain,
( ~ hBOOL(hAPP(U_3588,sK55(U_3592,U_3590,U_3588)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3590),U_3592))
| hBOOL(hAPP(U_3588,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3590),U_3592))) ),
inference(clausify,[status(thm)],[f_922_4]) ).
cnf(f_922_9,plain,
( U_3590 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3592),sK55(U_3592,U_3590,U_3588))
| ~ hBOOL(hAPP(U_3588,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_3588,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3590),U_3592))) ),
inference(clausify,[status(thm)],[f_922_4]) ).
cnf(f_922_10,plain,
( ~ hBOOL(hAPP(U_3588,sK55(U_3592,U_3590,U_3588)))
| ~ hBOOL(hAPP(U_3588,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_3588,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3590),U_3592))) ),
inference(clausify,[status(thm)],[f_922_4]) ).
fof(f_923_1,plain,
! [V_b_2,V_a_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
| ? [B_d] :
( ~ hBOOL(hAPP(V_P_2,B_d))
& V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
| ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) )
& ( ( ! [B_d] :
( hBOOL(hAPP(V_P_2,B_d))
| V_a_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
& ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) )
| ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__diff__split]) ).
fof(f_923_2,plain,
! [U_3597,U_3596,U_3595] :
( ( hBOOL(hAPP(U_3595,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3596),U_3597)))
| ? [U_3594] :
( ~ hBOOL(hAPP(U_3595,U_3594))
& U_3596 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3597),U_3594) )
| ( ~ hBOOL(hAPP(U_3595,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3596),U_3597)) ) )
& ( ( ! [U_3593] :
( hBOOL(hAPP(U_3595,U_3593))
| U_3596 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3597),U_3593) )
& ( hBOOL(hAPP(U_3595,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3596),U_3597)) ) )
| ~ hBOOL(hAPP(U_3595,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3596),U_3597))) ) ),
inference(variable_rename,[status(thm)],[f_923_1]) ).
fof(f_923_3,plain,
( ! [U_3603,U_3601,U_3599] :
( hBOOL(hAPP(U_3599,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3601),U_3603)))
| ? [U_3594] :
( ~ hBOOL(hAPP(U_3599,U_3594))
& U_3601 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3603),U_3594) )
| ( ~ hBOOL(hAPP(U_3599,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3601),U_3603)) ) )
& ! [U_3602,U_3600,U_3598] :
( ( ! [U_3593] :
( hBOOL(hAPP(U_3598,U_3593))
| U_3600 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3602),U_3593) )
& ( hBOOL(hAPP(U_3598,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3600),U_3602)) ) )
| ~ hBOOL(hAPP(U_3598,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3600),U_3602))) ) ),
inference(miniscope,[status(thm)],[f_923_2]) ).
fof(f_923_4,plain,
( ! [U_3603,U_3601,U_3599] :
( hBOOL(hAPP(U_3599,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3601),U_3603)))
| ( ~ hBOOL(hAPP(U_3599,sK56(U_3603,U_3601,U_3599)))
& U_3601 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3603),sK56(U_3603,U_3601,U_3599)) )
| ( ~ hBOOL(hAPP(U_3599,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3601),U_3603)) ) )
& ! [U_3602,U_3600,U_3598] :
( ( ! [U_3593] :
( hBOOL(hAPP(U_3598,U_3593))
| U_3600 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3602),U_3593) )
& ( hBOOL(hAPP(U_3598,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3600),U_3602)) ) )
| ~ hBOOL(hAPP(U_3598,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3600),U_3602))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_3594,sK56(U_3603,U_3601,U_3599))],[f_923_3]) ).
cnf(f_923_5,plain,
( hBOOL(hAPP(U_3598,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3600),U_3602))
| ~ hBOOL(hAPP(U_3598,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3600),U_3602))) ),
inference(clausify,[status(thm)],[f_923_4]) ).
cnf(f_923_6,plain,
( hBOOL(hAPP(U_3598,U_3593))
| U_3600 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3602),U_3593)
| ~ hBOOL(hAPP(U_3598,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3600),U_3602))) ),
inference(clausify,[status(thm)],[f_923_4]) ).
cnf(f_923_7,plain,
( U_3601 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3603),sK56(U_3603,U_3601,U_3599))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3601),U_3603))
| hBOOL(hAPP(U_3599,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3601),U_3603))) ),
inference(clausify,[status(thm)],[f_923_4]) ).
cnf(f_923_8,plain,
( ~ hBOOL(hAPP(U_3599,sK56(U_3603,U_3601,U_3599)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3601),U_3603))
| hBOOL(hAPP(U_3599,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3601),U_3603))) ),
inference(clausify,[status(thm)],[f_923_4]) ).
cnf(f_923_9,plain,
( U_3601 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3603),sK56(U_3603,U_3601,U_3599))
| ~ hBOOL(hAPP(U_3599,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_3599,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3601),U_3603))) ),
inference(clausify,[status(thm)],[f_923_4]) ).
cnf(f_923_10,plain,
( ~ hBOOL(hAPP(U_3599,sK56(U_3603,U_3601,U_3599)))
| ~ hBOOL(hAPP(U_3599,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_3599,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3601),U_3603))) ),
inference(clausify,[status(thm)],[f_923_4]) ).
fof(f_924_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_924_2,plain,
! [U_3606,U_3605,U_3604] :
( 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_3605),U_3604))),U_3606) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3605)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3604),U_3606))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3604),U_3605)) ),
inference(variable_rename,[status(thm)],[f_924_1]) ).
cnf(f_924_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_3605),U_3604))),U_3606) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3605)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3604),U_3606))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3604),U_3605)) ),
inference(clausify,[status(thm)],[f_924_2]) ).
fof(f_925_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_925_2,plain,
! [U_3609,U_3608,U_3607] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3609),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3608),U_3607))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3609),U_3607)),hAPP(c_Nat_OSuc,U_3608))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3607),U_3608)) ),
inference(variable_rename,[status(thm)],[f_925_1]) ).
cnf(f_925_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3609),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3608),U_3607))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3609),U_3607)),hAPP(c_Nat_OSuc,U_3608))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3607),U_3608)) ),
inference(clausify,[status(thm)],[f_925_2]) ).
fof(f_926_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_926_2,plain,
! [U_3614,U_3613,U_3612,U_3611,U_3610] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3610),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3610),U_3614),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3611),U_3612))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3610),U_3614),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3612),U_3613))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3610),U_3614),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3611),U_3613))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3612),U_3613))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3611),U_3612))
| ~ class_Groups_Ocomm__monoid__add(U_3610) ),
inference(variable_rename,[status(thm)],[f_926_1]) ).
cnf(f_926_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3610),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3610),U_3614),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3611),U_3612))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3610),U_3614),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3612),U_3613))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3610),U_3614),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3611),U_3613))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3612),U_3613))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3611),U_3612))
| ~ class_Groups_Ocomm__monoid__add(U_3610) ),
inference(clausify,[status(thm)],[f_926_2]) ).
fof(f_927_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_927_2,plain,
! [U_3621,U_3620,U_3619] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3619,tc_Nat_Onat),U_3621),U_3620) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ! [U_3618] :
( ? [U_3617] :
( hAPP(U_3621,U_3617) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_3618 != U_3617
& hBOOL(hAPP(hAPP(c_member(U_3619),U_3617),U_3620)) )
| hAPP(U_3621,U_3618) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_3619),U_3618),U_3620)) ) )
& ( ? [U_3616] :
( ! [U_3615] :
( hAPP(U_3621,U_3615) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3616 = U_3615
| ~ hBOOL(hAPP(hAPP(c_member(U_3619),U_3615),U_3620)) )
& hAPP(U_3621,U_3616) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& hBOOL(hAPP(hAPP(c_member(U_3619),U_3616),U_3620)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3619,tc_Nat_Onat),U_3621),U_3620) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3619),U_3620)) ),
inference(variable_rename,[status(thm)],[f_927_1]) ).
fof(f_927_3,plain,
! [U_3621,U_3620,U_3619] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3619,tc_Nat_Onat),U_3621),U_3620) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ! [U_3618] :
( ? [U_3617] :
( hAPP(U_3621,U_3617) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_3618 != U_3617
& hBOOL(hAPP(hAPP(c_member(U_3619),U_3617),U_3620)) )
| hAPP(U_3621,U_3618) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_3619),U_3618),U_3620)) ) )
& ( ( ! [U_3615] :
( hAPP(U_3621,U_3615) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK57(U_3621,U_3620,U_3619) = U_3615
| ~ hBOOL(hAPP(hAPP(c_member(U_3619),U_3615),U_3620)) )
& hAPP(U_3621,sK57(U_3621,U_3620,U_3619)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& hBOOL(hAPP(hAPP(c_member(U_3619),sK57(U_3621,U_3620,U_3619)),U_3620)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3619,tc_Nat_Onat),U_3621),U_3620) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3619),U_3620)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_3616,sK57(U_3621,U_3620,U_3619))],[f_927_2]) ).
fof(f_927_4,plain,
! [U_3621,U_3620,U_3619] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3619,tc_Nat_Onat),U_3621),U_3620) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ! [U_3618] :
( ( hAPP(U_3621,sK58(U_3621,U_3620,U_3619,U_3618)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_3618 != sK58(U_3621,U_3620,U_3619,U_3618)
& hBOOL(hAPP(hAPP(c_member(U_3619),sK58(U_3621,U_3620,U_3619,U_3618)),U_3620)) )
| hAPP(U_3621,U_3618) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_3619),U_3618),U_3620)) ) )
& ( ( ! [U_3615] :
( hAPP(U_3621,U_3615) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK57(U_3621,U_3620,U_3619) = U_3615
| ~ hBOOL(hAPP(hAPP(c_member(U_3619),U_3615),U_3620)) )
& hAPP(U_3621,sK57(U_3621,U_3620,U_3619)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& hBOOL(hAPP(hAPP(c_member(U_3619),sK57(U_3621,U_3620,U_3619)),U_3620)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3619,tc_Nat_Onat),U_3621),U_3620) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3619),U_3620)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_3617,sK58(U_3621,U_3620,U_3619,U_3618))],[f_927_3]) ).
cnf(f_927_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_3619),sK57(U_3621,U_3620,U_3619)),U_3620))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3619,tc_Nat_Onat),U_3621),U_3620) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3619),U_3620)) ),
inference(clausify,[status(thm)],[f_927_4]) ).
cnf(f_927_6,plain,
( hAPP(U_3621,sK57(U_3621,U_3620,U_3619)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3619,tc_Nat_Onat),U_3621),U_3620) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3619),U_3620)) ),
inference(clausify,[status(thm)],[f_927_4]) ).
cnf(f_927_7,plain,
( hAPP(U_3621,U_3615) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK57(U_3621,U_3620,U_3619) = U_3615
| ~ hBOOL(hAPP(hAPP(c_member(U_3619),U_3615),U_3620))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3619,tc_Nat_Onat),U_3621),U_3620) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3619),U_3620)) ),
inference(clausify,[status(thm)],[f_927_4]) ).
cnf(f_927_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_3619),sK58(U_3621,U_3620,U_3619,U_3618)),U_3620))
| hAPP(U_3621,U_3618) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_3619),U_3618),U_3620))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3619,tc_Nat_Onat),U_3621),U_3620) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3619),U_3620)) ),
inference(clausify,[status(thm)],[f_927_4]) ).
cnf(f_927_9,plain,
( U_3618 != sK58(U_3621,U_3620,U_3619,U_3618)
| hAPP(U_3621,U_3618) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_3619),U_3618),U_3620))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3619,tc_Nat_Onat),U_3621),U_3620) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3619),U_3620)) ),
inference(clausify,[status(thm)],[f_927_4]) ).
cnf(f_927_10,plain,
( hAPP(U_3621,sK58(U_3621,U_3620,U_3619,U_3618)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(U_3621,U_3618) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_3619),U_3618),U_3620))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3619,tc_Nat_Onat),U_3621),U_3620) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3619),U_3620)) ),
inference(clausify,[status(thm)],[f_927_4]) ).
fof(f_928_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_928_2,plain,
! [U_3627,U_3626,U_3625,U_3624,U_3623,U_3622] :
( c_Fun_Oinj__on(U_3622,U_3623,c_Fun_Ofun__upd(U_3622,U_3623,U_3624,U_3627,U_3626),U_3625)
| hBOOL(hAPP(hAPP(c_member(U_3623),U_3626),hAPP(c_Set_Oimage(U_3622,U_3623,U_3624),U_3625)))
| ~ c_Fun_Oinj__on(U_3622,U_3623,U_3624,U_3625) ),
inference(variable_rename,[status(thm)],[f_928_1]) ).
cnf(f_928_3,plain,
( c_Fun_Oinj__on(U_3622,U_3623,c_Fun_Ofun__upd(U_3622,U_3623,U_3624,U_3627,U_3626),U_3625)
| hBOOL(hAPP(hAPP(c_member(U_3623),U_3626),hAPP(c_Set_Oimage(U_3622,U_3623,U_3624),U_3625)))
| ~ c_Fun_Oinj__on(U_3622,U_3623,U_3624,U_3625) ),
inference(clausify,[status(thm)],[f_928_2]) ).
fof(f_929_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_929_2,plain,
! [U_3631,U_3630,U_3629,U_3628] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3628),U_3631),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3629),U_3630)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3628),hAPP(U_3631,U_3629)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3628),U_3631),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3629)),U_3630)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3629),U_3630))
| ~ class_Groups_Ocomm__monoid__add(U_3628) ),
inference(variable_rename,[status(thm)],[f_929_1]) ).
cnf(f_929_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3628),U_3631),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3629),U_3630)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3628),hAPP(U_3631,U_3629)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3628),U_3631),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3629)),U_3630)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3629),U_3630))
| ~ class_Groups_Ocomm__monoid__add(U_3628) ),
inference(clausify,[status(thm)],[f_929_2]) ).
fof(f_930_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_930_2,plain,
! [U_3635,U_3634,U_3633,U_3632] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3632),U_3635),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_3633,U_3634)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3632),hAPP(U_3635,U_3633)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3632),U_3635),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3633),U_3634)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3633),U_3634))
| ~ class_Groups_Ocomm__monoid__add(U_3632) ),
inference(variable_rename,[status(thm)],[f_930_1]) ).
cnf(f_930_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3632),U_3635),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_3633,U_3634)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3632),hAPP(U_3635,U_3633)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3632),U_3635),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3633),U_3634)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3633),U_3634))
| ~ class_Groups_Ocomm__monoid__add(U_3632) ),
inference(clausify,[status(thm)],[f_930_2]) ).
fof(f_931_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_931_2,plain,
! [U_3640,U_3639,U_3638,U_3637,U_3636] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3637,U_3636),U_3640),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3637,tc_HOL_Obool)),U_3638),U_3639)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3636),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3637,U_3636),U_3640),U_3638)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3637,U_3636),U_3640),U_3639))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3637,tc_HOL_Obool)),U_3639),U_3638))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3637),U_3638))
| ~ class_Groups_Oab__group__add(U_3636) ),
inference(variable_rename,[status(thm)],[f_931_1]) ).
cnf(f_931_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3637,U_3636),U_3640),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3637,tc_HOL_Obool)),U_3638),U_3639)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3636),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3637,U_3636),U_3640),U_3638)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3637,U_3636),U_3640),U_3639))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3637,tc_HOL_Obool)),U_3639),U_3638))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3637),U_3638))
| ~ class_Groups_Oab__group__add(U_3636) ),
inference(clausify,[status(thm)],[f_931_2]) ).
fof(f_932_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_932_2,plain,
! [U_3644,U_3643,U_3642,U_3641] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3641,tc_Nat_Onat),U_3644),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3641,tc_HOL_Obool)),U_3643),U_3642)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3641,tc_Nat_Onat),U_3644),U_3643)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3641,tc_Nat_Onat),U_3644),U_3642))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3641,tc_HOL_Obool)),U_3642),U_3643))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3641),U_3642)) ),
inference(variable_rename,[status(thm)],[f_932_1]) ).
cnf(f_932_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3641,tc_Nat_Onat),U_3644),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3641,tc_HOL_Obool)),U_3643),U_3642)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3641,tc_Nat_Onat),U_3644),U_3643)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3641,tc_Nat_Onat),U_3644),U_3642))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3641,tc_HOL_Obool)),U_3642),U_3643))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3641),U_3642)) ),
inference(clausify,[status(thm)],[f_932_2]) ).
fof(f_933_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_933_2,plain,
! [U_3648,U_3647,U_3646,U_3645] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3645),U_3648),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3647),hAPP(c_Nat_OSuc,U_3646))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3645),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3645),U_3648),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3647),U_3646))),hAPP(U_3648,U_3646))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3646),U_3647)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3645),U_3648),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3647),hAPP(c_Nat_OSuc,U_3646))) = c_Groups_Ozero__class_Ozero(U_3645)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3646),U_3647)) ) )
| ~ class_Groups_Ocomm__monoid__add(U_3645) ),
inference(variable_rename,[status(thm)],[f_933_1]) ).
cnf(f_933_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3645),U_3648),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3647),hAPP(c_Nat_OSuc,U_3646))) = c_Groups_Ozero__class_Ozero(U_3645)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3646),U_3647))
| ~ class_Groups_Ocomm__monoid__add(U_3645) ),
inference(clausify,[status(thm)],[f_933_2]) ).
cnf(f_933_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3645),U_3648),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3647),hAPP(c_Nat_OSuc,U_3646))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3645),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3645),U_3648),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3647),U_3646))),hAPP(U_3648,U_3646))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3646),U_3647))
| ~ class_Groups_Ocomm__monoid__add(U_3645) ),
inference(clausify,[status(thm)],[f_933_2]) ).
fof(f_934_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_934_2,plain,
! [U_3651,U_3650] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3650),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3650,tc_HOL_Obool),U_3651)))
| ! [U_3649] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3650),U_3649))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_3650,tc_HOL_Obool)),U_3649),U_3651)) ) ),
inference(variable_rename,[status(thm)],[f_934_1]) ).
cnf(f_934_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3650),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3650,tc_HOL_Obool),U_3651)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3650),U_3649))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_3650,tc_HOL_Obool)),U_3649),U_3651)) ),
inference(clausify,[status(thm)],[f_934_2]) ).
fof(f_935_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_935_2,plain,
! [U_3654,U_3653,U_3652] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3652),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3652,tc_HOL_Obool)),U_3653),U_3654)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3652),U_3653)) ),
inference(variable_rename,[status(thm)],[f_935_1]) ).
cnf(f_935_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3652),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3652,tc_HOL_Obool)),U_3653),U_3654)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3652),U_3653)) ),
inference(clausify,[status(thm)],[f_935_2]) ).
fof(f_936_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_936_2,plain,
! [U_3657,U_3656,U_3655] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3655),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3655,tc_HOL_Obool)),U_3656),U_3657)))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3655),U_3657))
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3655),U_3656)) ) ),
inference(variable_rename,[status(thm)],[f_936_1]) ).
cnf(f_936_3,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3655),U_3656))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3655),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3655,tc_HOL_Obool)),U_3656),U_3657))) ),
inference(clausify,[status(thm)],[f_936_2]) ).
cnf(f_936_4,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3655),U_3657))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3655),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3655,tc_HOL_Obool)),U_3656),U_3657))) ),
inference(clausify,[status(thm)],[f_936_2]) ).
fof(f_937_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_937_2,plain,
! [U_3661,U_3660,U_3659,U_3658] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3660),hAPP(c_Set_Oimage(U_3658,U_3660,U_3661),U_3659)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3658),U_3659)) ),
inference(variable_rename,[status(thm)],[f_937_1]) ).
cnf(f_937_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3660),hAPP(c_Set_Oimage(U_3658,U_3660,U_3661),U_3659)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3658),U_3659)) ),
inference(clausify,[status(thm)],[f_937_2]) ).
fof(f_938_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_938_2,plain,
! [U_3664,U_3663,U_3662] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3662),hAPP(hAPP(c_Set_Oinsert(U_3662),U_3664),U_3663)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3662),U_3663)) ),
inference(variable_rename,[status(thm)],[f_938_1]) ).
cnf(f_938_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3662),hAPP(hAPP(c_Set_Oinsert(U_3662),U_3664),U_3663)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3662),U_3663)) ),
inference(clausify,[status(thm)],[f_938_2]) ).
fof(f_939_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_939_2,plain,
! [U_3665] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_3665),c_Orderings_Obot__class_Obot(tc_fun(U_3665,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_939_1]) ).
cnf(f_939_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(U_3665),c_Orderings_Obot__class_Obot(tc_fun(U_3665,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_939_2]) ).
fof(f_940_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_940_2,plain,
! [U_3669,U_3668,U_3667,U_3666] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3668),hAPP(c_Set_Ovimage(U_3668,U_3666,U_3669),U_3667)))
| ~ c_Fun_Oinj__on(U_3668,U_3666,U_3669,c_Orderings_Otop__class_Otop(tc_fun(U_3668,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3666),U_3667)) ),
inference(variable_rename,[status(thm)],[f_940_1]) ).
cnf(f_940_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3668),hAPP(c_Set_Ovimage(U_3668,U_3666,U_3669),U_3667)))
| ~ c_Fun_Oinj__on(U_3668,U_3666,U_3669,c_Orderings_Otop__class_Otop(tc_fun(U_3668,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3666),U_3667)) ),
inference(clausify,[status(thm)],[f_940_2]) ).
fof(f_941_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_941_2,plain,
! [U_3673,U_3672,U_3671,U_3670] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3671),U_3673))
| hAPP(c_Set_Oimage(U_3670,U_3671,U_3672),c_Orderings_Otop__class_Otop(tc_fun(U_3670,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_3671,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3670),hAPP(c_Set_Ovimage(U_3670,U_3671,U_3672),U_3673))) ),
inference(variable_rename,[status(thm)],[f_941_1]) ).
cnf(f_941_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3671),U_3673))
| hAPP(c_Set_Oimage(U_3670,U_3671,U_3672),c_Orderings_Otop__class_Otop(tc_fun(U_3670,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_3671,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3670),hAPP(c_Set_Ovimage(U_3670,U_3671,U_3672),U_3673))) ),
inference(clausify,[status(thm)],[f_941_2]) ).
fof(f_942_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_942_2,plain,
! [U_3675,U_3674] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3674),U_3675) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3675),U_3674),
inference(variable_rename,[status(thm)],[f_942_1]) ).
cnf(f_942_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3674),U_3675) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3675),U_3674),
inference(clausify,[status(thm)],[f_942_2]) ).
fof(f_943_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_943_2,plain,
! [U_3678,U_3677,U_3676] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3676),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3677),U_3678)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3676),U_3678)),
inference(variable_rename,[status(thm)],[f_943_1]) ).
cnf(f_943_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3676),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3677),U_3678)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3676),U_3678)),
inference(clausify,[status(thm)],[f_943_2]) ).
fof(f_944_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_944_2,plain,
! [U_3681,U_3680,U_3679] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3679),U_3680)),U_3681) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3679),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3680),U_3681)),
inference(variable_rename,[status(thm)],[f_944_1]) ).
cnf(f_944_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3679),U_3680)),U_3681) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3679),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3680),U_3681)),
inference(clausify,[status(thm)],[f_944_2]) ).
fof(f_945_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_945_2,plain,
! [U_3684,U_3683,U_3682] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3682),U_3683) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3682),U_3684)
| U_3683 != U_3684 )
& ( U_3683 = U_3684
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3682),U_3683) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3682),U_3684) ) ),
inference(variable_rename,[status(thm)],[f_945_1]) ).
fof(f_945_3,plain,
( ! [U_3690,U_3688] :
( ! [U_3686] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3686),U_3688) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3686),U_3690)
| U_3688 != U_3690 )
& ! [U_3689,U_3687] :
( ! [U_3685] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3685),U_3687) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3685),U_3689)
| U_3687 = U_3689 ) ),
inference(miniscope,[status(thm)],[f_945_2]) ).
cnf(f_945_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3685),U_3687) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3685),U_3689)
| U_3687 = U_3689 ),
inference(clausify,[status(thm)],[f_945_3]) ).
cnf(f_945_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3686),U_3688) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3686),U_3690)
| U_3688 != U_3690 ),
inference(clausify,[status(thm)],[f_945_3]) ).
fof(f_946_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_946_2,plain,
! [U_3693,U_3692,U_3691] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3691),U_3692) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3693),U_3692)
| U_3691 != U_3693 )
& ( U_3691 = U_3693
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3691),U_3692) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3693),U_3692) ) ),
inference(variable_rename,[status(thm)],[f_946_1]) ).
fof(f_946_3,plain,
( ! [U_3699,U_3697,U_3695] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3695),U_3697) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3699),U_3697)
| U_3695 != U_3699 )
& ! [U_3698,U_3696,U_3694] :
( U_3694 = U_3698
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3694),U_3696) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3698),U_3696) ) ),
inference(miniscope,[status(thm)],[f_946_2]) ).
cnf(f_946_4,plain,
( U_3694 = U_3698
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3694),U_3696) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3698),U_3696) ),
inference(clausify,[status(thm)],[f_946_3]) ).
cnf(f_946_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3695),U_3697) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3699),U_3697)
| U_3695 != U_3699 ),
inference(clausify,[status(thm)],[f_946_3]) ).
fof(f_947_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_947_2,plain,
! [U_3705,U_3704,U_3703,U_3702] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3704),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3702,tc_fun(U_3704,tc_HOL_Obool)),U_3703),U_3705)))
| ? [U_3701] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3704),hAPP(U_3705,U_3701)))
& hBOOL(hAPP(hAPP(c_member(U_3702),U_3701),U_3703)) ) )
& ( ! [U_3700] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3704),hAPP(U_3705,U_3700)))
| ~ hBOOL(hAPP(hAPP(c_member(U_3702),U_3700),U_3703)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3704),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3702,tc_fun(U_3704,tc_HOL_Obool)),U_3703),U_3705))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3702),U_3703)) ),
inference(variable_rename,[status(thm)],[f_947_1]) ).
fof(f_947_3,plain,
! [U_3705,U_3704,U_3703,U_3702] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3704),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3702,tc_fun(U_3704,tc_HOL_Obool)),U_3703),U_3705)))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3704),hAPP(U_3705,sK59(U_3705,U_3704,U_3703,U_3702))))
& hBOOL(hAPP(hAPP(c_member(U_3702),sK59(U_3705,U_3704,U_3703,U_3702)),U_3703)) ) )
& ( ! [U_3700] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3704),hAPP(U_3705,U_3700)))
| ~ hBOOL(hAPP(hAPP(c_member(U_3702),U_3700),U_3703)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3704),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3702,tc_fun(U_3704,tc_HOL_Obool)),U_3703),U_3705))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3702),U_3703)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_3701,sK59(U_3705,U_3704,U_3703,U_3702))],[f_947_2]) ).
cnf(f_947_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3704),hAPP(U_3705,U_3700)))
| ~ hBOOL(hAPP(hAPP(c_member(U_3702),U_3700),U_3703))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3704),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3702,tc_fun(U_3704,tc_HOL_Obool)),U_3703),U_3705)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3702),U_3703)) ),
inference(clausify,[status(thm)],[f_947_3]) ).
cnf(f_947_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_3702),sK59(U_3705,U_3704,U_3703,U_3702)),U_3703))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3704),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3702,tc_fun(U_3704,tc_HOL_Obool)),U_3703),U_3705)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3702),U_3703)) ),
inference(clausify,[status(thm)],[f_947_3]) ).
cnf(f_947_6,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3704),hAPP(U_3705,sK59(U_3705,U_3704,U_3703,U_3702))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3704),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3702,tc_fun(U_3704,tc_HOL_Obool)),U_3703),U_3705)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3702),U_3703)) ),
inference(clausify,[status(thm)],[f_947_3]) ).
fof(f_948_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_948_2,plain,
! [U_3707,U_3706] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3706),U_3707))
| ~ class_Finite__Set_Ofinite(U_3706) ),
inference(variable_rename,[status(thm)],[f_948_1]) ).
cnf(f_948_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3706),U_3707))
| ~ class_Finite__Set_Ofinite(U_3706) ),
inference(clausify,[status(thm)],[f_948_2]) ).
fof(f_949_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_949_2,plain,
! [U_3709,U_3708] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3708),U_3709))
| ~ class_Finite__Set_Ofinite(U_3708) ),
inference(variable_rename,[status(thm)],[f_949_1]) ).
cnf(f_949_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3708),U_3709))
| ~ class_Finite__Set_Ofinite(U_3708) ),
inference(clausify,[status(thm)],[f_949_2]) ).
fof(f_950_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_950_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_950_1]) ).
fof(f_951_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_951_2,plain,
! [U_3710] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_3710),c_Orderings_Obot__class_Obot(tc_fun(U_3710,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_951_1]) ).
cnf(f_951_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(U_3710),c_Orderings_Obot__class_Obot(tc_fun(U_3710,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_951_2]) ).
fof(f_952_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_952_2,plain,
! [U_3713,U_3712,U_3711] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3711),hAPP(hAPP(c_Set_Oinsert(U_3711),U_3712),U_3713)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3711),U_3713)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3711),U_3713))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3711),hAPP(hAPP(c_Set_Oinsert(U_3711),U_3712),U_3713))) ) ),
inference(variable_rename,[status(thm)],[f_952_1]) ).
fof(f_952_3,plain,
( ! [U_3719,U_3717,U_3715] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3715),hAPP(hAPP(c_Set_Oinsert(U_3715),U_3717),U_3719)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3715),U_3719)) )
& ! [U_3718,U_3716,U_3714] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3714),U_3718))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3714),hAPP(hAPP(c_Set_Oinsert(U_3714),U_3716),U_3718))) ) ),
inference(miniscope,[status(thm)],[f_952_2]) ).
cnf(f_952_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3714),U_3718))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3714),hAPP(hAPP(c_Set_Oinsert(U_3714),U_3716),U_3718))) ),
inference(clausify,[status(thm)],[f_952_3]) ).
cnf(f_952_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3715),hAPP(hAPP(c_Set_Oinsert(U_3715),U_3717),U_3719)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3715),U_3719)) ),
inference(clausify,[status(thm)],[f_952_3]) ).
fof(f_953_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_953_2,plain,
! [U_3722,U_3721,U_3720] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3720),U_3722))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3720,tc_HOL_Obool)),U_3722),U_3721))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3720),U_3721)) ),
inference(variable_rename,[status(thm)],[f_953_1]) ).
cnf(f_953_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3720),U_3722))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3720,tc_HOL_Obool)),U_3722),U_3721))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3720),U_3721)) ),
inference(clausify,[status(thm)],[f_953_2]) ).
fof(f_954_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_954_2,plain,
! [U_3725,U_3724,U_3723] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3723),U_3724))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3723),U_3725))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3723,tc_HOL_Obool)),U_3724),U_3725)) ),
inference(variable_rename,[status(thm)],[f_954_1]) ).
cnf(f_954_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3723),U_3724))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3723),U_3725))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3723,tc_HOL_Obool)),U_3724),U_3725)) ),
inference(clausify,[status(thm)],[f_954_2]) ).
fof(f_955_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_955_2,plain,
! [U_3727,U_3726] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_3726,U_3727)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_3726,U_3727),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3727),c_Orderings_Otop__class_Otop(tc_fun(U_3727,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3726),c_Orderings_Otop__class_Otop(tc_fun(U_3726,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_955_1]) ).
cnf(f_955_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_3726,U_3727)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_3726,U_3727),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3727),c_Orderings_Otop__class_Otop(tc_fun(U_3727,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3726),c_Orderings_Otop__class_Otop(tc_fun(U_3726,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_955_2]) ).
fof(f_956_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_956_2,plain,
! [U_3729,U_3728] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3728,U_3729)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_3728,U_3729),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3729),c_Orderings_Otop__class_Otop(tc_fun(U_3729,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3728),c_Orderings_Otop__class_Otop(tc_fun(U_3728,tc_HOL_Obool)))) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3729),c_Orderings_Otop__class_Otop(tc_fun(U_3729,tc_HOL_Obool))))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_3728),c_Orderings_Otop__class_Otop(tc_fun(U_3728,tc_HOL_Obool)))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3728,U_3729)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_3728,U_3729),tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[f_956_1]) ).
fof(f_956_3,plain,
( ! [U_3733,U_3731] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3731,U_3733)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_3731,U_3733),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3733),c_Orderings_Otop__class_Otop(tc_fun(U_3733,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3731),c_Orderings_Otop__class_Otop(tc_fun(U_3731,tc_HOL_Obool)))) )
& ! [U_3732,U_3730] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3732),c_Orderings_Otop__class_Otop(tc_fun(U_3732,tc_HOL_Obool))))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_3730),c_Orderings_Otop__class_Otop(tc_fun(U_3730,tc_HOL_Obool)))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3730,U_3732)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_3730,U_3732),tc_HOL_Obool)))) ) ),
inference(miniscope,[status(thm)],[f_956_2]) ).
cnf(f_956_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3730),c_Orderings_Otop__class_Otop(tc_fun(U_3730,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3730,U_3732)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_3730,U_3732),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_956_3]) ).
cnf(f_956_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3732),c_Orderings_Otop__class_Otop(tc_fun(U_3732,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3730,U_3732)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_3730,U_3732),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_956_3]) ).
cnf(f_956_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_3731,U_3733)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_3731,U_3733),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3733),c_Orderings_Otop__class_Otop(tc_fun(U_3733,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3731),c_Orderings_Otop__class_Otop(tc_fun(U_3731,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_956_3]) ).
fof(f_957_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_957_2,plain,
! [U_3734] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_3734)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_3734),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3734),c_Orderings_Otop__class_Otop(tc_fun(U_3734,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3734),c_Orderings_Otop__class_Otop(tc_fun(U_3734,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_3734)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_3734),tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[f_957_1]) ).
fof(f_957_3,plain,
( ! [U_3736] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_3736)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_3736),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3736),c_Orderings_Otop__class_Otop(tc_fun(U_3736,tc_HOL_Obool)))) )
& ! [U_3735] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3735),c_Orderings_Otop__class_Otop(tc_fun(U_3735,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_3735)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_3735),tc_HOL_Obool)))) ) ),
inference(miniscope,[status(thm)],[f_957_2]) ).
cnf(f_957_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3735),c_Orderings_Otop__class_Otop(tc_fun(U_3735,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_3735)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_3735),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_957_3]) ).
cnf(f_957_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_3736)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_3736),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3736),c_Orderings_Otop__class_Otop(tc_fun(U_3736,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_957_3]) ).
fof(f_958_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_958_2,plain,
! [U_3737] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3737),c_Orderings_Otop__class_Otop(tc_fun(U_3737,tc_HOL_Obool))))
| ~ class_Finite__Set_Ofinite(U_3737) ),
inference(variable_rename,[status(thm)],[f_958_1]) ).
cnf(f_958_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3737),c_Orderings_Otop__class_Otop(tc_fun(U_3737,tc_HOL_Obool))))
| ~ class_Finite__Set_Ofinite(U_3737) ),
inference(clausify,[status(thm)],[f_958_2]) ).
fof(f_959_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_959_2,plain,
! [U_3740,U_3739,U_3738] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3738),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3738,tc_HOL_Obool)),U_3739),U_3740)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3738),U_3740))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3738),U_3739)) ),
inference(variable_rename,[status(thm)],[f_959_1]) ).
cnf(f_959_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3738),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3738,tc_HOL_Obool)),U_3739),U_3740)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3738),U_3740))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3738),U_3739)) ),
inference(clausify,[status(thm)],[f_959_2]) ).
fof(f_960_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_960_2,plain,
! [U_3743,U_3742,U_3741] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3741),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3741,tc_HOL_Obool)),U_3742),U_3743)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3741),U_3743))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3741),U_3742)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3741),U_3743))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_3741),U_3742)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3741),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3741,tc_HOL_Obool)),U_3742),U_3743))) ) ),
inference(variable_rename,[status(thm)],[f_960_1]) ).
fof(f_960_3,plain,
( ! [U_3749,U_3747,U_3745] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3745),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3745,tc_HOL_Obool)),U_3747),U_3749)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3745),U_3749))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3745),U_3747)) )
& ! [U_3748,U_3746,U_3744] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3744),U_3748))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_3744),U_3746)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3744),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3744,tc_HOL_Obool)),U_3746),U_3748))) ) ),
inference(miniscope,[status(thm)],[f_960_2]) ).
cnf(f_960_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3744),U_3746))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3744),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3744,tc_HOL_Obool)),U_3746),U_3748))) ),
inference(clausify,[status(thm)],[f_960_3]) ).
cnf(f_960_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3744),U_3748))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3744),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3744,tc_HOL_Obool)),U_3746),U_3748))) ),
inference(clausify,[status(thm)],[f_960_3]) ).
cnf(f_960_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3745),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3745,tc_HOL_Obool)),U_3747),U_3749)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3745),U_3749))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3745),U_3747)) ),
inference(clausify,[status(thm)],[f_960_3]) ).
fof(f_961_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_961_2,plain,
! [U_3752,U_3751,U_3750] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3750),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3750,tc_HOL_Obool)),U_3752),U_3751)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3750),U_3752)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3750),U_3752))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3750),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3750,tc_HOL_Obool)),U_3752),U_3751))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3750),U_3751)) ),
inference(variable_rename,[status(thm)],[f_961_1]) ).
cnf(f_961_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3750),U_3752))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3750),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3750,tc_HOL_Obool)),U_3752),U_3751)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3750),U_3751)) ),
inference(clausify,[status(thm)],[f_961_2]) ).
cnf(f_961_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3750),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3750,tc_HOL_Obool)),U_3752),U_3751)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3750),U_3752))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3750),U_3751)) ),
inference(clausify,[status(thm)],[f_961_2]) ).
fof(f_962_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_962_2,plain,
! [U_3754,U_3753] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3753,tc_HOL_Obool)),U_3754))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3753),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3753,tc_HOL_Obool),U_3754))) ),
inference(variable_rename,[status(thm)],[f_962_1]) ).
cnf(f_962_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3753,tc_HOL_Obool)),U_3754))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3753),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3753,tc_HOL_Obool),U_3754))) ),
inference(clausify,[status(thm)],[f_962_2]) ).
fof(f_963_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_963_2,plain,
! [U_3756,U_3755] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3755,tc_HOL_Obool)),hAPP(c_Set_OPow(U_3755),U_3756)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3755),U_3756)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3755),U_3756))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3755,tc_HOL_Obool)),hAPP(c_Set_OPow(U_3755),U_3756))) ) ),
inference(variable_rename,[status(thm)],[f_963_1]) ).
fof(f_963_3,plain,
( ! [U_3760,U_3758] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3758,tc_HOL_Obool)),hAPP(c_Set_OPow(U_3758),U_3760)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3758),U_3760)) )
& ! [U_3759,U_3757] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3757),U_3759))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3757,tc_HOL_Obool)),hAPP(c_Set_OPow(U_3757),U_3759))) ) ),
inference(miniscope,[status(thm)],[f_963_2]) ).
cnf(f_963_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3757),U_3759))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3757,tc_HOL_Obool)),hAPP(c_Set_OPow(U_3757),U_3759))) ),
inference(clausify,[status(thm)],[f_963_3]) ).
cnf(f_963_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3758,tc_HOL_Obool)),hAPP(c_Set_OPow(U_3758),U_3760)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3758),U_3760)) ),
inference(clausify,[status(thm)],[f_963_3]) ).
fof(f_964_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_964_2,plain,
! [U_3765,U_3764,U_3763,U_3762,U_3761] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3763),U_3764))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3763,tc_HOL_Obool)),U_3764),hAPP(c_Set_Oimage(U_3761,U_3763,U_3765),U_3762)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3761),U_3762)) ),
inference(variable_rename,[status(thm)],[f_964_1]) ).
cnf(f_964_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3763),U_3764))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3763,tc_HOL_Obool)),U_3764),hAPP(c_Set_Oimage(U_3761,U_3763,U_3765),U_3762)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3761),U_3762)) ),
inference(clausify,[status(thm)],[f_964_2]) ).
fof(f_965_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_965_2,plain,
! [U_3769,U_3768,U_3767,U_3766] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3766),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3766,tc_HOL_Obool)),U_3767),hAPP(hAPP(c_Set_Oinsert(U_3766),U_3768),U_3769))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3766),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3766,tc_HOL_Obool)),U_3767),U_3769))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3766),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3766,tc_HOL_Obool)),U_3767),U_3769)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3766),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3766,tc_HOL_Obool)),U_3767),hAPP(hAPP(c_Set_Oinsert(U_3766),U_3768),U_3769)))) ) ),
inference(variable_rename,[status(thm)],[f_965_1]) ).
fof(f_965_3,plain,
( ! [U_3777,U_3775,U_3773,U_3771] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3771),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3771,tc_HOL_Obool)),U_3773),hAPP(hAPP(c_Set_Oinsert(U_3771),U_3775),U_3777))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3771),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3771,tc_HOL_Obool)),U_3773),U_3777))) )
& ! [U_3776,U_3774,U_3772,U_3770] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3770),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3770,tc_HOL_Obool)),U_3772),U_3776)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3770),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3770,tc_HOL_Obool)),U_3772),hAPP(hAPP(c_Set_Oinsert(U_3770),U_3774),U_3776)))) ) ),
inference(miniscope,[status(thm)],[f_965_2]) ).
cnf(f_965_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3770),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3770,tc_HOL_Obool)),U_3772),U_3776)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3770),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3770,tc_HOL_Obool)),U_3772),hAPP(hAPP(c_Set_Oinsert(U_3770),U_3774),U_3776)))) ),
inference(clausify,[status(thm)],[f_965_3]) ).
cnf(f_965_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3771),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3771,tc_HOL_Obool)),U_3773),hAPP(hAPP(c_Set_Oinsert(U_3771),U_3775),U_3777))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3771),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3771,tc_HOL_Obool)),U_3773),U_3777))) ),
inference(clausify,[status(thm)],[f_965_3]) ).
fof(f_966_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_966_2,plain,
! [U_3781,U_3780,U_3779,U_3778] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3779),U_3781))
| ~ c_Fun_Oinj__on(U_3779,U_3778,U_3780,U_3781)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3778),hAPP(c_Set_Oimage(U_3779,U_3778,U_3780),U_3781))) ),
inference(variable_rename,[status(thm)],[f_966_1]) ).
cnf(f_966_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3779),U_3781))
| ~ c_Fun_Oinj__on(U_3779,U_3778,U_3780,U_3781)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3778),hAPP(c_Set_Oimage(U_3779,U_3778,U_3780),U_3781))) ),
inference(clausify,[status(thm)],[f_966_2]) ).
fof(f_967_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_967_2,plain,
! [U_3783,U_3782] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3782),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3782,tc_HOL_Obool)),U_3783)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3782),c_Orderings_Otop__class_Otop(tc_fun(U_3782,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3782),c_Orderings_Otop__class_Otop(tc_fun(U_3782,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3782),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3782,tc_HOL_Obool)),U_3783))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3782),U_3783)) ),
inference(variable_rename,[status(thm)],[f_967_1]) ).
cnf(f_967_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3782),c_Orderings_Otop__class_Otop(tc_fun(U_3782,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3782),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3782,tc_HOL_Obool)),U_3783)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3782),U_3783)) ),
inference(clausify,[status(thm)],[f_967_2]) ).
cnf(f_967_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3782),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3782,tc_HOL_Obool)),U_3783)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3782),c_Orderings_Otop__class_Otop(tc_fun(U_3782,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3782),U_3783)) ),
inference(clausify,[status(thm)],[f_967_2]) ).
fof(f_968_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_968_2,plain,
! [U_3785,U_3784] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3785),c_Orderings_Otop__class_Otop(tc_fun(U_3785,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3784,U_3785)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_3784,U_3785),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_968_1]) ).
fof(f_968_3,plain,
! [U_3785] :
( ! [U_3784] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3784,U_3785)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_3784,U_3785),tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3785),c_Orderings_Otop__class_Otop(tc_fun(U_3785,tc_HOL_Obool)))) ),
inference(miniscope,[status(thm)],[f_968_2]) ).
cnf(f_968_4,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3784,U_3785)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_3784,U_3785),tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3785),c_Orderings_Otop__class_Otop(tc_fun(U_3785,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_968_3]) ).
fof(f_969_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_969_2,plain,
! [U_3788,U_3787,U_3786] :
( hAPP(c_Set_Oimage(U_3786,U_3786,U_3788),U_3787) = U_3787
| ~ c_Fun_Oinj__on(U_3786,U_3786,U_3788,U_3787)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3786,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3786,U_3786,U_3788),U_3787)),U_3787))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3786),U_3787)) ),
inference(variable_rename,[status(thm)],[f_969_1]) ).
cnf(f_969_3,plain,
( hAPP(c_Set_Oimage(U_3786,U_3786,U_3788),U_3787) = U_3787
| ~ c_Fun_Oinj__on(U_3786,U_3786,U_3788,U_3787)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3786,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3786,U_3786,U_3788),U_3787)),U_3787))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3786),U_3787)) ),
inference(clausify,[status(thm)],[f_969_2]) ).
fof(f_970_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_970_2,plain,
! [U_3791,U_3790,U_3789] :
( c_Fun_Oinj__on(U_3789,U_3789,U_3791,U_3790)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3789,tc_HOL_Obool)),U_3790),hAPP(c_Set_Oimage(U_3789,U_3789,U_3791),U_3790)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3789),U_3790)) ),
inference(variable_rename,[status(thm)],[f_970_1]) ).
cnf(f_970_3,plain,
( c_Fun_Oinj__on(U_3789,U_3789,U_3791,U_3790)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3789,tc_HOL_Obool)),U_3790),hAPP(c_Set_Oimage(U_3789,U_3789,U_3791),U_3790)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3789),U_3790)) ),
inference(clausify,[status(thm)],[f_970_2]) ).
fof(f_971_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_971_2,plain,
! [U_3793,U_3792] :
( c_Fun_Oinj__on(U_3792,U_3792,U_3793,c_Orderings_Otop__class_Otop(tc_fun(U_3792,tc_HOL_Obool)))
| hAPP(c_Set_Oimage(U_3792,U_3792,U_3793),c_Orderings_Otop__class_Otop(tc_fun(U_3792,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_3792,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3792),c_Orderings_Otop__class_Otop(tc_fun(U_3792,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_971_1]) ).
cnf(f_971_3,plain,
( c_Fun_Oinj__on(U_3792,U_3792,U_3793,c_Orderings_Otop__class_Otop(tc_fun(U_3792,tc_HOL_Obool)))
| hAPP(c_Set_Oimage(U_3792,U_3792,U_3793),c_Orderings_Otop__class_Otop(tc_fun(U_3792,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_3792,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3792),c_Orderings_Otop__class_Otop(tc_fun(U_3792,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_971_2]) ).
fof(f_972_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_972_2,plain,
! [U_3795,U_3794] :
( hAPP(c_Set_Oimage(U_3794,U_3794,U_3795),c_Orderings_Otop__class_Otop(tc_fun(U_3794,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_3794,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(U_3794,U_3794,U_3795,c_Orderings_Otop__class_Otop(tc_fun(U_3794,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3794),c_Orderings_Otop__class_Otop(tc_fun(U_3794,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_972_1]) ).
cnf(f_972_3,plain,
( hAPP(c_Set_Oimage(U_3794,U_3794,U_3795),c_Orderings_Otop__class_Otop(tc_fun(U_3794,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_3794,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(U_3794,U_3794,U_3795,c_Orderings_Otop__class_Otop(tc_fun(U_3794,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3794),c_Orderings_Otop__class_Otop(tc_fun(U_3794,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_972_2]) ).
fof(f_973_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_973_2,plain,
! [U_3798,U_3797,U_3796] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3796),U_3797),U_3798) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3796),U_3797),hAPP(c_Groups_Ouminus__class_Ouminus(U_3796),U_3798))
| ~ class_Rings_Ocomm__ring__1(U_3796) ),
inference(variable_rename,[status(thm)],[f_973_1]) ).
cnf(f_973_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3796),U_3797),U_3798) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3796),U_3797),hAPP(c_Groups_Ouminus__class_Ouminus(U_3796),U_3798))
| ~ class_Rings_Ocomm__ring__1(U_3796) ),
inference(clausify,[status(thm)],[f_973_2]) ).
fof(f_974_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_974_2,plain,
! [U_3800,U_3799] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3799),U_3800),U_3800)),c_Groups_Ozero__class_Ozero(U_3799)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),U_3800),c_Groups_Ozero__class_Ozero(U_3799))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),U_3800),c_Groups_Ozero__class_Ozero(U_3799)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3799),U_3800),U_3800)),c_Groups_Ozero__class_Ozero(U_3799))) ) )
| ~ class_Rings_Olinordered__idom(U_3799) ),
inference(variable_rename,[status(thm)],[f_974_1]) ).
cnf(f_974_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),U_3800),c_Groups_Ozero__class_Ozero(U_3799)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3799),U_3800),U_3800)),c_Groups_Ozero__class_Ozero(U_3799)))
| ~ class_Rings_Olinordered__idom(U_3799) ),
inference(clausify,[status(thm)],[f_974_2]) ).
cnf(f_974_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3799),U_3800),U_3800)),c_Groups_Ozero__class_Ozero(U_3799)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3799),U_3800),c_Groups_Ozero__class_Ozero(U_3799)))
| ~ class_Rings_Olinordered__idom(U_3799) ),
inference(clausify,[status(thm)],[f_974_2]) ).
fof(f_975_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_975_2,plain,
! [U_3805,U_3804,U_3803,U_3802,U_3801] :
( ( ( hAPP(U_3803,U_3804) = hAPP(hAPP(U_3802,U_3805),hAPP(U_3803,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3801,tc_HOL_Obool)),U_3804),hAPP(hAPP(c_Set_Oinsert(U_3801),U_3805),c_Orderings_Obot__class_Obot(tc_fun(U_3801,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3801,tc_HOL_Obool)),U_3804),hAPP(hAPP(c_Set_Oinsert(U_3801),U_3805),c_Orderings_Obot__class_Obot(tc_fun(U_3801,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_3801,tc_HOL_Obool)) )
& ( hAPP(U_3803,U_3804) = U_3805
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3801,tc_HOL_Obool)),U_3804),hAPP(hAPP(c_Set_Oinsert(U_3801),U_3805),c_Orderings_Obot__class_Obot(tc_fun(U_3801,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_3801,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_3801),U_3805),U_3804))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3801),U_3804))
| ~ c_Finite__Set_Ofolding__one(U_3801,U_3802,U_3803) ),
inference(variable_rename,[status(thm)],[f_975_1]) ).
cnf(f_975_3,plain,
( hAPP(U_3803,U_3804) = U_3805
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3801,tc_HOL_Obool)),U_3804),hAPP(hAPP(c_Set_Oinsert(U_3801),U_3805),c_Orderings_Obot__class_Obot(tc_fun(U_3801,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_3801,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_3801),U_3805),U_3804))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3801),U_3804))
| ~ c_Finite__Set_Ofolding__one(U_3801,U_3802,U_3803) ),
inference(clausify,[status(thm)],[f_975_2]) ).
cnf(f_975_4,plain,
( hAPP(U_3803,U_3804) = hAPP(hAPP(U_3802,U_3805),hAPP(U_3803,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3801,tc_HOL_Obool)),U_3804),hAPP(hAPP(c_Set_Oinsert(U_3801),U_3805),c_Orderings_Obot__class_Obot(tc_fun(U_3801,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3801,tc_HOL_Obool)),U_3804),hAPP(hAPP(c_Set_Oinsert(U_3801),U_3805),c_Orderings_Obot__class_Obot(tc_fun(U_3801,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_3801,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_3801),U_3805),U_3804))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3801),U_3804))
| ~ c_Finite__Set_Ofolding__one(U_3801,U_3802,U_3803) ),
inference(clausify,[status(thm)],[f_975_2]) ).
fof(f_976_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_976_2,plain,
! [U_3813,U_3812,U_3811,U_3810,U_3809,U_3808,U_3807,U_3806] :
( hAPP(U_3811,U_3812) = hAPP(hAPP(U_3808,hAPP(U_3810,U_3813)),hAPP(U_3811,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3807,tc_HOL_Obool)),U_3812),hAPP(hAPP(c_Set_Oinsert(U_3807),U_3813),c_Orderings_Obot__class_Obot(tc_fun(U_3807,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_3807),U_3813),U_3812))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3807),U_3812))
| ~ c_Finite__Set_Ofolding__image__simple(U_3806,U_3807,U_3808,U_3809,U_3810,U_3811) ),
inference(variable_rename,[status(thm)],[f_976_1]) ).
fof(f_976_3,plain,
! [U_3813,U_3812,U_3811,U_3810,U_3809,U_3808,U_3807] :
( ! [U_3806] : ~ c_Finite__Set_Ofolding__image__simple(U_3806,U_3807,U_3808,U_3809,U_3810,U_3811)
| hAPP(U_3811,U_3812) = hAPP(hAPP(U_3808,hAPP(U_3810,U_3813)),hAPP(U_3811,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3807,tc_HOL_Obool)),U_3812),hAPP(hAPP(c_Set_Oinsert(U_3807),U_3813),c_Orderings_Obot__class_Obot(tc_fun(U_3807,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_3807),U_3813),U_3812))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3807),U_3812)) ),
inference(miniscope,[status(thm)],[f_976_2]) ).
cnf(f_976_4,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_3806,U_3807,U_3808,U_3809,U_3810,U_3811)
| hAPP(U_3811,U_3812) = hAPP(hAPP(U_3808,hAPP(U_3810,U_3813)),hAPP(U_3811,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3807,tc_HOL_Obool)),U_3812),hAPP(hAPP(c_Set_Oinsert(U_3807),U_3813),c_Orderings_Obot__class_Obot(tc_fun(U_3807,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_3807),U_3813),U_3812))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3807),U_3812)) ),
inference(clausify,[status(thm)],[f_976_3]) ).
fof(f_977_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_977_2,plain,
! [U_3819,U_3818,U_3817,U_3816,U_3815] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3815),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3816,U_3815),U_3819),U_3818)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3816,U_3815),U_3819),U_3817)))
| ? [U_3814] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3815),c_Groups_Ozero__class_Ozero(U_3815)),hAPP(U_3819,U_3814)))
& hBOOL(hAPP(hAPP(c_member(U_3816),U_3814),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3816,tc_HOL_Obool)),U_3817),U_3818))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3816,tc_HOL_Obool)),U_3818),U_3817))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3816),U_3817))
| ~ class_Groups_Oordered__comm__monoid__add(U_3815) ),
inference(variable_rename,[status(thm)],[f_977_1]) ).
fof(f_977_3,plain,
! [U_3819,U_3818,U_3817,U_3816,U_3815] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3815),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3816,U_3815),U_3819),U_3818)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3816,U_3815),U_3819),U_3817)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3815),c_Groups_Ozero__class_Ozero(U_3815)),hAPP(U_3819,sK60(U_3819,U_3818,U_3817,U_3816,U_3815))))
& hBOOL(hAPP(hAPP(c_member(U_3816),sK60(U_3819,U_3818,U_3817,U_3816,U_3815)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3816,tc_HOL_Obool)),U_3817),U_3818))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3816,tc_HOL_Obool)),U_3818),U_3817))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3816),U_3817))
| ~ class_Groups_Oordered__comm__monoid__add(U_3815) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_3814,sK60(U_3819,U_3818,U_3817,U_3816,U_3815))],[f_977_2]) ).
cnf(f_977_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_3816),sK60(U_3819,U_3818,U_3817,U_3816,U_3815)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3816,tc_HOL_Obool)),U_3817),U_3818)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3815),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3816,U_3815),U_3819),U_3818)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3816,U_3815),U_3819),U_3817)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3816,tc_HOL_Obool)),U_3818),U_3817))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3816),U_3817))
| ~ class_Groups_Oordered__comm__monoid__add(U_3815) ),
inference(clausify,[status(thm)],[f_977_3]) ).
cnf(f_977_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3815),c_Groups_Ozero__class_Ozero(U_3815)),hAPP(U_3819,sK60(U_3819,U_3818,U_3817,U_3816,U_3815))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3815),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3816,U_3815),U_3819),U_3818)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3816,U_3815),U_3819),U_3817)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3816,tc_HOL_Obool)),U_3818),U_3817))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3816),U_3817))
| ~ class_Groups_Oordered__comm__monoid__add(U_3815) ),
inference(clausify,[status(thm)],[f_977_3]) ).
fof(f_978_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_978_2,plain,
! [U_3825,U_3824,U_3823,U_3822,U_3821] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3822,U_3821),U_3825),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3822,tc_HOL_Obool)),U_3823),U_3824)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3821),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3822,U_3821),U_3825),U_3823)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3822,U_3821),U_3825),U_3824))
| ? [U_3820] :
( hAPP(U_3825,U_3820) != c_Groups_Ozero__class_Ozero(U_3821)
& hBOOL(hAPP(hAPP(c_member(U_3822),U_3820),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3822,tc_HOL_Obool)),U_3823),U_3824))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3822),U_3824))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3822),U_3823))
| ~ class_Groups_Ocomm__monoid__add(U_3821) ),
inference(variable_rename,[status(thm)],[f_978_1]) ).
fof(f_978_3,plain,
! [U_3825,U_3824,U_3823,U_3822,U_3821] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3822,U_3821),U_3825),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3822,tc_HOL_Obool)),U_3823),U_3824)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3821),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3822,U_3821),U_3825),U_3823)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3822,U_3821),U_3825),U_3824))
| ( hAPP(U_3825,sK61(U_3825,U_3824,U_3823,U_3822,U_3821)) != c_Groups_Ozero__class_Ozero(U_3821)
& hBOOL(hAPP(hAPP(c_member(U_3822),sK61(U_3825,U_3824,U_3823,U_3822,U_3821)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3822,tc_HOL_Obool)),U_3823),U_3824))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3822),U_3824))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3822),U_3823))
| ~ class_Groups_Ocomm__monoid__add(U_3821) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_3820,sK61(U_3825,U_3824,U_3823,U_3822,U_3821))],[f_978_2]) ).
cnf(f_978_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_3822),sK61(U_3825,U_3824,U_3823,U_3822,U_3821)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3822,tc_HOL_Obool)),U_3823),U_3824)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3822,U_3821),U_3825),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3822,tc_HOL_Obool)),U_3823),U_3824)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3821),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3822,U_3821),U_3825),U_3823)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3822,U_3821),U_3825),U_3824))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3822),U_3824))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3822),U_3823))
| ~ class_Groups_Ocomm__monoid__add(U_3821) ),
inference(clausify,[status(thm)],[f_978_3]) ).
cnf(f_978_5,plain,
( hAPP(U_3825,sK61(U_3825,U_3824,U_3823,U_3822,U_3821)) != c_Groups_Ozero__class_Ozero(U_3821)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3822,U_3821),U_3825),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3822,tc_HOL_Obool)),U_3823),U_3824)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3821),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3822,U_3821),U_3825),U_3823)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3822,U_3821),U_3825),U_3824))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3822),U_3824))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3822),U_3823))
| ~ class_Groups_Ocomm__monoid__add(U_3821) ),
inference(clausify,[status(thm)],[f_978_3]) ).
fof(f_979_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_979_2,plain,
! [U_3831,U_3830,U_3829,U_3828,U_3827] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3828,U_3827),U_3831),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3828,tc_HOL_Obool)),U_3829),U_3830)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3827),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3828,U_3827),U_3831),U_3829)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3828,U_3827),U_3831),U_3830))
| ? [U_3826] :
( hAPP(U_3831,U_3826) != c_Groups_Ozero__class_Ozero(U_3827)
& hBOOL(hAPP(hAPP(c_member(U_3828),U_3826),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3828,tc_HOL_Obool)),U_3829),U_3830))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3828),U_3830))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3828),U_3829))
| ~ class_Groups_Ocomm__monoid__add(U_3827) ),
inference(variable_rename,[status(thm)],[f_979_1]) ).
fof(f_979_3,plain,
! [U_3831,U_3830,U_3829,U_3828,U_3827] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3828,U_3827),U_3831),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3828,tc_HOL_Obool)),U_3829),U_3830)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3827),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3828,U_3827),U_3831),U_3829)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3828,U_3827),U_3831),U_3830))
| ( hAPP(U_3831,sK62(U_3831,U_3830,U_3829,U_3828,U_3827)) != c_Groups_Ozero__class_Ozero(U_3827)
& hBOOL(hAPP(hAPP(c_member(U_3828),sK62(U_3831,U_3830,U_3829,U_3828,U_3827)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3828,tc_HOL_Obool)),U_3829),U_3830))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3828),U_3830))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3828),U_3829))
| ~ class_Groups_Ocomm__monoid__add(U_3827) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_3826,sK62(U_3831,U_3830,U_3829,U_3828,U_3827))],[f_979_2]) ).
cnf(f_979_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_3828),sK62(U_3831,U_3830,U_3829,U_3828,U_3827)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3828,tc_HOL_Obool)),U_3829),U_3830)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3828,U_3827),U_3831),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3828,tc_HOL_Obool)),U_3829),U_3830)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3827),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3828,U_3827),U_3831),U_3829)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3828,U_3827),U_3831),U_3830))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3828),U_3830))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3828),U_3829))
| ~ class_Groups_Ocomm__monoid__add(U_3827) ),
inference(clausify,[status(thm)],[f_979_3]) ).
cnf(f_979_5,plain,
( hAPP(U_3831,sK62(U_3831,U_3830,U_3829,U_3828,U_3827)) != c_Groups_Ozero__class_Ozero(U_3827)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3828,U_3827),U_3831),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3828,tc_HOL_Obool)),U_3829),U_3830)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3827),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3828,U_3827),U_3831),U_3829)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3828,U_3827),U_3831),U_3830))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3828),U_3830))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3828),U_3829))
| ~ class_Groups_Ocomm__monoid__add(U_3827) ),
inference(clausify,[status(thm)],[f_979_3]) ).
fof(f_980_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_980_2,plain,
! [U_3837,U_3836,U_3835,U_3834,U_3833] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3833),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3834,U_3833),U_3837),U_3836)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3834,U_3833),U_3837),U_3835)))
| ? [U_3832] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3833),c_Groups_Ozero__class_Ozero(U_3833)),hAPP(U_3837,U_3832)))
& hBOOL(hAPP(hAPP(c_member(U_3834),U_3832),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3834,tc_HOL_Obool)),U_3835),U_3836))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3834,tc_HOL_Obool)),U_3836),U_3835))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3834),U_3835))
| ~ class_Groups_Oordered__ab__semigroup__add(U_3833)
| ~ class_Groups_Ocomm__monoid__add(U_3833) ),
inference(variable_rename,[status(thm)],[f_980_1]) ).
fof(f_980_3,plain,
! [U_3837,U_3836,U_3835,U_3834,U_3833] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3833),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3834,U_3833),U_3837),U_3836)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3834,U_3833),U_3837),U_3835)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3833),c_Groups_Ozero__class_Ozero(U_3833)),hAPP(U_3837,sK63(U_3837,U_3836,U_3835,U_3834,U_3833))))
& hBOOL(hAPP(hAPP(c_member(U_3834),sK63(U_3837,U_3836,U_3835,U_3834,U_3833)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3834,tc_HOL_Obool)),U_3835),U_3836))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3834,tc_HOL_Obool)),U_3836),U_3835))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3834),U_3835))
| ~ class_Groups_Oordered__ab__semigroup__add(U_3833)
| ~ class_Groups_Ocomm__monoid__add(U_3833) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_3832,sK63(U_3837,U_3836,U_3835,U_3834,U_3833))],[f_980_2]) ).
cnf(f_980_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_3834),sK63(U_3837,U_3836,U_3835,U_3834,U_3833)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3834,tc_HOL_Obool)),U_3835),U_3836)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3833),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3834,U_3833),U_3837),U_3836)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3834,U_3833),U_3837),U_3835)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3834,tc_HOL_Obool)),U_3836),U_3835))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3834),U_3835))
| ~ class_Groups_Oordered__ab__semigroup__add(U_3833)
| ~ class_Groups_Ocomm__monoid__add(U_3833) ),
inference(clausify,[status(thm)],[f_980_3]) ).
cnf(f_980_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3833),c_Groups_Ozero__class_Ozero(U_3833)),hAPP(U_3837,sK63(U_3837,U_3836,U_3835,U_3834,U_3833))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3833),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3834,U_3833),U_3837),U_3836)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3834,U_3833),U_3837),U_3835)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3834,tc_HOL_Obool)),U_3836),U_3835))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3834),U_3835))
| ~ class_Groups_Oordered__ab__semigroup__add(U_3833)
| ~ class_Groups_Ocomm__monoid__add(U_3833) ),
inference(clausify,[status(thm)],[f_980_3]) ).
fof(f_981_1,plain,
! [V_P_2,V_B_2,V_A_2,T_c,T_b] :
( ( ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
| ? [B_x] :
( ? [B_xa] :
( ~ hBOOL(hAPP(V_P_2,B_xa))
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x))) )
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ! [B_x] :
( ! [B_xa] :
( hBOOL(hAPP(V_P_2,B_xa))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x))) )
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
inference(fof_nnf,[status(thm)],[fact_ball__UN]) ).
fof(f_981_2,plain,
! [U_3848,U_3847,U_3846,U_3845,U_3844] :
( ( ! [U_3843] :
( hBOOL(hAPP(U_3848,U_3843))
| ~ hBOOL(hAPP(hAPP(c_member(U_3844),U_3843),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3845,tc_fun(U_3844,tc_HOL_Obool)),U_3846),U_3847))) )
| ? [U_3842] :
( ? [U_3841] :
( ~ hBOOL(hAPP(U_3848,U_3841))
& hBOOL(hAPP(hAPP(c_member(U_3844),U_3841),hAPP(U_3847,U_3842))) )
& hBOOL(hAPP(hAPP(c_member(U_3845),U_3842),U_3846)) ) )
& ( ! [U_3840] :
( ! [U_3839] :
( hBOOL(hAPP(U_3848,U_3839))
| ~ hBOOL(hAPP(hAPP(c_member(U_3844),U_3839),hAPP(U_3847,U_3840))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_3845),U_3840),U_3846)) )
| ? [U_3838] :
( ~ hBOOL(hAPP(U_3848,U_3838))
& hBOOL(hAPP(hAPP(c_member(U_3844),U_3838),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3845,tc_fun(U_3844,tc_HOL_Obool)),U_3846),U_3847))) ) ) ),
inference(variable_rename,[status(thm)],[f_981_1]) ).
fof(f_981_3,plain,
( ! [U_3858,U_3856,U_3854,U_3852,U_3850] :
( ! [U_3843] :
( hBOOL(hAPP(U_3858,U_3843))
| ~ hBOOL(hAPP(hAPP(c_member(U_3850),U_3843),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3852,tc_fun(U_3850,tc_HOL_Obool)),U_3854),U_3856))) )
| ? [U_3842] :
( ? [U_3841] :
( ~ hBOOL(hAPP(U_3858,U_3841))
& hBOOL(hAPP(hAPP(c_member(U_3850),U_3841),hAPP(U_3856,U_3842))) )
& hBOOL(hAPP(hAPP(c_member(U_3852),U_3842),U_3854)) ) )
& ! [U_3857,U_3855,U_3853,U_3851,U_3849] :
( ! [U_3840] :
( ! [U_3839] :
( hBOOL(hAPP(U_3857,U_3839))
| ~ hBOOL(hAPP(hAPP(c_member(U_3849),U_3839),hAPP(U_3855,U_3840))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_3851),U_3840),U_3853)) )
| ? [U_3838] :
( ~ hBOOL(hAPP(U_3857,U_3838))
& hBOOL(hAPP(hAPP(c_member(U_3849),U_3838),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3851,tc_fun(U_3849,tc_HOL_Obool)),U_3853),U_3855))) ) ) ),
inference(miniscope,[status(thm)],[f_981_2]) ).
fof(f_981_4,plain,
( ! [U_3858,U_3856,U_3854,U_3852,U_3850] :
( ! [U_3843] :
( hBOOL(hAPP(U_3858,U_3843))
| ~ hBOOL(hAPP(hAPP(c_member(U_3850),U_3843),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3852,tc_fun(U_3850,tc_HOL_Obool)),U_3854),U_3856))) )
| ? [U_3842] :
( ? [U_3841] :
( ~ hBOOL(hAPP(U_3858,U_3841))
& hBOOL(hAPP(hAPP(c_member(U_3850),U_3841),hAPP(U_3856,U_3842))) )
& hBOOL(hAPP(hAPP(c_member(U_3852),U_3842),U_3854)) ) )
& ! [U_3857,U_3855,U_3853,U_3851,U_3849] :
( ! [U_3840] :
( ! [U_3839] :
( hBOOL(hAPP(U_3857,U_3839))
| ~ hBOOL(hAPP(hAPP(c_member(U_3849),U_3839),hAPP(U_3855,U_3840))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_3851),U_3840),U_3853)) )
| ( ~ hBOOL(hAPP(U_3857,sK64(U_3857,U_3855,U_3853,U_3851,U_3849)))
& hBOOL(hAPP(hAPP(c_member(U_3849),sK64(U_3857,U_3855,U_3853,U_3851,U_3849)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3851,tc_fun(U_3849,tc_HOL_Obool)),U_3853),U_3855))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_3838,sK64(U_3857,U_3855,U_3853,U_3851,U_3849))],[f_981_3]) ).
fof(f_981_5,plain,
( ! [U_3858,U_3856,U_3854,U_3852,U_3850] :
( ! [U_3843] :
( hBOOL(hAPP(U_3858,U_3843))
| ~ hBOOL(hAPP(hAPP(c_member(U_3850),U_3843),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3852,tc_fun(U_3850,tc_HOL_Obool)),U_3854),U_3856))) )
| ( ? [U_3841] :
( ~ hBOOL(hAPP(U_3858,U_3841))
& hBOOL(hAPP(hAPP(c_member(U_3850),U_3841),hAPP(U_3856,sK65(U_3858,U_3856,U_3854,U_3852,U_3850)))) )
& hBOOL(hAPP(hAPP(c_member(U_3852),sK65(U_3858,U_3856,U_3854,U_3852,U_3850)),U_3854)) ) )
& ! [U_3857,U_3855,U_3853,U_3851,U_3849] :
( ! [U_3840] :
( ! [U_3839] :
( hBOOL(hAPP(U_3857,U_3839))
| ~ hBOOL(hAPP(hAPP(c_member(U_3849),U_3839),hAPP(U_3855,U_3840))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_3851),U_3840),U_3853)) )
| ( ~ hBOOL(hAPP(U_3857,sK64(U_3857,U_3855,U_3853,U_3851,U_3849)))
& hBOOL(hAPP(hAPP(c_member(U_3849),sK64(U_3857,U_3855,U_3853,U_3851,U_3849)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3851,tc_fun(U_3849,tc_HOL_Obool)),U_3853),U_3855))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_3842,sK65(U_3858,U_3856,U_3854,U_3852,U_3850))],[f_981_4]) ).
fof(f_981_6,plain,
( ! [U_3858,U_3856,U_3854,U_3852,U_3850] :
( ! [U_3843] :
( hBOOL(hAPP(U_3858,U_3843))
| ~ hBOOL(hAPP(hAPP(c_member(U_3850),U_3843),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3852,tc_fun(U_3850,tc_HOL_Obool)),U_3854),U_3856))) )
| ( ~ hBOOL(hAPP(U_3858,sK66(U_3858,U_3856,U_3854,U_3852,U_3850)))
& hBOOL(hAPP(hAPP(c_member(U_3850),sK66(U_3858,U_3856,U_3854,U_3852,U_3850)),hAPP(U_3856,sK65(U_3858,U_3856,U_3854,U_3852,U_3850))))
& hBOOL(hAPP(hAPP(c_member(U_3852),sK65(U_3858,U_3856,U_3854,U_3852,U_3850)),U_3854)) ) )
& ! [U_3857,U_3855,U_3853,U_3851,U_3849] :
( ! [U_3840] :
( ! [U_3839] :
( hBOOL(hAPP(U_3857,U_3839))
| ~ hBOOL(hAPP(hAPP(c_member(U_3849),U_3839),hAPP(U_3855,U_3840))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_3851),U_3840),U_3853)) )
| ( ~ hBOOL(hAPP(U_3857,sK64(U_3857,U_3855,U_3853,U_3851,U_3849)))
& hBOOL(hAPP(hAPP(c_member(U_3849),sK64(U_3857,U_3855,U_3853,U_3851,U_3849)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3851,tc_fun(U_3849,tc_HOL_Obool)),U_3853),U_3855))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_3841,sK66(U_3858,U_3856,U_3854,U_3852,U_3850))],[f_981_5]) ).
cnf(f_981_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_3849),sK64(U_3857,U_3855,U_3853,U_3851,U_3849)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3851,tc_fun(U_3849,tc_HOL_Obool)),U_3853),U_3855)))
| hBOOL(hAPP(U_3857,U_3839))
| ~ hBOOL(hAPP(hAPP(c_member(U_3849),U_3839),hAPP(U_3855,U_3840)))
| ~ hBOOL(hAPP(hAPP(c_member(U_3851),U_3840),U_3853)) ),
inference(clausify,[status(thm)],[f_981_6]) ).
cnf(f_981_8,plain,
( ~ hBOOL(hAPP(U_3857,sK64(U_3857,U_3855,U_3853,U_3851,U_3849)))
| hBOOL(hAPP(U_3857,U_3839))
| ~ hBOOL(hAPP(hAPP(c_member(U_3849),U_3839),hAPP(U_3855,U_3840)))
| ~ hBOOL(hAPP(hAPP(c_member(U_3851),U_3840),U_3853)) ),
inference(clausify,[status(thm)],[f_981_6]) ).
cnf(f_981_9,plain,
( hBOOL(hAPP(hAPP(c_member(U_3852),sK65(U_3858,U_3856,U_3854,U_3852,U_3850)),U_3854))
| hBOOL(hAPP(U_3858,U_3843))
| ~ hBOOL(hAPP(hAPP(c_member(U_3850),U_3843),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3852,tc_fun(U_3850,tc_HOL_Obool)),U_3854),U_3856))) ),
inference(clausify,[status(thm)],[f_981_6]) ).
cnf(f_981_10,plain,
( hBOOL(hAPP(hAPP(c_member(U_3850),sK66(U_3858,U_3856,U_3854,U_3852,U_3850)),hAPP(U_3856,sK65(U_3858,U_3856,U_3854,U_3852,U_3850))))
| hBOOL(hAPP(U_3858,U_3843))
| ~ hBOOL(hAPP(hAPP(c_member(U_3850),U_3843),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3852,tc_fun(U_3850,tc_HOL_Obool)),U_3854),U_3856))) ),
inference(clausify,[status(thm)],[f_981_6]) ).
cnf(f_981_11,plain,
( ~ hBOOL(hAPP(U_3858,sK66(U_3858,U_3856,U_3854,U_3852,U_3850)))
| hBOOL(hAPP(U_3858,U_3843))
| ~ hBOOL(hAPP(hAPP(c_member(U_3850),U_3843),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_3852,tc_fun(U_3850,tc_HOL_Obool)),U_3854),U_3856))) ),
inference(clausify,[status(thm)],[f_981_6]) ).
fof(f_982_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_982_2,plain,
! [U_3864,U_3863,U_3862,U_3861,U_3860,U_3859] :
( hAPP(U_3864,c_Orderings_Obot__class_Obot(tc_fun(U_3860,tc_HOL_Obool))) = U_3862
| ~ c_Finite__Set_Ofolding__image__simple(U_3859,U_3860,U_3861,U_3862,U_3863,U_3864) ),
inference(variable_rename,[status(thm)],[f_982_1]) ).
fof(f_982_3,plain,
! [U_3864,U_3863,U_3862,U_3861,U_3860] :
( ! [U_3859] : ~ c_Finite__Set_Ofolding__image__simple(U_3859,U_3860,U_3861,U_3862,U_3863,U_3864)
| hAPP(U_3864,c_Orderings_Obot__class_Obot(tc_fun(U_3860,tc_HOL_Obool))) = U_3862 ),
inference(miniscope,[status(thm)],[f_982_2]) ).
cnf(f_982_4,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_3859,U_3860,U_3861,U_3862,U_3863,U_3864)
| hAPP(U_3864,c_Orderings_Obot__class_Obot(tc_fun(U_3860,tc_HOL_Obool))) = U_3862 ),
inference(clausify,[status(thm)],[f_982_3]) ).
fof(f_983_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_983_2,plain,
! [U_3869,U_3868,U_3867,U_3866,U_3865] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3865),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3865),U_3866),U_3867)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3865),U_3868),U_3869)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3865),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3865),U_3866),U_3868)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3865),U_3867),U_3869))
| ~ class_Rings_Ocomm__semiring__1(U_3865) ),
inference(variable_rename,[status(thm)],[f_983_1]) ).
cnf(f_983_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3865),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3865),U_3866),U_3867)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3865),U_3868),U_3869)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3865),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3865),U_3866),U_3868)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3865),U_3867),U_3869))
| ~ class_Rings_Ocomm__semiring__1(U_3865) ),
inference(clausify,[status(thm)],[f_983_2]) ).
fof(f_984_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_984_2,plain,
! [U_3873,U_3872,U_3871,U_3870] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3870),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3870),U_3871),U_3872)),U_3873) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3870),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3870),U_3871),U_3873)),U_3872)
| ~ class_Rings_Ocomm__semiring__1(U_3870) ),
inference(variable_rename,[status(thm)],[f_984_1]) ).
cnf(f_984_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3870),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3870),U_3871),U_3872)),U_3873) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3870),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3870),U_3871),U_3873)),U_3872)
| ~ class_Rings_Ocomm__semiring__1(U_3870) ),
inference(clausify,[status(thm)],[f_984_2]) ).
fof(f_985_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_985_2,plain,
! [U_3877,U_3876,U_3875,U_3874] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3874),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3874),U_3875),U_3876)),U_3877) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3874),U_3875),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3874),U_3876),U_3877))
| ~ class_Rings_Ocomm__semiring__1(U_3874) ),
inference(variable_rename,[status(thm)],[f_985_1]) ).
cnf(f_985_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3874),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3874),U_3875),U_3876)),U_3877) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3874),U_3875),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3874),U_3876),U_3877))
| ~ class_Rings_Ocomm__semiring__1(U_3874) ),
inference(clausify,[status(thm)],[f_985_2]) ).
fof(f_986_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_986_2,plain,
! [U_3881,U_3880,U_3879,U_3878] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3878),U_3879),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3878),U_3880),U_3881)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3878),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3878),U_3879),U_3880)),U_3881)
| ~ class_Rings_Ocomm__semiring__1(U_3878) ),
inference(variable_rename,[status(thm)],[f_986_1]) ).
cnf(f_986_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3878),U_3879),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3878),U_3880),U_3881)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3878),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3878),U_3879),U_3880)),U_3881)
| ~ class_Rings_Ocomm__semiring__1(U_3878) ),
inference(clausify,[status(thm)],[f_986_2]) ).
fof(f_987_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_987_2,plain,
! [U_3885,U_3884,U_3883,U_3882] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3882),U_3883),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3882),U_3884),U_3885)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3882),U_3884),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3882),U_3883),U_3885))
| ~ class_Rings_Ocomm__semiring__1(U_3882) ),
inference(variable_rename,[status(thm)],[f_987_1]) ).
cnf(f_987_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3882),U_3883),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3882),U_3884),U_3885)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3882),U_3884),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3882),U_3883),U_3885))
| ~ class_Rings_Ocomm__semiring__1(U_3882) ),
inference(clausify,[status(thm)],[f_987_2]) ).
fof(f_988_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_988_2,plain,
! [U_3888,U_3887,U_3886] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3886),U_3887),U_3888) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3886),U_3888),U_3887)
| ~ class_Rings_Ocomm__semiring__1(U_3886) ),
inference(variable_rename,[status(thm)],[f_988_1]) ).
cnf(f_988_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3886),U_3887),U_3888) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3886),U_3888),U_3887)
| ~ class_Rings_Ocomm__semiring__1(U_3886) ),
inference(clausify,[status(thm)],[f_988_2]) ).
fof(f_989_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_989_2,plain,
! [U_3892,U_3891,U_3890,U_3889] :
( hAPP(U_3891,hAPP(hAPP(c_Set_Oinsert(U_3889),U_3892),c_Orderings_Obot__class_Obot(tc_fun(U_3889,tc_HOL_Obool)))) = U_3892
| ~ c_Finite__Set_Ofolding__one(U_3889,U_3890,U_3891) ),
inference(variable_rename,[status(thm)],[f_989_1]) ).
cnf(f_989_3,plain,
( hAPP(U_3891,hAPP(hAPP(c_Set_Oinsert(U_3889),U_3892),c_Orderings_Obot__class_Obot(tc_fun(U_3889,tc_HOL_Obool)))) = U_3892
| ~ c_Finite__Set_Ofolding__one(U_3889,U_3890,U_3891) ),
inference(clausify,[status(thm)],[f_989_2]) ).
fof(f_990_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_990_2,plain,
! [U_3900,U_3899,U_3898,U_3897,U_3896,U_3895,U_3894,U_3893] :
( hAPP(U_3898,hAPP(hAPP(c_Set_Oinsert(U_3894),U_3900),U_3899)) = hAPP(hAPP(U_3895,hAPP(U_3897,U_3900)),hAPP(U_3898,U_3899))
| hBOOL(hAPP(hAPP(c_member(U_3894),U_3900),U_3899))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3894),U_3899))
| ~ c_Finite__Set_Ofolding__image__simple(U_3893,U_3894,U_3895,U_3896,U_3897,U_3898) ),
inference(variable_rename,[status(thm)],[f_990_1]) ).
fof(f_990_3,plain,
! [U_3900,U_3899,U_3898,U_3897,U_3896,U_3895,U_3894] :
( ! [U_3893] : ~ c_Finite__Set_Ofolding__image__simple(U_3893,U_3894,U_3895,U_3896,U_3897,U_3898)
| hAPP(U_3898,hAPP(hAPP(c_Set_Oinsert(U_3894),U_3900),U_3899)) = hAPP(hAPP(U_3895,hAPP(U_3897,U_3900)),hAPP(U_3898,U_3899))
| hBOOL(hAPP(hAPP(c_member(U_3894),U_3900),U_3899))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3894),U_3899)) ),
inference(miniscope,[status(thm)],[f_990_2]) ).
cnf(f_990_4,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_3893,U_3894,U_3895,U_3896,U_3897,U_3898)
| hAPP(U_3898,hAPP(hAPP(c_Set_Oinsert(U_3894),U_3900),U_3899)) = hAPP(hAPP(U_3895,hAPP(U_3897,U_3900)),hAPP(U_3898,U_3899))
| hBOOL(hAPP(hAPP(c_member(U_3894),U_3900),U_3899))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3894),U_3899)) ),
inference(clausify,[status(thm)],[f_990_3]) ).
fof(f_991_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_991_2,plain,
! [U_3908,U_3907,U_3906,U_3905,U_3904,U_3903,U_3902,U_3901] :
( hAPP(hAPP(U_3903,hAPP(U_3906,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3902,tc_HOL_Obool)),U_3907),U_3908))),hAPP(U_3906,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3902,tc_HOL_Obool)),U_3907),U_3908))) = hAPP(hAPP(U_3903,hAPP(U_3906,U_3907)),hAPP(U_3906,U_3908))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3902),U_3908))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3902),U_3907))
| ~ c_Finite__Set_Ofolding__image__simple(U_3901,U_3902,U_3903,U_3904,U_3905,U_3906) ),
inference(variable_rename,[status(thm)],[f_991_1]) ).
fof(f_991_3,plain,
! [U_3908,U_3907,U_3906,U_3905,U_3904,U_3903,U_3902] :
( ! [U_3901] : ~ c_Finite__Set_Ofolding__image__simple(U_3901,U_3902,U_3903,U_3904,U_3905,U_3906)
| hAPP(hAPP(U_3903,hAPP(U_3906,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3902,tc_HOL_Obool)),U_3907),U_3908))),hAPP(U_3906,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3902,tc_HOL_Obool)),U_3907),U_3908))) = hAPP(hAPP(U_3903,hAPP(U_3906,U_3907)),hAPP(U_3906,U_3908))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3902),U_3908))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3902),U_3907)) ),
inference(miniscope,[status(thm)],[f_991_2]) ).
cnf(f_991_4,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_3901,U_3902,U_3903,U_3904,U_3905,U_3906)
| hAPP(hAPP(U_3903,hAPP(U_3906,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3902,tc_HOL_Obool)),U_3907),U_3908))),hAPP(U_3906,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3902,tc_HOL_Obool)),U_3907),U_3908))) = hAPP(hAPP(U_3903,hAPP(U_3906,U_3907)),hAPP(U_3906,U_3908))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3902),U_3908))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3902),U_3907)) ),
inference(clausify,[status(thm)],[f_991_3]) ).
fof(f_992_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_992_2,plain,
! [U_3910,U_3909] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3909),c_Groups_Ozero__class_Ozero(U_3909)),U_3910) = U_3910
| ~ class_Rings_Ocomm__semiring__1(U_3909) ),
inference(variable_rename,[status(thm)],[f_992_1]) ).
cnf(f_992_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3909),c_Groups_Ozero__class_Ozero(U_3909)),U_3910) = U_3910
| ~ class_Rings_Ocomm__semiring__1(U_3909) ),
inference(clausify,[status(thm)],[f_992_2]) ).
fof(f_993_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_993_2,plain,
! [U_3912,U_3911] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3911),U_3912),c_Groups_Ozero__class_Ozero(U_3911)) = U_3912
| ~ class_Rings_Ocomm__semiring__1(U_3911) ),
inference(variable_rename,[status(thm)],[f_993_1]) ).
cnf(f_993_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3911),U_3912),c_Groups_Ozero__class_Ozero(U_3911)) = U_3912
| ~ class_Rings_Ocomm__semiring__1(U_3911) ),
inference(clausify,[status(thm)],[f_993_2]) ).
fof(f_994_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_994_2,plain,
! [U_3915,U_3914,U_3913] :
( ( ( U_3914 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3913),U_3914),U_3915)
| U_3915 != c_Groups_Ozero__class_Ozero(U_3913) )
& ( U_3915 = c_Groups_Ozero__class_Ozero(U_3913)
| U_3914 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3913),U_3914),U_3915) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_3913) ),
inference(variable_rename,[status(thm)],[f_994_1]) ).
cnf(f_994_3,plain,
( U_3915 = c_Groups_Ozero__class_Ozero(U_3913)
| U_3914 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3913),U_3914),U_3915)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_3913) ),
inference(clausify,[status(thm)],[f_994_2]) ).
cnf(f_994_4,plain,
( U_3914 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3913),U_3914),U_3915)
| U_3915 != c_Groups_Ozero__class_Ozero(U_3913)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_3913) ),
inference(clausify,[status(thm)],[f_994_2]) ).
fof(f_995_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_995_2,plain,
! [U_3917,U_3916] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3916),U_3917),U_3917) = c_Groups_Ozero__class_Ozero(U_3916)
| U_3917 != c_Groups_Ozero__class_Ozero(U_3916) )
& ( U_3917 = c_Groups_Ozero__class_Ozero(U_3916)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3916),U_3917),U_3917) != c_Groups_Ozero__class_Ozero(U_3916) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_3916) ),
inference(variable_rename,[status(thm)],[f_995_1]) ).
cnf(f_995_3,plain,
( U_3917 = c_Groups_Ozero__class_Ozero(U_3916)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3916),U_3917),U_3917) != c_Groups_Ozero__class_Ozero(U_3916)
| ~ class_Groups_Olinordered__ab__group__add(U_3916) ),
inference(clausify,[status(thm)],[f_995_2]) ).
cnf(f_995_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3916),U_3917),U_3917) = c_Groups_Ozero__class_Ozero(U_3916)
| U_3917 != c_Groups_Ozero__class_Ozero(U_3916)
| ~ class_Groups_Olinordered__ab__group__add(U_3916) ),
inference(clausify,[status(thm)],[f_995_2]) ).
fof(f_996_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_996_2,plain,
! [U_3922,U_3921,U_3920,U_3919,U_3918] :
( hAPP(U_3920,hAPP(hAPP(c_Set_Oinsert(U_3918),U_3922),U_3921)) = hAPP(hAPP(U_3919,U_3922),hAPP(U_3920,U_3921))
| U_3921 = c_Orderings_Obot__class_Obot(tc_fun(U_3918,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_3918),U_3922),U_3921))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3918),U_3921))
| ~ c_Finite__Set_Ofolding__one(U_3918,U_3919,U_3920) ),
inference(variable_rename,[status(thm)],[f_996_1]) ).
cnf(f_996_3,plain,
( hAPP(U_3920,hAPP(hAPP(c_Set_Oinsert(U_3918),U_3922),U_3921)) = hAPP(hAPP(U_3919,U_3922),hAPP(U_3920,U_3921))
| U_3921 = c_Orderings_Obot__class_Obot(tc_fun(U_3918,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_3918),U_3922),U_3921))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3918),U_3921))
| ~ c_Finite__Set_Ofolding__one(U_3918,U_3919,U_3920) ),
inference(clausify,[status(thm)],[f_996_2]) ).
fof(f_997_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_997_2,plain,
! [U_3927,U_3926,U_3925,U_3924,U_3923] :
( ( ( hAPP(U_3925,hAPP(hAPP(c_Set_Oinsert(U_3923),U_3927),U_3926)) = hAPP(hAPP(U_3924,U_3927),hAPP(U_3925,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3923,tc_HOL_Obool)),U_3926),hAPP(hAPP(c_Set_Oinsert(U_3923),U_3927),c_Orderings_Obot__class_Obot(tc_fun(U_3923,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3923,tc_HOL_Obool)),U_3926),hAPP(hAPP(c_Set_Oinsert(U_3923),U_3927),c_Orderings_Obot__class_Obot(tc_fun(U_3923,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_3923,tc_HOL_Obool)) )
& ( hAPP(U_3925,hAPP(hAPP(c_Set_Oinsert(U_3923),U_3927),U_3926)) = U_3927
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3923,tc_HOL_Obool)),U_3926),hAPP(hAPP(c_Set_Oinsert(U_3923),U_3927),c_Orderings_Obot__class_Obot(tc_fun(U_3923,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_3923,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3923),U_3926))
| ~ c_Finite__Set_Ofolding__one(U_3923,U_3924,U_3925) ),
inference(variable_rename,[status(thm)],[f_997_1]) ).
cnf(f_997_3,plain,
( hAPP(U_3925,hAPP(hAPP(c_Set_Oinsert(U_3923),U_3927),U_3926)) = U_3927
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3923,tc_HOL_Obool)),U_3926),hAPP(hAPP(c_Set_Oinsert(U_3923),U_3927),c_Orderings_Obot__class_Obot(tc_fun(U_3923,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_3923,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3923),U_3926))
| ~ c_Finite__Set_Ofolding__one(U_3923,U_3924,U_3925) ),
inference(clausify,[status(thm)],[f_997_2]) ).
cnf(f_997_4,plain,
( hAPP(U_3925,hAPP(hAPP(c_Set_Oinsert(U_3923),U_3927),U_3926)) = hAPP(hAPP(U_3924,U_3927),hAPP(U_3925,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3923,tc_HOL_Obool)),U_3926),hAPP(hAPP(c_Set_Oinsert(U_3923),U_3927),c_Orderings_Obot__class_Obot(tc_fun(U_3923,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3923,tc_HOL_Obool)),U_3926),hAPP(hAPP(c_Set_Oinsert(U_3923),U_3927),c_Orderings_Obot__class_Obot(tc_fun(U_3923,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_3923,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3923),U_3926))
| ~ c_Finite__Set_Ofolding__one(U_3923,U_3924,U_3925) ),
inference(clausify,[status(thm)],[f_997_2]) ).
fof(f_998_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_998_2,plain,
! [U_3935,U_3934,U_3933,U_3932,U_3931,U_3930,U_3929,U_3928] :
( hAPP(U_3933,hAPP(hAPP(c_Set_Oinsert(U_3929),U_3935),U_3934)) = hAPP(hAPP(U_3930,hAPP(U_3932,U_3935)),hAPP(U_3933,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3929,tc_HOL_Obool)),U_3934),hAPP(hAPP(c_Set_Oinsert(U_3929),U_3935),c_Orderings_Obot__class_Obot(tc_fun(U_3929,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3929),U_3934))
| ~ c_Finite__Set_Ofolding__image__simple(U_3928,U_3929,U_3930,U_3931,U_3932,U_3933) ),
inference(variable_rename,[status(thm)],[f_998_1]) ).
fof(f_998_3,plain,
! [U_3935,U_3934,U_3933,U_3932,U_3931,U_3930,U_3929] :
( ! [U_3928] : ~ c_Finite__Set_Ofolding__image__simple(U_3928,U_3929,U_3930,U_3931,U_3932,U_3933)
| hAPP(U_3933,hAPP(hAPP(c_Set_Oinsert(U_3929),U_3935),U_3934)) = hAPP(hAPP(U_3930,hAPP(U_3932,U_3935)),hAPP(U_3933,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3929,tc_HOL_Obool)),U_3934),hAPP(hAPP(c_Set_Oinsert(U_3929),U_3935),c_Orderings_Obot__class_Obot(tc_fun(U_3929,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3929),U_3934)) ),
inference(miniscope,[status(thm)],[f_998_2]) ).
cnf(f_998_4,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_3928,U_3929,U_3930,U_3931,U_3932,U_3933)
| hAPP(U_3933,hAPP(hAPP(c_Set_Oinsert(U_3929),U_3935),U_3934)) = hAPP(hAPP(U_3930,hAPP(U_3932,U_3935)),hAPP(U_3933,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3929,tc_HOL_Obool)),U_3934),hAPP(hAPP(c_Set_Oinsert(U_3929),U_3935),c_Orderings_Obot__class_Obot(tc_fun(U_3929,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3929),U_3934)) ),
inference(clausify,[status(thm)],[f_998_3]) ).
fof(f_999_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_999_2,plain,
! [U_3940,U_3939,U_3938,U_3937,U_3936] :
( hAPP(hAPP(U_3937,hAPP(U_3938,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3936,tc_HOL_Obool)),U_3939),U_3940))),hAPP(U_3938,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3936,tc_HOL_Obool)),U_3939),U_3940))) = hAPP(hAPP(U_3937,hAPP(U_3938,U_3939)),hAPP(U_3938,U_3940))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3936,tc_HOL_Obool)),U_3939),U_3940) = c_Orderings_Obot__class_Obot(tc_fun(U_3936,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3936),U_3940))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3936),U_3939))
| ~ c_Finite__Set_Ofolding__one(U_3936,U_3937,U_3938) ),
inference(variable_rename,[status(thm)],[f_999_1]) ).
cnf(f_999_3,plain,
( hAPP(hAPP(U_3937,hAPP(U_3938,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3936,tc_HOL_Obool)),U_3939),U_3940))),hAPP(U_3938,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3936,tc_HOL_Obool)),U_3939),U_3940))) = hAPP(hAPP(U_3937,hAPP(U_3938,U_3939)),hAPP(U_3938,U_3940))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3936,tc_HOL_Obool)),U_3939),U_3940) = c_Orderings_Obot__class_Obot(tc_fun(U_3936,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3936),U_3940))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3936),U_3939))
| ~ c_Finite__Set_Ofolding__one(U_3936,U_3937,U_3938) ),
inference(clausify,[status(thm)],[f_999_2]) ).
fof(f_1000_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_1000_2,plain,
! [U_3945,U_3944,U_3943,U_3942,U_3941] :
( hAPP(U_3943,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3941,tc_HOL_Obool)),U_3944),U_3945)) = hAPP(hAPP(U_3942,hAPP(U_3943,U_3944)),hAPP(U_3943,U_3945))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3941,tc_HOL_Obool)),U_3944),U_3945) != c_Orderings_Obot__class_Obot(tc_fun(U_3941,tc_HOL_Obool))
| U_3945 = c_Orderings_Obot__class_Obot(tc_fun(U_3941,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3941),U_3945))
| U_3944 = c_Orderings_Obot__class_Obot(tc_fun(U_3941,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3941),U_3944))
| ~ c_Finite__Set_Ofolding__one(U_3941,U_3942,U_3943) ),
inference(variable_rename,[status(thm)],[f_1000_1]) ).
cnf(f_1000_3,plain,
( hAPP(U_3943,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3941,tc_HOL_Obool)),U_3944),U_3945)) = hAPP(hAPP(U_3942,hAPP(U_3943,U_3944)),hAPP(U_3943,U_3945))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3941,tc_HOL_Obool)),U_3944),U_3945) != c_Orderings_Obot__class_Obot(tc_fun(U_3941,tc_HOL_Obool))
| U_3945 = c_Orderings_Obot__class_Obot(tc_fun(U_3941,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3941),U_3945))
| U_3944 = c_Orderings_Obot__class_Obot(tc_fun(U_3941,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3941),U_3944))
| ~ c_Finite__Set_Ofolding__one(U_3941,U_3942,U_3943) ),
inference(clausify,[status(thm)],[f_1000_2]) ).
fof(f_1001_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_1001_2,plain,
! [U_3953,U_3952,U_3951,U_3950,U_3949,U_3948,U_3947,U_3946] :
( hAPP(U_3951,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3947,tc_HOL_Obool)),U_3952),U_3953)) = hAPP(hAPP(U_3948,hAPP(U_3951,U_3952)),hAPP(U_3951,U_3953))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3947,tc_HOL_Obool)),U_3952),U_3953) != c_Orderings_Obot__class_Obot(tc_fun(U_3947,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3947),U_3953))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3947),U_3952))
| ~ c_Finite__Set_Ofolding__image__simple(U_3946,U_3947,U_3948,U_3949,U_3950,U_3951) ),
inference(variable_rename,[status(thm)],[f_1001_1]) ).
fof(f_1001_3,plain,
! [U_3953,U_3952,U_3951,U_3950,U_3949,U_3948,U_3947] :
( ! [U_3946] : ~ c_Finite__Set_Ofolding__image__simple(U_3946,U_3947,U_3948,U_3949,U_3950,U_3951)
| hAPP(U_3951,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3947,tc_HOL_Obool)),U_3952),U_3953)) = hAPP(hAPP(U_3948,hAPP(U_3951,U_3952)),hAPP(U_3951,U_3953))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3947,tc_HOL_Obool)),U_3952),U_3953) != c_Orderings_Obot__class_Obot(tc_fun(U_3947,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3947),U_3953))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3947),U_3952)) ),
inference(miniscope,[status(thm)],[f_1001_2]) ).
cnf(f_1001_4,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_3946,U_3947,U_3948,U_3949,U_3950,U_3951)
| hAPP(U_3951,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3947,tc_HOL_Obool)),U_3952),U_3953)) = hAPP(hAPP(U_3948,hAPP(U_3951,U_3952)),hAPP(U_3951,U_3953))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3947,tc_HOL_Obool)),U_3952),U_3953) != c_Orderings_Obot__class_Obot(tc_fun(U_3947,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3947),U_3953))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3947),U_3952)) ),
inference(clausify,[status(thm)],[f_1001_3]) ).
fof(f_1002_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_1002_2,plain,
! [U_3956,U_3955] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3955),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3955,tc_HOL_Obool),U_3956)))
| ? [U_3954] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3955),U_3954))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_3955,tc_HOL_Obool)),U_3954),U_3956)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3955,tc_HOL_Obool)),U_3956)) ),
inference(variable_rename,[status(thm)],[f_1002_1]) ).
fof(f_1002_3,plain,
! [U_3956,U_3955] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3955),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3955,tc_HOL_Obool),U_3956)))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3955),sK67(U_3956,U_3955)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_3955,tc_HOL_Obool)),sK67(U_3956,U_3955)),U_3956)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3955,tc_HOL_Obool)),U_3956)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_3954,sK67(U_3956,U_3955))],[f_1002_2]) ).
cnf(f_1002_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_3955,tc_HOL_Obool)),sK67(U_3956,U_3955)),U_3956))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3955),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3955,tc_HOL_Obool),U_3956)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3955,tc_HOL_Obool)),U_3956)) ),
inference(clausify,[status(thm)],[f_1002_3]) ).
cnf(f_1002_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3955),sK67(U_3956,U_3955)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3955),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3955,tc_HOL_Obool),U_3956)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3955,tc_HOL_Obool)),U_3956)) ),
inference(clausify,[status(thm)],[f_1002_3]) ).
fof(f_1003_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_1003_2,plain,
! [U_3959,U_3958,U_3957] :
( ( ( c_Big__Operators_Olattice__class_OInf__fin(U_3957,U_3958) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3957),U_3959),c_Big__Operators_Olattice__class_OInf__fin(U_3957,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3957,tc_HOL_Obool)),U_3958),hAPP(hAPP(c_Set_Oinsert(U_3957),U_3959),c_Orderings_Obot__class_Obot(tc_fun(U_3957,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3957,tc_HOL_Obool)),U_3958),hAPP(hAPP(c_Set_Oinsert(U_3957),U_3959),c_Orderings_Obot__class_Obot(tc_fun(U_3957,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_3957,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice__class_OInf__fin(U_3957,U_3958) = U_3959
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3957,tc_HOL_Obool)),U_3958),hAPP(hAPP(c_Set_Oinsert(U_3957),U_3959),c_Orderings_Obot__class_Obot(tc_fun(U_3957,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_3957,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_3957),U_3959),U_3958))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3957),U_3958))
| ~ class_Lattices_Olattice(U_3957) ),
inference(variable_rename,[status(thm)],[f_1003_1]) ).
cnf(f_1003_3,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_3957,U_3958) = U_3959
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3957,tc_HOL_Obool)),U_3958),hAPP(hAPP(c_Set_Oinsert(U_3957),U_3959),c_Orderings_Obot__class_Obot(tc_fun(U_3957,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_3957,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_3957),U_3959),U_3958))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3957),U_3958))
| ~ class_Lattices_Olattice(U_3957) ),
inference(clausify,[status(thm)],[f_1003_2]) ).
cnf(f_1003_4,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_3957,U_3958) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3957),U_3959),c_Big__Operators_Olattice__class_OInf__fin(U_3957,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3957,tc_HOL_Obool)),U_3958),hAPP(hAPP(c_Set_Oinsert(U_3957),U_3959),c_Orderings_Obot__class_Obot(tc_fun(U_3957,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3957,tc_HOL_Obool)),U_3958),hAPP(hAPP(c_Set_Oinsert(U_3957),U_3959),c_Orderings_Obot__class_Obot(tc_fun(U_3957,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_3957,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_3957),U_3959),U_3958))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3957),U_3958))
| ~ class_Lattices_Olattice(U_3957) ),
inference(clausify,[status(thm)],[f_1003_2]) ).
fof(f_1004_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_1004_2,plain,
! [U_3962,U_3961,U_3960] :
( ( ( c_Big__Operators_Olattice__class_OSup__fin(U_3960,U_3961) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3960),U_3962),c_Big__Operators_Olattice__class_OSup__fin(U_3960,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3960,tc_HOL_Obool)),U_3961),hAPP(hAPP(c_Set_Oinsert(U_3960),U_3962),c_Orderings_Obot__class_Obot(tc_fun(U_3960,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3960,tc_HOL_Obool)),U_3961),hAPP(hAPP(c_Set_Oinsert(U_3960),U_3962),c_Orderings_Obot__class_Obot(tc_fun(U_3960,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_3960,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice__class_OSup__fin(U_3960,U_3961) = U_3962
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3960,tc_HOL_Obool)),U_3961),hAPP(hAPP(c_Set_Oinsert(U_3960),U_3962),c_Orderings_Obot__class_Obot(tc_fun(U_3960,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_3960,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_3960),U_3962),U_3961))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3960),U_3961))
| ~ class_Lattices_Olattice(U_3960) ),
inference(variable_rename,[status(thm)],[f_1004_1]) ).
cnf(f_1004_3,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_3960,U_3961) = U_3962
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3960,tc_HOL_Obool)),U_3961),hAPP(hAPP(c_Set_Oinsert(U_3960),U_3962),c_Orderings_Obot__class_Obot(tc_fun(U_3960,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_3960,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_3960),U_3962),U_3961))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3960),U_3961))
| ~ class_Lattices_Olattice(U_3960) ),
inference(clausify,[status(thm)],[f_1004_2]) ).
cnf(f_1004_4,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_3960,U_3961) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3960),U_3962),c_Big__Operators_Olattice__class_OSup__fin(U_3960,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3960,tc_HOL_Obool)),U_3961),hAPP(hAPP(c_Set_Oinsert(U_3960),U_3962),c_Orderings_Obot__class_Obot(tc_fun(U_3960,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3960,tc_HOL_Obool)),U_3961),hAPP(hAPP(c_Set_Oinsert(U_3960),U_3962),c_Orderings_Obot__class_Obot(tc_fun(U_3960,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_3960,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_3960),U_3962),U_3961))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3960),U_3961))
| ~ class_Lattices_Olattice(U_3960) ),
inference(clausify,[status(thm)],[f_1004_2]) ).
fof(f_1005_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_1005_2,plain,
! [U_3967,U_3966,U_3965] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3965,tc_HOL_Obool)),U_3966),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3965,tc_HOL_Obool),U_3967)) = c_Orderings_Obot__class_Obot(tc_fun(U_3965,tc_HOL_Obool))
| ? [U_3964] :
( ? [U_3963] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3965,tc_HOL_Obool)),U_3964),U_3963) != c_Orderings_Obot__class_Obot(tc_fun(U_3965,tc_HOL_Obool))
& U_3964 != U_3963
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_3965,tc_HOL_Obool)),U_3963),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_3965,tc_HOL_Obool)),U_3966),U_3967))) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_3965,tc_HOL_Obool)),U_3964),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_3965,tc_HOL_Obool)),U_3966),U_3967))) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_3965,tc_HOL_Obool)),U_3966),U_3967)) ),
inference(variable_rename,[status(thm)],[f_1005_1]) ).
fof(f_1005_3,plain,
! [U_3967,U_3966,U_3965] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3965,tc_HOL_Obool)),U_3966),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3965,tc_HOL_Obool),U_3967)) = c_Orderings_Obot__class_Obot(tc_fun(U_3965,tc_HOL_Obool))
| ( ? [U_3963] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3965,tc_HOL_Obool)),sK68(U_3967,U_3966,U_3965)),U_3963) != c_Orderings_Obot__class_Obot(tc_fun(U_3965,tc_HOL_Obool))
& sK68(U_3967,U_3966,U_3965) != U_3963
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_3965,tc_HOL_Obool)),U_3963),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_3965,tc_HOL_Obool)),U_3966),U_3967))) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_3965,tc_HOL_Obool)),sK68(U_3967,U_3966,U_3965)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_3965,tc_HOL_Obool)),U_3966),U_3967))) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_3965,tc_HOL_Obool)),U_3966),U_3967)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_3964,sK68(U_3967,U_3966,U_3965))],[f_1005_2]) ).
fof(f_1005_4,plain,
! [U_3967,U_3966,U_3965] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3965,tc_HOL_Obool)),U_3966),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3965,tc_HOL_Obool),U_3967)) = c_Orderings_Obot__class_Obot(tc_fun(U_3965,tc_HOL_Obool))
| ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3965,tc_HOL_Obool)),sK68(U_3967,U_3966,U_3965)),sK69(U_3967,U_3966,U_3965)) != c_Orderings_Obot__class_Obot(tc_fun(U_3965,tc_HOL_Obool))
& sK68(U_3967,U_3966,U_3965) != sK69(U_3967,U_3966,U_3965)
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_3965,tc_HOL_Obool)),sK69(U_3967,U_3966,U_3965)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_3965,tc_HOL_Obool)),U_3966),U_3967)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_3965,tc_HOL_Obool)),sK68(U_3967,U_3966,U_3965)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_3965,tc_HOL_Obool)),U_3966),U_3967))) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_3965,tc_HOL_Obool)),U_3966),U_3967)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_3963,sK69(U_3967,U_3966,U_3965))],[f_1005_3]) ).
cnf(f_1005_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_3965,tc_HOL_Obool)),sK68(U_3967,U_3966,U_3965)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_3965,tc_HOL_Obool)),U_3966),U_3967)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3965,tc_HOL_Obool)),U_3966),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3965,tc_HOL_Obool),U_3967)) = c_Orderings_Obot__class_Obot(tc_fun(U_3965,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_3965,tc_HOL_Obool)),U_3966),U_3967)) ),
inference(clausify,[status(thm)],[f_1005_4]) ).
cnf(f_1005_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_3965,tc_HOL_Obool)),sK69(U_3967,U_3966,U_3965)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_3965,tc_HOL_Obool)),U_3966),U_3967)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3965,tc_HOL_Obool)),U_3966),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3965,tc_HOL_Obool),U_3967)) = c_Orderings_Obot__class_Obot(tc_fun(U_3965,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_3965,tc_HOL_Obool)),U_3966),U_3967)) ),
inference(clausify,[status(thm)],[f_1005_4]) ).
cnf(f_1005_7,plain,
( sK68(U_3967,U_3966,U_3965) != sK69(U_3967,U_3966,U_3965)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3965,tc_HOL_Obool)),U_3966),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3965,tc_HOL_Obool),U_3967)) = c_Orderings_Obot__class_Obot(tc_fun(U_3965,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_3965,tc_HOL_Obool)),U_3966),U_3967)) ),
inference(clausify,[status(thm)],[f_1005_4]) ).
cnf(f_1005_8,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3965,tc_HOL_Obool)),sK68(U_3967,U_3966,U_3965)),sK69(U_3967,U_3966,U_3965)) != c_Orderings_Obot__class_Obot(tc_fun(U_3965,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3965,tc_HOL_Obool)),U_3966),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_3965,tc_HOL_Obool),U_3967)) = c_Orderings_Obot__class_Obot(tc_fun(U_3965,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_3965,tc_HOL_Obool)),U_3966),U_3967)) ),
inference(clausify,[status(thm)],[f_1005_4]) ).
fof(f_1006_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_1006_2,plain,
! [U_3973,U_3972,U_3971,U_3970] :
( hBOOL(hAPP(hAPP(c_member(U_3970),hAPP(U_3972,U_3973)),U_3973))
| ? [U_3969,U_3968] : ~ hBOOL(hAPP(hAPP(c_member(U_3970),hAPP(hAPP(U_3971,U_3969),U_3968)),hAPP(hAPP(c_Set_Oinsert(U_3970),U_3969),hAPP(hAPP(c_Set_Oinsert(U_3970),U_3968),c_Orderings_Obot__class_Obot(tc_fun(U_3970,tc_HOL_Obool))))))
| U_3973 = c_Orderings_Obot__class_Obot(tc_fun(U_3970,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3970),U_3973))
| ~ c_Finite__Set_Ofolding__one(U_3970,U_3971,U_3972) ),
inference(variable_rename,[status(thm)],[f_1006_1]) ).
fof(f_1006_3,plain,
! [U_3973,U_3972,U_3971,U_3970] :
( hBOOL(hAPP(hAPP(c_member(U_3970),hAPP(U_3972,U_3973)),U_3973))
| ? [U_3968] : ~ hBOOL(hAPP(hAPP(c_member(U_3970),hAPP(hAPP(U_3971,sK70(U_3973,U_3972,U_3971,U_3970)),U_3968)),hAPP(hAPP(c_Set_Oinsert(U_3970),sK70(U_3973,U_3972,U_3971,U_3970)),hAPP(hAPP(c_Set_Oinsert(U_3970),U_3968),c_Orderings_Obot__class_Obot(tc_fun(U_3970,tc_HOL_Obool))))))
| U_3973 = c_Orderings_Obot__class_Obot(tc_fun(U_3970,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3970),U_3973))
| ~ c_Finite__Set_Ofolding__one(U_3970,U_3971,U_3972) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_3969,sK70(U_3973,U_3972,U_3971,U_3970))],[f_1006_2]) ).
fof(f_1006_4,plain,
! [U_3973,U_3972,U_3971,U_3970] :
( hBOOL(hAPP(hAPP(c_member(U_3970),hAPP(U_3972,U_3973)),U_3973))
| ~ hBOOL(hAPP(hAPP(c_member(U_3970),hAPP(hAPP(U_3971,sK70(U_3973,U_3972,U_3971,U_3970)),sK71(U_3973,U_3972,U_3971,U_3970))),hAPP(hAPP(c_Set_Oinsert(U_3970),sK70(U_3973,U_3972,U_3971,U_3970)),hAPP(hAPP(c_Set_Oinsert(U_3970),sK71(U_3973,U_3972,U_3971,U_3970)),c_Orderings_Obot__class_Obot(tc_fun(U_3970,tc_HOL_Obool))))))
| U_3973 = c_Orderings_Obot__class_Obot(tc_fun(U_3970,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3970),U_3973))
| ~ c_Finite__Set_Ofolding__one(U_3970,U_3971,U_3972) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_3968,sK71(U_3973,U_3972,U_3971,U_3970))],[f_1006_3]) ).
cnf(f_1006_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_3970),hAPP(U_3972,U_3973)),U_3973))
| ~ hBOOL(hAPP(hAPP(c_member(U_3970),hAPP(hAPP(U_3971,sK70(U_3973,U_3972,U_3971,U_3970)),sK71(U_3973,U_3972,U_3971,U_3970))),hAPP(hAPP(c_Set_Oinsert(U_3970),sK70(U_3973,U_3972,U_3971,U_3970)),hAPP(hAPP(c_Set_Oinsert(U_3970),sK71(U_3973,U_3972,U_3971,U_3970)),c_Orderings_Obot__class_Obot(tc_fun(U_3970,tc_HOL_Obool))))))
| U_3973 = c_Orderings_Obot__class_Obot(tc_fun(U_3970,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3970),U_3973))
| ~ c_Finite__Set_Ofolding__one(U_3970,U_3971,U_3972) ),
inference(clausify,[status(thm)],[f_1006_4]) ).
fof(f_1007_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_1007_2,plain,
! [U_3975,U_3974] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3974),c_Orderings_Otop__class_Otop(tc_fun(U_3974,tc_HOL_Obool))))
| hAPP(c_Finite__Set_Ocard(U_3975),c_Orderings_Otop__class_Otop(tc_fun(U_3975,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3974,U_3975)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_3974,U_3975),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_1007_1]) ).
cnf(f_1007_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3974),c_Orderings_Otop__class_Otop(tc_fun(U_3974,tc_HOL_Obool))))
| hAPP(c_Finite__Set_Ocard(U_3975),c_Orderings_Otop__class_Otop(tc_fun(U_3975,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_3974,U_3975)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_3974,U_3975),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_1007_2]) ).
fof(f_1008_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_1008_2,plain,
! [U_3981,U_3980,U_3979,U_3978,U_3977] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3978,U_3977),U_3981),U_3980) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3978,U_3977),U_3981),U_3979)
| ? [U_3976] :
( hAPP(U_3981,U_3976) != c_Groups_Ozero__class_Ozero(U_3977)
& hBOOL(hAPP(hAPP(c_member(U_3978),U_3976),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3978,tc_HOL_Obool)),U_3979),U_3980))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3978,tc_HOL_Obool)),U_3980),U_3979))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3978),U_3979))
| ~ class_Groups_Ocomm__monoid__add(U_3977) ),
inference(variable_rename,[status(thm)],[f_1008_1]) ).
fof(f_1008_3,plain,
! [U_3981,U_3980,U_3979,U_3978,U_3977] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3978,U_3977),U_3981),U_3980) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3978,U_3977),U_3981),U_3979)
| ( hAPP(U_3981,sK72(U_3981,U_3980,U_3979,U_3978,U_3977)) != c_Groups_Ozero__class_Ozero(U_3977)
& hBOOL(hAPP(hAPP(c_member(U_3978),sK72(U_3981,U_3980,U_3979,U_3978,U_3977)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3978,tc_HOL_Obool)),U_3979),U_3980))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3978,tc_HOL_Obool)),U_3980),U_3979))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3978),U_3979))
| ~ class_Groups_Ocomm__monoid__add(U_3977) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_3976,sK72(U_3981,U_3980,U_3979,U_3978,U_3977))],[f_1008_2]) ).
cnf(f_1008_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_3978),sK72(U_3981,U_3980,U_3979,U_3978,U_3977)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3978,tc_HOL_Obool)),U_3979),U_3980)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3978,U_3977),U_3981),U_3980) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3978,U_3977),U_3981),U_3979)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3978,tc_HOL_Obool)),U_3980),U_3979))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3978),U_3979))
| ~ class_Groups_Ocomm__monoid__add(U_3977) ),
inference(clausify,[status(thm)],[f_1008_3]) ).
cnf(f_1008_5,plain,
( hAPP(U_3981,sK72(U_3981,U_3980,U_3979,U_3978,U_3977)) != c_Groups_Ozero__class_Ozero(U_3977)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3978,U_3977),U_3981),U_3980) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3978,U_3977),U_3981),U_3979)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3978,tc_HOL_Obool)),U_3980),U_3979))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3978),U_3979))
| ~ class_Groups_Ocomm__monoid__add(U_3977) ),
inference(clausify,[status(thm)],[f_1008_3]) ).
fof(f_1009_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_1009_2,plain,
! [U_3987,U_3986,U_3985,U_3984,U_3983] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3984,U_3983),U_3987),U_3985) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3984,U_3983),U_3987),U_3986)
| ? [U_3982] :
( hAPP(U_3987,U_3982) != c_Groups_Ozero__class_Ozero(U_3983)
& hBOOL(hAPP(hAPP(c_member(U_3984),U_3982),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3984,tc_HOL_Obool)),U_3985),U_3986))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3984,tc_HOL_Obool)),U_3986),U_3985))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3984),U_3985))
| ~ class_Groups_Ocomm__monoid__add(U_3983) ),
inference(variable_rename,[status(thm)],[f_1009_1]) ).
fof(f_1009_3,plain,
! [U_3987,U_3986,U_3985,U_3984,U_3983] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3984,U_3983),U_3987),U_3985) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3984,U_3983),U_3987),U_3986)
| ( hAPP(U_3987,sK73(U_3987,U_3986,U_3985,U_3984,U_3983)) != c_Groups_Ozero__class_Ozero(U_3983)
& hBOOL(hAPP(hAPP(c_member(U_3984),sK73(U_3987,U_3986,U_3985,U_3984,U_3983)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3984,tc_HOL_Obool)),U_3985),U_3986))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3984,tc_HOL_Obool)),U_3986),U_3985))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3984),U_3985))
| ~ class_Groups_Ocomm__monoid__add(U_3983) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_3982,sK73(U_3987,U_3986,U_3985,U_3984,U_3983))],[f_1009_2]) ).
cnf(f_1009_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_3984),sK73(U_3987,U_3986,U_3985,U_3984,U_3983)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3984,tc_HOL_Obool)),U_3985),U_3986)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3984,U_3983),U_3987),U_3985) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3984,U_3983),U_3987),U_3986)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3984,tc_HOL_Obool)),U_3986),U_3985))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3984),U_3985))
| ~ class_Groups_Ocomm__monoid__add(U_3983) ),
inference(clausify,[status(thm)],[f_1009_3]) ).
cnf(f_1009_5,plain,
( hAPP(U_3987,sK73(U_3987,U_3986,U_3985,U_3984,U_3983)) != c_Groups_Ozero__class_Ozero(U_3983)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3984,U_3983),U_3987),U_3985) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3984,U_3983),U_3987),U_3986)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3984,tc_HOL_Obool)),U_3986),U_3985))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3984),U_3985))
| ~ class_Groups_Ocomm__monoid__add(U_3983) ),
inference(clausify,[status(thm)],[f_1009_3]) ).
fof(f_1010_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_1010_2,plain,
! [U_3988] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_3988)) = U_3988,
inference(variable_rename,[status(thm)],[f_1010_1]) ).
cnf(f_1010_3,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_3988)) = U_3988,
inference(clausify,[status(thm)],[f_1010_2]) ).
fof(f_1011_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_1011_2,plain,
! [U_3990,U_3989] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3989),c_Big__Operators_Olattice__class_OInf__fin(U_3989,U_3990)),c_Big__Operators_Olattice__class_OSup__fin(U_3989,U_3990)))
| U_3990 = c_Orderings_Obot__class_Obot(tc_fun(U_3989,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3989),U_3990))
| ~ class_Lattices_Olattice(U_3989) ),
inference(variable_rename,[status(thm)],[f_1011_1]) ).
cnf(f_1011_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3989),c_Big__Operators_Olattice__class_OInf__fin(U_3989,U_3990)),c_Big__Operators_Olattice__class_OSup__fin(U_3989,U_3990)))
| U_3990 = c_Orderings_Obot__class_Obot(tc_fun(U_3989,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3989),U_3990))
| ~ class_Lattices_Olattice(U_3989) ),
inference(clausify,[status(thm)],[f_1011_2]) ).
fof(f_1012_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_1012_2,plain,
! [U_3991] : hAPP(c_Finite__Set_Ocard(U_3991),c_Orderings_Obot__class_Obot(tc_fun(U_3991,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1012_1]) ).
cnf(f_1012_3,plain,
hAPP(c_Finite__Set_Ocard(U_3991),c_Orderings_Obot__class_Obot(tc_fun(U_3991,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1012_2]) ).
fof(f_1013_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_1013_2,plain,
! [U_3993,U_3992] :
( hAPP(c_Finite__Set_Ocard(U_3992),U_3993) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3992),U_3993)) ),
inference(variable_rename,[status(thm)],[f_1013_1]) ).
cnf(f_1013_3,plain,
( hAPP(c_Finite__Set_Ocard(U_3992),U_3993) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3992),U_3993)) ),
inference(clausify,[status(thm)],[f_1013_2]) ).
fof(f_1014_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_1014_2,plain,
! [U_3995,U_3994] :
( U_3995 = c_Orderings_Otop__class_Otop(tc_fun(U_3994,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_3994),U_3995) != hAPP(c_Finite__Set_Ocard(U_3994),c_Orderings_Otop__class_Otop(tc_fun(U_3994,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3994),c_Orderings_Otop__class_Otop(tc_fun(U_3994,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_1014_1]) ).
cnf(f_1014_3,plain,
( U_3995 = c_Orderings_Otop__class_Otop(tc_fun(U_3994,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_3994),U_3995) != hAPP(c_Finite__Set_Ocard(U_3994),c_Orderings_Otop__class_Otop(tc_fun(U_3994,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3994),c_Orderings_Otop__class_Otop(tc_fun(U_3994,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_1014_2]) ).
fof(f_1015_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_1015_2,plain,
! [U_3999,U_3998,U_3997,U_3996] :
( hAPP(c_Finite__Set_Ocard(U_3997),hAPP(c_Set_Oimage(U_3996,U_3997,U_3998),U_3999)) = hAPP(c_Finite__Set_Ocard(U_3996),U_3999)
| ~ c_Fun_Oinj__on(U_3996,U_3997,U_3998,U_3999) ),
inference(variable_rename,[status(thm)],[f_1015_1]) ).
cnf(f_1015_3,plain,
( hAPP(c_Finite__Set_Ocard(U_3997),hAPP(c_Set_Oimage(U_3996,U_3997,U_3998),U_3999)) = hAPP(c_Finite__Set_Ocard(U_3996),U_3999)
| ~ c_Fun_Oinj__on(U_3996,U_3997,U_3998,U_3999) ),
inference(clausify,[status(thm)],[f_1015_2]) ).
fof(f_1016_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_1016_2,plain,
! [U_4001,U_4000] :
( U_4000 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4001),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4001),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_4000)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_4000),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4001),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4001),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_4000))))) ),
inference(variable_rename,[status(thm)],[f_1016_1]) ).
cnf(f_1016_3,plain,
( U_4000 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4001),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4001),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_4000)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_4000),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4001),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4001),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_4000))))) ),
inference(clausify,[status(thm)],[f_1016_2]) ).
fof(f_1017_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_1017_2,plain,
! [U_4003,U_4002] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4002),U_4003)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4003),U_4002),
inference(variable_rename,[status(thm)],[f_1017_1]) ).
cnf(f_1017_3,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4002),U_4003)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4003),U_4002),
inference(clausify,[status(thm)],[f_1017_2]) ).
fof(f_1018_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_1018_2,plain,
! [U_4004] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_4004)) = hAPP(c_Nat_OSuc,U_4004),
inference(variable_rename,[status(thm)],[f_1018_1]) ).
cnf(f_1018_3,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_4004)) = hAPP(c_Nat_OSuc,U_4004),
inference(clausify,[status(thm)],[f_1018_2]) ).
fof(f_1019_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_1019_2,plain,
! [U_4006,U_4005] :
( c_Big__Operators_Olattice__class_OInf__fin(U_4005,hAPP(hAPP(c_Set_Oinsert(U_4005),U_4006),c_Orderings_Obot__class_Obot(tc_fun(U_4005,tc_HOL_Obool)))) = U_4006
| ~ class_Lattices_Olattice(U_4005) ),
inference(variable_rename,[status(thm)],[f_1019_1]) ).
cnf(f_1019_3,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_4005,hAPP(hAPP(c_Set_Oinsert(U_4005),U_4006),c_Orderings_Obot__class_Obot(tc_fun(U_4005,tc_HOL_Obool)))) = U_4006
| ~ class_Lattices_Olattice(U_4005) ),
inference(clausify,[status(thm)],[f_1019_2]) ).
fof(f_1020_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_1020_2,plain,
! [U_4008,U_4007] :
( c_Big__Operators_Olattice__class_OSup__fin(U_4007,hAPP(hAPP(c_Set_Oinsert(U_4007),U_4008),c_Orderings_Obot__class_Obot(tc_fun(U_4007,tc_HOL_Obool)))) = U_4008
| ~ class_Lattices_Olattice(U_4007) ),
inference(variable_rename,[status(thm)],[f_1020_1]) ).
cnf(f_1020_3,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_4007,hAPP(hAPP(c_Set_Oinsert(U_4007),U_4008),c_Orderings_Obot__class_Obot(tc_fun(U_4007,tc_HOL_Obool)))) = U_4008
| ~ class_Lattices_Olattice(U_4007) ),
inference(clausify,[status(thm)],[f_1020_2]) ).
fof(f_1021_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_1021_2,plain,
! [U_4010,U_4009] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_4009,U_4010)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4010),U_4009),
inference(variable_rename,[status(thm)],[f_1021_1]) ).
cnf(f_1021_3,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_4009,U_4010)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4010),U_4009),
inference(clausify,[status(thm)],[f_1021_2]) ).
fof(f_1022_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_1022_2,plain,
! [U_4012,U_4011] :
( ( hAPP(c_Finite__Set_Ocard(U_4011),U_4012) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4011),U_4012))
& U_4012 != c_Orderings_Obot__class_Obot(tc_fun(U_4011,tc_HOL_Obool)) ) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4011),U_4012))
| U_4012 = c_Orderings_Obot__class_Obot(tc_fun(U_4011,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_4011),U_4012) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1022_1]) ).
fof(f_1022_3,plain,
( ! [U_4016,U_4014] :
( hAPP(c_Finite__Set_Ocard(U_4014),U_4016) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4014),U_4016))
& U_4016 != c_Orderings_Obot__class_Obot(tc_fun(U_4014,tc_HOL_Obool)) ) )
& ! [U_4015,U_4013] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4013),U_4015))
| U_4015 = c_Orderings_Obot__class_Obot(tc_fun(U_4013,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_4013),U_4015) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1022_2]) ).
cnf(f_1022_4,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4013),U_4015))
| U_4015 = c_Orderings_Obot__class_Obot(tc_fun(U_4013,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_4013),U_4015) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1022_3]) ).
cnf(f_1022_5,plain,
( U_4016 != c_Orderings_Obot__class_Obot(tc_fun(U_4014,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_4014),U_4016) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1022_3]) ).
cnf(f_1022_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4014),U_4016))
| hAPP(c_Finite__Set_Ocard(U_4014),U_4016) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1022_3]) ).
fof(f_1023_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_1023_2,plain,
! [U_4018,U_4017] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4017),U_4018))
| ~ 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_4017),U_4018))) ),
inference(variable_rename,[status(thm)],[f_1023_1]) ).
cnf(f_1023_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4017),U_4018))
| ~ 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_4017),U_4018))) ),
inference(clausify,[status(thm)],[f_1023_2]) ).
fof(f_1024_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_1024_2,plain,
! [U_4021,U_4020,U_4019] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4019),U_4020)),hAPP(c_Finite__Set_Ocard(U_4019),hAPP(hAPP(c_Set_Oinsert(U_4019),U_4021),U_4020))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4019),U_4020)) ),
inference(variable_rename,[status(thm)],[f_1024_1]) ).
cnf(f_1024_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4019),U_4020)),hAPP(c_Finite__Set_Ocard(U_4019),hAPP(hAPP(c_Set_Oinsert(U_4019),U_4021),U_4020))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4019),U_4020)) ),
inference(clausify,[status(thm)],[f_1024_2]) ).
fof(f_1025_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_1025_2,plain,
! [U_4024,U_4023,U_4022] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4022),U_4024)),hAPP(c_Finite__Set_Ocard(U_4022),U_4023)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4022,tc_HOL_Obool)),U_4024),U_4023))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4022),U_4023)) ),
inference(variable_rename,[status(thm)],[f_1025_1]) ).
cnf(f_1025_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4022),U_4024)),hAPP(c_Finite__Set_Ocard(U_4022),U_4023)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4022,tc_HOL_Obool)),U_4024),U_4023))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4022),U_4023)) ),
inference(clausify,[status(thm)],[f_1025_2]) ).
fof(f_1026_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_1026_2,plain,
! [U_4027,U_4026,U_4025] :
( U_4027 = U_4026
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4025),U_4026)),hAPP(c_Finite__Set_Ocard(U_4025),U_4027)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4025,tc_HOL_Obool)),U_4027),U_4026))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4025),U_4026)) ),
inference(variable_rename,[status(thm)],[f_1026_1]) ).
cnf(f_1026_3,plain,
( U_4027 = U_4026
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4025),U_4026)),hAPP(c_Finite__Set_Ocard(U_4025),U_4027)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4025,tc_HOL_Obool)),U_4027),U_4026))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4025),U_4026)) ),
inference(clausify,[status(thm)],[f_1026_2]) ).
fof(f_1027_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_1027_2,plain,
! [U_4031,U_4030,U_4029,U_4028] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4030),hAPP(c_Set_Oimage(U_4028,U_4030,U_4031),U_4029))),hAPP(c_Finite__Set_Ocard(U_4028),U_4029)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4028),U_4029)) ),
inference(variable_rename,[status(thm)],[f_1027_1]) ).
cnf(f_1027_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4030),hAPP(c_Set_Oimage(U_4028,U_4030,U_4031),U_4029))),hAPP(c_Finite__Set_Ocard(U_4028),U_4029)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4028),U_4029)) ),
inference(clausify,[status(thm)],[f_1027_2]) ).
fof(f_1028_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_1028_2,plain,
! [U_4035,U_4034,U_4033,U_4032] :
( ( ( c_Fun_Oinj__on(U_4032,U_4034,U_4035,U_4033)
| hAPP(c_Finite__Set_Ocard(U_4034),hAPP(c_Set_Oimage(U_4032,U_4034,U_4035),U_4033)) != hAPP(c_Finite__Set_Ocard(U_4032),U_4033) )
& ( hAPP(c_Finite__Set_Ocard(U_4034),hAPP(c_Set_Oimage(U_4032,U_4034,U_4035),U_4033)) = hAPP(c_Finite__Set_Ocard(U_4032),U_4033)
| ~ c_Fun_Oinj__on(U_4032,U_4034,U_4035,U_4033) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4032),U_4033)) ),
inference(variable_rename,[status(thm)],[f_1028_1]) ).
cnf(f_1028_3,plain,
( hAPP(c_Finite__Set_Ocard(U_4034),hAPP(c_Set_Oimage(U_4032,U_4034,U_4035),U_4033)) = hAPP(c_Finite__Set_Ocard(U_4032),U_4033)
| ~ c_Fun_Oinj__on(U_4032,U_4034,U_4035,U_4033)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4032),U_4033)) ),
inference(clausify,[status(thm)],[f_1028_2]) ).
cnf(f_1028_4,plain,
( c_Fun_Oinj__on(U_4032,U_4034,U_4035,U_4033)
| hAPP(c_Finite__Set_Ocard(U_4034),hAPP(c_Set_Oimage(U_4032,U_4034,U_4035),U_4033)) != hAPP(c_Finite__Set_Ocard(U_4032),U_4033)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4032),U_4033)) ),
inference(clausify,[status(thm)],[f_1028_2]) ).
fof(f_1029_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_1029_2,plain,
! [U_4039,U_4038,U_4037,U_4036] :
( c_Fun_Oinj__on(U_4036,U_4038,U_4039,U_4037)
| hAPP(c_Finite__Set_Ocard(U_4038),hAPP(c_Set_Oimage(U_4036,U_4038,U_4039),U_4037)) != hAPP(c_Finite__Set_Ocard(U_4036),U_4037)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4036),U_4037)) ),
inference(variable_rename,[status(thm)],[f_1029_1]) ).
cnf(f_1029_3,plain,
( c_Fun_Oinj__on(U_4036,U_4038,U_4039,U_4037)
| hAPP(c_Finite__Set_Ocard(U_4038),hAPP(c_Set_Oimage(U_4036,U_4038,U_4039),U_4037)) != hAPP(c_Finite__Set_Ocard(U_4036),U_4037)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4036),U_4037)) ),
inference(clausify,[status(thm)],[f_1029_2]) ).
fof(f_1030_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_1030_2,plain,
! [U_4043,U_4042,U_4041,U_4040] :
( ~ c_Fun_Oinj__on(U_4041,U_4040,U_4042,U_4043)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4040),hAPP(c_Set_Oimage(U_4041,U_4040,U_4042),U_4043))),hAPP(c_Finite__Set_Ocard(U_4041),U_4043))) ),
inference(variable_rename,[status(thm)],[f_1030_1]) ).
cnf(f_1030_3,plain,
( ~ c_Fun_Oinj__on(U_4041,U_4040,U_4042,U_4043)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4040),hAPP(c_Set_Oimage(U_4041,U_4040,U_4042),U_4043))),hAPP(c_Finite__Set_Ocard(U_4041),U_4043))) ),
inference(clausify,[status(thm)],[f_1030_2]) ).
fof(f_1031_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_1031_2,plain,
! [U_4046,U_4045,U_4044] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4044),U_4046)),hAPP(c_Finite__Set_Ocard(U_4044),U_4045)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4044,tc_HOL_Obool)),U_4046),U_4045))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4044),U_4045)) ),
inference(variable_rename,[status(thm)],[f_1031_1]) ).
cnf(f_1031_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4044),U_4046)),hAPP(c_Finite__Set_Ocard(U_4044),U_4045)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4044,tc_HOL_Obool)),U_4046),U_4045))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4044),U_4045)) ),
inference(clausify,[status(thm)],[f_1031_2]) ).
fof(f_1032_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_1032_2,plain,
! [U_4048,U_4047] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4047,U_4048)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4048)),U_4047),
inference(variable_rename,[status(thm)],[f_1032_1]) ).
cnf(f_1032_3,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4047,U_4048)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4048)),U_4047),
inference(clausify,[status(thm)],[f_1032_2]) ).
fof(f_1033_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_1033_2,plain,
! [U_4051,U_4050,U_4049] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4049),U_4051),c_Big__Operators_Olattice__class_OInf__fin(U_4049,U_4050)) = U_4051
| ~ hBOOL(hAPP(hAPP(c_member(U_4049),U_4051),U_4050))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4049),U_4050))
| ~ class_Lattices_Olattice(U_4049) ),
inference(variable_rename,[status(thm)],[f_1033_1]) ).
cnf(f_1033_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4049),U_4051),c_Big__Operators_Olattice__class_OInf__fin(U_4049,U_4050)) = U_4051
| ~ hBOOL(hAPP(hAPP(c_member(U_4049),U_4051),U_4050))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4049),U_4050))
| ~ class_Lattices_Olattice(U_4049) ),
inference(clausify,[status(thm)],[f_1033_2]) ).
fof(f_1034_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_1034_2,plain,
! [U_4054,U_4053,U_4052] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4052),U_4054),c_Big__Operators_Olattice__class_OSup__fin(U_4052,U_4053)) = c_Big__Operators_Olattice__class_OSup__fin(U_4052,U_4053)
| ~ hBOOL(hAPP(hAPP(c_member(U_4052),U_4054),U_4053))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4052),U_4053))
| ~ class_Lattices_Olattice(U_4052) ),
inference(variable_rename,[status(thm)],[f_1034_1]) ).
cnf(f_1034_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4052),U_4054),c_Big__Operators_Olattice__class_OSup__fin(U_4052,U_4053)) = c_Big__Operators_Olattice__class_OSup__fin(U_4052,U_4053)
| ~ hBOOL(hAPP(hAPP(c_member(U_4052),U_4054),U_4053))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4052),U_4053))
| ~ class_Lattices_Olattice(U_4052) ),
inference(clausify,[status(thm)],[f_1034_2]) ).
fof(f_1035_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_1035_2,plain,
! [U_4057,U_4056,U_4055] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4055),U_4057),c_Big__Operators_Olattice__class_OSup__fin(U_4055,U_4056)) = U_4057
| ~ hBOOL(hAPP(hAPP(c_member(U_4055),U_4057),U_4056))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4055),U_4056))
| ~ class_Lattices_Olattice(U_4055) ),
inference(variable_rename,[status(thm)],[f_1035_1]) ).
cnf(f_1035_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4055),U_4057),c_Big__Operators_Olattice__class_OSup__fin(U_4055,U_4056)) = U_4057
| ~ hBOOL(hAPP(hAPP(c_member(U_4055),U_4057),U_4056))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4055),U_4056))
| ~ class_Lattices_Olattice(U_4055) ),
inference(clausify,[status(thm)],[f_1035_2]) ).
fof(f_1036_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_1036_2,plain,
! [U_4060,U_4059,U_4058] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4058),U_4060),c_Big__Operators_Olattice__class_OInf__fin(U_4058,U_4059)) = c_Big__Operators_Olattice__class_OInf__fin(U_4058,U_4059)
| ~ hBOOL(hAPP(hAPP(c_member(U_4058),U_4060),U_4059))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4058),U_4059))
| ~ class_Lattices_Olattice(U_4058) ),
inference(variable_rename,[status(thm)],[f_1036_1]) ).
cnf(f_1036_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4058),U_4060),c_Big__Operators_Olattice__class_OInf__fin(U_4058,U_4059)) = c_Big__Operators_Olattice__class_OInf__fin(U_4058,U_4059)
| ~ hBOOL(hAPP(hAPP(c_member(U_4058),U_4060),U_4059))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4058),U_4059))
| ~ class_Lattices_Olattice(U_4058) ),
inference(clausify,[status(thm)],[f_1036_2]) ).
fof(f_1037_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_1037_2,plain,
! [U_4062,U_4061] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_4061,U_4062)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4062),hAPP(c_Nat_OSuc,U_4061)),
inference(variable_rename,[status(thm)],[f_1037_1]) ).
cnf(f_1037_3,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_4061,U_4062)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4062),hAPP(c_Nat_OSuc,U_4061)),
inference(clausify,[status(thm)],[f_1037_2]) ).
fof(f_1038_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_1038_2,plain,
! [U_4064,U_4063] :
( c_Big__Operators_Olattice__class_OSup__fin(U_4063,U_4064) = c_Complete__Lattice_OSup__class_OSup(U_4063,U_4064)
| U_4064 = c_Orderings_Obot__class_Obot(tc_fun(U_4063,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4063),U_4064))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4063) ),
inference(variable_rename,[status(thm)],[f_1038_1]) ).
cnf(f_1038_3,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_4063,U_4064) = c_Complete__Lattice_OSup__class_OSup(U_4063,U_4064)
| U_4064 = c_Orderings_Obot__class_Obot(tc_fun(U_4063,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4063),U_4064))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4063) ),
inference(clausify,[status(thm)],[f_1038_2]) ).
fof(f_1039_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_1039_2,plain,
! [U_4066,U_4065] :
( c_Big__Operators_Olattice__class_OInf__fin(U_4065,U_4066) = c_Complete__Lattice_OInf__class_OInf(U_4065,U_4066)
| U_4066 = c_Orderings_Obot__class_Obot(tc_fun(U_4065,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4065),U_4066))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4065) ),
inference(variable_rename,[status(thm)],[f_1039_1]) ).
cnf(f_1039_3,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_4065,U_4066) = c_Complete__Lattice_OInf__class_OInf(U_4065,U_4066)
| U_4066 = c_Orderings_Obot__class_Obot(tc_fun(U_4065,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4065),U_4066))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4065) ),
inference(clausify,[status(thm)],[f_1039_2]) ).
fof(f_1040_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_1040_2,plain,
! [U_4069,U_4068,U_4067] :
( ( ( hAPP(c_Finite__Set_Ocard(U_4067),hAPP(hAPP(c_Set_Oinsert(U_4067),U_4069),U_4068)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4067),U_4068))
| hBOOL(hAPP(hAPP(c_member(U_4067),U_4069),U_4068)) )
& ( hAPP(c_Finite__Set_Ocard(U_4067),hAPP(hAPP(c_Set_Oinsert(U_4067),U_4069),U_4068)) = hAPP(c_Finite__Set_Ocard(U_4067),U_4068)
| ~ hBOOL(hAPP(hAPP(c_member(U_4067),U_4069),U_4068)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4067),U_4068)) ),
inference(variable_rename,[status(thm)],[f_1040_1]) ).
cnf(f_1040_3,plain,
( hAPP(c_Finite__Set_Ocard(U_4067),hAPP(hAPP(c_Set_Oinsert(U_4067),U_4069),U_4068)) = hAPP(c_Finite__Set_Ocard(U_4067),U_4068)
| ~ hBOOL(hAPP(hAPP(c_member(U_4067),U_4069),U_4068))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4067),U_4068)) ),
inference(clausify,[status(thm)],[f_1040_2]) ).
cnf(f_1040_4,plain,
( hAPP(c_Finite__Set_Ocard(U_4067),hAPP(hAPP(c_Set_Oinsert(U_4067),U_4069),U_4068)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4067),U_4068))
| hBOOL(hAPP(hAPP(c_member(U_4067),U_4069),U_4068))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4067),U_4068)) ),
inference(clausify,[status(thm)],[f_1040_2]) ).
fof(f_1041_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_1041_2,plain,
! [U_4072,U_4071,U_4070] :
( hAPP(c_Finite__Set_Ocard(U_4070),hAPP(hAPP(c_Set_Oinsert(U_4070),U_4072),U_4071)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4070),U_4071))
| hBOOL(hAPP(hAPP(c_member(U_4070),U_4072),U_4071))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4070),U_4071)) ),
inference(variable_rename,[status(thm)],[f_1041_1]) ).
cnf(f_1041_3,plain,
( hAPP(c_Finite__Set_Ocard(U_4070),hAPP(hAPP(c_Set_Oinsert(U_4070),U_4072),U_4071)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4070),U_4071))
| hBOOL(hAPP(hAPP(c_member(U_4070),U_4072),U_4071))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4070),U_4071)) ),
inference(clausify,[status(thm)],[f_1041_2]) ).
fof(f_1042_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_1042_2,plain,
! [U_4074,U_4073] :
( ( 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_4073),U_4074)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4073),U_4074))
| U_4074 = c_Orderings_Obot__class_Obot(tc_fun(U_4073,tc_HOL_Obool)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4073),U_4074))
& U_4074 != c_Orderings_Obot__class_Obot(tc_fun(U_4073,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_4073),U_4074))) ) ),
inference(variable_rename,[status(thm)],[f_1042_1]) ).
fof(f_1042_3,plain,
( ! [U_4078,U_4076] :
( 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_4076),U_4078)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4076),U_4078))
| U_4078 = c_Orderings_Obot__class_Obot(tc_fun(U_4076,tc_HOL_Obool)) )
& ! [U_4077,U_4075] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4075),U_4077))
& U_4077 != c_Orderings_Obot__class_Obot(tc_fun(U_4075,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_4075),U_4077))) ) ),
inference(miniscope,[status(thm)],[f_1042_2]) ).
cnf(f_1042_4,plain,
( U_4077 != c_Orderings_Obot__class_Obot(tc_fun(U_4075,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_4075),U_4077))) ),
inference(clausify,[status(thm)],[f_1042_3]) ).
cnf(f_1042_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4075),U_4077))
| ~ 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_4075),U_4077))) ),
inference(clausify,[status(thm)],[f_1042_3]) ).
cnf(f_1042_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_4076),U_4078)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4076),U_4078))
| U_4078 = c_Orderings_Obot__class_Obot(tc_fun(U_4076,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1042_3]) ).
fof(f_1043_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_1043_2,plain,
! [U_4079] :
( 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_4079),c_Orderings_Otop__class_Otop(tc_fun(U_4079,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4079),c_Orderings_Otop__class_Otop(tc_fun(U_4079,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_1043_1]) ).
cnf(f_1043_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_4079),c_Orderings_Otop__class_Otop(tc_fun(U_4079,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4079),c_Orderings_Otop__class_Otop(tc_fun(U_4079,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_1043_2]) ).
fof(f_1044_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_1044_2,plain,
! [U_4082,U_4081,U_4080] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4080),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4080,tc_HOL_Obool)),U_4081),U_4082))),hAPP(c_Finite__Set_Ocard(U_4080),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4080,tc_HOL_Obool)),U_4081),U_4082))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4080),U_4081)),hAPP(c_Finite__Set_Ocard(U_4080),U_4082))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4080),U_4082))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4080),U_4081)) ),
inference(variable_rename,[status(thm)],[f_1044_1]) ).
cnf(f_1044_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4080),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4080,tc_HOL_Obool)),U_4081),U_4082))),hAPP(c_Finite__Set_Ocard(U_4080),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4080,tc_HOL_Obool)),U_4081),U_4082))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4080),U_4081)),hAPP(c_Finite__Set_Ocard(U_4080),U_4082))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4080),U_4082))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4080),U_4081)) ),
inference(clausify,[status(thm)],[f_1044_2]) ).
fof(f_1045_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_1045_2,plain,
! [U_4085,U_4084,U_4083] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4083),U_4084)),hAPP(c_Finite__Set_Ocard(U_4083),U_4085)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4083),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4083,tc_HOL_Obool)),U_4084),U_4085))),hAPP(c_Finite__Set_Ocard(U_4083),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4083,tc_HOL_Obool)),U_4084),U_4085)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4083),U_4085))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4083),U_4084)) ),
inference(variable_rename,[status(thm)],[f_1045_1]) ).
cnf(f_1045_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4083),U_4084)),hAPP(c_Finite__Set_Ocard(U_4083),U_4085)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4083),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4083,tc_HOL_Obool)),U_4084),U_4085))),hAPP(c_Finite__Set_Ocard(U_4083),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4083,tc_HOL_Obool)),U_4084),U_4085)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4083),U_4085))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4083),U_4084)) ),
inference(clausify,[status(thm)],[f_1045_2]) ).
fof(f_1046_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_1046_2,plain,
! [U_4091,U_4090,U_4089,U_4088,U_4087,U_4086] :
( hAPP(c_Finite__Set_Ocard(U_4086),U_4089) = hAPP(c_Finite__Set_Ocard(U_4087),U_4090)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4087),U_4090))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4086),U_4089))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4086,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4087,U_4086,U_4091),U_4090)),U_4089))
| ~ c_Fun_Oinj__on(U_4087,U_4086,U_4091,U_4090)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4087,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4086,U_4087,U_4088),U_4089)),U_4090))
| ~ c_Fun_Oinj__on(U_4086,U_4087,U_4088,U_4089) ),
inference(variable_rename,[status(thm)],[f_1046_1]) ).
cnf(f_1046_3,plain,
( hAPP(c_Finite__Set_Ocard(U_4086),U_4089) = hAPP(c_Finite__Set_Ocard(U_4087),U_4090)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4087),U_4090))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4086),U_4089))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4086,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4087,U_4086,U_4091),U_4090)),U_4089))
| ~ c_Fun_Oinj__on(U_4087,U_4086,U_4091,U_4090)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4087,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4086,U_4087,U_4088),U_4089)),U_4090))
| ~ c_Fun_Oinj__on(U_4086,U_4087,U_4088,U_4089) ),
inference(clausify,[status(thm)],[f_1046_2]) ).
fof(f_1047_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_1047_2,plain,
! [U_4094,U_4093,U_4092] :
( hAPP(c_Finite__Set_Ocard(U_4092),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4092,tc_HOL_Obool)),U_4094),U_4093)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4092),U_4094)),hAPP(c_Finite__Set_Ocard(U_4092),U_4093))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4092,tc_HOL_Obool)),U_4093),U_4094))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4092),U_4093)) ),
inference(variable_rename,[status(thm)],[f_1047_1]) ).
cnf(f_1047_3,plain,
( hAPP(c_Finite__Set_Ocard(U_4092),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4092,tc_HOL_Obool)),U_4094),U_4093)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4092),U_4094)),hAPP(c_Finite__Set_Ocard(U_4092),U_4093))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4092,tc_HOL_Obool)),U_4093),U_4094))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4092),U_4093)) ),
inference(clausify,[status(thm)],[f_1047_2]) ).
fof(f_1048_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_1048_2,plain,
! [U_4097,U_4096,U_4095] :
( hAPP(c_Finite__Set_Ocard(U_4095),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4095,tc_HOL_Obool)),U_4096),U_4097)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4095),U_4096)),hAPP(c_Finite__Set_Ocard(U_4095),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4095,tc_HOL_Obool)),U_4096),U_4097)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4095),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4095,tc_HOL_Obool)),U_4096),U_4097))) ),
inference(variable_rename,[status(thm)],[f_1048_1]) ).
cnf(f_1048_3,plain,
( hAPP(c_Finite__Set_Ocard(U_4095),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4095,tc_HOL_Obool)),U_4096),U_4097)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4095),U_4096)),hAPP(c_Finite__Set_Ocard(U_4095),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4095,tc_HOL_Obool)),U_4096),U_4097)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4095),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4095,tc_HOL_Obool)),U_4096),U_4097))) ),
inference(clausify,[status(thm)],[f_1048_2]) ).
fof(f_1049_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_1049_2,plain,
! [U_4100,U_4099,U_4098] :
( 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_4098),U_4100)),hAPP(c_Finite__Set_Ocard(U_4098),U_4099))),hAPP(c_Finite__Set_Ocard(U_4098),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4098,tc_HOL_Obool)),U_4100),U_4099))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4098),U_4099)) ),
inference(variable_rename,[status(thm)],[f_1049_1]) ).
cnf(f_1049_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_4098),U_4100)),hAPP(c_Finite__Set_Ocard(U_4098),U_4099))),hAPP(c_Finite__Set_Ocard(U_4098),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4098,tc_HOL_Obool)),U_4100),U_4099))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4098),U_4099)) ),
inference(clausify,[status(thm)],[f_1049_2]) ).
fof(f_1050_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_1050_2,plain,
! [U_4103,U_4102,U_4101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4101,tc_HOL_Obool)),U_4103),U_4102))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4101),U_4103)),hAPP(c_Finite__Set_Ocard(U_4101),U_4102)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4101,tc_HOL_Obool)),U_4103),U_4102))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4101),U_4102)) ),
inference(variable_rename,[status(thm)],[f_1050_1]) ).
cnf(f_1050_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4101,tc_HOL_Obool)),U_4103),U_4102))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4101),U_4103)),hAPP(c_Finite__Set_Ocard(U_4101),U_4102)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4101,tc_HOL_Obool)),U_4103),U_4102))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4101),U_4102)) ),
inference(clausify,[status(thm)],[f_1050_2]) ).
fof(f_1051_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_1051_2,plain,
! [U_4106,U_4105,U_4104] :
( c_Big__Operators_Olattice__class_OSup__fin(U_4104,hAPP(hAPP(c_Set_Oinsert(U_4104),U_4106),U_4105)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4104),U_4106),c_Big__Operators_Olattice__class_OSup__fin(U_4104,U_4105))
| U_4105 = c_Orderings_Obot__class_Obot(tc_fun(U_4104,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4104),U_4105))
| ~ class_Lattices_Olattice(U_4104) ),
inference(variable_rename,[status(thm)],[f_1051_1]) ).
cnf(f_1051_3,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_4104,hAPP(hAPP(c_Set_Oinsert(U_4104),U_4106),U_4105)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4104),U_4106),c_Big__Operators_Olattice__class_OSup__fin(U_4104,U_4105))
| U_4105 = c_Orderings_Obot__class_Obot(tc_fun(U_4104,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4104),U_4105))
| ~ class_Lattices_Olattice(U_4104) ),
inference(clausify,[status(thm)],[f_1051_2]) ).
fof(f_1052_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_1052_2,plain,
! [U_4109,U_4108,U_4107] :
( c_Big__Operators_Olattice__class_OInf__fin(U_4107,hAPP(hAPP(c_Set_Oinsert(U_4107),U_4109),U_4108)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4107),U_4109),c_Big__Operators_Olattice__class_OInf__fin(U_4107,U_4108))
| U_4108 = c_Orderings_Obot__class_Obot(tc_fun(U_4107,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4107),U_4108))
| ~ class_Lattices_Olattice(U_4107) ),
inference(variable_rename,[status(thm)],[f_1052_1]) ).
cnf(f_1052_3,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_4107,hAPP(hAPP(c_Set_Oinsert(U_4107),U_4109),U_4108)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4107),U_4109),c_Big__Operators_Olattice__class_OInf__fin(U_4107,U_4108))
| U_4108 = c_Orderings_Obot__class_Obot(tc_fun(U_4107,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4107),U_4108))
| ~ class_Lattices_Olattice(U_4107) ),
inference(clausify,[status(thm)],[f_1052_2]) ).
fof(f_1053_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_1053_2,plain,
! [U_4112,U_4111,U_4110] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4110),c_Big__Operators_Olattice__class_OSup__fin(U_4110,U_4112)),c_Big__Operators_Olattice__class_OSup__fin(U_4110,U_4111)) = c_Big__Operators_Olattice__class_OSup__fin(U_4110,U_4111)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4110,tc_HOL_Obool)),U_4112),U_4111))
| U_4112 = c_Orderings_Obot__class_Obot(tc_fun(U_4110,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4110),U_4111))
| ~ class_Lattices_Olattice(U_4110) ),
inference(variable_rename,[status(thm)],[f_1053_1]) ).
cnf(f_1053_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4110),c_Big__Operators_Olattice__class_OSup__fin(U_4110,U_4112)),c_Big__Operators_Olattice__class_OSup__fin(U_4110,U_4111)) = c_Big__Operators_Olattice__class_OSup__fin(U_4110,U_4111)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4110,tc_HOL_Obool)),U_4112),U_4111))
| U_4112 = c_Orderings_Obot__class_Obot(tc_fun(U_4110,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4110),U_4111))
| ~ class_Lattices_Olattice(U_4110) ),
inference(clausify,[status(thm)],[f_1053_2]) ).
fof(f_1054_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_1054_2,plain,
! [U_4115,U_4114,U_4113] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4113),c_Big__Operators_Olattice__class_OInf__fin(U_4113,U_4115)),c_Big__Operators_Olattice__class_OInf__fin(U_4113,U_4114)) = c_Big__Operators_Olattice__class_OInf__fin(U_4113,U_4114)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4113,tc_HOL_Obool)),U_4115),U_4114))
| U_4115 = c_Orderings_Obot__class_Obot(tc_fun(U_4113,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4113),U_4114))
| ~ class_Lattices_Olattice(U_4113) ),
inference(variable_rename,[status(thm)],[f_1054_1]) ).
cnf(f_1054_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4113),c_Big__Operators_Olattice__class_OInf__fin(U_4113,U_4115)),c_Big__Operators_Olattice__class_OInf__fin(U_4113,U_4114)) = c_Big__Operators_Olattice__class_OInf__fin(U_4113,U_4114)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4113,tc_HOL_Obool)),U_4115),U_4114))
| U_4115 = c_Orderings_Obot__class_Obot(tc_fun(U_4113,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4113),U_4114))
| ~ class_Lattices_Olattice(U_4113) ),
inference(clausify,[status(thm)],[f_1054_2]) ).
fof(f_1055_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_1055_2,plain,
! [U_4118,U_4117,U_4116] :
( c_Big__Operators_Olattice__class_OSup__fin(U_4116,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4116,tc_HOL_Obool)),U_4117),U_4118)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4116),c_Big__Operators_Olattice__class_OSup__fin(U_4116,U_4117)),c_Big__Operators_Olattice__class_OSup__fin(U_4116,U_4118))
| U_4118 = c_Orderings_Obot__class_Obot(tc_fun(U_4116,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4116),U_4118))
| U_4117 = c_Orderings_Obot__class_Obot(tc_fun(U_4116,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4116),U_4117))
| ~ class_Lattices_Olattice(U_4116) ),
inference(variable_rename,[status(thm)],[f_1055_1]) ).
cnf(f_1055_3,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_4116,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4116,tc_HOL_Obool)),U_4117),U_4118)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4116),c_Big__Operators_Olattice__class_OSup__fin(U_4116,U_4117)),c_Big__Operators_Olattice__class_OSup__fin(U_4116,U_4118))
| U_4118 = c_Orderings_Obot__class_Obot(tc_fun(U_4116,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4116),U_4118))
| U_4117 = c_Orderings_Obot__class_Obot(tc_fun(U_4116,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4116),U_4117))
| ~ class_Lattices_Olattice(U_4116) ),
inference(clausify,[status(thm)],[f_1055_2]) ).
fof(f_1056_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_1056_2,plain,
! [U_4121,U_4120,U_4119] :
( c_Big__Operators_Olattice__class_OInf__fin(U_4119,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4119,tc_HOL_Obool)),U_4120),U_4121)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4119),c_Big__Operators_Olattice__class_OInf__fin(U_4119,U_4120)),c_Big__Operators_Olattice__class_OInf__fin(U_4119,U_4121))
| U_4121 = c_Orderings_Obot__class_Obot(tc_fun(U_4119,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4119),U_4121))
| U_4120 = c_Orderings_Obot__class_Obot(tc_fun(U_4119,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4119),U_4120))
| ~ class_Lattices_Olattice(U_4119) ),
inference(variable_rename,[status(thm)],[f_1056_1]) ).
cnf(f_1056_3,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_4119,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4119,tc_HOL_Obool)),U_4120),U_4121)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4119),c_Big__Operators_Olattice__class_OInf__fin(U_4119,U_4120)),c_Big__Operators_Olattice__class_OInf__fin(U_4119,U_4121))
| U_4121 = c_Orderings_Obot__class_Obot(tc_fun(U_4119,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4119),U_4121))
| U_4120 = c_Orderings_Obot__class_Obot(tc_fun(U_4119,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4119),U_4120))
| ~ class_Lattices_Olattice(U_4119) ),
inference(clausify,[status(thm)],[f_1056_2]) ).
fof(f_1057_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_1057_2,plain,
! [U_4124,U_4123,U_4122] :
( hAPP(c_Finite__Set_Ocard(U_4122),hAPP(hAPP(c_Set_Oinsert(U_4122),U_4124),U_4123)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4122),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4122,tc_HOL_Obool)),U_4123),hAPP(hAPP(c_Set_Oinsert(U_4122),U_4124),c_Orderings_Obot__class_Obot(tc_fun(U_4122,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4122),U_4123)) ),
inference(variable_rename,[status(thm)],[f_1057_1]) ).
cnf(f_1057_3,plain,
( hAPP(c_Finite__Set_Ocard(U_4122),hAPP(hAPP(c_Set_Oinsert(U_4122),U_4124),U_4123)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4122),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4122,tc_HOL_Obool)),U_4123),hAPP(hAPP(c_Set_Oinsert(U_4122),U_4124),c_Orderings_Obot__class_Obot(tc_fun(U_4122,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4122),U_4123)) ),
inference(clausify,[status(thm)],[f_1057_2]) ).
fof(f_1058_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_1058_2,plain,
! [U_4127,U_4126,U_4125] :
( hAPP(c_Finite__Set_Ocard(U_4125),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4125,tc_HOL_Obool)),U_4126),U_4127)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4125),U_4126)),hAPP(c_Finite__Set_Ocard(U_4125),U_4127))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4125,tc_HOL_Obool)),U_4126),U_4127) != c_Orderings_Obot__class_Obot(tc_fun(U_4125,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4125),U_4127))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4125),U_4126)) ),
inference(variable_rename,[status(thm)],[f_1058_1]) ).
cnf(f_1058_3,plain,
( hAPP(c_Finite__Set_Ocard(U_4125),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4125,tc_HOL_Obool)),U_4126),U_4127)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4125),U_4126)),hAPP(c_Finite__Set_Ocard(U_4125),U_4127))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4125,tc_HOL_Obool)),U_4126),U_4127) != c_Orderings_Obot__class_Obot(tc_fun(U_4125,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4125),U_4127))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4125),U_4126)) ),
inference(clausify,[status(thm)],[f_1058_2]) ).
fof(f_1059_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_1059_2,plain,
! [U_4130,U_4129,U_4128] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4128),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4128,tc_HOL_Obool)),U_4129),hAPP(hAPP(c_Set_Oinsert(U_4128),U_4130),c_Orderings_Obot__class_Obot(tc_fun(U_4128,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_4128),U_4129)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4128),U_4129)) ),
inference(variable_rename,[status(thm)],[f_1059_1]) ).
cnf(f_1059_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4128),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4128,tc_HOL_Obool)),U_4129),hAPP(hAPP(c_Set_Oinsert(U_4128),U_4130),c_Orderings_Obot__class_Obot(tc_fun(U_4128,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_4128),U_4129)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4128),U_4129)) ),
inference(clausify,[status(thm)],[f_1059_2]) ).
fof(f_1060_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_1060_2,plain,
! [U_4135,U_4134,U_4133,U_4132,U_4131] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4131),U_4134)),hAPP(c_Finite__Set_Ocard(U_4132),U_4135)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4132),U_4135))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4132,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4131,U_4132,U_4133),U_4134)),U_4135))
| ~ c_Fun_Oinj__on(U_4131,U_4132,U_4133,U_4134) ),
inference(variable_rename,[status(thm)],[f_1060_1]) ).
cnf(f_1060_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4131),U_4134)),hAPP(c_Finite__Set_Ocard(U_4132),U_4135)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4132),U_4135))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4132,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4131,U_4132,U_4133),U_4134)),U_4135))
| ~ c_Fun_Oinj__on(U_4131,U_4132,U_4133,U_4134) ),
inference(clausify,[status(thm)],[f_1060_2]) ).
fof(f_1061_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_1061_2,plain,
! [U_4141,U_4140,U_4139,U_4138] :
( ( ( ? [U_4137] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4140,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4138,U_4140,U_4137),U_4139)),U_4141))
& c_Fun_Oinj__on(U_4138,U_4140,U_4137,U_4139) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4138),U_4139)),hAPP(c_Finite__Set_Ocard(U_4140),U_4141))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4138),U_4139)),hAPP(c_Finite__Set_Ocard(U_4140),U_4141)))
| ! [U_4136] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4140,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4138,U_4140,U_4136),U_4139)),U_4141))
| ~ c_Fun_Oinj__on(U_4138,U_4140,U_4136,U_4139) ) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4140),U_4141))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4138),U_4139)) ),
inference(variable_rename,[status(thm)],[f_1061_1]) ).
fof(f_1061_3,plain,
! [U_4141,U_4140,U_4139,U_4138] :
( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4140,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4138,U_4140,sK74(U_4141,U_4140,U_4139,U_4138)),U_4139)),U_4141))
& c_Fun_Oinj__on(U_4138,U_4140,sK74(U_4141,U_4140,U_4139,U_4138),U_4139) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4138),U_4139)),hAPP(c_Finite__Set_Ocard(U_4140),U_4141))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4138),U_4139)),hAPP(c_Finite__Set_Ocard(U_4140),U_4141)))
| ! [U_4136] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4140,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4138,U_4140,U_4136),U_4139)),U_4141))
| ~ c_Fun_Oinj__on(U_4138,U_4140,U_4136,U_4139) ) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4140),U_4141))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4138),U_4139)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_4137,sK74(U_4141,U_4140,U_4139,U_4138))],[f_1061_2]) ).
cnf(f_1061_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4138),U_4139)),hAPP(c_Finite__Set_Ocard(U_4140),U_4141)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4140,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4138,U_4140,U_4136),U_4139)),U_4141))
| ~ c_Fun_Oinj__on(U_4138,U_4140,U_4136,U_4139)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4140),U_4141))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4138),U_4139)) ),
inference(clausify,[status(thm)],[f_1061_3]) ).
cnf(f_1061_5,plain,
( c_Fun_Oinj__on(U_4138,U_4140,sK74(U_4141,U_4140,U_4139,U_4138),U_4139)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4138),U_4139)),hAPP(c_Finite__Set_Ocard(U_4140),U_4141)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4140),U_4141))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4138),U_4139)) ),
inference(clausify,[status(thm)],[f_1061_3]) ).
cnf(f_1061_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4140,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4138,U_4140,sK74(U_4141,U_4140,U_4139,U_4138)),U_4139)),U_4141))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4138),U_4139)),hAPP(c_Finite__Set_Ocard(U_4140),U_4141)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4140),U_4141))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4138),U_4139)) ),
inference(clausify,[status(thm)],[f_1061_3]) ).
fof(f_1062_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_1062_2,plain,
! [U_4144,U_4143,U_4142] :
( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4142),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4142,tc_HOL_Obool)),U_4143),hAPP(hAPP(c_Set_Oinsert(U_4142),U_4144),c_Orderings_Obot__class_Obot(tc_fun(U_4142,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_4142),U_4143)
| ~ hBOOL(hAPP(hAPP(c_member(U_4142),U_4144),U_4143))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4142),U_4143)) ),
inference(variable_rename,[status(thm)],[f_1062_1]) ).
cnf(f_1062_3,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4142),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4142,tc_HOL_Obool)),U_4143),hAPP(hAPP(c_Set_Oinsert(U_4142),U_4144),c_Orderings_Obot__class_Obot(tc_fun(U_4142,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_4142),U_4143)
| ~ hBOOL(hAPP(hAPP(c_member(U_4142),U_4144),U_4143))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4142),U_4143)) ),
inference(clausify,[status(thm)],[f_1062_2]) ).
fof(f_1063_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_1063_2,plain,
! [U_4148,U_4147,U_4146,U_4145] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4145),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4145,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4145,tc_HOL_Obool)),U_4146),hAPP(hAPP(c_Set_Oinsert(U_4145),U_4147),c_Orderings_Obot__class_Obot(tc_fun(U_4145,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_4145),U_4148),c_Orderings_Obot__class_Obot(tc_fun(U_4145,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_4145),U_4146)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4145),U_4148),U_4146))
| ~ hBOOL(hAPP(hAPP(c_member(U_4145),U_4147),U_4146))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4145),U_4146)) ),
inference(variable_rename,[status(thm)],[f_1063_1]) ).
cnf(f_1063_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4145),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4145,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4145,tc_HOL_Obool)),U_4146),hAPP(hAPP(c_Set_Oinsert(U_4145),U_4147),c_Orderings_Obot__class_Obot(tc_fun(U_4145,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_4145),U_4148),c_Orderings_Obot__class_Obot(tc_fun(U_4145,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_4145),U_4146)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4145),U_4148),U_4146))
| ~ hBOOL(hAPP(hAPP(c_member(U_4145),U_4147),U_4146))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4145),U_4146)) ),
inference(clausify,[status(thm)],[f_1063_2]) ).
fof(f_1064_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_1064_2,plain,
! [U_4151,U_4150,U_4149] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4149),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4149,tc_HOL_Obool)),U_4150),hAPP(hAPP(c_Set_Oinsert(U_4149),U_4151),c_Orderings_Obot__class_Obot(tc_fun(U_4149,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_4149),U_4150)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4149),U_4151),U_4150))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4149),U_4150)) ),
inference(variable_rename,[status(thm)],[f_1064_1]) ).
cnf(f_1064_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4149),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4149,tc_HOL_Obool)),U_4150),hAPP(hAPP(c_Set_Oinsert(U_4149),U_4151),c_Orderings_Obot__class_Obot(tc_fun(U_4149,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_4149),U_4150)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4149),U_4151),U_4150))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4149),U_4150)) ),
inference(clausify,[status(thm)],[f_1064_2]) ).
fof(f_1065_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_1065_2,plain,
! [U_4154,U_4153,U_4152] :
( c_Big__Operators_Olattice__class_OSup__fin(U_4152,hAPP(hAPP(c_Set_Oinsert(U_4152),U_4154),U_4153)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4152),U_4154),c_Big__Operators_Olattice__class_OSup__fin(U_4152,U_4153))
| U_4153 = c_Orderings_Obot__class_Obot(tc_fun(U_4152,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_4152),U_4154),U_4153))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4152),U_4153))
| ~ class_Lattices_Olattice(U_4152) ),
inference(variable_rename,[status(thm)],[f_1065_1]) ).
cnf(f_1065_3,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_4152,hAPP(hAPP(c_Set_Oinsert(U_4152),U_4154),U_4153)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4152),U_4154),c_Big__Operators_Olattice__class_OSup__fin(U_4152,U_4153))
| U_4153 = c_Orderings_Obot__class_Obot(tc_fun(U_4152,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_4152),U_4154),U_4153))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4152),U_4153))
| ~ class_Lattices_Olattice(U_4152) ),
inference(clausify,[status(thm)],[f_1065_2]) ).
fof(f_1066_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_1066_2,plain,
! [U_4157,U_4156,U_4155] :
( c_Big__Operators_Olattice__class_OInf__fin(U_4155,hAPP(hAPP(c_Set_Oinsert(U_4155),U_4157),U_4156)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4155),U_4157),c_Big__Operators_Olattice__class_OInf__fin(U_4155,U_4156))
| U_4156 = c_Orderings_Obot__class_Obot(tc_fun(U_4155,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_4155),U_4157),U_4156))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4155),U_4156))
| ~ class_Lattices_Olattice(U_4155) ),
inference(variable_rename,[status(thm)],[f_1066_1]) ).
cnf(f_1066_3,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_4155,hAPP(hAPP(c_Set_Oinsert(U_4155),U_4157),U_4156)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4155),U_4157),c_Big__Operators_Olattice__class_OInf__fin(U_4155,U_4156))
| U_4156 = c_Orderings_Obot__class_Obot(tc_fun(U_4155,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_4155),U_4157),U_4156))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4155),U_4156))
| ~ class_Lattices_Olattice(U_4155) ),
inference(clausify,[status(thm)],[f_1066_2]) ).
fof(f_1067_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_1067_2,plain,
! [U_4160,U_4159,U_4158] :
( ( ( c_Big__Operators_Olattice__class_OSup__fin(U_4158,hAPP(hAPP(c_Set_Oinsert(U_4158),U_4160),U_4159)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4158),U_4160),c_Big__Operators_Olattice__class_OSup__fin(U_4158,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4158,tc_HOL_Obool)),U_4159),hAPP(hAPP(c_Set_Oinsert(U_4158),U_4160),c_Orderings_Obot__class_Obot(tc_fun(U_4158,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4158,tc_HOL_Obool)),U_4159),hAPP(hAPP(c_Set_Oinsert(U_4158),U_4160),c_Orderings_Obot__class_Obot(tc_fun(U_4158,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_4158,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice__class_OSup__fin(U_4158,hAPP(hAPP(c_Set_Oinsert(U_4158),U_4160),U_4159)) = U_4160
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4158,tc_HOL_Obool)),U_4159),hAPP(hAPP(c_Set_Oinsert(U_4158),U_4160),c_Orderings_Obot__class_Obot(tc_fun(U_4158,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_4158,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4158),U_4159))
| ~ class_Lattices_Olattice(U_4158) ),
inference(variable_rename,[status(thm)],[f_1067_1]) ).
cnf(f_1067_3,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_4158,hAPP(hAPP(c_Set_Oinsert(U_4158),U_4160),U_4159)) = U_4160
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4158,tc_HOL_Obool)),U_4159),hAPP(hAPP(c_Set_Oinsert(U_4158),U_4160),c_Orderings_Obot__class_Obot(tc_fun(U_4158,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_4158,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4158),U_4159))
| ~ class_Lattices_Olattice(U_4158) ),
inference(clausify,[status(thm)],[f_1067_2]) ).
cnf(f_1067_4,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_4158,hAPP(hAPP(c_Set_Oinsert(U_4158),U_4160),U_4159)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4158),U_4160),c_Big__Operators_Olattice__class_OSup__fin(U_4158,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4158,tc_HOL_Obool)),U_4159),hAPP(hAPP(c_Set_Oinsert(U_4158),U_4160),c_Orderings_Obot__class_Obot(tc_fun(U_4158,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4158,tc_HOL_Obool)),U_4159),hAPP(hAPP(c_Set_Oinsert(U_4158),U_4160),c_Orderings_Obot__class_Obot(tc_fun(U_4158,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_4158,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4158),U_4159))
| ~ class_Lattices_Olattice(U_4158) ),
inference(clausify,[status(thm)],[f_1067_2]) ).
fof(f_1068_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_1068_2,plain,
! [U_4163,U_4162,U_4161] :
( ( ( c_Big__Operators_Olattice__class_OInf__fin(U_4161,hAPP(hAPP(c_Set_Oinsert(U_4161),U_4163),U_4162)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4161),U_4163),c_Big__Operators_Olattice__class_OInf__fin(U_4161,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4161,tc_HOL_Obool)),U_4162),hAPP(hAPP(c_Set_Oinsert(U_4161),U_4163),c_Orderings_Obot__class_Obot(tc_fun(U_4161,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4161,tc_HOL_Obool)),U_4162),hAPP(hAPP(c_Set_Oinsert(U_4161),U_4163),c_Orderings_Obot__class_Obot(tc_fun(U_4161,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_4161,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice__class_OInf__fin(U_4161,hAPP(hAPP(c_Set_Oinsert(U_4161),U_4163),U_4162)) = U_4163
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4161,tc_HOL_Obool)),U_4162),hAPP(hAPP(c_Set_Oinsert(U_4161),U_4163),c_Orderings_Obot__class_Obot(tc_fun(U_4161,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_4161,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4161),U_4162))
| ~ class_Lattices_Olattice(U_4161) ),
inference(variable_rename,[status(thm)],[f_1068_1]) ).
cnf(f_1068_3,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_4161,hAPP(hAPP(c_Set_Oinsert(U_4161),U_4163),U_4162)) = U_4163
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4161,tc_HOL_Obool)),U_4162),hAPP(hAPP(c_Set_Oinsert(U_4161),U_4163),c_Orderings_Obot__class_Obot(tc_fun(U_4161,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_4161,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4161),U_4162))
| ~ class_Lattices_Olattice(U_4161) ),
inference(clausify,[status(thm)],[f_1068_2]) ).
cnf(f_1068_4,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_4161,hAPP(hAPP(c_Set_Oinsert(U_4161),U_4163),U_4162)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4161),U_4163),c_Big__Operators_Olattice__class_OInf__fin(U_4161,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4161,tc_HOL_Obool)),U_4162),hAPP(hAPP(c_Set_Oinsert(U_4161),U_4163),c_Orderings_Obot__class_Obot(tc_fun(U_4161,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4161,tc_HOL_Obool)),U_4162),hAPP(hAPP(c_Set_Oinsert(U_4161),U_4163),c_Orderings_Obot__class_Obot(tc_fun(U_4161,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_4161,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4161),U_4162))
| ~ class_Lattices_Olattice(U_4161) ),
inference(clausify,[status(thm)],[f_1068_2]) ).
fof(f_1069_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_1069_2,plain,
! [U_4166,U_4165,U_4164] :
( c_Big__Operators_Olattice__class_OSup__fin(U_4164,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4164,tc_HOL_Obool)),U_4165),U_4166)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4164),c_Big__Operators_Olattice__class_OSup__fin(U_4164,U_4165)),c_Big__Operators_Olattice__class_OSup__fin(U_4164,U_4166))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4164,tc_HOL_Obool)),U_4165),U_4166) != c_Orderings_Obot__class_Obot(tc_fun(U_4164,tc_HOL_Obool))
| U_4166 = c_Orderings_Obot__class_Obot(tc_fun(U_4164,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4164),U_4166))
| U_4165 = c_Orderings_Obot__class_Obot(tc_fun(U_4164,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4164),U_4165))
| ~ class_Lattices_Olattice(U_4164) ),
inference(variable_rename,[status(thm)],[f_1069_1]) ).
cnf(f_1069_3,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_4164,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4164,tc_HOL_Obool)),U_4165),U_4166)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4164),c_Big__Operators_Olattice__class_OSup__fin(U_4164,U_4165)),c_Big__Operators_Olattice__class_OSup__fin(U_4164,U_4166))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4164,tc_HOL_Obool)),U_4165),U_4166) != c_Orderings_Obot__class_Obot(tc_fun(U_4164,tc_HOL_Obool))
| U_4166 = c_Orderings_Obot__class_Obot(tc_fun(U_4164,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4164),U_4166))
| U_4165 = c_Orderings_Obot__class_Obot(tc_fun(U_4164,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4164),U_4165))
| ~ class_Lattices_Olattice(U_4164) ),
inference(clausify,[status(thm)],[f_1069_2]) ).
fof(f_1070_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_1070_2,plain,
! [U_4169,U_4168,U_4167] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4167),c_Big__Operators_Olattice__class_OSup__fin(U_4167,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4167,tc_HOL_Obool)),U_4168),U_4169))),c_Big__Operators_Olattice__class_OSup__fin(U_4167,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4167,tc_HOL_Obool)),U_4168),U_4169))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4167),c_Big__Operators_Olattice__class_OSup__fin(U_4167,U_4168)),c_Big__Operators_Olattice__class_OSup__fin(U_4167,U_4169))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4167,tc_HOL_Obool)),U_4168),U_4169) = c_Orderings_Obot__class_Obot(tc_fun(U_4167,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4167),U_4169))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4167),U_4168))
| ~ class_Lattices_Olattice(U_4167) ),
inference(variable_rename,[status(thm)],[f_1070_1]) ).
cnf(f_1070_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4167),c_Big__Operators_Olattice__class_OSup__fin(U_4167,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4167,tc_HOL_Obool)),U_4168),U_4169))),c_Big__Operators_Olattice__class_OSup__fin(U_4167,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4167,tc_HOL_Obool)),U_4168),U_4169))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4167),c_Big__Operators_Olattice__class_OSup__fin(U_4167,U_4168)),c_Big__Operators_Olattice__class_OSup__fin(U_4167,U_4169))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4167,tc_HOL_Obool)),U_4168),U_4169) = c_Orderings_Obot__class_Obot(tc_fun(U_4167,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4167),U_4169))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4167),U_4168))
| ~ class_Lattices_Olattice(U_4167) ),
inference(clausify,[status(thm)],[f_1070_2]) ).
fof(f_1071_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_1071_2,plain,
! [U_4172,U_4171,U_4170] :
( c_Big__Operators_Olattice__class_OInf__fin(U_4170,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4170,tc_HOL_Obool)),U_4171),U_4172)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4170),c_Big__Operators_Olattice__class_OInf__fin(U_4170,U_4171)),c_Big__Operators_Olattice__class_OInf__fin(U_4170,U_4172))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4170,tc_HOL_Obool)),U_4171),U_4172) != c_Orderings_Obot__class_Obot(tc_fun(U_4170,tc_HOL_Obool))
| U_4172 = c_Orderings_Obot__class_Obot(tc_fun(U_4170,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4170),U_4172))
| U_4171 = c_Orderings_Obot__class_Obot(tc_fun(U_4170,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4170),U_4171))
| ~ class_Lattices_Olattice(U_4170) ),
inference(variable_rename,[status(thm)],[f_1071_1]) ).
cnf(f_1071_3,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_4170,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4170,tc_HOL_Obool)),U_4171),U_4172)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4170),c_Big__Operators_Olattice__class_OInf__fin(U_4170,U_4171)),c_Big__Operators_Olattice__class_OInf__fin(U_4170,U_4172))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4170,tc_HOL_Obool)),U_4171),U_4172) != c_Orderings_Obot__class_Obot(tc_fun(U_4170,tc_HOL_Obool))
| U_4172 = c_Orderings_Obot__class_Obot(tc_fun(U_4170,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4170),U_4172))
| U_4171 = c_Orderings_Obot__class_Obot(tc_fun(U_4170,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4170),U_4171))
| ~ class_Lattices_Olattice(U_4170) ),
inference(clausify,[status(thm)],[f_1071_2]) ).
fof(f_1072_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_1072_2,plain,
! [U_4175,U_4174,U_4173] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4173),c_Big__Operators_Olattice__class_OInf__fin(U_4173,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4173,tc_HOL_Obool)),U_4174),U_4175))),c_Big__Operators_Olattice__class_OInf__fin(U_4173,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4173,tc_HOL_Obool)),U_4174),U_4175))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4173),c_Big__Operators_Olattice__class_OInf__fin(U_4173,U_4174)),c_Big__Operators_Olattice__class_OInf__fin(U_4173,U_4175))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4173,tc_HOL_Obool)),U_4174),U_4175) = c_Orderings_Obot__class_Obot(tc_fun(U_4173,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4173),U_4175))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4173),U_4174))
| ~ class_Lattices_Olattice(U_4173) ),
inference(variable_rename,[status(thm)],[f_1072_1]) ).
cnf(f_1072_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4173),c_Big__Operators_Olattice__class_OInf__fin(U_4173,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4173,tc_HOL_Obool)),U_4174),U_4175))),c_Big__Operators_Olattice__class_OInf__fin(U_4173,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4173,tc_HOL_Obool)),U_4174),U_4175))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4173),c_Big__Operators_Olattice__class_OInf__fin(U_4173,U_4174)),c_Big__Operators_Olattice__class_OInf__fin(U_4173,U_4175))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4173,tc_HOL_Obool)),U_4174),U_4175) = c_Orderings_Obot__class_Obot(tc_fun(U_4173,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4173),U_4175))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4173),U_4174))
| ~ class_Lattices_Olattice(U_4173) ),
inference(clausify,[status(thm)],[f_1072_2]) ).
fof(f_1073_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_1073_2,plain,
! [U_4179,U_4178] :
( hBOOL(hAPP(hAPP(c_member(U_4178),c_Big__Operators_Olattice__class_OInf__fin(U_4178,U_4179)),U_4179))
| ? [U_4177,U_4176] : ~ hBOOL(hAPP(hAPP(c_member(U_4178),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4178),U_4177),U_4176)),hAPP(hAPP(c_Set_Oinsert(U_4178),U_4177),hAPP(hAPP(c_Set_Oinsert(U_4178),U_4176),c_Orderings_Obot__class_Obot(tc_fun(U_4178,tc_HOL_Obool))))))
| U_4179 = c_Orderings_Obot__class_Obot(tc_fun(U_4178,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4178),U_4179))
| ~ class_Lattices_Olattice(U_4178) ),
inference(variable_rename,[status(thm)],[f_1073_1]) ).
fof(f_1073_3,plain,
! [U_4179,U_4178] :
( hBOOL(hAPP(hAPP(c_member(U_4178),c_Big__Operators_Olattice__class_OInf__fin(U_4178,U_4179)),U_4179))
| ? [U_4176] : ~ hBOOL(hAPP(hAPP(c_member(U_4178),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4178),sK75(U_4179,U_4178)),U_4176)),hAPP(hAPP(c_Set_Oinsert(U_4178),sK75(U_4179,U_4178)),hAPP(hAPP(c_Set_Oinsert(U_4178),U_4176),c_Orderings_Obot__class_Obot(tc_fun(U_4178,tc_HOL_Obool))))))
| U_4179 = c_Orderings_Obot__class_Obot(tc_fun(U_4178,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4178),U_4179))
| ~ class_Lattices_Olattice(U_4178) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_4177,sK75(U_4179,U_4178))],[f_1073_2]) ).
fof(f_1073_4,plain,
! [U_4179,U_4178] :
( hBOOL(hAPP(hAPP(c_member(U_4178),c_Big__Operators_Olattice__class_OInf__fin(U_4178,U_4179)),U_4179))
| ~ hBOOL(hAPP(hAPP(c_member(U_4178),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4178),sK75(U_4179,U_4178)),sK76(U_4179,U_4178))),hAPP(hAPP(c_Set_Oinsert(U_4178),sK75(U_4179,U_4178)),hAPP(hAPP(c_Set_Oinsert(U_4178),sK76(U_4179,U_4178)),c_Orderings_Obot__class_Obot(tc_fun(U_4178,tc_HOL_Obool))))))
| U_4179 = c_Orderings_Obot__class_Obot(tc_fun(U_4178,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4178),U_4179))
| ~ class_Lattices_Olattice(U_4178) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_4176,sK76(U_4179,U_4178))],[f_1073_3]) ).
cnf(f_1073_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_4178),c_Big__Operators_Olattice__class_OInf__fin(U_4178,U_4179)),U_4179))
| ~ hBOOL(hAPP(hAPP(c_member(U_4178),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4178),sK75(U_4179,U_4178)),sK76(U_4179,U_4178))),hAPP(hAPP(c_Set_Oinsert(U_4178),sK75(U_4179,U_4178)),hAPP(hAPP(c_Set_Oinsert(U_4178),sK76(U_4179,U_4178)),c_Orderings_Obot__class_Obot(tc_fun(U_4178,tc_HOL_Obool))))))
| U_4179 = c_Orderings_Obot__class_Obot(tc_fun(U_4178,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4178),U_4179))
| ~ class_Lattices_Olattice(U_4178) ),
inference(clausify,[status(thm)],[f_1073_4]) ).
fof(f_1074_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_1074_2,plain,
! [U_4183,U_4182] :
( hBOOL(hAPP(hAPP(c_member(U_4182),c_Big__Operators_Olattice__class_OSup__fin(U_4182,U_4183)),U_4183))
| ? [U_4181,U_4180] : ~ hBOOL(hAPP(hAPP(c_member(U_4182),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4182),U_4181),U_4180)),hAPP(hAPP(c_Set_Oinsert(U_4182),U_4181),hAPP(hAPP(c_Set_Oinsert(U_4182),U_4180),c_Orderings_Obot__class_Obot(tc_fun(U_4182,tc_HOL_Obool))))))
| U_4183 = c_Orderings_Obot__class_Obot(tc_fun(U_4182,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4182),U_4183))
| ~ class_Lattices_Olattice(U_4182) ),
inference(variable_rename,[status(thm)],[f_1074_1]) ).
fof(f_1074_3,plain,
! [U_4183,U_4182] :
( hBOOL(hAPP(hAPP(c_member(U_4182),c_Big__Operators_Olattice__class_OSup__fin(U_4182,U_4183)),U_4183))
| ? [U_4180] : ~ hBOOL(hAPP(hAPP(c_member(U_4182),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4182),sK77(U_4183,U_4182)),U_4180)),hAPP(hAPP(c_Set_Oinsert(U_4182),sK77(U_4183,U_4182)),hAPP(hAPP(c_Set_Oinsert(U_4182),U_4180),c_Orderings_Obot__class_Obot(tc_fun(U_4182,tc_HOL_Obool))))))
| U_4183 = c_Orderings_Obot__class_Obot(tc_fun(U_4182,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4182),U_4183))
| ~ class_Lattices_Olattice(U_4182) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_4181,sK77(U_4183,U_4182))],[f_1074_2]) ).
fof(f_1074_4,plain,
! [U_4183,U_4182] :
( hBOOL(hAPP(hAPP(c_member(U_4182),c_Big__Operators_Olattice__class_OSup__fin(U_4182,U_4183)),U_4183))
| ~ hBOOL(hAPP(hAPP(c_member(U_4182),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4182),sK77(U_4183,U_4182)),sK78(U_4183,U_4182))),hAPP(hAPP(c_Set_Oinsert(U_4182),sK77(U_4183,U_4182)),hAPP(hAPP(c_Set_Oinsert(U_4182),sK78(U_4183,U_4182)),c_Orderings_Obot__class_Obot(tc_fun(U_4182,tc_HOL_Obool))))))
| U_4183 = c_Orderings_Obot__class_Obot(tc_fun(U_4182,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4182),U_4183))
| ~ class_Lattices_Olattice(U_4182) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_4180,sK78(U_4183,U_4182))],[f_1074_3]) ).
cnf(f_1074_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_4182),c_Big__Operators_Olattice__class_OSup__fin(U_4182,U_4183)),U_4183))
| ~ hBOOL(hAPP(hAPP(c_member(U_4182),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4182),sK77(U_4183,U_4182)),sK78(U_4183,U_4182))),hAPP(hAPP(c_Set_Oinsert(U_4182),sK77(U_4183,U_4182)),hAPP(hAPP(c_Set_Oinsert(U_4182),sK78(U_4183,U_4182)),c_Orderings_Obot__class_Obot(tc_fun(U_4182,tc_HOL_Obool))))))
| U_4183 = c_Orderings_Obot__class_Obot(tc_fun(U_4182,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4182),U_4183))
| ~ class_Lattices_Olattice(U_4182) ),
inference(clausify,[status(thm)],[f_1074_4]) ).
fof(f_1075_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_1075_2,plain,
! [U_4190,U_4189,U_4188] :
( ( hAPP(c_Finite__Set_Ocard(U_4188),U_4189) = hAPP(c_Nat_OSuc,U_4190)
| ! [U_4187,U_4186] :
( ( U_4186 != c_Orderings_Obot__class_Obot(tc_fun(U_4188,tc_HOL_Obool))
& U_4190 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(c_Finite__Set_Ocard(U_4188),U_4186) != U_4190
| hBOOL(hAPP(hAPP(c_member(U_4188),U_4187),U_4186))
| U_4189 != hAPP(hAPP(c_Set_Oinsert(U_4188),U_4187),U_4186) ) )
& ( ? [U_4185,U_4184] :
( ( U_4184 = c_Orderings_Obot__class_Obot(tc_fun(U_4188,tc_HOL_Obool))
| U_4190 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& hAPP(c_Finite__Set_Ocard(U_4188),U_4184) = U_4190
& ~ hBOOL(hAPP(hAPP(c_member(U_4188),U_4185),U_4184))
& U_4189 = hAPP(hAPP(c_Set_Oinsert(U_4188),U_4185),U_4184) )
| hAPP(c_Finite__Set_Ocard(U_4188),U_4189) != hAPP(c_Nat_OSuc,U_4190) ) ),
inference(variable_rename,[status(thm)],[f_1075_1]) ).
fof(f_1075_3,plain,
( ! [U_4196,U_4194,U_4192] :
( hAPP(c_Finite__Set_Ocard(U_4192),U_4194) = hAPP(c_Nat_OSuc,U_4196)
| ! [U_4187,U_4186] :
( ( U_4186 != c_Orderings_Obot__class_Obot(tc_fun(U_4192,tc_HOL_Obool))
& U_4196 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(c_Finite__Set_Ocard(U_4192),U_4186) != U_4196
| hBOOL(hAPP(hAPP(c_member(U_4192),U_4187),U_4186))
| U_4194 != hAPP(hAPP(c_Set_Oinsert(U_4192),U_4187),U_4186) ) )
& ! [U_4195,U_4193,U_4191] :
( ? [U_4185,U_4184] :
( ( U_4184 = c_Orderings_Obot__class_Obot(tc_fun(U_4191,tc_HOL_Obool))
| U_4195 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& hAPP(c_Finite__Set_Ocard(U_4191),U_4184) = U_4195
& ~ hBOOL(hAPP(hAPP(c_member(U_4191),U_4185),U_4184))
& U_4193 = hAPP(hAPP(c_Set_Oinsert(U_4191),U_4185),U_4184) )
| hAPP(c_Finite__Set_Ocard(U_4191),U_4193) != hAPP(c_Nat_OSuc,U_4195) ) ),
inference(miniscope,[status(thm)],[f_1075_2]) ).
fof(f_1075_4,plain,
( ! [U_4196,U_4194,U_4192] :
( hAPP(c_Finite__Set_Ocard(U_4192),U_4194) = hAPP(c_Nat_OSuc,U_4196)
| ! [U_4187,U_4186] :
( ( U_4186 != c_Orderings_Obot__class_Obot(tc_fun(U_4192,tc_HOL_Obool))
& U_4196 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(c_Finite__Set_Ocard(U_4192),U_4186) != U_4196
| hBOOL(hAPP(hAPP(c_member(U_4192),U_4187),U_4186))
| U_4194 != hAPP(hAPP(c_Set_Oinsert(U_4192),U_4187),U_4186) ) )
& ! [U_4195,U_4193,U_4191] :
( ? [U_4184] :
( ( U_4184 = c_Orderings_Obot__class_Obot(tc_fun(U_4191,tc_HOL_Obool))
| U_4195 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& hAPP(c_Finite__Set_Ocard(U_4191),U_4184) = U_4195
& ~ hBOOL(hAPP(hAPP(c_member(U_4191),sK79(U_4195,U_4193,U_4191)),U_4184))
& U_4193 = hAPP(hAPP(c_Set_Oinsert(U_4191),sK79(U_4195,U_4193,U_4191)),U_4184) )
| hAPP(c_Finite__Set_Ocard(U_4191),U_4193) != hAPP(c_Nat_OSuc,U_4195) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_4185,sK79(U_4195,U_4193,U_4191))],[f_1075_3]) ).
fof(f_1075_5,plain,
( ! [U_4196,U_4194,U_4192] :
( hAPP(c_Finite__Set_Ocard(U_4192),U_4194) = hAPP(c_Nat_OSuc,U_4196)
| ! [U_4187,U_4186] :
( ( U_4186 != c_Orderings_Obot__class_Obot(tc_fun(U_4192,tc_HOL_Obool))
& U_4196 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(c_Finite__Set_Ocard(U_4192),U_4186) != U_4196
| hBOOL(hAPP(hAPP(c_member(U_4192),U_4187),U_4186))
| U_4194 != hAPP(hAPP(c_Set_Oinsert(U_4192),U_4187),U_4186) ) )
& ! [U_4195,U_4193,U_4191] :
( ( ( sK80(U_4195,U_4193,U_4191) = c_Orderings_Obot__class_Obot(tc_fun(U_4191,tc_HOL_Obool))
| U_4195 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& hAPP(c_Finite__Set_Ocard(U_4191),sK80(U_4195,U_4193,U_4191)) = U_4195
& ~ hBOOL(hAPP(hAPP(c_member(U_4191),sK79(U_4195,U_4193,U_4191)),sK80(U_4195,U_4193,U_4191)))
& U_4193 = hAPP(hAPP(c_Set_Oinsert(U_4191),sK79(U_4195,U_4193,U_4191)),sK80(U_4195,U_4193,U_4191)) )
| hAPP(c_Finite__Set_Ocard(U_4191),U_4193) != hAPP(c_Nat_OSuc,U_4195) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_4184,sK80(U_4195,U_4193,U_4191))],[f_1075_4]) ).
cnf(f_1075_6,plain,
( U_4193 = hAPP(hAPP(c_Set_Oinsert(U_4191),sK79(U_4195,U_4193,U_4191)),sK80(U_4195,U_4193,U_4191))
| hAPP(c_Finite__Set_Ocard(U_4191),U_4193) != hAPP(c_Nat_OSuc,U_4195) ),
inference(clausify,[status(thm)],[f_1075_5]) ).
cnf(f_1075_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_4191),sK79(U_4195,U_4193,U_4191)),sK80(U_4195,U_4193,U_4191)))
| hAPP(c_Finite__Set_Ocard(U_4191),U_4193) != hAPP(c_Nat_OSuc,U_4195) ),
inference(clausify,[status(thm)],[f_1075_5]) ).
cnf(f_1075_8,plain,
( hAPP(c_Finite__Set_Ocard(U_4191),sK80(U_4195,U_4193,U_4191)) = U_4195
| hAPP(c_Finite__Set_Ocard(U_4191),U_4193) != hAPP(c_Nat_OSuc,U_4195) ),
inference(clausify,[status(thm)],[f_1075_5]) ).
cnf(f_1075_9,plain,
( sK80(U_4195,U_4193,U_4191) = c_Orderings_Obot__class_Obot(tc_fun(U_4191,tc_HOL_Obool))
| U_4195 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Finite__Set_Ocard(U_4191),U_4193) != hAPP(c_Nat_OSuc,U_4195) ),
inference(clausify,[status(thm)],[f_1075_5]) ).
cnf(f_1075_10,plain,
( U_4196 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Finite__Set_Ocard(U_4192),U_4186) != U_4196
| hBOOL(hAPP(hAPP(c_member(U_4192),U_4187),U_4186))
| U_4194 != hAPP(hAPP(c_Set_Oinsert(U_4192),U_4187),U_4186)
| hAPP(c_Finite__Set_Ocard(U_4192),U_4194) = hAPP(c_Nat_OSuc,U_4196) ),
inference(clausify,[status(thm)],[f_1075_5]) ).
cnf(f_1075_11,plain,
( U_4186 != c_Orderings_Obot__class_Obot(tc_fun(U_4192,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_4192),U_4186) != U_4196
| hBOOL(hAPP(hAPP(c_member(U_4192),U_4187),U_4186))
| U_4194 != hAPP(hAPP(c_Set_Oinsert(U_4192),U_4187),U_4186)
| hAPP(c_Finite__Set_Ocard(U_4192),U_4194) = hAPP(c_Nat_OSuc,U_4196) ),
inference(clausify,[status(thm)],[f_1075_5]) ).
fof(f_1076_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_1076_2,plain,
! [U_4199,U_4198,U_4197] :
( ( ( hAPP(c_Finite__Set_Ocard(U_4197),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4197,tc_HOL_Obool)),U_4198),hAPP(hAPP(c_Set_Oinsert(U_4197),U_4199),c_Orderings_Obot__class_Obot(tc_fun(U_4197,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_4197),U_4198)
| hBOOL(hAPP(hAPP(c_member(U_4197),U_4199),U_4198)) )
& ( hAPP(c_Finite__Set_Ocard(U_4197),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4197,tc_HOL_Obool)),U_4198),hAPP(hAPP(c_Set_Oinsert(U_4197),U_4199),c_Orderings_Obot__class_Obot(tc_fun(U_4197,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4197),U_4198)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_4197),U_4199),U_4198)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4197),U_4198)) ),
inference(variable_rename,[status(thm)],[f_1076_1]) ).
cnf(f_1076_3,plain,
( hAPP(c_Finite__Set_Ocard(U_4197),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4197,tc_HOL_Obool)),U_4198),hAPP(hAPP(c_Set_Oinsert(U_4197),U_4199),c_Orderings_Obot__class_Obot(tc_fun(U_4197,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4197),U_4198)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_4197),U_4199),U_4198))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4197),U_4198)) ),
inference(clausify,[status(thm)],[f_1076_2]) ).
cnf(f_1076_4,plain,
( hAPP(c_Finite__Set_Ocard(U_4197),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4197,tc_HOL_Obool)),U_4198),hAPP(hAPP(c_Set_Oinsert(U_4197),U_4199),c_Orderings_Obot__class_Obot(tc_fun(U_4197,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_4197),U_4198)
| hBOOL(hAPP(hAPP(c_member(U_4197),U_4199),U_4198))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4197),U_4198)) ),
inference(clausify,[status(thm)],[f_1076_2]) ).
fof(f_1077_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_1077_2,plain,
! [U_4202,U_4201,U_4200] :
( hAPP(c_Finite__Set_Ocard(U_4200),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4200,tc_HOL_Obool)),U_4201),hAPP(hAPP(c_Set_Oinsert(U_4200),U_4202),c_Orderings_Obot__class_Obot(tc_fun(U_4200,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4200),U_4201)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_4200),U_4202),U_4201))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4200),U_4201)) ),
inference(variable_rename,[status(thm)],[f_1077_1]) ).
cnf(f_1077_3,plain,
( hAPP(c_Finite__Set_Ocard(U_4200),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4200,tc_HOL_Obool)),U_4201),hAPP(hAPP(c_Set_Oinsert(U_4200),U_4202),c_Orderings_Obot__class_Obot(tc_fun(U_4200,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4200),U_4201)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_4200),U_4202),U_4201))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4200),U_4201)) ),
inference(clausify,[status(thm)],[f_1077_2]) ).
fof(f_1078_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_1078_2,plain,
! [U_4205,U_4204,U_4203] :
( hAPP(c_Finite__Set_Ocard(U_4203),U_4204) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_4203),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4203,tc_HOL_Obool)),U_4204),hAPP(hAPP(c_Set_Oinsert(U_4203),U_4205),c_Orderings_Obot__class_Obot(tc_fun(U_4203,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_4203),U_4205),U_4204))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4203),U_4204)) ),
inference(variable_rename,[status(thm)],[f_1078_1]) ).
cnf(f_1078_3,plain,
( hAPP(c_Finite__Set_Ocard(U_4203),U_4204) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_4203),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4203,tc_HOL_Obool)),U_4204),hAPP(hAPP(c_Set_Oinsert(U_4203),U_4205),c_Orderings_Obot__class_Obot(tc_fun(U_4203,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_4203),U_4205),U_4204))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4203),U_4204)) ),
inference(clausify,[status(thm)],[f_1078_2]) ).
fof(f_1079_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_1079_2,plain,
! [U_4209,U_4208,U_4207,U_4206] :
( ( hAPP(c_Finite__Set_Ocard(tc_sum(U_4206,U_4208)),c_Sum__Type_OPlus(U_4206,U_4208,U_4207,U_4209)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4208),U_4209))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_4206),U_4207)) ) )
& ( hAPP(c_Finite__Set_Ocard(tc_sum(U_4206,U_4208)),c_Sum__Type_OPlus(U_4206,U_4208,U_4207,U_4209)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4206),U_4207)),hAPP(c_Finite__Set_Ocard(U_4208),U_4209))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4208),U_4209))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4206),U_4207)) ) ),
inference(variable_rename,[status(thm)],[f_1079_1]) ).
fof(f_1079_3,plain,
( ! [U_4217,U_4215,U_4213,U_4211] :
( hAPP(c_Finite__Set_Ocard(tc_sum(U_4211,U_4215)),c_Sum__Type_OPlus(U_4211,U_4215,U_4213,U_4217)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4215),U_4217))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_4211),U_4213)) ) )
& ! [U_4216,U_4214,U_4212,U_4210] :
( hAPP(c_Finite__Set_Ocard(tc_sum(U_4210,U_4214)),c_Sum__Type_OPlus(U_4210,U_4214,U_4212,U_4216)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4210),U_4212)),hAPP(c_Finite__Set_Ocard(U_4214),U_4216))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4214),U_4216))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4210),U_4212)) ) ),
inference(miniscope,[status(thm)],[f_1079_2]) ).
cnf(f_1079_4,plain,
( hAPP(c_Finite__Set_Ocard(tc_sum(U_4210,U_4214)),c_Sum__Type_OPlus(U_4210,U_4214,U_4212,U_4216)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4210),U_4212)),hAPP(c_Finite__Set_Ocard(U_4214),U_4216))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4214),U_4216))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4210),U_4212)) ),
inference(clausify,[status(thm)],[f_1079_3]) ).
cnf(f_1079_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4211),U_4213))
| hAPP(c_Finite__Set_Ocard(tc_sum(U_4211,U_4215)),c_Sum__Type_OPlus(U_4211,U_4215,U_4213,U_4217)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1079_3]) ).
cnf(f_1079_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4215),U_4217))
| hAPP(c_Finite__Set_Ocard(tc_sum(U_4211,U_4215)),c_Sum__Type_OPlus(U_4211,U_4215,U_4213,U_4217)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1079_3]) ).
fof(f_1080_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_1080_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_1080_1]) ).
fof(f_1081_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_1081_2,plain,
! [U_4219,U_4218] :
( ( ( c_Groups_Oone__class_Oone(U_4218) = U_4219
| U_4219 != c_Groups_Oone__class_Oone(U_4218) )
& ( U_4219 = c_Groups_Oone__class_Oone(U_4218)
| c_Groups_Oone__class_Oone(U_4218) != U_4219 ) )
| ~ class_Groups_Oone(U_4218) ),
inference(variable_rename,[status(thm)],[f_1081_1]) ).
cnf(f_1081_3,plain,
( U_4219 = c_Groups_Oone__class_Oone(U_4218)
| c_Groups_Oone__class_Oone(U_4218) != U_4219
| ~ class_Groups_Oone(U_4218) ),
inference(clausify,[status(thm)],[f_1081_2]) ).
cnf(f_1081_4,plain,
( c_Groups_Oone__class_Oone(U_4218) = U_4219
| U_4219 != c_Groups_Oone__class_Oone(U_4218)
| ~ class_Groups_Oone(U_4218) ),
inference(clausify,[status(thm)],[f_1081_2]) ).
fof(f_1082_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_1082_2,plain,
! [U_4220] :
( c_Groups_Ozero__class_Ozero(U_4220) != c_Groups_Oone__class_Oone(U_4220)
| ~ class_Rings_Ozero__neq__one(U_4220) ),
inference(variable_rename,[status(thm)],[f_1082_1]) ).
cnf(f_1082_3,plain,
( c_Groups_Ozero__class_Ozero(U_4220) != c_Groups_Oone__class_Oone(U_4220)
| ~ class_Rings_Ozero__neq__one(U_4220) ),
inference(clausify,[status(thm)],[f_1082_2]) ).
fof(f_1083_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_1083_2,plain,
! [U_4221] :
( c_Groups_Oone__class_Oone(U_4221) != c_Groups_Ozero__class_Ozero(U_4221)
| ~ class_Rings_Ozero__neq__one(U_4221) ),
inference(variable_rename,[status(thm)],[f_1083_1]) ).
cnf(f_1083_3,plain,
( c_Groups_Oone__class_Oone(U_4221) != c_Groups_Ozero__class_Ozero(U_4221)
| ~ class_Rings_Ozero__neq__one(U_4221) ),
inference(clausify,[status(thm)],[f_1083_2]) ).
fof(f_1084_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_1084_2,plain,
! [U_4222] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4222),c_Groups_Oone__class_Oone(U_4222)),c_Groups_Ozero__class_Ozero(U_4222)))
| ~ class_Rings_Olinordered__semidom(U_4222) ),
inference(variable_rename,[status(thm)],[f_1084_1]) ).
cnf(f_1084_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4222),c_Groups_Oone__class_Oone(U_4222)),c_Groups_Ozero__class_Ozero(U_4222)))
| ~ class_Rings_Olinordered__semidom(U_4222) ),
inference(clausify,[status(thm)],[f_1084_2]) ).
fof(f_1085_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_1085_2,plain,
! [U_4223] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4223),c_Groups_Ozero__class_Ozero(U_4223)),c_Groups_Oone__class_Oone(U_4223)))
| ~ class_Rings_Olinordered__semidom(U_4223) ),
inference(variable_rename,[status(thm)],[f_1085_1]) ).
cnf(f_1085_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4223),c_Groups_Ozero__class_Ozero(U_4223)),c_Groups_Oone__class_Oone(U_4223)))
| ~ class_Rings_Olinordered__semidom(U_4223) ),
inference(clausify,[status(thm)],[f_1085_2]) ).
fof(f_1086_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_1086_2,plain,
! [U_4224] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4224),c_Groups_Ozero__class_Ozero(U_4224)),c_Groups_Oone__class_Oone(U_4224)))
| ~ class_Rings_Olinordered__semidom(U_4224) ),
inference(variable_rename,[status(thm)],[f_1086_1]) ).
cnf(f_1086_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4224),c_Groups_Ozero__class_Ozero(U_4224)),c_Groups_Oone__class_Oone(U_4224)))
| ~ class_Rings_Olinordered__semidom(U_4224) ),
inference(clausify,[status(thm)],[f_1086_2]) ).
fof(f_1087_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_1087_2,plain,
! [U_4225] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4225),c_Groups_Oone__class_Oone(U_4225)),c_Groups_Ozero__class_Ozero(U_4225)))
| ~ class_Rings_Olinordered__semidom(U_4225) ),
inference(variable_rename,[status(thm)],[f_1087_1]) ).
cnf(f_1087_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4225),c_Groups_Oone__class_Oone(U_4225)),c_Groups_Ozero__class_Ozero(U_4225)))
| ~ class_Rings_Olinordered__semidom(U_4225) ),
inference(clausify,[status(thm)],[f_1087_2]) ).
fof(f_1088_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_1088_2,plain,
! [U_4227,U_4226] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4226),U_4227),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4226),U_4227),c_Groups_Oone__class_Oone(U_4226))))
| ~ class_Rings_Olinordered__semidom(U_4226) ),
inference(variable_rename,[status(thm)],[f_1088_1]) ).
cnf(f_1088_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4226),U_4227),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4226),U_4227),c_Groups_Oone__class_Oone(U_4226))))
| ~ class_Rings_Olinordered__semidom(U_4226) ),
inference(clausify,[status(thm)],[f_1088_2]) ).
fof(f_1089_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_1089_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_1089_1]) ).
fof(f_1090_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_1090_2,plain,
! [U_4228] : hAPP(c_Nat_OSuc,U_4228) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4228),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_1090_1]) ).
cnf(f_1090_3,plain,
hAPP(c_Nat_OSuc,U_4228) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4228),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_1090_2]) ).
fof(f_1091_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_1091_2,plain,
! [U_4229] : hAPP(c_Nat_OSuc,U_4229) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4229),
inference(variable_rename,[status(thm)],[f_1091_1]) ).
cnf(f_1091_3,plain,
hAPP(c_Nat_OSuc,U_4229) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4229),
inference(clausify,[status(thm)],[f_1091_2]) ).
fof(f_1092_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_1092_2,plain,
! [U_4230] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4230)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4230,
inference(variable_rename,[status(thm)],[f_1092_1]) ).
cnf(f_1092_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4230)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4230,
inference(clausify,[status(thm)],[f_1092_2]) ).
fof(f_1093_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_1093_2,plain,
! [U_4232,U_4231] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4231),hAPP(c_Nat_OSuc,U_4232)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4231),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4232),
inference(variable_rename,[status(thm)],[f_1093_1]) ).
cnf(f_1093_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4231),hAPP(c_Nat_OSuc,U_4232)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4231),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4232),
inference(clausify,[status(thm)],[f_1093_2]) ).
fof(f_1094_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_1094_2,plain,
! [U_4233] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4233),c_Groups_Ozero__class_Ozero(U_4233)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4233),c_Groups_Oone__class_Oone(U_4233)),c_Groups_Oone__class_Oone(U_4233))))
| ~ class_Rings_Olinordered__semidom(U_4233) ),
inference(variable_rename,[status(thm)],[f_1094_1]) ).
cnf(f_1094_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4233),c_Groups_Ozero__class_Ozero(U_4233)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4233),c_Groups_Oone__class_Oone(U_4233)),c_Groups_Oone__class_Oone(U_4233))))
| ~ class_Rings_Olinordered__semidom(U_4233) ),
inference(clausify,[status(thm)],[f_1094_2]) ).
fof(f_1095_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_1095_2,plain,
! [U_4240,U_4239,U_4238] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4238,tc_Nat_Onat),U_4240),U_4239) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ! [U_4237] :
( ? [U_4236] :
( hAPP(U_4240,U_4236) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_4237 != U_4236
& hBOOL(hAPP(hAPP(c_member(U_4238),U_4236),U_4239)) )
| hAPP(U_4240,U_4237) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_4238),U_4237),U_4239)) ) )
& ( ? [U_4235] :
( ! [U_4234] :
( hAPP(U_4240,U_4234) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4235 = U_4234
| ~ hBOOL(hAPP(hAPP(c_member(U_4238),U_4234),U_4239)) )
& hAPP(U_4240,U_4235) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_4238),U_4235),U_4239)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4238,tc_Nat_Onat),U_4240),U_4239) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4238),U_4239)) ),
inference(variable_rename,[status(thm)],[f_1095_1]) ).
fof(f_1095_3,plain,
! [U_4240,U_4239,U_4238] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4238,tc_Nat_Onat),U_4240),U_4239) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ! [U_4237] :
( ? [U_4236] :
( hAPP(U_4240,U_4236) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_4237 != U_4236
& hBOOL(hAPP(hAPP(c_member(U_4238),U_4236),U_4239)) )
| hAPP(U_4240,U_4237) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_4238),U_4237),U_4239)) ) )
& ( ( ! [U_4234] :
( hAPP(U_4240,U_4234) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK81(U_4240,U_4239,U_4238) = U_4234
| ~ hBOOL(hAPP(hAPP(c_member(U_4238),U_4234),U_4239)) )
& hAPP(U_4240,sK81(U_4240,U_4239,U_4238)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_4238),sK81(U_4240,U_4239,U_4238)),U_4239)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4238,tc_Nat_Onat),U_4240),U_4239) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4238),U_4239)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_4235,sK81(U_4240,U_4239,U_4238))],[f_1095_2]) ).
fof(f_1095_4,plain,
! [U_4240,U_4239,U_4238] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4238,tc_Nat_Onat),U_4240),U_4239) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ! [U_4237] :
( ( hAPP(U_4240,sK82(U_4240,U_4239,U_4238,U_4237)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_4237 != sK82(U_4240,U_4239,U_4238,U_4237)
& hBOOL(hAPP(hAPP(c_member(U_4238),sK82(U_4240,U_4239,U_4238,U_4237)),U_4239)) )
| hAPP(U_4240,U_4237) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_4238),U_4237),U_4239)) ) )
& ( ( ! [U_4234] :
( hAPP(U_4240,U_4234) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK81(U_4240,U_4239,U_4238) = U_4234
| ~ hBOOL(hAPP(hAPP(c_member(U_4238),U_4234),U_4239)) )
& hAPP(U_4240,sK81(U_4240,U_4239,U_4238)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_4238),sK81(U_4240,U_4239,U_4238)),U_4239)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4238,tc_Nat_Onat),U_4240),U_4239) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4238),U_4239)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_4236,sK82(U_4240,U_4239,U_4238,U_4237))],[f_1095_3]) ).
cnf(f_1095_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_4238),sK81(U_4240,U_4239,U_4238)),U_4239))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4238,tc_Nat_Onat),U_4240),U_4239) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4238),U_4239)) ),
inference(clausify,[status(thm)],[f_1095_4]) ).
cnf(f_1095_6,plain,
( hAPP(U_4240,sK81(U_4240,U_4239,U_4238)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4238,tc_Nat_Onat),U_4240),U_4239) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4238),U_4239)) ),
inference(clausify,[status(thm)],[f_1095_4]) ).
cnf(f_1095_7,plain,
( hAPP(U_4240,U_4234) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK81(U_4240,U_4239,U_4238) = U_4234
| ~ hBOOL(hAPP(hAPP(c_member(U_4238),U_4234),U_4239))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4238,tc_Nat_Onat),U_4240),U_4239) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4238),U_4239)) ),
inference(clausify,[status(thm)],[f_1095_4]) ).
cnf(f_1095_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_4238),sK82(U_4240,U_4239,U_4238,U_4237)),U_4239))
| hAPP(U_4240,U_4237) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_4238),U_4237),U_4239))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4238,tc_Nat_Onat),U_4240),U_4239) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4238),U_4239)) ),
inference(clausify,[status(thm)],[f_1095_4]) ).
cnf(f_1095_9,plain,
( U_4237 != sK82(U_4240,U_4239,U_4238,U_4237)
| hAPP(U_4240,U_4237) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_4238),U_4237),U_4239))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4238,tc_Nat_Onat),U_4240),U_4239) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4238),U_4239)) ),
inference(clausify,[status(thm)],[f_1095_4]) ).
cnf(f_1095_10,plain,
( hAPP(U_4240,sK82(U_4240,U_4239,U_4238,U_4237)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(U_4240,U_4237) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_4238),U_4237),U_4239))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4238,tc_Nat_Onat),U_4240),U_4239) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4238),U_4239)) ),
inference(clausify,[status(thm)],[f_1095_4]) ).
fof(f_1096_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_1096_2,plain,
! [U_4241] :
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4241),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_4241
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4241)) ),
inference(variable_rename,[status(thm)],[f_1096_1]) ).
cnf(f_1096_3,plain,
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4241),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_4241
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4241)) ),
inference(clausify,[status(thm)],[f_1096_2]) ).
fof(f_1097_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_1097_2,plain,
! [U_4242] :
( U_4242 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4242),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_4242)) ),
inference(variable_rename,[status(thm)],[f_1097_1]) ).
cnf(f_1097_3,plain,
( U_4242 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4242),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_4242)) ),
inference(clausify,[status(thm)],[f_1097_2]) ).
fof(f_1098_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_1098_2,plain,
! [U_4244,U_4243] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4243),U_4244) = 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_4243),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4244))
| U_4243 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4243),U_4244) = U_4244
| U_4243 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1098_1]) ).
fof(f_1098_3,plain,
( ! [U_4248,U_4246] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4246),U_4248) = 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_4246),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4248))
| U_4246 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_4247,U_4245] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4245),U_4247) = U_4247
| U_4245 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1098_2]) ).
cnf(f_1098_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4245),U_4247) = U_4247
| U_4245 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1098_3]) ).
cnf(f_1098_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4246),U_4248) = 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_4246),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4248))
| U_4246 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1098_3]) ).
fof(f_1099_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_1099_2,plain,
! [U_4252,U_4251,U_4250,U_4249] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4250),U_4252))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4249,U_4250)),c_Sum__Type_OPlus(U_4249,U_4250,U_4251,U_4252))) ),
inference(variable_rename,[status(thm)],[f_1099_1]) ).
fof(f_1099_3,plain,
! [U_4252,U_4251,U_4250] :
( ! [U_4249] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4249,U_4250)),c_Sum__Type_OPlus(U_4249,U_4250,U_4251,U_4252)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_4250),U_4252)) ),
inference(miniscope,[status(thm)],[f_1099_2]) ).
cnf(f_1099_4,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4249,U_4250)),c_Sum__Type_OPlus(U_4249,U_4250,U_4251,U_4252)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_4250),U_4252)) ),
inference(clausify,[status(thm)],[f_1099_3]) ).
fof(f_1100_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_1100_2,plain,
! [U_4256,U_4255,U_4254,U_4253] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4253),U_4255))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4253,U_4254)),c_Sum__Type_OPlus(U_4253,U_4254,U_4255,U_4256))) ),
inference(variable_rename,[status(thm)],[f_1100_1]) ).
cnf(f_1100_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4253),U_4255))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4253,U_4254)),c_Sum__Type_OPlus(U_4253,U_4254,U_4255,U_4256))) ),
inference(clausify,[status(thm)],[f_1100_2]) ).
fof(f_1101_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_1101_2,plain,
! [U_4260,U_4259,U_4258,U_4257] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4257,U_4259)),c_Sum__Type_OPlus(U_4257,U_4259,U_4258,U_4260)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4259),U_4260))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4257),U_4258)) ),
inference(variable_rename,[status(thm)],[f_1101_1]) ).
cnf(f_1101_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4257,U_4259)),c_Sum__Type_OPlus(U_4257,U_4259,U_4258,U_4260)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4259),U_4260))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4257),U_4258)) ),
inference(clausify,[status(thm)],[f_1101_2]) ).
fof(f_1102_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_1102_2,plain,
! [U_4264,U_4263,U_4262,U_4261] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4261,U_4262)),c_Sum__Type_OPlus(U_4261,U_4262,U_4263,U_4264)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4262),U_4264))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4261),U_4263)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4262),U_4264))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_4261),U_4263)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4261,U_4262)),c_Sum__Type_OPlus(U_4261,U_4262,U_4263,U_4264))) ) ),
inference(variable_rename,[status(thm)],[f_1102_1]) ).
fof(f_1102_3,plain,
( ! [U_4272,U_4270,U_4268,U_4266] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4266,U_4268)),c_Sum__Type_OPlus(U_4266,U_4268,U_4270,U_4272)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4268),U_4272))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4266),U_4270)) )
& ! [U_4271,U_4269,U_4267,U_4265] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4267),U_4271))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_4265),U_4269)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4265,U_4267)),c_Sum__Type_OPlus(U_4265,U_4267,U_4269,U_4271))) ) ),
inference(miniscope,[status(thm)],[f_1102_2]) ).
cnf(f_1102_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4265),U_4269))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4265,U_4267)),c_Sum__Type_OPlus(U_4265,U_4267,U_4269,U_4271))) ),
inference(clausify,[status(thm)],[f_1102_3]) ).
cnf(f_1102_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4267),U_4271))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4265,U_4267)),c_Sum__Type_OPlus(U_4265,U_4267,U_4269,U_4271))) ),
inference(clausify,[status(thm)],[f_1102_3]) ).
cnf(f_1102_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_4266,U_4268)),c_Sum__Type_OPlus(U_4266,U_4268,U_4270,U_4272)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4268),U_4272))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4266),U_4270)) ),
inference(clausify,[status(thm)],[f_1102_3]) ).
fof(f_1103_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_1103_2,plain,
! [U_4276,U_4275,U_4274,U_4273] :
( hAPP(c_Finite__Set_Ocard(tc_sum(U_4273,U_4275)),c_Sum__Type_OPlus(U_4273,U_4275,U_4274,U_4276)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4273),U_4274)),hAPP(c_Finite__Set_Ocard(U_4275),U_4276))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4275),U_4276))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4273),U_4274)) ),
inference(variable_rename,[status(thm)],[f_1103_1]) ).
cnf(f_1103_3,plain,
( hAPP(c_Finite__Set_Ocard(tc_sum(U_4273,U_4275)),c_Sum__Type_OPlus(U_4273,U_4275,U_4274,U_4276)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4273),U_4274)),hAPP(c_Finite__Set_Ocard(U_4275),U_4276))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4275),U_4276))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4273),U_4274)) ),
inference(clausify,[status(thm)],[f_1103_2]) ).
fof(f_1104_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_1104_2,plain,
! [U_4279,U_4278,U_4277] :
( hAPP(c_Finite__Set_Ocard(U_4277),hAPP(hAPP(c_Set_Oinsert(U_4277),U_4279),U_4278)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_4277),U_4278))
| hBOOL(hAPP(hAPP(c_member(U_4277),U_4279),U_4278))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4277),U_4278)) ),
inference(variable_rename,[status(thm)],[f_1104_1]) ).
cnf(f_1104_3,plain,
( hAPP(c_Finite__Set_Ocard(U_4277),hAPP(hAPP(c_Set_Oinsert(U_4277),U_4279),U_4278)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_4277),U_4278))
| hBOOL(hAPP(hAPP(c_member(U_4277),U_4279),U_4278))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4277),U_4278)) ),
inference(clausify,[status(thm)],[f_1104_2]) ).
fof(f_1105_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_1105_2,plain,
! [U_4284,U_4283,U_4282,U_4281,U_4280] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4280),U_4283),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4281,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4282),U_4284))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4280),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4280),U_4283),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4281,U_4282))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4280),U_4283),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4282),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4282),U_4284))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4281),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4282),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Groups_Ocomm__monoid__add(U_4280) ),
inference(variable_rename,[status(thm)],[f_1105_1]) ).
cnf(f_1105_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4280),U_4283),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4281,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4282),U_4284))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4280),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4280),U_4283),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4281,U_4282))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4280),U_4283),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4282),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4282),U_4284))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4281),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4282),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Groups_Ocomm__monoid__add(U_4280) ),
inference(clausify,[status(thm)],[f_1105_2]) ).
fof(f_1106_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_1106_2,plain,
! [U_4288,U_4287,U_4286,U_4285] :
( hAPP(c_Finite__Set_Ocard(U_4285),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4285,tc_HOL_Obool)),U_4286),hAPP(hAPP(c_Set_Oinsert(U_4285),U_4287),U_4288))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4285),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4285,tc_HOL_Obool)),U_4286),U_4288))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| hBOOL(hAPP(hAPP(c_member(U_4285),U_4287),U_4288))
| ~ hBOOL(hAPP(hAPP(c_member(U_4285),U_4287),U_4286))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4285),U_4286)) ),
inference(variable_rename,[status(thm)],[f_1106_1]) ).
cnf(f_1106_3,plain,
( hAPP(c_Finite__Set_Ocard(U_4285),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4285,tc_HOL_Obool)),U_4286),hAPP(hAPP(c_Set_Oinsert(U_4285),U_4287),U_4288))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4285),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4285,tc_HOL_Obool)),U_4286),U_4288))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| hBOOL(hAPP(hAPP(c_member(U_4285),U_4287),U_4288))
| ~ hBOOL(hAPP(hAPP(c_member(U_4285),U_4287),U_4286))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4285),U_4286)) ),
inference(clausify,[status(thm)],[f_1106_2]) ).
fof(f_1107_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_1107_2,plain,
! [U_4291,U_4290,U_4289] :
( hAPP(c_Finite__Set_Ocard(U_4289),hAPP(hAPP(c_Set_Oinsert(U_4289),U_4291),U_4290)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_4289),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4289,tc_HOL_Obool)),U_4290),hAPP(hAPP(c_Set_Oinsert(U_4289),U_4291),c_Orderings_Obot__class_Obot(tc_fun(U_4289,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4289),U_4290)) ),
inference(variable_rename,[status(thm)],[f_1107_1]) ).
cnf(f_1107_3,plain,
( hAPP(c_Finite__Set_Ocard(U_4289),hAPP(hAPP(c_Set_Oinsert(U_4289),U_4291),U_4290)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_4289),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4289,tc_HOL_Obool)),U_4290),hAPP(hAPP(c_Set_Oinsert(U_4289),U_4291),c_Orderings_Obot__class_Obot(tc_fun(U_4289,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4289),U_4290)) ),
inference(clausify,[status(thm)],[f_1107_2]) ).
fof(f_1108_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_1108_2,plain,
! [U_4293,U_4292] : c_Sum__Type_OPlus(U_4292,U_4293,c_Orderings_Otop__class_Otop(tc_fun(U_4292,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_4293,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_4292,U_4293),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_1108_1]) ).
cnf(f_1108_3,plain,
c_Sum__Type_OPlus(U_4292,U_4293,c_Orderings_Otop__class_Otop(tc_fun(U_4292,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_4293,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_4292,U_4293),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_1108_2]) ).
fof(f_1109_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_1109_2,plain,
! [U_4297,U_4296,U_4295] :
( hAPP(c_Finite__Set_Ocard(U_4295),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4295,tc_HOL_Obool)),U_4296),U_4297)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4295),U_4296)),hAPP(c_Finite__Set_Ocard(U_4295),U_4297))
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ? [U_4294] : hBOOL(hAPP(hAPP(c_member(U_4295),U_4294),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4295,tc_HOL_Obool)),U_4296),U_4297))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4295),U_4297))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4295),U_4296)) ),
inference(variable_rename,[status(thm)],[f_1109_1]) ).
fof(f_1109_3,plain,
! [U_4297,U_4296,U_4295] :
( hAPP(c_Finite__Set_Ocard(U_4295),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4295,tc_HOL_Obool)),U_4296),U_4297)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4295),U_4296)),hAPP(c_Finite__Set_Ocard(U_4295),U_4297))
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_4295),sK83(U_4297,U_4296,U_4295)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4295,tc_HOL_Obool)),U_4296),U_4297))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4295),U_4297))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4295),U_4296)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_4294,sK83(U_4297,U_4296,U_4295))],[f_1109_2]) ).
cnf(f_1109_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_4295),sK83(U_4297,U_4296,U_4295)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4295,tc_HOL_Obool)),U_4296),U_4297)))
| hAPP(c_Finite__Set_Ocard(U_4295),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4295,tc_HOL_Obool)),U_4296),U_4297)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4295),U_4296)),hAPP(c_Finite__Set_Ocard(U_4295),U_4297))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4295),U_4297))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4295),U_4296)) ),
inference(clausify,[status(thm)],[f_1109_3]) ).
cnf(f_1109_5,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Finite__Set_Ocard(U_4295),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4295,tc_HOL_Obool)),U_4296),U_4297)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4295),U_4296)),hAPP(c_Finite__Set_Ocard(U_4295),U_4297))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4295),U_4297))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4295),U_4296)) ),
inference(clausify,[status(thm)],[f_1109_3]) ).
fof(f_1110_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_1110_2,plain,
! [U_4301,U_4300,U_4299,U_4298] :
( ( c_Sum__Type_OPlus(U_4298,U_4299,U_4300,U_4301) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_4298,U_4299),tc_HOL_Obool))
| U_4301 != c_Orderings_Obot__class_Obot(tc_fun(U_4299,tc_HOL_Obool))
| U_4300 != c_Orderings_Obot__class_Obot(tc_fun(U_4298,tc_HOL_Obool)) )
& ( ( U_4301 = c_Orderings_Obot__class_Obot(tc_fun(U_4299,tc_HOL_Obool))
& U_4300 = c_Orderings_Obot__class_Obot(tc_fun(U_4298,tc_HOL_Obool)) )
| c_Sum__Type_OPlus(U_4298,U_4299,U_4300,U_4301) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_4298,U_4299),tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_1110_1]) ).
fof(f_1110_3,plain,
( ! [U_4309,U_4307,U_4305,U_4303] :
( c_Sum__Type_OPlus(U_4303,U_4305,U_4307,U_4309) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_4303,U_4305),tc_HOL_Obool))
| U_4309 != c_Orderings_Obot__class_Obot(tc_fun(U_4305,tc_HOL_Obool))
| U_4307 != c_Orderings_Obot__class_Obot(tc_fun(U_4303,tc_HOL_Obool)) )
& ! [U_4308,U_4306,U_4304,U_4302] :
( ( U_4308 = c_Orderings_Obot__class_Obot(tc_fun(U_4304,tc_HOL_Obool))
& U_4306 = c_Orderings_Obot__class_Obot(tc_fun(U_4302,tc_HOL_Obool)) )
| c_Sum__Type_OPlus(U_4302,U_4304,U_4306,U_4308) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_4302,U_4304),tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_1110_2]) ).
cnf(f_1110_4,plain,
( U_4306 = c_Orderings_Obot__class_Obot(tc_fun(U_4302,tc_HOL_Obool))
| c_Sum__Type_OPlus(U_4302,U_4304,U_4306,U_4308) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_4302,U_4304),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1110_3]) ).
cnf(f_1110_5,plain,
( U_4308 = c_Orderings_Obot__class_Obot(tc_fun(U_4304,tc_HOL_Obool))
| c_Sum__Type_OPlus(U_4302,U_4304,U_4306,U_4308) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_4302,U_4304),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1110_3]) ).
cnf(f_1110_6,plain,
( c_Sum__Type_OPlus(U_4303,U_4305,U_4307,U_4309) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_4303,U_4305),tc_HOL_Obool))
| U_4309 != c_Orderings_Obot__class_Obot(tc_fun(U_4305,tc_HOL_Obool))
| U_4307 != c_Orderings_Obot__class_Obot(tc_fun(U_4303,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1110_3]) ).
fof(f_1111_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_1111_2,plain,
! [U_4311,U_4310] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4310),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4310),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4310),c_Groups_Oone__class_Oone(U_4310)),U_4311)),U_4311)),c_Groups_Ozero__class_Ozero(U_4310)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4310),U_4311),c_Groups_Ozero__class_Ozero(U_4310))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4310),U_4311),c_Groups_Ozero__class_Ozero(U_4310)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4310),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4310),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4310),c_Groups_Oone__class_Oone(U_4310)),U_4311)),U_4311)),c_Groups_Ozero__class_Ozero(U_4310))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_4310),U_4311),c_Int_Oring__1__class_OInts(U_4310)))
| ~ class_Rings_Olinordered__idom(U_4310) ),
inference(variable_rename,[status(thm)],[f_1111_1]) ).
cnf(f_1111_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4310),U_4311),c_Groups_Ozero__class_Ozero(U_4310)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4310),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4310),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4310),c_Groups_Oone__class_Oone(U_4310)),U_4311)),U_4311)),c_Groups_Ozero__class_Ozero(U_4310)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4310),U_4311),c_Int_Oring__1__class_OInts(U_4310)))
| ~ class_Rings_Olinordered__idom(U_4310) ),
inference(clausify,[status(thm)],[f_1111_2]) ).
cnf(f_1111_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4310),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4310),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4310),c_Groups_Oone__class_Oone(U_4310)),U_4311)),U_4311)),c_Groups_Ozero__class_Ozero(U_4310)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4310),U_4311),c_Groups_Ozero__class_Ozero(U_4310)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4310),U_4311),c_Int_Oring__1__class_OInts(U_4310)))
| ~ class_Rings_Olinordered__idom(U_4310) ),
inference(clausify,[status(thm)],[f_1111_2]) ).
fof(f_1112_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_1112_2,plain,
! [U_4316,U_4315,U_4314] :
( hAPP(U_4315,c_Big__Operators_Olattice__class_OInf__fin(U_4314,U_4316)) = c_Big__Operators_Olattice__class_OInf__fin(U_4314,hAPP(c_Set_Oimage(U_4314,U_4314,U_4315),U_4316))
| U_4316 = c_Orderings_Obot__class_Obot(tc_fun(U_4314,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4314),U_4316))
| ? [U_4313,U_4312] : hAPP(U_4315,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4314),U_4313),U_4312)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4314),hAPP(U_4315,U_4313)),hAPP(U_4315,U_4312))
| ~ class_Lattices_Olattice(U_4314) ),
inference(variable_rename,[status(thm)],[f_1112_1]) ).
fof(f_1112_3,plain,
! [U_4316,U_4315,U_4314] :
( hAPP(U_4315,c_Big__Operators_Olattice__class_OInf__fin(U_4314,U_4316)) = c_Big__Operators_Olattice__class_OInf__fin(U_4314,hAPP(c_Set_Oimage(U_4314,U_4314,U_4315),U_4316))
| U_4316 = c_Orderings_Obot__class_Obot(tc_fun(U_4314,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4314),U_4316))
| ? [U_4312] : hAPP(U_4315,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4314),sK84(U_4316,U_4315,U_4314)),U_4312)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4314),hAPP(U_4315,sK84(U_4316,U_4315,U_4314))),hAPP(U_4315,U_4312))
| ~ class_Lattices_Olattice(U_4314) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_4313,sK84(U_4316,U_4315,U_4314))],[f_1112_2]) ).
fof(f_1112_4,plain,
! [U_4316,U_4315,U_4314] :
( hAPP(U_4315,c_Big__Operators_Olattice__class_OInf__fin(U_4314,U_4316)) = c_Big__Operators_Olattice__class_OInf__fin(U_4314,hAPP(c_Set_Oimage(U_4314,U_4314,U_4315),U_4316))
| U_4316 = c_Orderings_Obot__class_Obot(tc_fun(U_4314,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4314),U_4316))
| hAPP(U_4315,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4314),sK84(U_4316,U_4315,U_4314)),sK85(U_4316,U_4315,U_4314))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4314),hAPP(U_4315,sK84(U_4316,U_4315,U_4314))),hAPP(U_4315,sK85(U_4316,U_4315,U_4314)))
| ~ class_Lattices_Olattice(U_4314) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_4312,sK85(U_4316,U_4315,U_4314))],[f_1112_3]) ).
cnf(f_1112_5,plain,
( hAPP(U_4315,c_Big__Operators_Olattice__class_OInf__fin(U_4314,U_4316)) = c_Big__Operators_Olattice__class_OInf__fin(U_4314,hAPP(c_Set_Oimage(U_4314,U_4314,U_4315),U_4316))
| U_4316 = c_Orderings_Obot__class_Obot(tc_fun(U_4314,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4314),U_4316))
| hAPP(U_4315,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4314),sK84(U_4316,U_4315,U_4314)),sK85(U_4316,U_4315,U_4314))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4314),hAPP(U_4315,sK84(U_4316,U_4315,U_4314))),hAPP(U_4315,sK85(U_4316,U_4315,U_4314)))
| ~ class_Lattices_Olattice(U_4314) ),
inference(clausify,[status(thm)],[f_1112_4]) ).
fof(f_1113_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_1113_2,plain,
! [U_4321,U_4320,U_4319] :
( hAPP(U_4320,c_Big__Operators_Olattice__class_OSup__fin(U_4319,U_4321)) = c_Big__Operators_Olattice__class_OSup__fin(U_4319,hAPP(c_Set_Oimage(U_4319,U_4319,U_4320),U_4321))
| U_4321 = c_Orderings_Obot__class_Obot(tc_fun(U_4319,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4319),U_4321))
| ? [U_4318,U_4317] : hAPP(U_4320,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4319),U_4318),U_4317)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4319),hAPP(U_4320,U_4318)),hAPP(U_4320,U_4317))
| ~ class_Lattices_Olattice(U_4319) ),
inference(variable_rename,[status(thm)],[f_1113_1]) ).
fof(f_1113_3,plain,
! [U_4321,U_4320,U_4319] :
( hAPP(U_4320,c_Big__Operators_Olattice__class_OSup__fin(U_4319,U_4321)) = c_Big__Operators_Olattice__class_OSup__fin(U_4319,hAPP(c_Set_Oimage(U_4319,U_4319,U_4320),U_4321))
| U_4321 = c_Orderings_Obot__class_Obot(tc_fun(U_4319,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4319),U_4321))
| ? [U_4317] : hAPP(U_4320,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4319),sK86(U_4321,U_4320,U_4319)),U_4317)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4319),hAPP(U_4320,sK86(U_4321,U_4320,U_4319))),hAPP(U_4320,U_4317))
| ~ class_Lattices_Olattice(U_4319) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_4318,sK86(U_4321,U_4320,U_4319))],[f_1113_2]) ).
fof(f_1113_4,plain,
! [U_4321,U_4320,U_4319] :
( hAPP(U_4320,c_Big__Operators_Olattice__class_OSup__fin(U_4319,U_4321)) = c_Big__Operators_Olattice__class_OSup__fin(U_4319,hAPP(c_Set_Oimage(U_4319,U_4319,U_4320),U_4321))
| U_4321 = c_Orderings_Obot__class_Obot(tc_fun(U_4319,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4319),U_4321))
| hAPP(U_4320,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4319),sK86(U_4321,U_4320,U_4319)),sK87(U_4321,U_4320,U_4319))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4319),hAPP(U_4320,sK86(U_4321,U_4320,U_4319))),hAPP(U_4320,sK87(U_4321,U_4320,U_4319)))
| ~ class_Lattices_Olattice(U_4319) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_4317,sK87(U_4321,U_4320,U_4319))],[f_1113_3]) ).
cnf(f_1113_5,plain,
( hAPP(U_4320,c_Big__Operators_Olattice__class_OSup__fin(U_4319,U_4321)) = c_Big__Operators_Olattice__class_OSup__fin(U_4319,hAPP(c_Set_Oimage(U_4319,U_4319,U_4320),U_4321))
| U_4321 = c_Orderings_Obot__class_Obot(tc_fun(U_4319,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4319),U_4321))
| hAPP(U_4320,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4319),sK86(U_4321,U_4320,U_4319)),sK87(U_4321,U_4320,U_4319))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4319),hAPP(U_4320,sK86(U_4321,U_4320,U_4319))),hAPP(U_4320,sK87(U_4321,U_4320,U_4319)))
| ~ class_Lattices_Olattice(U_4319) ),
inference(clausify,[status(thm)],[f_1113_4]) ).
fof(f_1114_1,plain,
! [V_n_2,V_P_2] :
( ? [B_k] :
( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [B_i] :
( ~ hBOOL(hAPP(V_P_2,B_i))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) )
| ~ hBOOL(hAPP(V_P_2,V_n_2))
| hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(fof_nnf,[status(thm)],[fact_ex__least__nat__less]) ).
fof(f_1114_2,plain,
! [U_4325,U_4324] :
( ? [U_4323] :
( hBOOL(hAPP(U_4324,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4323),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [U_4322] :
( ~ hBOOL(hAPP(U_4324,U_4322))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4322),U_4323)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4323),U_4325)) )
| ~ hBOOL(hAPP(U_4324,U_4325))
| hBOOL(hAPP(U_4324,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(variable_rename,[status(thm)],[f_1114_1]) ).
fof(f_1114_3,plain,
! [U_4325,U_4324] :
( ( hBOOL(hAPP(U_4324,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK88(U_4325,U_4324)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [U_4322] :
( ~ hBOOL(hAPP(U_4324,U_4322))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4322),sK88(U_4325,U_4324))) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK88(U_4325,U_4324)),U_4325)) )
| ~ hBOOL(hAPP(U_4324,U_4325))
| hBOOL(hAPP(U_4324,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_4323,sK88(U_4325,U_4324))],[f_1114_2]) ).
cnf(f_1114_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK88(U_4325,U_4324)),U_4325))
| ~ hBOOL(hAPP(U_4324,U_4325))
| hBOOL(hAPP(U_4324,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_1114_3]) ).
cnf(f_1114_5,plain,
( ~ hBOOL(hAPP(U_4324,U_4322))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4322),sK88(U_4325,U_4324)))
| ~ hBOOL(hAPP(U_4324,U_4325))
| hBOOL(hAPP(U_4324,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_1114_3]) ).
cnf(f_1114_6,plain,
( hBOOL(hAPP(U_4324,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK88(U_4325,U_4324)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(U_4324,U_4325))
| hBOOL(hAPP(U_4324,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_1114_3]) ).
fof(f_1115_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_1115_2,plain,
! [U_4326] :
( hBOOL(hAPP(hAPP(c_member(U_4326),c_Groups_Ozero__class_Ozero(U_4326)),c_Int_Oring__1__class_OInts(U_4326)))
| ~ class_Rings_Oring__1(U_4326) ),
inference(variable_rename,[status(thm)],[f_1115_1]) ).
cnf(f_1115_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_4326),c_Groups_Ozero__class_Ozero(U_4326)),c_Int_Oring__1__class_OInts(U_4326)))
| ~ class_Rings_Oring__1(U_4326) ),
inference(clausify,[status(thm)],[f_1115_2]) ).
fof(f_1116_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_1116_2,plain,
! [U_4329,U_4328,U_4327] :
( hBOOL(hAPP(hAPP(c_member(U_4327),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4327),U_4328),U_4329)),c_Int_Oring__1__class_OInts(U_4327)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4327),U_4329),c_Int_Oring__1__class_OInts(U_4327)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4327),U_4328),c_Int_Oring__1__class_OInts(U_4327)))
| ~ class_Rings_Oring__1(U_4327) ),
inference(variable_rename,[status(thm)],[f_1116_1]) ).
cnf(f_1116_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_4327),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4327),U_4328),U_4329)),c_Int_Oring__1__class_OInts(U_4327)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4327),U_4329),c_Int_Oring__1__class_OInts(U_4327)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4327),U_4328),c_Int_Oring__1__class_OInts(U_4327)))
| ~ class_Rings_Oring__1(U_4327) ),
inference(clausify,[status(thm)],[f_1116_2]) ).
fof(f_1117_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_1117_2,plain,
! [U_4332,U_4331,U_4330] :
( hBOOL(hAPP(hAPP(c_member(U_4330),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4330),U_4331),U_4332)),c_Int_Oring__1__class_OInts(U_4330)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4330),U_4332),c_Int_Oring__1__class_OInts(U_4330)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4330),U_4331),c_Int_Oring__1__class_OInts(U_4330)))
| ~ class_Rings_Oring__1(U_4330) ),
inference(variable_rename,[status(thm)],[f_1117_1]) ).
cnf(f_1117_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_4330),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4330),U_4331),U_4332)),c_Int_Oring__1__class_OInts(U_4330)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4330),U_4332),c_Int_Oring__1__class_OInts(U_4330)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4330),U_4331),c_Int_Oring__1__class_OInts(U_4330)))
| ~ class_Rings_Oring__1(U_4330) ),
inference(clausify,[status(thm)],[f_1117_2]) ).
fof(f_1118_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_1118_2,plain,
! [U_4333] :
( hBOOL(hAPP(hAPP(c_member(U_4333),c_Groups_Oone__class_Oone(U_4333)),c_Int_Oring__1__class_OInts(U_4333)))
| ~ class_Rings_Oring__1(U_4333) ),
inference(variable_rename,[status(thm)],[f_1118_1]) ).
cnf(f_1118_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_4333),c_Groups_Oone__class_Oone(U_4333)),c_Int_Oring__1__class_OInts(U_4333)))
| ~ class_Rings_Oring__1(U_4333) ),
inference(clausify,[status(thm)],[f_1118_2]) ).
fof(f_1119_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_1119_2,plain,
! [U_4335,U_4334] :
( hBOOL(hAPP(hAPP(c_member(U_4334),hAPP(c_Groups_Ouminus__class_Ouminus(U_4334),U_4335)),c_Int_Oring__1__class_OInts(U_4334)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4334),U_4335),c_Int_Oring__1__class_OInts(U_4334)))
| ~ class_Rings_Oring__1(U_4334) ),
inference(variable_rename,[status(thm)],[f_1119_1]) ).
cnf(f_1119_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_4334),hAPP(c_Groups_Ouminus__class_Ouminus(U_4334),U_4335)),c_Int_Oring__1__class_OInts(U_4334)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4334),U_4335),c_Int_Oring__1__class_OInts(U_4334)))
| ~ class_Rings_Oring__1(U_4334) ),
inference(clausify,[status(thm)],[f_1119_2]) ).
fof(f_1120_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_1120_2,plain,
! [U_4337,U_4336] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4336),U_4337),U_4337) = c_Groups_Ozero__class_Ozero(U_4336)
| U_4337 != c_Groups_Ozero__class_Ozero(U_4336) )
& ( U_4337 = c_Groups_Ozero__class_Ozero(U_4336)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4336),U_4337),U_4337) != c_Groups_Ozero__class_Ozero(U_4336) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_4336),U_4337),c_Int_Oring__1__class_OInts(U_4336)))
| ~ class_Int_Oring__char__0(U_4336) ),
inference(variable_rename,[status(thm)],[f_1120_1]) ).
cnf(f_1120_3,plain,
( U_4337 = c_Groups_Ozero__class_Ozero(U_4336)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4336),U_4337),U_4337) != c_Groups_Ozero__class_Ozero(U_4336)
| ~ hBOOL(hAPP(hAPP(c_member(U_4336),U_4337),c_Int_Oring__1__class_OInts(U_4336)))
| ~ class_Int_Oring__char__0(U_4336) ),
inference(clausify,[status(thm)],[f_1120_2]) ).
cnf(f_1120_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4336),U_4337),U_4337) = c_Groups_Ozero__class_Ozero(U_4336)
| U_4337 != c_Groups_Ozero__class_Ozero(U_4336)
| ~ hBOOL(hAPP(hAPP(c_member(U_4336),U_4337),c_Int_Oring__1__class_OInts(U_4336)))
| ~ class_Int_Oring__char__0(U_4336) ),
inference(clausify,[status(thm)],[f_1120_2]) ).
fof(f_1121_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_1121_2,plain,
! [U_4339,U_4338] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4338),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4338),c_Groups_Oone__class_Oone(U_4338)),U_4339)),U_4339) != c_Groups_Ozero__class_Ozero(U_4338)
| ~ hBOOL(hAPP(hAPP(c_member(U_4338),U_4339),c_Int_Oring__1__class_OInts(U_4338)))
| ~ class_Int_Oring__char__0(U_4338) ),
inference(variable_rename,[status(thm)],[f_1121_1]) ).
cnf(f_1121_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4338),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4338),c_Groups_Oone__class_Oone(U_4338)),U_4339)),U_4339) != c_Groups_Ozero__class_Ozero(U_4338)
| ~ hBOOL(hAPP(hAPP(c_member(U_4338),U_4339),c_Int_Oring__1__class_OInts(U_4338)))
| ~ class_Int_Oring__char__0(U_4338) ),
inference(clausify,[status(thm)],[f_1121_2]) ).
fof(f_1122_1,plain,
! [V_P_2,V_A_2,T_b] :
( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
| ? [B_a,B_A] :
( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_b),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
& hBOOL(hAPP(V_P_2,B_A))
& hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A)) )
| ~ hBOOL(hAPP(V_P_2,V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__empty__induct]) ).
fof(f_1122_2,plain,
! [U_4344,U_4343,U_4342] :
( hBOOL(hAPP(U_4344,c_Orderings_Obot__class_Obot(tc_fun(U_4342,tc_HOL_Obool))))
| ? [U_4341,U_4340] :
( ~ hBOOL(hAPP(U_4344,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4342,tc_HOL_Obool)),U_4340),hAPP(hAPP(c_Set_Oinsert(U_4342),U_4341),c_Orderings_Obot__class_Obot(tc_fun(U_4342,tc_HOL_Obool))))))
& hBOOL(hAPP(U_4344,U_4340))
& hBOOL(hAPP(hAPP(c_member(U_4342),U_4341),U_4340))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_4342),U_4340)) )
| ~ hBOOL(hAPP(U_4344,U_4343))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4342),U_4343)) ),
inference(variable_rename,[status(thm)],[f_1122_1]) ).
fof(f_1122_3,plain,
! [U_4344,U_4343,U_4342] :
( hBOOL(hAPP(U_4344,c_Orderings_Obot__class_Obot(tc_fun(U_4342,tc_HOL_Obool))))
| ? [U_4340] :
( ~ hBOOL(hAPP(U_4344,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4342,tc_HOL_Obool)),U_4340),hAPP(hAPP(c_Set_Oinsert(U_4342),sK89(U_4344,U_4343,U_4342)),c_Orderings_Obot__class_Obot(tc_fun(U_4342,tc_HOL_Obool))))))
& hBOOL(hAPP(U_4344,U_4340))
& hBOOL(hAPP(hAPP(c_member(U_4342),sK89(U_4344,U_4343,U_4342)),U_4340))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_4342),U_4340)) )
| ~ hBOOL(hAPP(U_4344,U_4343))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4342),U_4343)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_4341,sK89(U_4344,U_4343,U_4342))],[f_1122_2]) ).
fof(f_1122_4,plain,
! [U_4344,U_4343,U_4342] :
( hBOOL(hAPP(U_4344,c_Orderings_Obot__class_Obot(tc_fun(U_4342,tc_HOL_Obool))))
| ( ~ hBOOL(hAPP(U_4344,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4342,tc_HOL_Obool)),sK90(U_4344,U_4343,U_4342)),hAPP(hAPP(c_Set_Oinsert(U_4342),sK89(U_4344,U_4343,U_4342)),c_Orderings_Obot__class_Obot(tc_fun(U_4342,tc_HOL_Obool))))))
& hBOOL(hAPP(U_4344,sK90(U_4344,U_4343,U_4342)))
& hBOOL(hAPP(hAPP(c_member(U_4342),sK89(U_4344,U_4343,U_4342)),sK90(U_4344,U_4343,U_4342)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_4342),sK90(U_4344,U_4343,U_4342))) )
| ~ hBOOL(hAPP(U_4344,U_4343))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4342),U_4343)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_4340,sK90(U_4344,U_4343,U_4342))],[f_1122_3]) ).
cnf(f_1122_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4342),sK90(U_4344,U_4343,U_4342)))
| hBOOL(hAPP(U_4344,c_Orderings_Obot__class_Obot(tc_fun(U_4342,tc_HOL_Obool))))
| ~ hBOOL(hAPP(U_4344,U_4343))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4342),U_4343)) ),
inference(clausify,[status(thm)],[f_1122_4]) ).
cnf(f_1122_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_4342),sK89(U_4344,U_4343,U_4342)),sK90(U_4344,U_4343,U_4342)))
| hBOOL(hAPP(U_4344,c_Orderings_Obot__class_Obot(tc_fun(U_4342,tc_HOL_Obool))))
| ~ hBOOL(hAPP(U_4344,U_4343))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4342),U_4343)) ),
inference(clausify,[status(thm)],[f_1122_4]) ).
cnf(f_1122_7,plain,
( hBOOL(hAPP(U_4344,sK90(U_4344,U_4343,U_4342)))
| hBOOL(hAPP(U_4344,c_Orderings_Obot__class_Obot(tc_fun(U_4342,tc_HOL_Obool))))
| ~ hBOOL(hAPP(U_4344,U_4343))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4342),U_4343)) ),
inference(clausify,[status(thm)],[f_1122_4]) ).
cnf(f_1122_8,plain,
( ~ hBOOL(hAPP(U_4344,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4342,tc_HOL_Obool)),sK90(U_4344,U_4343,U_4342)),hAPP(hAPP(c_Set_Oinsert(U_4342),sK89(U_4344,U_4343,U_4342)),c_Orderings_Obot__class_Obot(tc_fun(U_4342,tc_HOL_Obool))))))
| hBOOL(hAPP(U_4344,c_Orderings_Obot__class_Obot(tc_fun(U_4342,tc_HOL_Obool))))
| ~ hBOOL(hAPP(U_4344,U_4343))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4342),U_4343)) ),
inference(clausify,[status(thm)],[f_1122_4]) ).
fof(f_1123_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_1123_2,plain,
! [U_4349,U_4348,U_4347,U_4346,U_4345] :
( hAPP(U_4347,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4345,tc_HOL_Obool)),U_4348),U_4349)) = hAPP(hAPP(U_4346,hAPP(U_4347,U_4348)),hAPP(U_4347,U_4349))
| U_4349 = c_Orderings_Obot__class_Obot(tc_fun(U_4345,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4345),U_4349))
| U_4348 = c_Orderings_Obot__class_Obot(tc_fun(U_4345,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4345),U_4348))
| ~ c_Finite__Set_Ofolding__one__idem(U_4345,U_4346,U_4347) ),
inference(variable_rename,[status(thm)],[f_1123_1]) ).
cnf(f_1123_3,plain,
( hAPP(U_4347,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4345,tc_HOL_Obool)),U_4348),U_4349)) = hAPP(hAPP(U_4346,hAPP(U_4347,U_4348)),hAPP(U_4347,U_4349))
| U_4349 = c_Orderings_Obot__class_Obot(tc_fun(U_4345,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4345),U_4349))
| U_4348 = c_Orderings_Obot__class_Obot(tc_fun(U_4345,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4345),U_4348))
| ~ c_Finite__Set_Ofolding__one__idem(U_4345,U_4346,U_4347) ),
inference(clausify,[status(thm)],[f_1123_2]) ).
fof(f_1124_1,plain,
! [V_P_2,V_A_2,V_F_2,T_b] :
( hBOOL(hAPP(V_P_2,V_F_2))
| ? [B_a,B_F] :
( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F)))
& hBOOL(hAPP(V_P_2,B_F))
& ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
& hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F)) )
| ~ hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__subset__induct]) ).
fof(f_1124_2,plain,
! [U_4355,U_4354,U_4353,U_4352] :
( hBOOL(hAPP(U_4355,U_4353))
| ? [U_4351,U_4350] :
( ~ hBOOL(hAPP(U_4355,hAPP(hAPP(c_Set_Oinsert(U_4352),U_4351),U_4350)))
& hBOOL(hAPP(U_4355,U_4350))
& ~ hBOOL(hAPP(hAPP(c_member(U_4352),U_4351),U_4350))
& hBOOL(hAPP(hAPP(c_member(U_4352),U_4351),U_4354))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_4352),U_4350)) )
| ~ hBOOL(hAPP(U_4355,c_Orderings_Obot__class_Obot(tc_fun(U_4352,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4352,tc_HOL_Obool)),U_4353),U_4354))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4352),U_4353)) ),
inference(variable_rename,[status(thm)],[f_1124_1]) ).
fof(f_1124_3,plain,
! [U_4355,U_4354,U_4353,U_4352] :
( hBOOL(hAPP(U_4355,U_4353))
| ? [U_4350] :
( ~ hBOOL(hAPP(U_4355,hAPP(hAPP(c_Set_Oinsert(U_4352),sK91(U_4355,U_4354,U_4353,U_4352)),U_4350)))
& hBOOL(hAPP(U_4355,U_4350))
& ~ hBOOL(hAPP(hAPP(c_member(U_4352),sK91(U_4355,U_4354,U_4353,U_4352)),U_4350))
& hBOOL(hAPP(hAPP(c_member(U_4352),sK91(U_4355,U_4354,U_4353,U_4352)),U_4354))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_4352),U_4350)) )
| ~ hBOOL(hAPP(U_4355,c_Orderings_Obot__class_Obot(tc_fun(U_4352,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4352,tc_HOL_Obool)),U_4353),U_4354))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4352),U_4353)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_4351,sK91(U_4355,U_4354,U_4353,U_4352))],[f_1124_2]) ).
fof(f_1124_4,plain,
! [U_4355,U_4354,U_4353,U_4352] :
( hBOOL(hAPP(U_4355,U_4353))
| ( ~ hBOOL(hAPP(U_4355,hAPP(hAPP(c_Set_Oinsert(U_4352),sK91(U_4355,U_4354,U_4353,U_4352)),sK92(U_4355,U_4354,U_4353,U_4352))))
& hBOOL(hAPP(U_4355,sK92(U_4355,U_4354,U_4353,U_4352)))
& ~ hBOOL(hAPP(hAPP(c_member(U_4352),sK91(U_4355,U_4354,U_4353,U_4352)),sK92(U_4355,U_4354,U_4353,U_4352)))
& hBOOL(hAPP(hAPP(c_member(U_4352),sK91(U_4355,U_4354,U_4353,U_4352)),U_4354))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_4352),sK92(U_4355,U_4354,U_4353,U_4352))) )
| ~ hBOOL(hAPP(U_4355,c_Orderings_Obot__class_Obot(tc_fun(U_4352,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4352,tc_HOL_Obool)),U_4353),U_4354))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4352),U_4353)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_4350,sK92(U_4355,U_4354,U_4353,U_4352))],[f_1124_3]) ).
cnf(f_1124_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4352),sK92(U_4355,U_4354,U_4353,U_4352)))
| hBOOL(hAPP(U_4355,U_4353))
| ~ hBOOL(hAPP(U_4355,c_Orderings_Obot__class_Obot(tc_fun(U_4352,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4352,tc_HOL_Obool)),U_4353),U_4354))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4352),U_4353)) ),
inference(clausify,[status(thm)],[f_1124_4]) ).
cnf(f_1124_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_4352),sK91(U_4355,U_4354,U_4353,U_4352)),U_4354))
| hBOOL(hAPP(U_4355,U_4353))
| ~ hBOOL(hAPP(U_4355,c_Orderings_Obot__class_Obot(tc_fun(U_4352,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4352,tc_HOL_Obool)),U_4353),U_4354))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4352),U_4353)) ),
inference(clausify,[status(thm)],[f_1124_4]) ).
cnf(f_1124_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_4352),sK91(U_4355,U_4354,U_4353,U_4352)),sK92(U_4355,U_4354,U_4353,U_4352)))
| hBOOL(hAPP(U_4355,U_4353))
| ~ hBOOL(hAPP(U_4355,c_Orderings_Obot__class_Obot(tc_fun(U_4352,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4352,tc_HOL_Obool)),U_4353),U_4354))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4352),U_4353)) ),
inference(clausify,[status(thm)],[f_1124_4]) ).
cnf(f_1124_8,plain,
( hBOOL(hAPP(U_4355,sK92(U_4355,U_4354,U_4353,U_4352)))
| hBOOL(hAPP(U_4355,U_4353))
| ~ hBOOL(hAPP(U_4355,c_Orderings_Obot__class_Obot(tc_fun(U_4352,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4352,tc_HOL_Obool)),U_4353),U_4354))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4352),U_4353)) ),
inference(clausify,[status(thm)],[f_1124_4]) ).
cnf(f_1124_9,plain,
( ~ hBOOL(hAPP(U_4355,hAPP(hAPP(c_Set_Oinsert(U_4352),sK91(U_4355,U_4354,U_4353,U_4352)),sK92(U_4355,U_4354,U_4353,U_4352))))
| hBOOL(hAPP(U_4355,U_4353))
| ~ hBOOL(hAPP(U_4355,c_Orderings_Obot__class_Obot(tc_fun(U_4352,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4352,tc_HOL_Obool)),U_4353),U_4354))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4352),U_4353)) ),
inference(clausify,[status(thm)],[f_1124_4]) ).
fof(f_1125_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_1125_2,plain,
! [U_4360,U_4359,U_4358,U_4357,U_4356] :
( hAPP(hAPP(U_4357,hAPP(U_4358,U_4360)),hAPP(U_4358,U_4359)) = hAPP(U_4358,U_4359)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4356,tc_HOL_Obool)),U_4360),U_4359))
| U_4360 = c_Orderings_Obot__class_Obot(tc_fun(U_4356,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4356),U_4359))
| ~ c_Finite__Set_Ofolding__one__idem(U_4356,U_4357,U_4358) ),
inference(variable_rename,[status(thm)],[f_1125_1]) ).
cnf(f_1125_3,plain,
( hAPP(hAPP(U_4357,hAPP(U_4358,U_4360)),hAPP(U_4358,U_4359)) = hAPP(U_4358,U_4359)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4356,tc_HOL_Obool)),U_4360),U_4359))
| U_4360 = c_Orderings_Obot__class_Obot(tc_fun(U_4356,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4356),U_4359))
| ~ c_Finite__Set_Ofolding__one__idem(U_4356,U_4357,U_4358) ),
inference(clausify,[status(thm)],[f_1125_2]) ).
fof(f_1126_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_1126_2,plain,
! [U_4366,U_4365,U_4364,U_4363,U_4362] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4362),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4363,U_4362),U_4365),U_4364)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4363,U_4362),U_4366),U_4364)))
| ? [U_4361] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4362),hAPP(U_4365,U_4361)),hAPP(U_4366,U_4361)))
& hBOOL(hAPP(hAPP(c_member(U_4363),U_4361),U_4364)) )
| U_4364 = c_Orderings_Obot__class_Obot(tc_fun(U_4363,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4363),U_4364))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_4362)
| ~ class_Groups_Ocomm__monoid__add(U_4362) ),
inference(variable_rename,[status(thm)],[f_1126_1]) ).
fof(f_1126_3,plain,
! [U_4366,U_4365,U_4364,U_4363,U_4362] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4362),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4363,U_4362),U_4365),U_4364)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4363,U_4362),U_4366),U_4364)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4362),hAPP(U_4365,sK93(U_4366,U_4365,U_4364,U_4363,U_4362))),hAPP(U_4366,sK93(U_4366,U_4365,U_4364,U_4363,U_4362))))
& hBOOL(hAPP(hAPP(c_member(U_4363),sK93(U_4366,U_4365,U_4364,U_4363,U_4362)),U_4364)) )
| U_4364 = c_Orderings_Obot__class_Obot(tc_fun(U_4363,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4363),U_4364))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_4362)
| ~ class_Groups_Ocomm__monoid__add(U_4362) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_4361,sK93(U_4366,U_4365,U_4364,U_4363,U_4362))],[f_1126_2]) ).
cnf(f_1126_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_4363),sK93(U_4366,U_4365,U_4364,U_4363,U_4362)),U_4364))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4362),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4363,U_4362),U_4365),U_4364)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4363,U_4362),U_4366),U_4364)))
| U_4364 = c_Orderings_Obot__class_Obot(tc_fun(U_4363,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4363),U_4364))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_4362)
| ~ class_Groups_Ocomm__monoid__add(U_4362) ),
inference(clausify,[status(thm)],[f_1126_3]) ).
cnf(f_1126_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4362),hAPP(U_4365,sK93(U_4366,U_4365,U_4364,U_4363,U_4362))),hAPP(U_4366,sK93(U_4366,U_4365,U_4364,U_4363,U_4362))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4362),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4363,U_4362),U_4365),U_4364)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4363,U_4362),U_4366),U_4364)))
| U_4364 = c_Orderings_Obot__class_Obot(tc_fun(U_4363,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4363),U_4364))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_4362)
| ~ class_Groups_Ocomm__monoid__add(U_4362) ),
inference(clausify,[status(thm)],[f_1126_3]) ).
fof(f_1127_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_1127_2,plain,
! [U_4371,U_4370,U_4369,U_4368,U_4367] :
( hAPP(U_4369,hAPP(hAPP(c_Set_Oinsert(U_4367),U_4371),U_4370)) = hAPP(hAPP(U_4368,U_4371),hAPP(U_4369,U_4370))
| U_4370 = c_Orderings_Obot__class_Obot(tc_fun(U_4367,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4367),U_4370))
| ~ c_Finite__Set_Ofolding__one__idem(U_4367,U_4368,U_4369) ),
inference(variable_rename,[status(thm)],[f_1127_1]) ).
cnf(f_1127_3,plain,
( hAPP(U_4369,hAPP(hAPP(c_Set_Oinsert(U_4367),U_4371),U_4370)) = hAPP(hAPP(U_4368,U_4371),hAPP(U_4369,U_4370))
| U_4370 = c_Orderings_Obot__class_Obot(tc_fun(U_4367,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4367),U_4370))
| ~ c_Finite__Set_Ofolding__one__idem(U_4367,U_4368,U_4369) ),
inference(clausify,[status(thm)],[f_1127_2]) ).
fof(f_1128_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_1128_2,plain,
! [U_4373,U_4372] :
( ( ( ( ( c_Groups_Osgn__class_Osgn(U_4372,U_4373) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4372),c_Groups_Oone__class_Oone(U_4372))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4373)) )
& ( c_Groups_Osgn__class_Osgn(U_4372,U_4373) = c_Groups_Oone__class_Oone(U_4372)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4373)) ) )
| U_4373 = c_Groups_Ozero__class_Ozero(U_4372) )
& ( c_Groups_Osgn__class_Osgn(U_4372,U_4373) = c_Groups_Ozero__class_Ozero(U_4372)
| U_4373 != c_Groups_Ozero__class_Ozero(U_4372) ) )
| ~ class_Groups_Osgn__if(U_4372) ),
inference(variable_rename,[status(thm)],[f_1128_1]) ).
cnf(f_1128_3,plain,
( c_Groups_Osgn__class_Osgn(U_4372,U_4373) = c_Groups_Ozero__class_Ozero(U_4372)
| U_4373 != c_Groups_Ozero__class_Ozero(U_4372)
| ~ class_Groups_Osgn__if(U_4372) ),
inference(clausify,[status(thm)],[f_1128_2]) ).
cnf(f_1128_4,plain,
( c_Groups_Osgn__class_Osgn(U_4372,U_4373) = c_Groups_Oone__class_Oone(U_4372)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4373))
| U_4373 = c_Groups_Ozero__class_Ozero(U_4372)
| ~ class_Groups_Osgn__if(U_4372) ),
inference(clausify,[status(thm)],[f_1128_2]) ).
cnf(f_1128_5,plain,
( c_Groups_Osgn__class_Osgn(U_4372,U_4373) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4372),c_Groups_Oone__class_Oone(U_4372))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4373))
| U_4373 = c_Groups_Ozero__class_Ozero(U_4372)
| ~ class_Groups_Osgn__if(U_4372) ),
inference(clausify,[status(thm)],[f_1128_2]) ).
fof(f_1129_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_1129_2,plain,
! [U_4377,U_4376,U_4375,U_4374] :
( hAPP(hAPP(U_4375,U_4377),U_4377) = U_4377
| ~ c_Finite__Set_Ofolding__one__idem(U_4374,U_4375,U_4376) ),
inference(variable_rename,[status(thm)],[f_1129_1]) ).
fof(f_1129_3,plain,
! [U_4377,U_4376,U_4375] :
( ! [U_4374] : ~ c_Finite__Set_Ofolding__one__idem(U_4374,U_4375,U_4376)
| hAPP(hAPP(U_4375,U_4377),U_4377) = U_4377 ),
inference(miniscope,[status(thm)],[f_1129_2]) ).
cnf(f_1129_4,plain,
( ~ c_Finite__Set_Ofolding__one__idem(U_4374,U_4375,U_4376)
| hAPP(hAPP(U_4375,U_4377),U_4377) = U_4377 ),
inference(clausify,[status(thm)],[f_1129_3]) ).
fof(f_1130_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_1130_2,plain,
! [U_4379,U_4378] :
( c_Groups_Osgn__class_Osgn(U_4378,c_Groups_Osgn__class_Osgn(U_4378,U_4379)) = c_Groups_Osgn__class_Osgn(U_4378,U_4379)
| ~ class_Rings_Olinordered__idom(U_4378) ),
inference(variable_rename,[status(thm)],[f_1130_1]) ).
cnf(f_1130_3,plain,
( c_Groups_Osgn__class_Osgn(U_4378,c_Groups_Osgn__class_Osgn(U_4378,U_4379)) = c_Groups_Osgn__class_Osgn(U_4378,U_4379)
| ~ class_Rings_Olinordered__idom(U_4378) ),
inference(clausify,[status(thm)],[f_1130_2]) ).
fof(f_1131_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_1131_2,plain,
! [U_4381,U_4380] :
( ( ( c_Groups_Osgn__class_Osgn(U_4380,U_4381) = c_Groups_Ozero__class_Ozero(U_4380)
| U_4381 != c_Groups_Ozero__class_Ozero(U_4380) )
& ( U_4381 = c_Groups_Ozero__class_Ozero(U_4380)
| c_Groups_Osgn__class_Osgn(U_4380,U_4381) != c_Groups_Ozero__class_Ozero(U_4380) ) )
| ~ class_Rings_Olinordered__idom(U_4380) ),
inference(variable_rename,[status(thm)],[f_1131_1]) ).
cnf(f_1131_3,plain,
( U_4381 = c_Groups_Ozero__class_Ozero(U_4380)
| c_Groups_Osgn__class_Osgn(U_4380,U_4381) != c_Groups_Ozero__class_Ozero(U_4380)
| ~ class_Rings_Olinordered__idom(U_4380) ),
inference(clausify,[status(thm)],[f_1131_2]) ).
cnf(f_1131_4,plain,
( c_Groups_Osgn__class_Osgn(U_4380,U_4381) = c_Groups_Ozero__class_Ozero(U_4380)
| U_4381 != c_Groups_Ozero__class_Ozero(U_4380)
| ~ class_Rings_Olinordered__idom(U_4380) ),
inference(clausify,[status(thm)],[f_1131_2]) ).
fof(f_1132_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_1132_2,plain,
! [U_4382] :
( c_Groups_Osgn__class_Osgn(U_4382,c_Groups_Ozero__class_Ozero(U_4382)) = c_Groups_Ozero__class_Ozero(U_4382)
| ~ class_Groups_Osgn__if(U_4382) ),
inference(variable_rename,[status(thm)],[f_1132_1]) ).
cnf(f_1132_3,plain,
( c_Groups_Osgn__class_Osgn(U_4382,c_Groups_Ozero__class_Ozero(U_4382)) = c_Groups_Ozero__class_Ozero(U_4382)
| ~ class_Groups_Osgn__if(U_4382) ),
inference(clausify,[status(thm)],[f_1132_2]) ).
fof(f_1133_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_1133_2,plain,
! [U_4384,U_4383] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4383),c_Groups_Osgn__class_Osgn(U_4383,U_4384)),c_Groups_Ozero__class_Ozero(U_4383)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4383),U_4384),c_Groups_Ozero__class_Ozero(U_4383))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4383),U_4384),c_Groups_Ozero__class_Ozero(U_4383)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4383),c_Groups_Osgn__class_Osgn(U_4383,U_4384)),c_Groups_Ozero__class_Ozero(U_4383))) ) )
| ~ class_Rings_Olinordered__idom(U_4383) ),
inference(variable_rename,[status(thm)],[f_1133_1]) ).
cnf(f_1133_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4383),U_4384),c_Groups_Ozero__class_Ozero(U_4383)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4383),c_Groups_Osgn__class_Osgn(U_4383,U_4384)),c_Groups_Ozero__class_Ozero(U_4383)))
| ~ class_Rings_Olinordered__idom(U_4383) ),
inference(clausify,[status(thm)],[f_1133_2]) ).
cnf(f_1133_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4383),c_Groups_Osgn__class_Osgn(U_4383,U_4384)),c_Groups_Ozero__class_Ozero(U_4383)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4383),U_4384),c_Groups_Ozero__class_Ozero(U_4383)))
| ~ class_Rings_Olinordered__idom(U_4383) ),
inference(clausify,[status(thm)],[f_1133_2]) ).
fof(f_1134_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_1134_2,plain,
! [U_4386,U_4385] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4385),c_Groups_Ozero__class_Ozero(U_4385)),c_Groups_Osgn__class_Osgn(U_4385,U_4386)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4385),c_Groups_Ozero__class_Ozero(U_4385)),U_4386)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4385),c_Groups_Ozero__class_Ozero(U_4385)),U_4386))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4385),c_Groups_Ozero__class_Ozero(U_4385)),c_Groups_Osgn__class_Osgn(U_4385,U_4386))) ) )
| ~ class_Rings_Olinordered__idom(U_4385) ),
inference(variable_rename,[status(thm)],[f_1134_1]) ).
cnf(f_1134_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4385),c_Groups_Ozero__class_Ozero(U_4385)),U_4386))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4385),c_Groups_Ozero__class_Ozero(U_4385)),c_Groups_Osgn__class_Osgn(U_4385,U_4386)))
| ~ class_Rings_Olinordered__idom(U_4385) ),
inference(clausify,[status(thm)],[f_1134_2]) ).
cnf(f_1134_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4385),c_Groups_Ozero__class_Ozero(U_4385)),c_Groups_Osgn__class_Osgn(U_4385,U_4386)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4385),c_Groups_Ozero__class_Ozero(U_4385)),U_4386))
| ~ class_Rings_Olinordered__idom(U_4385) ),
inference(clausify,[status(thm)],[f_1134_2]) ).
fof(f_1135_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_1135_2,plain,
! [U_4391,U_4390,U_4389,U_4388,U_4387] :
( hAPP(hAPP(U_4388,U_4391),hAPP(U_4389,U_4390)) = hAPP(U_4389,U_4390)
| ~ hBOOL(hAPP(hAPP(c_member(U_4387),U_4391),U_4390))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4387),U_4390))
| ~ c_Finite__Set_Ofolding__one__idem(U_4387,U_4388,U_4389) ),
inference(variable_rename,[status(thm)],[f_1135_1]) ).
cnf(f_1135_3,plain,
( hAPP(hAPP(U_4388,U_4391),hAPP(U_4389,U_4390)) = hAPP(U_4389,U_4390)
| ~ hBOOL(hAPP(hAPP(c_member(U_4387),U_4391),U_4390))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4387),U_4390))
| ~ c_Finite__Set_Ofolding__one__idem(U_4387,U_4388,U_4389) ),
inference(clausify,[status(thm)],[f_1135_2]) ).
fof(f_1136_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_1136_2,plain,
! [U_4393,U_4392] :
( c_Groups_Osgn__class_Osgn(U_4392,U_4393) = c_Groups_Oone__class_Oone(U_4392)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),c_Groups_Ozero__class_Ozero(U_4392)),U_4393))
| ~ class_Rings_Olinordered__idom(U_4392) ),
inference(variable_rename,[status(thm)],[f_1136_1]) ).
cnf(f_1136_3,plain,
( c_Groups_Osgn__class_Osgn(U_4392,U_4393) = c_Groups_Oone__class_Oone(U_4392)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),c_Groups_Ozero__class_Ozero(U_4392)),U_4393))
| ~ class_Rings_Olinordered__idom(U_4392) ),
inference(clausify,[status(thm)],[f_1136_2]) ).
fof(f_1137_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_1137_2,plain,
! [U_4395,U_4394] :
( ( ( c_Groups_Osgn__class_Osgn(U_4394,U_4395) = c_Groups_Oone__class_Oone(U_4394)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),U_4395)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),U_4395))
| c_Groups_Osgn__class_Osgn(U_4394,U_4395) != c_Groups_Oone__class_Oone(U_4394) ) )
| ~ class_Rings_Olinordered__idom(U_4394) ),
inference(variable_rename,[status(thm)],[f_1137_1]) ).
cnf(f_1137_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),U_4395))
| c_Groups_Osgn__class_Osgn(U_4394,U_4395) != c_Groups_Oone__class_Oone(U_4394)
| ~ class_Rings_Olinordered__idom(U_4394) ),
inference(clausify,[status(thm)],[f_1137_2]) ).
cnf(f_1137_4,plain,
( c_Groups_Osgn__class_Osgn(U_4394,U_4395) = c_Groups_Oone__class_Oone(U_4394)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4394),c_Groups_Ozero__class_Ozero(U_4394)),U_4395))
| ~ class_Rings_Olinordered__idom(U_4394) ),
inference(clausify,[status(thm)],[f_1137_2]) ).
fof(f_1138_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_1138_2,plain,
! [U_4397,U_4396] :
( ( ( c_Groups_Osgn__class_Osgn(U_4396,U_4397) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4396),c_Groups_Oone__class_Oone(U_4396))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4396),U_4397),c_Groups_Ozero__class_Ozero(U_4396))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4396),U_4397),c_Groups_Ozero__class_Ozero(U_4396)))
| c_Groups_Osgn__class_Osgn(U_4396,U_4397) != hAPP(c_Groups_Ouminus__class_Ouminus(U_4396),c_Groups_Oone__class_Oone(U_4396)) ) )
| ~ class_Rings_Olinordered__idom(U_4396) ),
inference(variable_rename,[status(thm)],[f_1138_1]) ).
cnf(f_1138_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4396),U_4397),c_Groups_Ozero__class_Ozero(U_4396)))
| c_Groups_Osgn__class_Osgn(U_4396,U_4397) != hAPP(c_Groups_Ouminus__class_Ouminus(U_4396),c_Groups_Oone__class_Oone(U_4396))
| ~ class_Rings_Olinordered__idom(U_4396) ),
inference(clausify,[status(thm)],[f_1138_2]) ).
cnf(f_1138_4,plain,
( c_Groups_Osgn__class_Osgn(U_4396,U_4397) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4396),c_Groups_Oone__class_Oone(U_4396))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4396),U_4397),c_Groups_Ozero__class_Ozero(U_4396)))
| ~ class_Rings_Olinordered__idom(U_4396) ),
inference(clausify,[status(thm)],[f_1138_2]) ).
fof(f_1139_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_1139_2,plain,
! [U_4399,U_4398] :
( c_Groups_Osgn__class_Osgn(U_4398,U_4399) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4398),c_Groups_Oone__class_Oone(U_4398))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),U_4399),c_Groups_Ozero__class_Ozero(U_4398)))
| ~ class_Rings_Olinordered__idom(U_4398) ),
inference(variable_rename,[status(thm)],[f_1139_1]) ).
cnf(f_1139_3,plain,
( c_Groups_Osgn__class_Osgn(U_4398,U_4399) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4398),c_Groups_Oone__class_Oone(U_4398))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4398),U_4399),c_Groups_Ozero__class_Ozero(U_4398)))
| ~ class_Rings_Olinordered__idom(U_4398) ),
inference(clausify,[status(thm)],[f_1139_2]) ).
fof(f_1140_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_1140_2,plain,
! [U_4406,U_4405,U_4404,U_4403,U_4402] :
( hAPP(U_4405,hAPP(U_4404,U_4406)) = hAPP(U_4404,hAPP(c_Set_Oimage(U_4402,U_4402,U_4405),U_4406))
| U_4406 = c_Orderings_Obot__class_Obot(tc_fun(U_4402,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4402),U_4406))
| ? [U_4401,U_4400] : hAPP(U_4405,hAPP(hAPP(U_4403,U_4401),U_4400)) != hAPP(hAPP(U_4403,hAPP(U_4405,U_4401)),hAPP(U_4405,U_4400))
| ~ c_Finite__Set_Ofolding__one__idem(U_4402,U_4403,U_4404) ),
inference(variable_rename,[status(thm)],[f_1140_1]) ).
fof(f_1140_3,plain,
! [U_4406,U_4405,U_4404,U_4403,U_4402] :
( hAPP(U_4405,hAPP(U_4404,U_4406)) = hAPP(U_4404,hAPP(c_Set_Oimage(U_4402,U_4402,U_4405),U_4406))
| U_4406 = c_Orderings_Obot__class_Obot(tc_fun(U_4402,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4402),U_4406))
| ? [U_4400] : hAPP(U_4405,hAPP(hAPP(U_4403,sK94(U_4406,U_4405,U_4404,U_4403,U_4402)),U_4400)) != hAPP(hAPP(U_4403,hAPP(U_4405,sK94(U_4406,U_4405,U_4404,U_4403,U_4402))),hAPP(U_4405,U_4400))
| ~ c_Finite__Set_Ofolding__one__idem(U_4402,U_4403,U_4404) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_4401,sK94(U_4406,U_4405,U_4404,U_4403,U_4402))],[f_1140_2]) ).
fof(f_1140_4,plain,
! [U_4406,U_4405,U_4404,U_4403,U_4402] :
( hAPP(U_4405,hAPP(U_4404,U_4406)) = hAPP(U_4404,hAPP(c_Set_Oimage(U_4402,U_4402,U_4405),U_4406))
| U_4406 = c_Orderings_Obot__class_Obot(tc_fun(U_4402,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4402),U_4406))
| hAPP(U_4405,hAPP(hAPP(U_4403,sK94(U_4406,U_4405,U_4404,U_4403,U_4402)),sK95(U_4406,U_4405,U_4404,U_4403,U_4402))) != hAPP(hAPP(U_4403,hAPP(U_4405,sK94(U_4406,U_4405,U_4404,U_4403,U_4402))),hAPP(U_4405,sK95(U_4406,U_4405,U_4404,U_4403,U_4402)))
| ~ c_Finite__Set_Ofolding__one__idem(U_4402,U_4403,U_4404) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_4400,sK95(U_4406,U_4405,U_4404,U_4403,U_4402))],[f_1140_3]) ).
cnf(f_1140_5,plain,
( hAPP(U_4405,hAPP(U_4404,U_4406)) = hAPP(U_4404,hAPP(c_Set_Oimage(U_4402,U_4402,U_4405),U_4406))
| U_4406 = c_Orderings_Obot__class_Obot(tc_fun(U_4402,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4402),U_4406))
| hAPP(U_4405,hAPP(hAPP(U_4403,sK94(U_4406,U_4405,U_4404,U_4403,U_4402)),sK95(U_4406,U_4405,U_4404,U_4403,U_4402))) != hAPP(hAPP(U_4403,hAPP(U_4405,sK94(U_4406,U_4405,U_4404,U_4403,U_4402))),hAPP(U_4405,sK95(U_4406,U_4405,U_4404,U_4403,U_4402)))
| ~ c_Finite__Set_Ofolding__one__idem(U_4402,U_4403,U_4404) ),
inference(clausify,[status(thm)],[f_1140_4]) ).
fof(f_1141_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_1141_2,plain,
! [U_4415,U_4414,U_4413,U_4412,U_4411,U_4410,U_4409,U_4408] :
( hAPP(U_4413,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4409,tc_HOL_Obool)),U_4414),U_4415)) = hAPP(hAPP(U_4410,hAPP(U_4413,U_4414)),hAPP(U_4413,U_4415))
| ? [U_4407] :
( hAPP(U_4412,U_4407) != U_4411
& hBOOL(hAPP(hAPP(c_member(U_4409),U_4407),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4409,tc_HOL_Obool)),U_4414),U_4415))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4409),U_4415))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4409),U_4414))
| ~ c_Finite__Set_Ofolding__image__simple(U_4408,U_4409,U_4410,U_4411,U_4412,U_4413) ),
inference(variable_rename,[status(thm)],[f_1141_1]) ).
fof(f_1141_3,plain,
! [U_4415,U_4414,U_4413,U_4412,U_4411,U_4410,U_4409] :
( ! [U_4408] : ~ c_Finite__Set_Ofolding__image__simple(U_4408,U_4409,U_4410,U_4411,U_4412,U_4413)
| hAPP(U_4413,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4409,tc_HOL_Obool)),U_4414),U_4415)) = hAPP(hAPP(U_4410,hAPP(U_4413,U_4414)),hAPP(U_4413,U_4415))
| ? [U_4407] :
( hAPP(U_4412,U_4407) != U_4411
& hBOOL(hAPP(hAPP(c_member(U_4409),U_4407),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4409,tc_HOL_Obool)),U_4414),U_4415))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4409),U_4415))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4409),U_4414)) ),
inference(miniscope,[status(thm)],[f_1141_2]) ).
fof(f_1141_4,plain,
! [U_4415,U_4414,U_4413,U_4412,U_4411,U_4410,U_4409] :
( ! [U_4408] : ~ c_Finite__Set_Ofolding__image__simple(U_4408,U_4409,U_4410,U_4411,U_4412,U_4413)
| hAPP(U_4413,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4409,tc_HOL_Obool)),U_4414),U_4415)) = hAPP(hAPP(U_4410,hAPP(U_4413,U_4414)),hAPP(U_4413,U_4415))
| ( hAPP(U_4412,sK96(U_4415,U_4414,U_4413,U_4412,U_4411,U_4410,U_4409)) != U_4411
& hBOOL(hAPP(hAPP(c_member(U_4409),sK96(U_4415,U_4414,U_4413,U_4412,U_4411,U_4410,U_4409)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4409,tc_HOL_Obool)),U_4414),U_4415))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4409),U_4415))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4409),U_4414)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_4407,sK96(U_4415,U_4414,U_4413,U_4412,U_4411,U_4410,U_4409))],[f_1141_3]) ).
cnf(f_1141_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_4409),sK96(U_4415,U_4414,U_4413,U_4412,U_4411,U_4410,U_4409)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4409,tc_HOL_Obool)),U_4414),U_4415)))
| hAPP(U_4413,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4409,tc_HOL_Obool)),U_4414),U_4415)) = hAPP(hAPP(U_4410,hAPP(U_4413,U_4414)),hAPP(U_4413,U_4415))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4409),U_4415))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4409),U_4414))
| ~ c_Finite__Set_Ofolding__image__simple(U_4408,U_4409,U_4410,U_4411,U_4412,U_4413) ),
inference(clausify,[status(thm)],[f_1141_4]) ).
cnf(f_1141_6,plain,
( hAPP(U_4412,sK96(U_4415,U_4414,U_4413,U_4412,U_4411,U_4410,U_4409)) != U_4411
| hAPP(U_4413,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4409,tc_HOL_Obool)),U_4414),U_4415)) = hAPP(hAPP(U_4410,hAPP(U_4413,U_4414)),hAPP(U_4413,U_4415))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4409),U_4415))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4409),U_4414))
| ~ c_Finite__Set_Ofolding__image__simple(U_4408,U_4409,U_4410,U_4411,U_4412,U_4413) ),
inference(clausify,[status(thm)],[f_1141_4]) ).
fof(f_1142_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_1142_2,plain,
! [U_4418,U_4417] :
( hAPP(c_Finite__Set_Ocard(U_4417),U_4418) = 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_4416] : hBOOL(hAPP(hAPP(c_member(U_4417),U_4416),U_4418)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4417),U_4418)) ),
inference(variable_rename,[status(thm)],[f_1142_1]) ).
fof(f_1142_3,plain,
! [U_4418,U_4417] :
( hAPP(c_Finite__Set_Ocard(U_4417),U_4418) = 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_4417),sK97(U_4418,U_4417)),U_4418)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4417),U_4418)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_4416,sK97(U_4418,U_4417))],[f_1142_2]) ).
cnf(f_1142_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_4417),sK97(U_4418,U_4417)),U_4418))
| hAPP(c_Finite__Set_Ocard(U_4417),U_4418) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4417),U_4418)) ),
inference(clausify,[status(thm)],[f_1142_3]) ).
cnf(f_1142_5,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Finite__Set_Ocard(U_4417),U_4418) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4417),U_4418)) ),
inference(clausify,[status(thm)],[f_1142_3]) ).
fof(f_1143_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_1143_2,plain,
! [U_4422,U_4421,U_4420] :
( hBOOL(hAPP(hAPP(c_member(U_4420),U_4422),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_4420,tc_HOL_Obool),U_4421)))
| ? [U_4419] :
( ~ hBOOL(hAPP(hAPP(c_member(U_4420),U_4422),U_4419))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_4420,tc_HOL_Obool)),U_4419),U_4421)) ) ),
inference(variable_rename,[status(thm)],[f_1143_1]) ).
fof(f_1143_3,plain,
! [U_4422,U_4421,U_4420] :
( hBOOL(hAPP(hAPP(c_member(U_4420),U_4422),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_4420,tc_HOL_Obool),U_4421)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_4420),U_4422),sK98(U_4422,U_4421,U_4420)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_4420,tc_HOL_Obool)),sK98(U_4422,U_4421,U_4420)),U_4421)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_4419,sK98(U_4422,U_4421,U_4420))],[f_1143_2]) ).
cnf(f_1143_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_4420,tc_HOL_Obool)),sK98(U_4422,U_4421,U_4420)),U_4421))
| hBOOL(hAPP(hAPP(c_member(U_4420),U_4422),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_4420,tc_HOL_Obool),U_4421))) ),
inference(clausify,[status(thm)],[f_1143_3]) ).
cnf(f_1143_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_4420),U_4422),sK98(U_4422,U_4421,U_4420)))
| hBOOL(hAPP(hAPP(c_member(U_4420),U_4422),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_4420,tc_HOL_Obool),U_4421))) ),
inference(clausify,[status(thm)],[f_1143_3]) ).
fof(f_1144_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_1144_2,plain,
! [U_4423] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4423) = 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_4423)),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_4423))) ),
inference(variable_rename,[status(thm)],[f_1144_1]) ).
cnf(f_1144_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4423) = 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_4423)),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_4423))) ),
inference(clausify,[status(thm)],[f_1144_2]) ).
fof(f_1145_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_1145_2,plain,
! [U_4432,U_4431,U_4430,U_4429,U_4428,U_4427,U_4426,U_4425] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4427,U_4425),U_4432),U_4430) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4426,U_4425),U_4431),U_4429)
| ? [U_4424] :
( hAPP(U_4431,U_4424) != hAPP(U_4432,hAPP(U_4428,U_4424))
& hBOOL(hAPP(hAPP(c_member(U_4426),U_4424),U_4429)) )
| U_4430 != hAPP(c_Set_Oimage(U_4426,U_4427,U_4428),U_4429)
| ~ c_Fun_Oinj__on(U_4426,U_4427,U_4428,U_4429)
| ~ class_Groups_Ocomm__monoid__add(U_4425) ),
inference(variable_rename,[status(thm)],[f_1145_1]) ).
fof(f_1145_3,plain,
! [U_4432,U_4431,U_4430,U_4429,U_4428,U_4427,U_4426,U_4425] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4427,U_4425),U_4432),U_4430) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4426,U_4425),U_4431),U_4429)
| ( hAPP(U_4431,sK99(U_4432,U_4431,U_4430,U_4429,U_4428,U_4427,U_4426,U_4425)) != hAPP(U_4432,hAPP(U_4428,sK99(U_4432,U_4431,U_4430,U_4429,U_4428,U_4427,U_4426,U_4425)))
& hBOOL(hAPP(hAPP(c_member(U_4426),sK99(U_4432,U_4431,U_4430,U_4429,U_4428,U_4427,U_4426,U_4425)),U_4429)) )
| U_4430 != hAPP(c_Set_Oimage(U_4426,U_4427,U_4428),U_4429)
| ~ c_Fun_Oinj__on(U_4426,U_4427,U_4428,U_4429)
| ~ class_Groups_Ocomm__monoid__add(U_4425) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_4424,sK99(U_4432,U_4431,U_4430,U_4429,U_4428,U_4427,U_4426,U_4425))],[f_1145_2]) ).
cnf(f_1145_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_4426),sK99(U_4432,U_4431,U_4430,U_4429,U_4428,U_4427,U_4426,U_4425)),U_4429))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4427,U_4425),U_4432),U_4430) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4426,U_4425),U_4431),U_4429)
| U_4430 != hAPP(c_Set_Oimage(U_4426,U_4427,U_4428),U_4429)
| ~ c_Fun_Oinj__on(U_4426,U_4427,U_4428,U_4429)
| ~ class_Groups_Ocomm__monoid__add(U_4425) ),
inference(clausify,[status(thm)],[f_1145_3]) ).
cnf(f_1145_5,plain,
( hAPP(U_4431,sK99(U_4432,U_4431,U_4430,U_4429,U_4428,U_4427,U_4426,U_4425)) != hAPP(U_4432,hAPP(U_4428,sK99(U_4432,U_4431,U_4430,U_4429,U_4428,U_4427,U_4426,U_4425)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4427,U_4425),U_4432),U_4430) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4426,U_4425),U_4431),U_4429)
| U_4430 != hAPP(c_Set_Oimage(U_4426,U_4427,U_4428),U_4429)
| ~ c_Fun_Oinj__on(U_4426,U_4427,U_4428,U_4429)
| ~ class_Groups_Ocomm__monoid__add(U_4425) ),
inference(clausify,[status(thm)],[f_1145_3]) ).
fof(f_1146_1,plain,
! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2))
| ? [B_x] :
( hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),B_x)) )
| V_b_2 != V_d_2
| V_a_2 != V_c_2
| ~ class_Orderings_Oord(T_b)
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__ivl__cong]) ).
fof(f_1146_2,plain,
! [U_4441,U_4440,U_4439,U_4438,U_4437,U_4436,U_4435,U_4434] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4435,U_4434),U_4440),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_4435,U_4436),U_4438)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4435,U_4434),U_4441),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_4435,U_4437),U_4439))
| ? [U_4433] :
( hAPP(U_4440,U_4433) != hAPP(U_4441,U_4433)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4435),U_4433),U_4439))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4435),U_4437),U_4433)) )
| U_4438 != U_4439
| U_4436 != U_4437
| ~ class_Orderings_Oord(U_4435)
| ~ class_Groups_Ocomm__monoid__add(U_4434) ),
inference(variable_rename,[status(thm)],[f_1146_1]) ).
fof(f_1146_3,plain,
! [U_4441,U_4440,U_4439,U_4438,U_4437,U_4436,U_4435,U_4434] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4435,U_4434),U_4440),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_4435,U_4436),U_4438)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4435,U_4434),U_4441),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_4435,U_4437),U_4439))
| ( hAPP(U_4440,sK100(U_4441,U_4440,U_4439,U_4438,U_4437,U_4436,U_4435,U_4434)) != hAPP(U_4441,sK100(U_4441,U_4440,U_4439,U_4438,U_4437,U_4436,U_4435,U_4434))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4435),sK100(U_4441,U_4440,U_4439,U_4438,U_4437,U_4436,U_4435,U_4434)),U_4439))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4435),U_4437),sK100(U_4441,U_4440,U_4439,U_4438,U_4437,U_4436,U_4435,U_4434))) )
| U_4438 != U_4439
| U_4436 != U_4437
| ~ class_Orderings_Oord(U_4435)
| ~ class_Groups_Ocomm__monoid__add(U_4434) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_4433,sK100(U_4441,U_4440,U_4439,U_4438,U_4437,U_4436,U_4435,U_4434))],[f_1146_2]) ).
cnf(f_1146_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4435),U_4437),sK100(U_4441,U_4440,U_4439,U_4438,U_4437,U_4436,U_4435,U_4434)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4435,U_4434),U_4440),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_4435,U_4436),U_4438)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4435,U_4434),U_4441),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_4435,U_4437),U_4439))
| U_4438 != U_4439
| U_4436 != U_4437
| ~ class_Orderings_Oord(U_4435)
| ~ class_Groups_Ocomm__monoid__add(U_4434) ),
inference(clausify,[status(thm)],[f_1146_3]) ).
cnf(f_1146_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4435),sK100(U_4441,U_4440,U_4439,U_4438,U_4437,U_4436,U_4435,U_4434)),U_4439))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4435,U_4434),U_4440),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_4435,U_4436),U_4438)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4435,U_4434),U_4441),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_4435,U_4437),U_4439))
| U_4438 != U_4439
| U_4436 != U_4437
| ~ class_Orderings_Oord(U_4435)
| ~ class_Groups_Ocomm__monoid__add(U_4434) ),
inference(clausify,[status(thm)],[f_1146_3]) ).
cnf(f_1146_6,plain,
( hAPP(U_4440,sK100(U_4441,U_4440,U_4439,U_4438,U_4437,U_4436,U_4435,U_4434)) != hAPP(U_4441,sK100(U_4441,U_4440,U_4439,U_4438,U_4437,U_4436,U_4435,U_4434))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4435,U_4434),U_4440),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_4435,U_4436),U_4438)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4435,U_4434),U_4441),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_4435,U_4437),U_4439))
| U_4438 != U_4439
| U_4436 != U_4437
| ~ class_Orderings_Oord(U_4435)
| ~ class_Groups_Ocomm__monoid__add(U_4434) ),
inference(clausify,[status(thm)],[f_1146_3]) ).
fof(f_1147_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_1147_2,plain,
! [U_4444,U_4443,U_4442] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_4442),U_4443) = hAPP(c_Int_Onumber__class_Onumber__of(U_4442),U_4444)
| U_4443 != U_4444 )
& ( U_4443 = U_4444
| hAPP(c_Int_Onumber__class_Onumber__of(U_4442),U_4443) != hAPP(c_Int_Onumber__class_Onumber__of(U_4442),U_4444) ) )
| ~ class_Int_Oring__char__0(U_4442)
| ~ class_Int_Onumber__ring(U_4442) ),
inference(variable_rename,[status(thm)],[f_1147_1]) ).
cnf(f_1147_3,plain,
( U_4443 = U_4444
| hAPP(c_Int_Onumber__class_Onumber__of(U_4442),U_4443) != hAPP(c_Int_Onumber__class_Onumber__of(U_4442),U_4444)
| ~ class_Int_Oring__char__0(U_4442)
| ~ class_Int_Onumber__ring(U_4442) ),
inference(clausify,[status(thm)],[f_1147_2]) ).
cnf(f_1147_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_4442),U_4443) = hAPP(c_Int_Onumber__class_Onumber__of(U_4442),U_4444)
| U_4443 != U_4444
| ~ class_Int_Oring__char__0(U_4442)
| ~ class_Int_Onumber__ring(U_4442) ),
inference(clausify,[status(thm)],[f_1147_2]) ).
fof(f_1148_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_1148_2,plain,
! [U_4447,U_4446,U_4445] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_4445),U_4446) = U_4447
| U_4447 != hAPP(c_Int_Onumber__class_Onumber__of(U_4445),U_4446) )
& ( U_4447 = hAPP(c_Int_Onumber__class_Onumber__of(U_4445),U_4446)
| hAPP(c_Int_Onumber__class_Onumber__of(U_4445),U_4446) != U_4447 ) )
| ~ class_Int_Onumber(U_4445) ),
inference(variable_rename,[status(thm)],[f_1148_1]) ).
cnf(f_1148_3,plain,
( U_4447 = hAPP(c_Int_Onumber__class_Onumber__of(U_4445),U_4446)
| hAPP(c_Int_Onumber__class_Onumber__of(U_4445),U_4446) != U_4447
| ~ class_Int_Onumber(U_4445) ),
inference(clausify,[status(thm)],[f_1148_2]) ).
cnf(f_1148_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_4445),U_4446) = U_4447
| U_4447 != hAPP(c_Int_Onumber__class_Onumber__of(U_4445),U_4446)
| ~ class_Int_Onumber(U_4445) ),
inference(clausify,[status(thm)],[f_1148_2]) ).
fof(f_1149_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_1149_2,plain,
! [U_4450,U_4449,U_4448] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4448),hAPP(c_Int_Onumber__class_Onumber__of(U_4448),U_4449)),hAPP(c_Int_Onumber__class_Onumber__of(U_4448),U_4450)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4449),U_4450)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4449),U_4450))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4448),hAPP(c_Int_Onumber__class_Onumber__of(U_4448),U_4449)),hAPP(c_Int_Onumber__class_Onumber__of(U_4448),U_4450))) ) )
| ~ class_Rings_Olinordered__idom(U_4448)
| ~ class_Int_Onumber__ring(U_4448) ),
inference(variable_rename,[status(thm)],[f_1149_1]) ).
cnf(f_1149_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4449),U_4450))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4448),hAPP(c_Int_Onumber__class_Onumber__of(U_4448),U_4449)),hAPP(c_Int_Onumber__class_Onumber__of(U_4448),U_4450)))
| ~ class_Rings_Olinordered__idom(U_4448)
| ~ class_Int_Onumber__ring(U_4448) ),
inference(clausify,[status(thm)],[f_1149_2]) ).
cnf(f_1149_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4448),hAPP(c_Int_Onumber__class_Onumber__of(U_4448),U_4449)),hAPP(c_Int_Onumber__class_Onumber__of(U_4448),U_4450)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4449),U_4450))
| ~ class_Rings_Olinordered__idom(U_4448)
| ~ class_Int_Onumber__ring(U_4448) ),
inference(clausify,[status(thm)],[f_1149_2]) ).
fof(f_1150_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_1150_2,plain,
! [U_4453,U_4452,U_4451] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4451),hAPP(c_Int_Onumber__class_Onumber__of(U_4451),U_4452)),hAPP(c_Int_Onumber__class_Onumber__of(U_4451),U_4453)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4452),U_4453)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4452),U_4453))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4451),hAPP(c_Int_Onumber__class_Onumber__of(U_4451),U_4452)),hAPP(c_Int_Onumber__class_Onumber__of(U_4451),U_4453))) ) )
| ~ class_Rings_Olinordered__idom(U_4451)
| ~ class_Int_Onumber__ring(U_4451) ),
inference(variable_rename,[status(thm)],[f_1150_1]) ).
cnf(f_1150_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4452),U_4453))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4451),hAPP(c_Int_Onumber__class_Onumber__of(U_4451),U_4452)),hAPP(c_Int_Onumber__class_Onumber__of(U_4451),U_4453)))
| ~ class_Rings_Olinordered__idom(U_4451)
| ~ class_Int_Onumber__ring(U_4451) ),
inference(clausify,[status(thm)],[f_1150_2]) ).
cnf(f_1150_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4451),hAPP(c_Int_Onumber__class_Onumber__of(U_4451),U_4452)),hAPP(c_Int_Onumber__class_Onumber__of(U_4451),U_4453)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4452),U_4453))
| ~ class_Rings_Olinordered__idom(U_4451)
| ~ class_Int_Onumber__ring(U_4451) ),
inference(clausify,[status(thm)],[f_1150_2]) ).
fof(f_1151_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_1151_2,plain,
! [U_4456,U_4455,U_4454] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_4454),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4455),U_4456)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4454),hAPP(c_Int_Onumber__class_Onumber__of(U_4454),U_4455)),hAPP(c_Int_Onumber__class_Onumber__of(U_4454),U_4456))
| ~ class_Int_Onumber__ring(U_4454) ),
inference(variable_rename,[status(thm)],[f_1151_1]) ).
cnf(f_1151_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_4454),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4455),U_4456)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4454),hAPP(c_Int_Onumber__class_Onumber__of(U_4454),U_4455)),hAPP(c_Int_Onumber__class_Onumber__of(U_4454),U_4456))
| ~ class_Int_Onumber__ring(U_4454) ),
inference(clausify,[status(thm)],[f_1151_2]) ).
fof(f_1152_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_1152_2,plain,
! [U_4459,U_4458,U_4457] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4457),hAPP(c_Int_Onumber__class_Onumber__of(U_4457),U_4458)),hAPP(c_Int_Onumber__class_Onumber__of(U_4457),U_4459)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4457),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4458),U_4459))
| ~ class_Int_Onumber__ring(U_4457) ),
inference(variable_rename,[status(thm)],[f_1152_1]) ).
cnf(f_1152_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4457),hAPP(c_Int_Onumber__class_Onumber__of(U_4457),U_4458)),hAPP(c_Int_Onumber__class_Onumber__of(U_4457),U_4459)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4457),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4458),U_4459))
| ~ class_Int_Onumber__ring(U_4457) ),
inference(clausify,[status(thm)],[f_1152_2]) ).
fof(f_1153_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_1153_2,plain,
! [U_4463,U_4462,U_4461,U_4460] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4460),hAPP(c_Int_Onumber__class_Onumber__of(U_4460),U_4461)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4460),hAPP(c_Int_Onumber__class_Onumber__of(U_4460),U_4462)),U_4463)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4460),hAPP(c_Int_Onumber__class_Onumber__of(U_4460),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4461),U_4462))),U_4463)
| ~ class_Int_Onumber__ring(U_4460) ),
inference(variable_rename,[status(thm)],[f_1153_1]) ).
cnf(f_1153_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4460),hAPP(c_Int_Onumber__class_Onumber__of(U_4460),U_4461)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4460),hAPP(c_Int_Onumber__class_Onumber__of(U_4460),U_4462)),U_4463)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4460),hAPP(c_Int_Onumber__class_Onumber__of(U_4460),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4461),U_4462))),U_4463)
| ~ class_Int_Onumber__ring(U_4460) ),
inference(clausify,[status(thm)],[f_1153_2]) ).
fof(f_1154_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_1154_2,plain,
! [U_4466,U_4465,U_4464] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_4464),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4465),U_4466)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4464),hAPP(c_Int_Onumber__class_Onumber__of(U_4464),U_4465)),hAPP(c_Int_Onumber__class_Onumber__of(U_4464),U_4466))
| ~ class_Int_Onumber__ring(U_4464) ),
inference(variable_rename,[status(thm)],[f_1154_1]) ).
cnf(f_1154_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_4464),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4465),U_4466)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4464),hAPP(c_Int_Onumber__class_Onumber__of(U_4464),U_4465)),hAPP(c_Int_Onumber__class_Onumber__of(U_4464),U_4466))
| ~ class_Int_Onumber__ring(U_4464) ),
inference(clausify,[status(thm)],[f_1154_2]) ).
fof(f_1155_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_1155_2,plain,
! [U_4469,U_4468,U_4467] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4467),hAPP(c_Int_Onumber__class_Onumber__of(U_4467),U_4468)),hAPP(c_Int_Onumber__class_Onumber__of(U_4467),U_4469)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4467),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4468),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4469)))
| ~ class_Int_Onumber__ring(U_4467) ),
inference(variable_rename,[status(thm)],[f_1155_1]) ).
cnf(f_1155_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4467),hAPP(c_Int_Onumber__class_Onumber__of(U_4467),U_4468)),hAPP(c_Int_Onumber__class_Onumber__of(U_4467),U_4469)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4467),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4468),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4469)))
| ~ class_Int_Onumber__ring(U_4467) ),
inference(clausify,[status(thm)],[f_1155_2]) ).
fof(f_1156_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_1156_2,plain,
! [U_4471,U_4470] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_4470),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4471)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4470),hAPP(c_Int_Onumber__class_Onumber__of(U_4470),U_4471))
| ~ class_Int_Onumber__ring(U_4470) ),
inference(variable_rename,[status(thm)],[f_1156_1]) ).
cnf(f_1156_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_4470),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4471)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4470),hAPP(c_Int_Onumber__class_Onumber__of(U_4470),U_4471))
| ~ class_Int_Onumber__ring(U_4470) ),
inference(clausify,[status(thm)],[f_1156_2]) ).
fof(f_1157_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_1157_2,plain,
! [U_4473,U_4472] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4472),hAPP(c_Int_Onumber__class_Onumber__of(U_4472),U_4473)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4472),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4473))
| ~ class_Int_Onumber__ring(U_4472) ),
inference(variable_rename,[status(thm)],[f_1157_1]) ).
cnf(f_1157_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4472),hAPP(c_Int_Onumber__class_Onumber__of(U_4472),U_4473)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4472),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4473))
| ~ class_Int_Onumber__ring(U_4472) ),
inference(clausify,[status(thm)],[f_1157_2]) ).
fof(f_1158_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_1158_2,plain,
! [U_4476,U_4475,U_4474] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4474),hAPP(c_Int_Onumber__class_Onumber__of(U_4474),U_4475)),hAPP(c_Int_Onumber__class_Onumber__of(U_4474),U_4476)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4474),hAPP(c_Int_Onumber__class_Onumber__of(U_4474),U_4476)),hAPP(c_Int_Onumber__class_Onumber__of(U_4474),U_4475))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4474),hAPP(c_Int_Onumber__class_Onumber__of(U_4474),U_4476)),hAPP(c_Int_Onumber__class_Onumber__of(U_4474),U_4475)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4474),hAPP(c_Int_Onumber__class_Onumber__of(U_4474),U_4475)),hAPP(c_Int_Onumber__class_Onumber__of(U_4474),U_4476))) ) )
| ~ class_Orderings_Olinorder(U_4474)
| ~ class_Int_Onumber(U_4474) ),
inference(variable_rename,[status(thm)],[f_1158_1]) ).
cnf(f_1158_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4474),hAPP(c_Int_Onumber__class_Onumber__of(U_4474),U_4476)),hAPP(c_Int_Onumber__class_Onumber__of(U_4474),U_4475)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4474),hAPP(c_Int_Onumber__class_Onumber__of(U_4474),U_4475)),hAPP(c_Int_Onumber__class_Onumber__of(U_4474),U_4476)))
| ~ class_Orderings_Olinorder(U_4474)
| ~ class_Int_Onumber(U_4474) ),
inference(clausify,[status(thm)],[f_1158_2]) ).
cnf(f_1158_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4474),hAPP(c_Int_Onumber__class_Onumber__of(U_4474),U_4475)),hAPP(c_Int_Onumber__class_Onumber__of(U_4474),U_4476)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4474),hAPP(c_Int_Onumber__class_Onumber__of(U_4474),U_4476)),hAPP(c_Int_Onumber__class_Onumber__of(U_4474),U_4475)))
| ~ class_Orderings_Olinorder(U_4474)
| ~ class_Int_Onumber(U_4474) ),
inference(clausify,[status(thm)],[f_1158_2]) ).
fof(f_1159_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_1159_2,plain,
! [U_4480,U_4479,U_4478,U_4477] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4477),hAPP(c_Int_Onumber__class_Onumber__of(U_4477),U_4478)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4477),U_4479),hAPP(c_Int_Onumber__class_Onumber__of(U_4477),U_4480))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4477),hAPP(c_Int_Onumber__class_Onumber__of(U_4477),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4478),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4480)))),U_4479)
| ~ class_Int_Onumber__ring(U_4477) ),
inference(variable_rename,[status(thm)],[f_1159_1]) ).
cnf(f_1159_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4477),hAPP(c_Int_Onumber__class_Onumber__of(U_4477),U_4478)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4477),U_4479),hAPP(c_Int_Onumber__class_Onumber__of(U_4477),U_4480))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4477),hAPP(c_Int_Onumber__class_Onumber__of(U_4477),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4478),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4480)))),U_4479)
| ~ class_Int_Onumber__ring(U_4477) ),
inference(clausify,[status(thm)],[f_1159_2]) ).
fof(f_1160_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_1160_2,plain,
! [U_4484,U_4483,U_4482,U_4481] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4481),hAPP(c_Int_Onumber__class_Onumber__of(U_4481),U_4482)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4481),hAPP(c_Int_Onumber__class_Onumber__of(U_4481),U_4483)),U_4484)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4481),hAPP(c_Int_Onumber__class_Onumber__of(U_4481),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4482),U_4483))),U_4484)
| ~ class_Int_Onumber__ring(U_4481) ),
inference(variable_rename,[status(thm)],[f_1160_1]) ).
cnf(f_1160_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4481),hAPP(c_Int_Onumber__class_Onumber__of(U_4481),U_4482)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4481),hAPP(c_Int_Onumber__class_Onumber__of(U_4481),U_4483)),U_4484)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4481),hAPP(c_Int_Onumber__class_Onumber__of(U_4481),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4482),U_4483))),U_4484)
| ~ class_Int_Onumber__ring(U_4481) ),
inference(clausify,[status(thm)],[f_1160_2]) ).
fof(f_1161_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_1161_2,plain,
! [U_4486,U_4485] :
( hBOOL(hAPP(hAPP(c_member(U_4485),hAPP(c_Int_Onumber__class_Onumber__of(U_4485),U_4486)),c_Int_Oring__1__class_OInts(U_4485)))
| ~ class_Int_Onumber__ring(U_4485) ),
inference(variable_rename,[status(thm)],[f_1161_1]) ).
cnf(f_1161_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_4485),hAPP(c_Int_Onumber__class_Onumber__of(U_4485),U_4486)),c_Int_Oring__1__class_OInts(U_4485)))
| ~ class_Int_Onumber__ring(U_4485) ),
inference(clausify,[status(thm)],[f_1161_2]) ).
fof(f_1162_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_1162_2,plain,
! [U_4488,U_4487] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_4487),c_Int_Opred(U_4488)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4487),hAPP(c_Groups_Ouminus__class_Ouminus(U_4487),c_Groups_Oone__class_Oone(U_4487))),hAPP(c_Int_Onumber__class_Onumber__of(U_4487),U_4488))
| ~ class_Int_Onumber__ring(U_4487) ),
inference(variable_rename,[status(thm)],[f_1162_1]) ).
cnf(f_1162_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_4487),c_Int_Opred(U_4488)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4487),hAPP(c_Groups_Ouminus__class_Ouminus(U_4487),c_Groups_Oone__class_Oone(U_4487))),hAPP(c_Int_Onumber__class_Onumber__of(U_4487),U_4488))
| ~ class_Int_Onumber__ring(U_4487) ),
inference(clausify,[status(thm)],[f_1162_2]) ).
fof(f_1163_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_1163_2,plain,
! [U_4496,U_4495,U_4494,U_4493,U_4492,U_4491,U_4490,U_4489] :
( hAPP(U_4494,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4490,tc_HOL_Obool)),U_4495),U_4496)) = hAPP(hAPP(U_4491,hAPP(U_4494,U_4495)),hAPP(U_4494,U_4496))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4490),U_4496))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4490),U_4495))
| ~ c_Finite__Set_Ofolding__image__simple__idem(U_4489,U_4490,U_4491,U_4492,U_4493,U_4494) ),
inference(variable_rename,[status(thm)],[f_1163_1]) ).
fof(f_1163_3,plain,
! [U_4496,U_4495,U_4494,U_4493,U_4492,U_4491,U_4490] :
( ! [U_4489] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_4489,U_4490,U_4491,U_4492,U_4493,U_4494)
| hAPP(U_4494,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4490,tc_HOL_Obool)),U_4495),U_4496)) = hAPP(hAPP(U_4491,hAPP(U_4494,U_4495)),hAPP(U_4494,U_4496))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4490),U_4496))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4490),U_4495)) ),
inference(miniscope,[status(thm)],[f_1163_2]) ).
cnf(f_1163_4,plain,
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_4489,U_4490,U_4491,U_4492,U_4493,U_4494)
| hAPP(U_4494,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4490,tc_HOL_Obool)),U_4495),U_4496)) = hAPP(hAPP(U_4491,hAPP(U_4494,U_4495)),hAPP(U_4494,U_4496))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4490),U_4496))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4490),U_4495)) ),
inference(clausify,[status(thm)],[f_1163_3]) ).
fof(f_1164_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_1164_2,plain,
! [U_4498,U_4497] :
( hAPP(c_Finite__Set_Ocard(tc_fun(U_4497,tc_HOL_Obool)),hAPP(c_Set_OPow(U_4497),U_4498)) = 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_4497),U_4498))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4497),U_4498)) ),
inference(variable_rename,[status(thm)],[f_1164_1]) ).
cnf(f_1164_3,plain,
( hAPP(c_Finite__Set_Ocard(tc_fun(U_4497,tc_HOL_Obool)),hAPP(c_Set_OPow(U_4497),U_4498)) = 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_4497),U_4498))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4497),U_4498)) ),
inference(clausify,[status(thm)],[f_1164_2]) ).
fof(f_1165_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_1165_2,plain,
! [U_4502,U_4501,U_4500] :
( ? [U_4499] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_4500,tc_HOL_Obool)),U_4499),U_4502))
& hBOOL(hAPP(hAPP(c_member(U_4500),U_4501),U_4499)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_4500),U_4501),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_4500,tc_HOL_Obool),U_4502))) ),
inference(variable_rename,[status(thm)],[f_1165_1]) ).
fof(f_1165_3,plain,
! [U_4502,U_4501,U_4500] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_4500,tc_HOL_Obool)),sK101(U_4502,U_4501,U_4500)),U_4502))
& hBOOL(hAPP(hAPP(c_member(U_4500),U_4501),sK101(U_4502,U_4501,U_4500))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_4500),U_4501),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_4500,tc_HOL_Obool),U_4502))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_4499,sK101(U_4502,U_4501,U_4500))],[f_1165_2]) ).
cnf(f_1165_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_4500),U_4501),sK101(U_4502,U_4501,U_4500)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4500),U_4501),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_4500,tc_HOL_Obool),U_4502))) ),
inference(clausify,[status(thm)],[f_1165_3]) ).
cnf(f_1165_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_4500,tc_HOL_Obool)),sK101(U_4502,U_4501,U_4500)),U_4502))
| ~ hBOOL(hAPP(hAPP(c_member(U_4500),U_4501),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_4500,tc_HOL_Obool),U_4502))) ),
inference(clausify,[status(thm)],[f_1165_3]) ).
fof(f_1166_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_1166_2,plain,
! [U_4510,U_4509,U_4508,U_4507,U_4506,U_4505,U_4504,U_4503] :
( hAPP(hAPP(U_4505,hAPP(U_4508,U_4510)),hAPP(U_4508,U_4509)) = hAPP(U_4508,U_4509)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4504,tc_HOL_Obool)),U_4510),U_4509))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4504),U_4509))
| ~ c_Finite__Set_Ofolding__image__simple__idem(U_4503,U_4504,U_4505,U_4506,U_4507,U_4508) ),
inference(variable_rename,[status(thm)],[f_1166_1]) ).
fof(f_1166_3,plain,
! [U_4510,U_4509,U_4508,U_4507,U_4506,U_4505,U_4504] :
( ! [U_4503] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_4503,U_4504,U_4505,U_4506,U_4507,U_4508)
| hAPP(hAPP(U_4505,hAPP(U_4508,U_4510)),hAPP(U_4508,U_4509)) = hAPP(U_4508,U_4509)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4504,tc_HOL_Obool)),U_4510),U_4509))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4504),U_4509)) ),
inference(miniscope,[status(thm)],[f_1166_2]) ).
cnf(f_1166_4,plain,
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_4503,U_4504,U_4505,U_4506,U_4507,U_4508)
| hAPP(hAPP(U_4505,hAPP(U_4508,U_4510)),hAPP(U_4508,U_4509)) = hAPP(U_4508,U_4509)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4504,tc_HOL_Obool)),U_4510),U_4509))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4504),U_4509)) ),
inference(clausify,[status(thm)],[f_1166_3]) ).
fof(f_1167_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_1167_2,plain,
! [U_4513,U_4512,U_4511] :
( c_Big__Operators_Olattice__class_OInf__fin(U_4511,hAPP(hAPP(c_Set_Oinsert(U_4511),U_4513),U_4512)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4511,U_4511,c_Lattices_Osemilattice__inf__class_Oinf(U_4511)),U_4513),U_4512)
| hBOOL(hAPP(hAPP(c_member(U_4511),U_4513),U_4512))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4511),U_4512))
| ~ class_Lattices_Olattice(U_4511) ),
inference(variable_rename,[status(thm)],[f_1167_1]) ).
cnf(f_1167_3,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_4511,hAPP(hAPP(c_Set_Oinsert(U_4511),U_4513),U_4512)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4511,U_4511,c_Lattices_Osemilattice__inf__class_Oinf(U_4511)),U_4513),U_4512)
| hBOOL(hAPP(hAPP(c_member(U_4511),U_4513),U_4512))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4511),U_4512))
| ~ class_Lattices_Olattice(U_4511) ),
inference(clausify,[status(thm)],[f_1167_2]) ).
fof(f_1168_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_1168_2,plain,
! [U_4516,U_4515,U_4514] :
( c_Big__Operators_Olattice__class_OSup__fin(U_4514,hAPP(hAPP(c_Set_Oinsert(U_4514),U_4516),U_4515)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4514,U_4514,c_Lattices_Osemilattice__sup__class_Osup(U_4514)),U_4516),U_4515)
| hBOOL(hAPP(hAPP(c_member(U_4514),U_4516),U_4515))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4514),U_4515))
| ~ class_Lattices_Olattice(U_4514) ),
inference(variable_rename,[status(thm)],[f_1168_1]) ).
cnf(f_1168_3,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_4514,hAPP(hAPP(c_Set_Oinsert(U_4514),U_4516),U_4515)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4514,U_4514,c_Lattices_Osemilattice__sup__class_Osup(U_4514)),U_4516),U_4515)
| hBOOL(hAPP(hAPP(c_member(U_4514),U_4516),U_4515))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4514),U_4515))
| ~ class_Lattices_Olattice(U_4514) ),
inference(clausify,[status(thm)],[f_1168_2]) ).
fof(f_1169_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_1169_2,plain,
! [U_4518,U_4517] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4517)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4518)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4517),U_4518)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4517),U_4518))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4517)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4518))) ) ),
inference(variable_rename,[status(thm)],[f_1169_1]) ).
fof(f_1169_3,plain,
( ! [U_4522,U_4520] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4520)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4522)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4520),U_4522)) )
& ! [U_4521,U_4519] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4519),U_4521))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4519)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4521))) ) ),
inference(miniscope,[status(thm)],[f_1169_2]) ).
cnf(f_1169_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4519),U_4521))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4519)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4521))) ),
inference(clausify,[status(thm)],[f_1169_3]) ).
cnf(f_1169_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_4520)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4522)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4520),U_4522)) ),
inference(clausify,[status(thm)],[f_1169_3]) ).
fof(f_1170_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_1170_2,plain,
! [U_4524,U_4523] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4523)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4524)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4523),U_4524)),
inference(variable_rename,[status(thm)],[f_1170_1]) ).
cnf(f_1170_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4523)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4524)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4523),U_4524)),
inference(clausify,[status(thm)],[f_1170_2]) ).
fof(f_1171_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_1171_2,plain,
! [U_4526,U_4525] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4525)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4526)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4525),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4526))),
inference(variable_rename,[status(thm)],[f_1171_1]) ).
cnf(f_1171_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4525)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4526)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4525),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4526))),
inference(clausify,[status(thm)],[f_1171_2]) ).
fof(f_1172_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_1172_2,plain,
! [U_4527] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4527)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4527)),
inference(variable_rename,[status(thm)],[f_1172_1]) ).
cnf(f_1172_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4527)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4527)),
inference(clausify,[status(thm)],[f_1172_2]) ).
fof(f_1173_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_1173_2,plain,
! [U_4529,U_4528] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4528)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4529)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4528),U_4529)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4528),U_4529))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4528)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4529))) ) ),
inference(variable_rename,[status(thm)],[f_1173_1]) ).
fof(f_1173_3,plain,
( ! [U_4533,U_4531] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4531)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4533)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4531),U_4533)) )
& ! [U_4532,U_4530] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4530),U_4532))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4530)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4532))) ) ),
inference(miniscope,[status(thm)],[f_1173_2]) ).
cnf(f_1173_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4530),U_4532))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4530)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4532))) ),
inference(clausify,[status(thm)],[f_1173_3]) ).
cnf(f_1173_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4531)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4533)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4531),U_4533)) ),
inference(clausify,[status(thm)],[f_1173_3]) ).
fof(f_1174_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_1174_2,plain,
! [U_4535,U_4534] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4534),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4535) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_4534,U_4535),
inference(variable_rename,[status(thm)],[f_1174_1]) ).
cnf(f_1174_3,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4534),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4535) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_4534,U_4535),
inference(clausify,[status(thm)],[f_1174_2]) ).
fof(f_1175_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_1175_2,plain,
! [U_4537,U_4536] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4536),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4537) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_4536,U_4537),
inference(variable_rename,[status(thm)],[f_1175_1]) ).
cnf(f_1175_3,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4536),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4537) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_4536,U_4537),
inference(clausify,[status(thm)],[f_1175_2]) ).
fof(f_1176_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_1176_2,plain,
! [U_4539,U_4538] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_4538),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4539),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_4538,U_4539),
inference(variable_rename,[status(thm)],[f_1176_1]) ).
cnf(f_1176_3,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_4538),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4539),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_4538,U_4539),
inference(clausify,[status(thm)],[f_1176_2]) ).
fof(f_1177_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_1177_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_1177_1]) ).
fof(f_1178_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_1178_2,plain,
! [U_4540] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4540))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4540)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4540))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4540)) ) ),
inference(variable_rename,[status(thm)],[f_1178_1]) ).
fof(f_1178_3,plain,
( ! [U_4542] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4542))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4542)) )
& ! [U_4541] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4541))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4541)) ) ),
inference(miniscope,[status(thm)],[f_1178_2]) ).
cnf(f_1178_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4541))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4541)) ),
inference(clausify,[status(thm)],[f_1178_3]) ).
cnf(f_1178_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4542))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4542)) ),
inference(clausify,[status(thm)],[f_1178_3]) ).
fof(f_1179_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_1179_2,plain,
! [U_4544,U_4543] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4543),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4544),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4543),U_4544)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4543),U_4544))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4543),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4544),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(variable_rename,[status(thm)],[f_1179_1]) ).
fof(f_1179_3,plain,
( ! [U_4548,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_4548),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4546),U_4548)) )
& ! [U_4547,U_4545] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4545),U_4547))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4545),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4547),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(miniscope,[status(thm)],[f_1179_2]) ).
cnf(f_1179_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4545),U_4547))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4545),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4547),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(clausify,[status(thm)],[f_1179_3]) ).
cnf(f_1179_5,plain,
( 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_4548),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4546),U_4548)) ),
inference(clausify,[status(thm)],[f_1179_3]) ).
fof(f_1180_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_1180_2,plain,
! [U_4549] : c_Int_Opred(U_4549) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4549),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(variable_rename,[status(thm)],[f_1180_1]) ).
cnf(f_1180_3,plain,
c_Int_Opred(U_4549) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4549),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_1180_2]) ).
fof(f_1181_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_1181_2,plain,
! [U_4550] :
( ( 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_4550)),U_4550)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4550),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4550),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_4550)),U_4550)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_1181_1]) ).
fof(f_1181_3,plain,
( ! [U_4552] :
( 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_4552)),U_4552)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4552),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_4551] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4551),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_4551)),U_4551)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_1181_2]) ).
cnf(f_1181_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4551),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_4551)),U_4551)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1181_3]) ).
cnf(f_1181_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_4552)),U_4552)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4552),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1181_3]) ).
fof(f_1182_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_1182_2,plain,
! [U_4553] :
( 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_4553)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4553)) ),
inference(variable_rename,[status(thm)],[f_1182_1]) ).
cnf(f_1182_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_4553)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4553)) ),
inference(clausify,[status(thm)],[f_1182_2]) ).
fof(f_1183_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_1183_2,plain,
! [U_4555,U_4554] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4554),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4555),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ( U_4554 != U_4555
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4554),U_4555)) ) )
& ( U_4554 = U_4555
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4554),U_4555))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4554),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4555),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(variable_rename,[status(thm)],[f_1183_1]) ).
fof(f_1183_3,plain,
( ! [U_4559,U_4557] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4557),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4559),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ( U_4557 != U_4559
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4557),U_4559)) ) )
& ! [U_4558,U_4556] :
( U_4556 = U_4558
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4556),U_4558))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4556),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4558),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(miniscope,[status(thm)],[f_1183_2]) ).
cnf(f_1183_4,plain,
( U_4556 = U_4558
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4556),U_4558))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4556),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4558),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(clausify,[status(thm)],[f_1183_3]) ).
cnf(f_1183_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4557),U_4559))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4557),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4559),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(clausify,[status(thm)],[f_1183_3]) ).
cnf(f_1183_6,plain,
( U_4557 != U_4559
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4557),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4559),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(clausify,[status(thm)],[f_1183_3]) ).
fof(f_1184_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_1184_2,plain,
! [U_4561,U_4560] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4560),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4561))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4560),U_4561)) ),
inference(variable_rename,[status(thm)],[f_1184_1]) ).
cnf(f_1184_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_4560),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4561))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4560),U_4561)) ),
inference(clausify,[status(thm)],[f_1184_2]) ).
fof(f_1185_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_1185_2,plain,
! [U_4563,U_4562] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4562),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4563))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4562),U_4563)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4562),U_4563))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4562),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4563)) ) ),
inference(variable_rename,[status(thm)],[f_1185_1]) ).
fof(f_1185_3,plain,
( ! [U_4567,U_4565] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4565),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4567))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4565),U_4567)) )
& ! [U_4566,U_4564] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4564),U_4566))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4564),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4566)) ) ),
inference(miniscope,[status(thm)],[f_1185_2]) ).
cnf(f_1185_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4564),U_4566))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4564),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4566)) ),
inference(clausify,[status(thm)],[f_1185_3]) ).
cnf(f_1185_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_4565),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4567))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4565),U_4567)) ),
inference(clausify,[status(thm)],[f_1185_3]) ).
fof(f_1186_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_1186_2,plain,
! [U_4569,U_4568] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4568),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4569),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4568),U_4569)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4568),U_4569))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4568),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4569),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(variable_rename,[status(thm)],[f_1186_1]) ).
fof(f_1186_3,plain,
( ! [U_4573,U_4571] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4571),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4573),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4571),U_4573)) )
& ! [U_4572,U_4570] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4570),U_4572))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4570),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4572),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(miniscope,[status(thm)],[f_1186_2]) ).
cnf(f_1186_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4570),U_4572))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4570),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4572),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(clausify,[status(thm)],[f_1186_3]) ).
cnf(f_1186_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4571),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4573),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4571),U_4573)) ),
inference(clausify,[status(thm)],[f_1186_3]) ).
fof(f_1187_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_1187_2,plain,
! [U_4574] : 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_4574)),U_4574) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_1187_1]) ).
cnf(f_1187_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_4574)),U_4574) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1187_2]) ).
fof(f_1188_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_1188_2,plain,
! [U_4581,U_4580,U_4579,U_4578,U_4577,U_4576,U_4575] :
( hAPP(hAPP(U_4577,U_4581),U_4581) = U_4581
| ~ c_Finite__Set_Ofolding__image__simple__idem(U_4575,U_4576,U_4577,U_4578,U_4579,U_4580) ),
inference(variable_rename,[status(thm)],[f_1188_1]) ).
fof(f_1188_3,plain,
! [U_4581,U_4580,U_4579,U_4578,U_4577] :
( ! [U_4576,U_4575] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_4575,U_4576,U_4577,U_4578,U_4579,U_4580)
| hAPP(hAPP(U_4577,U_4581),U_4581) = U_4581 ),
inference(miniscope,[status(thm)],[f_1188_2]) ).
cnf(f_1188_4,plain,
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_4575,U_4576,U_4577,U_4578,U_4579,U_4580)
| hAPP(hAPP(U_4577,U_4581),U_4581) = U_4581 ),
inference(clausify,[status(thm)],[f_1188_3]) ).
fof(f_1189_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_1189_2,plain,
! [U_4583,U_4582] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4582),U_4583))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4582),U_4583)),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_4582),U_4583)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4582),U_4583)) ) ),
inference(variable_rename,[status(thm)],[f_1189_1]) ).
fof(f_1189_3,plain,
( ! [U_4587,U_4585] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4585),U_4587))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4585),U_4587)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_4586,U_4584] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4584),U_4586)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4584),U_4586)) ) ),
inference(miniscope,[status(thm)],[f_1189_2]) ).
cnf(f_1189_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4584),U_4586)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4584),U_4586)) ),
inference(clausify,[status(thm)],[f_1189_3]) ).
cnf(f_1189_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4585),U_4587))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4585),U_4587)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1189_3]) ).
fof(f_1190_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_1190_2,plain,
! [U_4589,U_4588] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4589),U_4588))
| U_4588 = U_4589
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4588),U_4589)) ),
inference(variable_rename,[status(thm)],[f_1190_1]) ).
cnf(f_1190_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4589),U_4588))
| U_4588 = U_4589
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4588),U_4589)) ),
inference(clausify,[status(thm)],[f_1190_2]) ).
fof(f_1191_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_1191_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_1191_1]) ).
fof(f_1192_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_1192_2,plain,
! [U_4590] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4590)) = U_4590,
inference(variable_rename,[status(thm)],[f_1192_1]) ).
cnf(f_1192_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4590)) = U_4590,
inference(clausify,[status(thm)],[f_1192_2]) ).
fof(f_1193_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_1193_2,plain,
! [U_4592,U_4591] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4591),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4592)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4591),U_4592),
inference(variable_rename,[status(thm)],[f_1193_1]) ).
cnf(f_1193_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4591),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4592)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4591),U_4592),
inference(clausify,[status(thm)],[f_1193_2]) ).
fof(f_1194_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_1194_2,plain,
! [U_4594,U_4593] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4593),U_4594) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4593),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4594)),
inference(variable_rename,[status(thm)],[f_1194_1]) ).
cnf(f_1194_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4593),U_4594) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4593),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4594)),
inference(clausify,[status(thm)],[f_1194_2]) ).
fof(f_1195_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_1195_2,plain,
! [U_4597,U_4596,U_4595] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4595),U_4597)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4596),U_4597)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4595),U_4596)) ),
inference(variable_rename,[status(thm)],[f_1195_1]) ).
cnf(f_1195_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4595),U_4597)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4596),U_4597)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4595),U_4596)) ),
inference(clausify,[status(thm)],[f_1195_2]) ).
fof(f_1196_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_1196_2,plain,
! [U_4598] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4598) = U_4598,
inference(variable_rename,[status(thm)],[f_1196_1]) ).
cnf(f_1196_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4598) = U_4598,
inference(clausify,[status(thm)],[f_1196_2]) ).
fof(f_1197_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_1197_2,plain,
! [U_4599] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4599),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_4599,
inference(variable_rename,[status(thm)],[f_1197_1]) ).
cnf(f_1197_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4599),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_4599,
inference(clausify,[status(thm)],[f_1197_2]) ).
fof(f_1198_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_1198_2,plain,
! [U_4600] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4600)),U_4600) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_1198_1]) ).
cnf(f_1198_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4600)),U_4600) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1198_2]) ).
fof(f_1199_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_1199_2,plain,
! [U_4602,U_4601] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4601),U_4602) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4602),U_4601),
inference(variable_rename,[status(thm)],[f_1199_1]) ).
cnf(f_1199_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4601),U_4602) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4602),U_4601),
inference(clausify,[status(thm)],[f_1199_2]) ).
fof(f_1200_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_1200_2,plain,
! [U_4605,U_4604,U_4603] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4603),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4604),U_4605)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4604),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4603),U_4605)),
inference(variable_rename,[status(thm)],[f_1200_1]) ).
cnf(f_1200_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4603),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4604),U_4605)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4604),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4603),U_4605)),
inference(clausify,[status(thm)],[f_1200_2]) ).
fof(f_1201_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_1201_2,plain,
! [U_4608,U_4607,U_4606] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4606),U_4607)),U_4608) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4606),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4607),U_4608)),
inference(variable_rename,[status(thm)],[f_1201_1]) ).
cnf(f_1201_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4606),U_4607)),U_4608) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4606),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4607),U_4608)),
inference(clausify,[status(thm)],[f_1201_2]) ).
fof(f_1202_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_1202_2,plain,
! [U_4610,U_4609] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4609),U_4610)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4609)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4610)),
inference(variable_rename,[status(thm)],[f_1202_1]) ).
cnf(f_1202_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4609),U_4610)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4609)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4610)),
inference(clausify,[status(thm)],[f_1202_2]) ).
fof(f_1203_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_1203_2,plain,
! [U_4613,U_4612,U_4611] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4613),U_4611)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4613),U_4612)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4611),U_4612)) ),
inference(variable_rename,[status(thm)],[f_1203_1]) ).
cnf(f_1203_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_4613),U_4611)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4613),U_4612)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4611),U_4612)) ),
inference(clausify,[status(thm)],[f_1203_2]) ).
fof(f_1204_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_1204_2,plain,
! [U_4617,U_4616,U_4615,U_4614] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4614),U_4616)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4615),U_4617)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4616),U_4617))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4614),U_4615)) ),
inference(variable_rename,[status(thm)],[f_1204_1]) ).
cnf(f_1204_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4614),U_4616)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4615),U_4617)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4616),U_4617))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4614),U_4615)) ),
inference(clausify,[status(thm)],[f_1204_2]) ).
fof(f_1205_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_1205_2,plain,
! [U_4618] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4618),U_4618)),
inference(variable_rename,[status(thm)],[f_1205_1]) ).
cnf(f_1205_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4618),U_4618)),
inference(clausify,[status(thm)],[f_1205_2]) ).
fof(f_1206_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_1206_2,plain,
! [U_4620,U_4619] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4620),U_4619))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4619),U_4620)) ),
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),U_4620),U_4619))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4619),U_4620)) ),
inference(clausify,[status(thm)],[f_1206_2]) ).
fof(f_1207_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_1207_2,plain,
! [U_4623,U_4622,U_4621] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4621),U_4623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4622),U_4623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4621),U_4622)) ),
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_4621),U_4623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4622),U_4623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4621),U_4622)) ),
inference(clausify,[status(thm)],[f_1207_2]) ).
fof(f_1208_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_1208_2,plain,
! [U_4625,U_4624] :
( U_4624 = U_4625
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4625),U_4624))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4624),U_4625)) ),
inference(variable_rename,[status(thm)],[f_1208_1]) ).
cnf(f_1208_3,plain,
( U_4624 = U_4625
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4625),U_4624))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4624),U_4625)) ),
inference(clausify,[status(thm)],[f_1208_2]) ).
fof(f_1209_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_1209_2,plain,
! [U_4627,U_4626] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4626),U_4627))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_4626)),U_4627)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_4626)),U_4627))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4626),U_4627)) ) ),
inference(variable_rename,[status(thm)],[f_1209_1]) ).
fof(f_1209_3,plain,
( ! [U_4631,U_4629] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4629),U_4631))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_4629)),U_4631)) )
& ! [U_4630,U_4628] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_4628)),U_4630))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4628),U_4630)) ) ),
inference(miniscope,[status(thm)],[f_1209_2]) ).
cnf(f_1209_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_4628)),U_4630))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4628),U_4630)) ),
inference(clausify,[status(thm)],[f_1209_3]) ).
cnf(f_1209_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4629),U_4631))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_4629)),U_4631)) ),
inference(clausify,[status(thm)],[f_1209_3]) ).
fof(f_1210_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_1210_2,plain,
! [U_4633,U_4632] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4632),U_4633))
| U_4632 = U_4633
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4632),U_4633)) )
& ( ( U_4632 != U_4633
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4632),U_4633)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4632),U_4633)) ) ),
inference(variable_rename,[status(thm)],[f_1210_1]) ).
fof(f_1210_3,plain,
( ! [U_4637,U_4635] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4635),U_4637))
| U_4635 = U_4637
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4635),U_4637)) )
& ! [U_4636,U_4634] :
( ( U_4634 != U_4636
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4634),U_4636)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4634),U_4636)) ) ),
inference(miniscope,[status(thm)],[f_1210_2]) ).
cnf(f_1210_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4634),U_4636))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4634),U_4636)) ),
inference(clausify,[status(thm)],[f_1210_3]) ).
cnf(f_1210_5,plain,
( U_4634 != U_4636
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4634),U_4636)) ),
inference(clausify,[status(thm)],[f_1210_3]) ).
cnf(f_1210_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4635),U_4637))
| U_4635 = U_4637
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4635),U_4637)) ),
inference(clausify,[status(thm)],[f_1210_3]) ).
fof(f_1211_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_1211_2,plain,
! [U_4638] :
( ( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_4638) = 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_4638)) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_4638) = 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_4638)) ) )
| U_4638 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_4638) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_4638 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_1211_1]) ).
fof(f_1211_3,plain,
( ! [U_4640] :
( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_4640) = 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_4640)) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_4640) = 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_4640)) ) )
| U_4640 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_4639] :
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_4639) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_4639 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_1211_2]) ).
cnf(f_1211_4,plain,
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_4639) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_4639 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1211_3]) ).
cnf(f_1211_5,plain,
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_4640) = 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_4640))
| U_4640 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1211_3]) ).
cnf(f_1211_6,plain,
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_4640) = 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_4640))
| U_4640 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1211_3]) ).
fof(f_1212_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_1212_2,plain,
! [U_4644,U_4643,U_4642,U_4641] : hAPP(hAPP(c_Finite__Set_Ofold(U_4641,U_4642,U_4643),U_4644),c_Orderings_Obot__class_Obot(tc_fun(U_4641,tc_HOL_Obool))) = U_4644,
inference(variable_rename,[status(thm)],[f_1212_1]) ).
cnf(f_1212_3,plain,
hAPP(hAPP(c_Finite__Set_Ofold(U_4641,U_4642,U_4643),U_4644),c_Orderings_Obot__class_Obot(tc_fun(U_4641,tc_HOL_Obool))) = U_4644,
inference(clausify,[status(thm)],[f_1212_2]) ).
fof(f_1213_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_1213_2,plain,
! [U_4646,U_4645] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4645),U_4646),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4646
| ~ class_Rings_Ocomm__semiring__1(U_4645) ),
inference(variable_rename,[status(thm)],[f_1213_1]) ).
cnf(f_1213_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4645),U_4646),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4646
| ~ class_Rings_Ocomm__semiring__1(U_4645) ),
inference(clausify,[status(thm)],[f_1213_2]) ).
fof(f_1214_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_1214_2,plain,
! [U_4648,U_4647] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4647),U_4648),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_4647)
| ~ class_Rings_Ocomm__semiring__1(U_4647) ),
inference(variable_rename,[status(thm)],[f_1214_1]) ).
cnf(f_1214_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4647),U_4648),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_4647)
| ~ class_Rings_Ocomm__semiring__1(U_4647) ),
inference(clausify,[status(thm)],[f_1214_2]) ).
fof(f_1215_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_1215_2,plain,
! [U_4651,U_4650,U_4649] :
( hBOOL(hAPP(hAPP(c_member(U_4649),hAPP(hAPP(c_Power_Opower__class_Opower(U_4649),U_4650),U_4651)),c_Int_Oring__1__class_OInts(U_4649)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4649),U_4650),c_Int_Oring__1__class_OInts(U_4649)))
| ~ class_Rings_Oring__1(U_4649) ),
inference(variable_rename,[status(thm)],[f_1215_1]) ).
cnf(f_1215_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_4649),hAPP(hAPP(c_Power_Opower__class_Opower(U_4649),U_4650),U_4651)),c_Int_Oring__1__class_OInts(U_4649)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4649),U_4650),c_Int_Oring__1__class_OInts(U_4649)))
| ~ class_Rings_Oring__1(U_4649) ),
inference(clausify,[status(thm)],[f_1215_2]) ).
fof(f_1216_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_1216_2,plain,
! [U_4654,U_4653,U_4652] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4652,tc_HOL_Obool)),U_4653),U_4654) = hAPP(hAPP(c_Finite__Set_Ofold(U_4652,tc_fun(U_4652,tc_HOL_Obool),c_Set_Oinsert(U_4652)),U_4654),U_4653)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4652),U_4653)) ),
inference(variable_rename,[status(thm)],[f_1216_1]) ).
cnf(f_1216_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4652,tc_HOL_Obool)),U_4653),U_4654) = hAPP(hAPP(c_Finite__Set_Ofold(U_4652,tc_fun(U_4652,tc_HOL_Obool),c_Set_Oinsert(U_4652)),U_4654),U_4653)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4652),U_4653)) ),
inference(clausify,[status(thm)],[f_1216_2]) ).
fof(f_1217_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_1217_2,plain,
! [U_4658,U_4657,U_4656,U_4655] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_4655,U_4655,c_Lattices_Osemilattice__sup__class_Osup(U_4655)),U_4657),hAPP(hAPP(c_Set_Oinsert(U_4655),U_4658),U_4656)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4655),U_4658),hAPP(hAPP(c_Finite__Set_Ofold(U_4655,U_4655,c_Lattices_Osemilattice__sup__class_Osup(U_4655)),U_4657),U_4656))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4655),U_4656))
| ~ class_Lattices_Osemilattice__sup(U_4655) ),
inference(variable_rename,[status(thm)],[f_1217_1]) ).
cnf(f_1217_3,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_4655,U_4655,c_Lattices_Osemilattice__sup__class_Osup(U_4655)),U_4657),hAPP(hAPP(c_Set_Oinsert(U_4655),U_4658),U_4656)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4655),U_4658),hAPP(hAPP(c_Finite__Set_Ofold(U_4655,U_4655,c_Lattices_Osemilattice__sup__class_Osup(U_4655)),U_4657),U_4656))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4655),U_4656))
| ~ class_Lattices_Osemilattice__sup(U_4655) ),
inference(clausify,[status(thm)],[f_1217_2]) ).
fof(f_1218_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_1218_2,plain,
! [U_4662,U_4661,U_4660,U_4659] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_4659,U_4659,c_Lattices_Osemilattice__inf__class_Oinf(U_4659)),U_4661),hAPP(hAPP(c_Set_Oinsert(U_4659),U_4662),U_4660)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4659),U_4662),hAPP(hAPP(c_Finite__Set_Ofold(U_4659,U_4659,c_Lattices_Osemilattice__inf__class_Oinf(U_4659)),U_4661),U_4660))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4659),U_4660))
| ~ class_Lattices_Osemilattice__inf(U_4659) ),
inference(variable_rename,[status(thm)],[f_1218_1]) ).
cnf(f_1218_3,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_4659,U_4659,c_Lattices_Osemilattice__inf__class_Oinf(U_4659)),U_4661),hAPP(hAPP(c_Set_Oinsert(U_4659),U_4662),U_4660)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4659),U_4662),hAPP(hAPP(c_Finite__Set_Ofold(U_4659,U_4659,c_Lattices_Osemilattice__inf__class_Oinf(U_4659)),U_4661),U_4660))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4659),U_4660))
| ~ class_Lattices_Osemilattice__inf(U_4659) ),
inference(clausify,[status(thm)],[f_1218_2]) ).
fof(f_1219_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_1219_2,plain,
! [U_4665,U_4664,U_4663] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4663),U_4665),c_Complete__Lattice_OSup__class_OSup(U_4663,U_4664)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4663,U_4663,c_Lattices_Osemilattice__sup__class_Osup(U_4663)),U_4665),U_4664)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4663),U_4664))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4663) ),
inference(variable_rename,[status(thm)],[f_1219_1]) ).
cnf(f_1219_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4663),U_4665),c_Complete__Lattice_OSup__class_OSup(U_4663,U_4664)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4663,U_4663,c_Lattices_Osemilattice__sup__class_Osup(U_4663)),U_4665),U_4664)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4663),U_4664))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4663) ),
inference(clausify,[status(thm)],[f_1219_2]) ).
fof(f_1220_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_1220_2,plain,
! [U_4668,U_4667,U_4666] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4666),U_4668),c_Complete__Lattice_OInf__class_OInf(U_4666,U_4667)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4666,U_4666,c_Lattices_Osemilattice__inf__class_Oinf(U_4666)),U_4668),U_4667)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4666),U_4667))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4666) ),
inference(variable_rename,[status(thm)],[f_1220_1]) ).
cnf(f_1220_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4666),U_4668),c_Complete__Lattice_OInf__class_OInf(U_4666,U_4667)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4666,U_4666,c_Lattices_Osemilattice__inf__class_Oinf(U_4666)),U_4668),U_4667)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4666),U_4667))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4666) ),
inference(clausify,[status(thm)],[f_1220_2]) ).
fof(f_1221_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_1221_2,plain,
! [U_4673,U_4672,U_4671,U_4670,U_4669] :
( hAPP(U_4671,hAPP(hAPP(c_Set_Oinsert(U_4669),U_4673),U_4672)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4669,U_4669,U_4670),U_4673),U_4672)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4669),U_4672))
| ~ c_Finite__Set_Ofolding__one__idem(U_4669,U_4670,U_4671) ),
inference(variable_rename,[status(thm)],[f_1221_1]) ).
cnf(f_1221_3,plain,
( hAPP(U_4671,hAPP(hAPP(c_Set_Oinsert(U_4669),U_4673),U_4672)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4669,U_4669,U_4670),U_4673),U_4672)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4669),U_4672))
| ~ c_Finite__Set_Ofolding__one__idem(U_4669,U_4670,U_4671) ),
inference(clausify,[status(thm)],[f_1221_2]) ).
fof(f_1222_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_1222_2,plain,
! [U_4677,U_4676,U_4675,U_4674] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4674),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4674),U_4676),U_4677)),hAPP(hAPP(c_Finite__Set_Ofold(U_4674,U_4674,c_Lattices_Osemilattice__sup__class_Osup(U_4674)),U_4677),U_4675)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4674),U_4676),U_4675))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4674),U_4675))
| ~ class_Lattices_Osemilattice__sup(U_4674) ),
inference(variable_rename,[status(thm)],[f_1222_1]) ).
cnf(f_1222_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4674),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4674),U_4676),U_4677)),hAPP(hAPP(c_Finite__Set_Ofold(U_4674,U_4674,c_Lattices_Osemilattice__sup__class_Osup(U_4674)),U_4677),U_4675)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4674),U_4676),U_4675))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4674),U_4675))
| ~ class_Lattices_Osemilattice__sup(U_4674) ),
inference(clausify,[status(thm)],[f_1222_2]) ).
fof(f_1223_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_1223_2,plain,
! [U_4681,U_4680,U_4679,U_4678] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4678),hAPP(hAPP(c_Finite__Set_Ofold(U_4678,U_4678,c_Lattices_Osemilattice__inf__class_Oinf(U_4678)),U_4681),U_4679)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4678),U_4680),U_4681)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4678),U_4680),U_4679))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4678),U_4679))
| ~ class_Lattices_Osemilattice__inf(U_4678) ),
inference(variable_rename,[status(thm)],[f_1223_1]) ).
cnf(f_1223_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4678),hAPP(hAPP(c_Finite__Set_Ofold(U_4678,U_4678,c_Lattices_Osemilattice__inf__class_Oinf(U_4678)),U_4681),U_4679)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4678),U_4680),U_4681)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4678),U_4680),U_4679))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4678),U_4679))
| ~ class_Lattices_Osemilattice__inf(U_4678) ),
inference(clausify,[status(thm)],[f_1223_2]) ).
fof(f_1224_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_1224_2,plain,
! [U_4683,U_4682] :
( c_Complete__Lattice_OSup__class_OSup(U_4682,U_4683) = hAPP(hAPP(c_Finite__Set_Ofold(U_4682,U_4682,c_Lattices_Osemilattice__sup__class_Osup(U_4682)),c_Orderings_Obot__class_Obot(U_4682)),U_4683)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4682),U_4683))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4682) ),
inference(variable_rename,[status(thm)],[f_1224_1]) ).
cnf(f_1224_3,plain,
( c_Complete__Lattice_OSup__class_OSup(U_4682,U_4683) = hAPP(hAPP(c_Finite__Set_Ofold(U_4682,U_4682,c_Lattices_Osemilattice__sup__class_Osup(U_4682)),c_Orderings_Obot__class_Obot(U_4682)),U_4683)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4682),U_4683))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4682) ),
inference(clausify,[status(thm)],[f_1224_2]) ).
fof(f_1225_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_1225_2,plain,
! [U_4685,U_4684] :
( c_Complete__Lattice_OInf__class_OInf(U_4684,U_4685) = hAPP(hAPP(c_Finite__Set_Ofold(U_4684,U_4684,c_Lattices_Osemilattice__inf__class_Oinf(U_4684)),c_Orderings_Otop__class_Otop(U_4684)),U_4685)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4684),U_4685))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4684) ),
inference(variable_rename,[status(thm)],[f_1225_1]) ).
cnf(f_1225_3,plain,
( c_Complete__Lattice_OInf__class_OInf(U_4684,U_4685) = hAPP(hAPP(c_Finite__Set_Ofold(U_4684,U_4684,c_Lattices_Osemilattice__inf__class_Oinf(U_4684)),c_Orderings_Otop__class_Otop(U_4684)),U_4685)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4684),U_4685))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4684) ),
inference(clausify,[status(thm)],[f_1225_2]) ).
fof(f_1226_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_1226_2,plain,
! [U_4688,U_4687,U_4686] :
( c_Big__Operators_Olattice__class_OSup__fin(U_4686,hAPP(hAPP(c_Set_Oinsert(U_4686),U_4688),U_4687)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4686,U_4686,c_Lattices_Osemilattice__sup__class_Osup(U_4686)),U_4688),U_4687)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4686),U_4687))
| ~ class_Lattices_Olattice(U_4686) ),
inference(variable_rename,[status(thm)],[f_1226_1]) ).
cnf(f_1226_3,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_4686,hAPP(hAPP(c_Set_Oinsert(U_4686),U_4688),U_4687)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4686,U_4686,c_Lattices_Osemilattice__sup__class_Osup(U_4686)),U_4688),U_4687)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4686),U_4687))
| ~ class_Lattices_Olattice(U_4686) ),
inference(clausify,[status(thm)],[f_1226_2]) ).
fof(f_1227_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_1227_2,plain,
! [U_4691,U_4690,U_4689] :
( c_Big__Operators_Olattice__class_OInf__fin(U_4689,hAPP(hAPP(c_Set_Oinsert(U_4689),U_4691),U_4690)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4689,U_4689,c_Lattices_Osemilattice__inf__class_Oinf(U_4689)),U_4691),U_4690)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4689),U_4690))
| ~ class_Lattices_Olattice(U_4689) ),
inference(variable_rename,[status(thm)],[f_1227_1]) ).
cnf(f_1227_3,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_4689,hAPP(hAPP(c_Set_Oinsert(U_4689),U_4691),U_4690)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4689,U_4689,c_Lattices_Osemilattice__inf__class_Oinf(U_4689)),U_4691),U_4690)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4689),U_4690))
| ~ class_Lattices_Olattice(U_4689) ),
inference(clausify,[status(thm)],[f_1227_2]) ).
fof(f_1228_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_1228_2,plain,
! [U_4696,U_4695,U_4694,U_4693,U_4692] :
( hAPP(U_4694,hAPP(hAPP(c_Set_Oinsert(U_4692),U_4696),U_4695)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4692,U_4692,U_4693),U_4696),U_4695)
| hBOOL(hAPP(hAPP(c_member(U_4692),U_4696),U_4695))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4692),U_4695))
| ~ c_Finite__Set_Ofolding__one(U_4692,U_4693,U_4694) ),
inference(variable_rename,[status(thm)],[f_1228_1]) ).
cnf(f_1228_3,plain,
( hAPP(U_4694,hAPP(hAPP(c_Set_Oinsert(U_4692),U_4696),U_4695)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4692,U_4692,U_4693),U_4696),U_4695)
| hBOOL(hAPP(hAPP(c_member(U_4692),U_4696),U_4695))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4692),U_4695))
| ~ c_Finite__Set_Ofolding__one(U_4692,U_4693,U_4694) ),
inference(clausify,[status(thm)],[f_1228_2]) ).
fof(f_1229_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_1229_2,plain,
! [U_4704,U_4703,U_4702,U_4701,U_4700,U_4699,U_4698,U_4697] :
( hAPP(hAPP(U_4699,hAPP(U_4701,U_4704)),hAPP(U_4702,U_4703)) = hAPP(U_4702,U_4703)
| ~ hBOOL(hAPP(hAPP(c_member(U_4698),U_4704),U_4703))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4698),U_4703))
| ~ c_Finite__Set_Ofolding__image__simple__idem(U_4697,U_4698,U_4699,U_4700,U_4701,U_4702) ),
inference(variable_rename,[status(thm)],[f_1229_1]) ).
fof(f_1229_3,plain,
! [U_4704,U_4703,U_4702,U_4701,U_4700,U_4699,U_4698] :
( ! [U_4697] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_4697,U_4698,U_4699,U_4700,U_4701,U_4702)
| hAPP(hAPP(U_4699,hAPP(U_4701,U_4704)),hAPP(U_4702,U_4703)) = hAPP(U_4702,U_4703)
| ~ hBOOL(hAPP(hAPP(c_member(U_4698),U_4704),U_4703))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4698),U_4703)) ),
inference(miniscope,[status(thm)],[f_1229_2]) ).
cnf(f_1229_4,plain,
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_4697,U_4698,U_4699,U_4700,U_4701,U_4702)
| hAPP(hAPP(U_4699,hAPP(U_4701,U_4704)),hAPP(U_4702,U_4703)) = hAPP(U_4702,U_4703)
| ~ hBOOL(hAPP(hAPP(c_member(U_4698),U_4704),U_4703))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4698),U_4703)) ),
inference(clausify,[status(thm)],[f_1229_3]) ).
fof(f_1230_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_1230_2,plain,
! [U_4712,U_4711,U_4710,U_4709,U_4708,U_4707,U_4706,U_4705] :
( hAPP(U_4710,hAPP(hAPP(c_Set_Oinsert(U_4706),U_4712),U_4711)) = hAPP(hAPP(U_4707,hAPP(U_4709,U_4712)),hAPP(U_4710,U_4711))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4706),U_4711))
| ~ c_Finite__Set_Ofolding__image__simple__idem(U_4705,U_4706,U_4707,U_4708,U_4709,U_4710) ),
inference(variable_rename,[status(thm)],[f_1230_1]) ).
fof(f_1230_3,plain,
! [U_4712,U_4711,U_4710,U_4709,U_4708,U_4707,U_4706] :
( ! [U_4705] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_4705,U_4706,U_4707,U_4708,U_4709,U_4710)
| hAPP(U_4710,hAPP(hAPP(c_Set_Oinsert(U_4706),U_4712),U_4711)) = hAPP(hAPP(U_4707,hAPP(U_4709,U_4712)),hAPP(U_4710,U_4711))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4706),U_4711)) ),
inference(miniscope,[status(thm)],[f_1230_2]) ).
cnf(f_1230_4,plain,
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_4705,U_4706,U_4707,U_4708,U_4709,U_4710)
| hAPP(U_4710,hAPP(hAPP(c_Set_Oinsert(U_4706),U_4712),U_4711)) = hAPP(hAPP(U_4707,hAPP(U_4709,U_4712)),hAPP(U_4710,U_4711))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4706),U_4711)) ),
inference(clausify,[status(thm)],[f_1230_3]) ).
fof(f_1231_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_1231_2,plain,
! [U_4716,U_4715,U_4714,U_4713] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4713),hAPP(hAPP(c_Power_Opower__class_Opower(U_4713),U_4714),U_4716)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4713),U_4715),U_4716)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4716))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4713),c_Groups_Ozero__class_Ozero(U_4713)),U_4714))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4713),U_4714),U_4715))
| ~ class_Rings_Olinordered__semidom(U_4713) ),
inference(variable_rename,[status(thm)],[f_1231_1]) ).
cnf(f_1231_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4713),hAPP(hAPP(c_Power_Opower__class_Opower(U_4713),U_4714),U_4716)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4713),U_4715),U_4716)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4716))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4713),c_Groups_Ozero__class_Ozero(U_4713)),U_4714))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4713),U_4714),U_4715))
| ~ class_Rings_Olinordered__semidom(U_4713) ),
inference(clausify,[status(thm)],[f_1231_2]) ).
fof(f_1232_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_1232_2,plain,
! [U_4719,U_4718,U_4717] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4717),c_Groups_Oone__class_Oone(U_4717)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4717),U_4718),U_4719)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4719))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4717),c_Groups_Oone__class_Oone(U_4717)),U_4718))
| ~ class_Rings_Olinordered__semidom(U_4717) ),
inference(variable_rename,[status(thm)],[f_1232_1]) ).
cnf(f_1232_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4717),c_Groups_Oone__class_Oone(U_4717)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4717),U_4718),U_4719)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4719))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4717),c_Groups_Oone__class_Oone(U_4717)),U_4718))
| ~ class_Rings_Olinordered__semidom(U_4717) ),
inference(clausify,[status(thm)],[f_1232_2]) ).
fof(f_1233_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_1233_2,plain,
! [U_4723,U_4722,U_4721,U_4720] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4720),hAPP(hAPP(c_Power_Opower__class_Opower(U_4720),U_4721),U_4722)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4720),U_4721),U_4723)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4722),U_4723)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4722),U_4723))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4720),hAPP(hAPP(c_Power_Opower__class_Opower(U_4720),U_4721),U_4722)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4720),U_4721),U_4723))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4720),c_Groups_Oone__class_Oone(U_4720)),U_4721))
| ~ class_Rings_Olinordered__semidom(U_4720) ),
inference(variable_rename,[status(thm)],[f_1233_1]) ).
cnf(f_1233_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4722),U_4723))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4720),hAPP(hAPP(c_Power_Opower__class_Opower(U_4720),U_4721),U_4722)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4720),U_4721),U_4723)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4720),c_Groups_Oone__class_Oone(U_4720)),U_4721))
| ~ class_Rings_Olinordered__semidom(U_4720) ),
inference(clausify,[status(thm)],[f_1233_2]) ).
cnf(f_1233_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4720),hAPP(hAPP(c_Power_Opower__class_Opower(U_4720),U_4721),U_4722)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4720),U_4721),U_4723)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4722),U_4723))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4720),c_Groups_Oone__class_Oone(U_4720)),U_4721))
| ~ class_Rings_Olinordered__semidom(U_4720) ),
inference(clausify,[status(thm)],[f_1233_2]) ).
fof(f_1234_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_1234_2,plain,
! [U_4727,U_4726,U_4725,U_4724] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4726),U_4727))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4724),hAPP(hAPP(c_Power_Opower__class_Opower(U_4724),U_4725),U_4726)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4724),U_4725),U_4727)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4724),c_Groups_Oone__class_Oone(U_4724)),U_4725))
| ~ class_Rings_Olinordered__semidom(U_4724) ),
inference(variable_rename,[status(thm)],[f_1234_1]) ).
cnf(f_1234_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4726),U_4727))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4724),hAPP(hAPP(c_Power_Opower__class_Opower(U_4724),U_4725),U_4726)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4724),U_4725),U_4727)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4724),c_Groups_Oone__class_Oone(U_4724)),U_4725))
| ~ class_Rings_Olinordered__semidom(U_4724) ),
inference(clausify,[status(thm)],[f_1234_2]) ).
fof(f_1235_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_1235_2,plain,
! [U_4731,U_4730,U_4729,U_4728] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4728),hAPP(hAPP(c_Power_Opower__class_Opower(U_4728),U_4731),U_4730)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4728),U_4731),U_4729)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4728),U_4731),c_Groups_Oone__class_Oone(U_4728)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4728),c_Groups_Ozero__class_Ozero(U_4728)),U_4731))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4729),U_4730))
| ~ class_Rings_Olinordered__semidom(U_4728) ),
inference(variable_rename,[status(thm)],[f_1235_1]) ).
cnf(f_1235_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4728),hAPP(hAPP(c_Power_Opower__class_Opower(U_4728),U_4731),U_4730)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4728),U_4731),U_4729)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4728),U_4731),c_Groups_Oone__class_Oone(U_4728)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4728),c_Groups_Ozero__class_Ozero(U_4728)),U_4731))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4729),U_4730))
| ~ class_Rings_Olinordered__semidom(U_4728) ),
inference(clausify,[status(thm)],[f_1235_2]) ).
fof(f_1236_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_1236_2,plain,
! [U_4735,U_4734,U_4733,U_4732] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4732),hAPP(hAPP(c_Power_Opower__class_Opower(U_4732),U_4735),U_4734)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4732),U_4735),U_4733)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4732),U_4735),c_Groups_Oone__class_Oone(U_4732)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4732),c_Groups_Ozero__class_Ozero(U_4732)),U_4735))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4733),U_4734))
| ~ class_Rings_Olinordered__semidom(U_4732) ),
inference(variable_rename,[status(thm)],[f_1236_1]) ).
cnf(f_1236_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4732),hAPP(hAPP(c_Power_Opower__class_Opower(U_4732),U_4735),U_4734)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4732),U_4735),U_4733)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4732),U_4735),c_Groups_Oone__class_Oone(U_4732)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4732),c_Groups_Ozero__class_Ozero(U_4732)),U_4735))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4733),U_4734))
| ~ class_Rings_Olinordered__semidom(U_4732) ),
inference(clausify,[status(thm)],[f_1236_2]) ).
fof(f_1237_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_1237_2,plain,
! [U_4738,U_4737,U_4736] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4736),hAPP(hAPP(c_Power_Opower__class_Opower(U_4736),U_4737),hAPP(c_Nat_OSuc,U_4738))),c_Groups_Oone__class_Oone(U_4736)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4736),U_4737),c_Groups_Oone__class_Oone(U_4736)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4736),c_Groups_Ozero__class_Ozero(U_4736)),U_4737))
| ~ class_Rings_Olinordered__semidom(U_4736) ),
inference(variable_rename,[status(thm)],[f_1237_1]) ).
cnf(f_1237_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4736),hAPP(hAPP(c_Power_Opower__class_Opower(U_4736),U_4737),hAPP(c_Nat_OSuc,U_4738))),c_Groups_Oone__class_Oone(U_4736)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4736),U_4737),c_Groups_Oone__class_Oone(U_4736)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4736),c_Groups_Ozero__class_Ozero(U_4736)),U_4737))
| ~ class_Rings_Olinordered__semidom(U_4736) ),
inference(clausify,[status(thm)],[f_1237_2]) ).
fof(f_1238_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_1238_2,plain,
! [U_4740,U_4739] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_4739,U_4740))),
inference(variable_rename,[status(thm)],[f_1238_1]) ).
cnf(f_1238_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_4739,U_4740))),
inference(clausify,[status(thm)],[f_1238_2]) ).
fof(f_1239_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_1239_2,plain,
! [U_4742,U_4741] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_4741),U_4742))),
inference(variable_rename,[status(thm)],[f_1239_1]) ).
cnf(f_1239_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_4741),U_4742))),
inference(clausify,[status(thm)],[f_1239_2]) ).
fof(f_1240_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_1240_2,plain,
! [U_4744,U_4743] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_4743,U_4744))),
inference(variable_rename,[status(thm)],[f_1240_1]) ).
cnf(f_1240_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_4743,U_4744))),
inference(clausify,[status(thm)],[f_1240_2]) ).
fof(f_1241_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_1241_2,plain,
! [U_4746,U_4745] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_4745,U_4746))),
inference(variable_rename,[status(thm)],[f_1241_1]) ).
cnf(f_1241_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_4745,U_4746))),
inference(clausify,[status(thm)],[f_1241_2]) ).
fof(f_1242_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_1242_2,plain,
! [U_4747] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4747) = U_4747,
inference(variable_rename,[status(thm)],[f_1242_1]) ).
cnf(f_1242_3,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4747) = U_4747,
inference(clausify,[status(thm)],[f_1242_2]) ).
fof(f_1243_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_1243_2,plain,
! [U_4748] : 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_4748))),
inference(variable_rename,[status(thm)],[f_1243_1]) ).
cnf(f_1243_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_4748))),
inference(clausify,[status(thm)],[f_1243_2]) ).
fof(f_1244_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_1244_2,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1244_1]) ).
fof(f_1245_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_1245_2,plain,
! [U_4751,U_4750,U_4749] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4749),U_4750),U_4751) != c_Groups_Ozero__class_Ozero(U_4749)
| U_4750 = c_Groups_Ozero__class_Ozero(U_4749)
| ~ class_Rings_Oring__1__no__zero__divisors(U_4749) ),
inference(variable_rename,[status(thm)],[f_1245_1]) ).
cnf(f_1245_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4749),U_4750),U_4751) != c_Groups_Ozero__class_Ozero(U_4749)
| U_4750 = c_Groups_Ozero__class_Ozero(U_4749)
| ~ class_Rings_Oring__1__no__zero__divisors(U_4749) ),
inference(clausify,[status(thm)],[f_1245_2]) ).
fof(f_1246_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_1246_2,plain,
! [U_4753,U_4752] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4752),c_Groups_Oone__class_Oone(U_4752)),U_4753) = c_Groups_Oone__class_Oone(U_4752)
| ~ class_Groups_Omonoid__mult(U_4752) ),
inference(variable_rename,[status(thm)],[f_1246_1]) ).
cnf(f_1246_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4752),c_Groups_Oone__class_Oone(U_4752)),U_4753) = c_Groups_Oone__class_Oone(U_4752)
| ~ class_Groups_Omonoid__mult(U_4752) ),
inference(clausify,[status(thm)],[f_1246_2]) ).
fof(f_1247_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_1247_2,plain,
! [U_4755,U_4754] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4754),U_4755),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4755
| ~ class_Groups_Omonoid__mult(U_4754) ),
inference(variable_rename,[status(thm)],[f_1247_1]) ).
cnf(f_1247_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4754),U_4755),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4755
| ~ class_Groups_Omonoid__mult(U_4754) ),
inference(clausify,[status(thm)],[f_1247_2]) ).
fof(f_1248_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_1248_2,plain,
! [U_4759,U_4758,U_4757,U_4756] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4756),hAPP(hAPP(c_Power_Opower__class_Opower(U_4756),U_4757),U_4759)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4756),U_4758),U_4759)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4756),c_Groups_Ozero__class_Ozero(U_4756)),U_4757))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4756),U_4757),U_4758))
| ~ class_Rings_Olinordered__semidom(U_4756) ),
inference(variable_rename,[status(thm)],[f_1248_1]) ).
cnf(f_1248_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4756),hAPP(hAPP(c_Power_Opower__class_Opower(U_4756),U_4757),U_4759)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4756),U_4758),U_4759)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4756),c_Groups_Ozero__class_Ozero(U_4756)),U_4757))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4756),U_4757),U_4758))
| ~ class_Rings_Olinordered__semidom(U_4756) ),
inference(clausify,[status(thm)],[f_1248_2]) ).
fof(f_1249_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_1249_2,plain,
! [U_4762,U_4761,U_4760] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4760),c_Groups_Ozero__class_Ozero(U_4760)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4760),U_4761),U_4762)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4760),c_Groups_Ozero__class_Ozero(U_4760)),U_4761))
| ~ class_Rings_Olinordered__semidom(U_4760) ),
inference(variable_rename,[status(thm)],[f_1249_1]) ).
cnf(f_1249_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4760),c_Groups_Ozero__class_Ozero(U_4760)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4760),U_4761),U_4762)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4760),c_Groups_Ozero__class_Ozero(U_4760)),U_4761))
| ~ class_Rings_Olinordered__semidom(U_4760) ),
inference(clausify,[status(thm)],[f_1249_2]) ).
fof(f_1250_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_1250_2,plain,
! [U_4765,U_4764,U_4763] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4763),c_Groups_Ozero__class_Ozero(U_4763)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4763),U_4764),U_4765)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4763),c_Groups_Ozero__class_Ozero(U_4763)),U_4764))
| ~ class_Rings_Olinordered__semidom(U_4763) ),
inference(variable_rename,[status(thm)],[f_1250_1]) ).
cnf(f_1250_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4763),c_Groups_Ozero__class_Ozero(U_4763)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4763),U_4764),U_4765)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4763),c_Groups_Ozero__class_Ozero(U_4763)),U_4764))
| ~ class_Rings_Olinordered__semidom(U_4763) ),
inference(clausify,[status(thm)],[f_1250_2]) ).
fof(f_1251_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_1251_2,plain,
! [U_4768,U_4767,U_4766] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4766),U_4767),U_4768) = c_Groups_Ozero__class_Ozero(U_4766)
| U_4768 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4767 != c_Groups_Ozero__class_Ozero(U_4766) )
& ( ( U_4768 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_4767 = c_Groups_Ozero__class_Ozero(U_4766) )
| hAPP(hAPP(c_Power_Opower__class_Opower(U_4766),U_4767),U_4768) != c_Groups_Ozero__class_Ozero(U_4766) ) )
| ~ class_Rings_Ozero__neq__one(U_4766)
| ~ class_Rings_Ono__zero__divisors(U_4766)
| ~ class_Rings_Omult__zero(U_4766)
| ~ class_Power_Opower(U_4766) ),
inference(variable_rename,[status(thm)],[f_1251_1]) ).
cnf(f_1251_3,plain,
( U_4767 = c_Groups_Ozero__class_Ozero(U_4766)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_4766),U_4767),U_4768) != c_Groups_Ozero__class_Ozero(U_4766)
| ~ class_Rings_Ozero__neq__one(U_4766)
| ~ class_Rings_Ono__zero__divisors(U_4766)
| ~ class_Rings_Omult__zero(U_4766)
| ~ class_Power_Opower(U_4766) ),
inference(clausify,[status(thm)],[f_1251_2]) ).
cnf(f_1251_4,plain,
( U_4768 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_4766),U_4767),U_4768) != c_Groups_Ozero__class_Ozero(U_4766)
| ~ class_Rings_Ozero__neq__one(U_4766)
| ~ class_Rings_Ono__zero__divisors(U_4766)
| ~ class_Rings_Omult__zero(U_4766)
| ~ class_Power_Opower(U_4766) ),
inference(clausify,[status(thm)],[f_1251_2]) ).
cnf(f_1251_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4766),U_4767),U_4768) = c_Groups_Ozero__class_Ozero(U_4766)
| U_4768 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_4767 != c_Groups_Ozero__class_Ozero(U_4766)
| ~ class_Rings_Ozero__neq__one(U_4766)
| ~ class_Rings_Ono__zero__divisors(U_4766)
| ~ class_Rings_Omult__zero(U_4766)
| ~ class_Power_Opower(U_4766) ),
inference(clausify,[status(thm)],[f_1251_2]) ).
fof(f_1252_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_1252_2,plain,
! [U_4771,U_4770,U_4769] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4769),c_Groups_Oone__class_Oone(U_4769)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4769),U_4770),U_4771)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4769),c_Groups_Oone__class_Oone(U_4769)),U_4770))
| ~ class_Rings_Olinordered__semidom(U_4769) ),
inference(variable_rename,[status(thm)],[f_1252_1]) ).
cnf(f_1252_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4769),c_Groups_Oone__class_Oone(U_4769)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4769),U_4770),U_4771)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4769),c_Groups_Oone__class_Oone(U_4769)),U_4770))
| ~ class_Rings_Olinordered__semidom(U_4769) ),
inference(clausify,[status(thm)],[f_1252_2]) ).
fof(f_1253_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_1253_2,plain,
! [U_4773,U_4772] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4772),c_Groups_Ozero__class_Ozero(U_4772)),hAPP(c_Nat_OSuc,U_4773)) = c_Groups_Ozero__class_Ozero(U_4772)
| ~ class_Rings_Osemiring__0(U_4772)
| ~ class_Power_Opower(U_4772) ),
inference(variable_rename,[status(thm)],[f_1253_1]) ).
cnf(f_1253_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4772),c_Groups_Ozero__class_Ozero(U_4772)),hAPP(c_Nat_OSuc,U_4773)) = c_Groups_Ozero__class_Ozero(U_4772)
| ~ class_Rings_Osemiring__0(U_4772)
| ~ class_Power_Opower(U_4772) ),
inference(clausify,[status(thm)],[f_1253_2]) ).
fof(f_1254_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_1254_2,plain,
! [U_4777,U_4776,U_4775,U_4774] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4774),U_4775),U_4776) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4774),U_4775),U_4777)
| U_4776 != U_4777 )
& ( U_4776 = U_4777
| hAPP(hAPP(c_Power_Opower__class_Opower(U_4774),U_4775),U_4776) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4774),U_4775),U_4777) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4774),c_Groups_Oone__class_Oone(U_4774)),U_4775))
| ~ class_Rings_Olinordered__semidom(U_4774) ),
inference(variable_rename,[status(thm)],[f_1254_1]) ).
cnf(f_1254_3,plain,
( U_4776 = U_4777
| hAPP(hAPP(c_Power_Opower__class_Opower(U_4774),U_4775),U_4776) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4774),U_4775),U_4777)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4774),c_Groups_Oone__class_Oone(U_4774)),U_4775))
| ~ class_Rings_Olinordered__semidom(U_4774) ),
inference(clausify,[status(thm)],[f_1254_2]) ).
cnf(f_1254_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4774),U_4775),U_4776) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4774),U_4775),U_4777)
| U_4776 != U_4777
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4774),c_Groups_Oone__class_Oone(U_4774)),U_4775))
| ~ class_Rings_Olinordered__semidom(U_4774) ),
inference(clausify,[status(thm)],[f_1254_2]) ).
fof(f_1255_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_1255_2,plain,
! [U_4779,U_4778] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4778),U_4779),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_4778)
| ~ class_Power_Opower(U_4778) ),
inference(variable_rename,[status(thm)],[f_1255_1]) ).
cnf(f_1255_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4778),U_4779),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_4778)
| ~ class_Power_Opower(U_4778) ),
inference(clausify,[status(thm)],[f_1255_2]) ).
fof(f_1256_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_1256_2,plain,
! [U_4781,U_4780] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4780),U_4781) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( U_4780 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_4781 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_4780 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_4781 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4780),U_4781) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_1256_1]) ).
fof(f_1256_3,plain,
( ! [U_4785,U_4783] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4783),U_4785) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( U_4783 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_4785 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_4784,U_4782] :
( U_4782 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_4784 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4782),U_4784) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_1256_2]) ).
cnf(f_1256_4,plain,
( U_4782 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_4784 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4782),U_4784) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_1256_3]) ).
cnf(f_1256_5,plain,
( U_4785 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4783),U_4785) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_1256_3]) ).
cnf(f_1256_6,plain,
( U_4783 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4783),U_4785) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_1256_3]) ).
fof(f_1257_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_1257_2,plain,
! [U_4786] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4786) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_1257_1]) ).
cnf(f_1257_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_4786) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_1257_2]) ).
fof(f_1258_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_1258_2,plain,
! [U_4788,U_4787] :
( ( 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_4787),U_4788)))
| ( U_4788 != 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_4787)) ) )
& ( U_4788 = 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_4787))
| ~ 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_4787),U_4788))) ) ),
inference(variable_rename,[status(thm)],[f_1258_1]) ).
fof(f_1258_3,plain,
( ! [U_4792,U_4790] :
( 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_4790),U_4792)))
| ( U_4792 != 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_4790)) ) )
& ! [U_4791,U_4789] :
( U_4791 = 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_4789))
| ~ 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_4789),U_4791))) ) ),
inference(miniscope,[status(thm)],[f_1258_2]) ).
cnf(f_1258_4,plain,
( U_4791 = 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_4789))
| ~ 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_4789),U_4791))) ),
inference(clausify,[status(thm)],[f_1258_3]) ).
cnf(f_1258_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4790))
| 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_4790),U_4792))) ),
inference(clausify,[status(thm)],[f_1258_3]) ).
cnf(f_1258_6,plain,
( U_4792 != 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_4790),U_4792))) ),
inference(clausify,[status(thm)],[f_1258_3]) ).
fof(f_1259_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_1259_2,plain,
! [U_4795,U_4794,U_4793] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4794),U_4795))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4793),U_4794)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4793),U_4795)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4793)) ),
inference(variable_rename,[status(thm)],[f_1259_1]) ).
cnf(f_1259_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4794),U_4795))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4793),U_4794)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4793),U_4795)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4793)) ),
inference(clausify,[status(thm)],[f_1259_2]) ).
fof(f_1260_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_1260_2,plain,
! [U_4799,U_4798,U_4797,U_4796] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4796),U_4797),U_4799))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4796),c_Groups_Ozero__class_Ozero(U_4796)),U_4799))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4796),hAPP(hAPP(c_Power_Opower__class_Opower(U_4796),U_4797),U_4798)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4796),U_4799),U_4798)))
| ~ class_Rings_Olinordered__semidom(U_4796) ),
inference(variable_rename,[status(thm)],[f_1260_1]) ).
cnf(f_1260_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4796),U_4797),U_4799))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4796),c_Groups_Ozero__class_Ozero(U_4796)),U_4799))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4796),hAPP(hAPP(c_Power_Opower__class_Opower(U_4796),U_4797),U_4798)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4796),U_4799),U_4798)))
| ~ class_Rings_Olinordered__semidom(U_4796) ),
inference(clausify,[status(thm)],[f_1260_2]) ).
fof(f_1261_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_1261_2,plain,
! [U_4803,U_4802,U_4801,U_4800] :
( U_4801 = U_4803
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4800),c_Groups_Ozero__class_Ozero(U_4800)),U_4803))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4800),c_Groups_Ozero__class_Ozero(U_4800)),U_4801))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_4800),U_4801),hAPP(c_Nat_OSuc,U_4802)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4800),U_4803),hAPP(c_Nat_OSuc,U_4802))
| ~ class_Rings_Olinordered__semidom(U_4800) ),
inference(variable_rename,[status(thm)],[f_1261_1]) ).
cnf(f_1261_3,plain,
( U_4801 = U_4803
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4800),c_Groups_Ozero__class_Ozero(U_4800)),U_4803))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4800),c_Groups_Ozero__class_Ozero(U_4800)),U_4801))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_4800),U_4801),hAPP(c_Nat_OSuc,U_4802)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4800),U_4803),hAPP(c_Nat_OSuc,U_4802))
| ~ class_Rings_Olinordered__semidom(U_4800) ),
inference(clausify,[status(thm)],[f_1261_2]) ).
fof(f_1262_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_1262_2,plain,
! [U_4807,U_4806,U_4805,U_4804] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4804),U_4805),U_4807))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4804),c_Groups_Ozero__class_Ozero(U_4804)),U_4807))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4804),hAPP(hAPP(c_Power_Opower__class_Opower(U_4804),U_4805),hAPP(c_Nat_OSuc,U_4806))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4804),U_4807),hAPP(c_Nat_OSuc,U_4806))))
| ~ class_Rings_Olinordered__semidom(U_4804) ),
inference(variable_rename,[status(thm)],[f_1262_1]) ).
cnf(f_1262_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4804),U_4805),U_4807))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4804),c_Groups_Ozero__class_Ozero(U_4804)),U_4807))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4804),hAPP(hAPP(c_Power_Opower__class_Opower(U_4804),U_4805),hAPP(c_Nat_OSuc,U_4806))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4804),U_4807),hAPP(c_Nat_OSuc,U_4806))))
| ~ class_Rings_Olinordered__semidom(U_4804) ),
inference(clausify,[status(thm)],[f_1262_2]) ).
fof(f_1263_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_1263_2,plain,
! [U_4809,U_4808] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4808),c_Groups_Ozero__class_Ozero(U_4808)),U_4809) = c_Groups_Ozero__class_Ozero(U_4808)
| U_4809 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4808),c_Groups_Ozero__class_Ozero(U_4808)),U_4809) = c_Groups_Oone__class_Oone(U_4808)
| U_4809 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Rings_Osemiring__0(U_4808)
| ~ class_Power_Opower(U_4808) ),
inference(variable_rename,[status(thm)],[f_1263_1]) ).
cnf(f_1263_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4808),c_Groups_Ozero__class_Ozero(U_4808)),U_4809) = c_Groups_Oone__class_Oone(U_4808)
| U_4809 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Osemiring__0(U_4808)
| ~ class_Power_Opower(U_4808) ),
inference(clausify,[status(thm)],[f_1263_2]) ).
cnf(f_1263_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4808),c_Groups_Ozero__class_Ozero(U_4808)),U_4809) = c_Groups_Ozero__class_Ozero(U_4808)
| U_4809 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Osemiring__0(U_4808)
| ~ class_Power_Opower(U_4808) ),
inference(clausify,[status(thm)],[f_1263_2]) ).
fof(f_1264_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_1264_2,plain,
! [U_4812,U_4811,U_4810] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4810),c_Groups_Oone__class_Oone(U_4810)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4810),U_4811),hAPP(c_Nat_OSuc,U_4812))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4810),c_Groups_Oone__class_Oone(U_4810)),U_4811))
| ~ class_Rings_Olinordered__semidom(U_4810) ),
inference(variable_rename,[status(thm)],[f_1264_1]) ).
cnf(f_1264_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4810),c_Groups_Oone__class_Oone(U_4810)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4810),U_4811),hAPP(c_Nat_OSuc,U_4812))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4810),c_Groups_Oone__class_Oone(U_4810)),U_4811))
| ~ class_Rings_Olinordered__semidom(U_4810) ),
inference(clausify,[status(thm)],[f_1264_2]) ).
fof(f_1265_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_1265_2,plain,
! [U_4816,U_4815,U_4814,U_4813] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4813),hAPP(hAPP(c_Power_Opower__class_Opower(U_4813),U_4814),U_4815)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4813),U_4814),U_4816)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4815),U_4816)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4815),U_4816))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4813),hAPP(hAPP(c_Power_Opower__class_Opower(U_4813),U_4814),U_4815)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4813),U_4814),U_4816))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4813),c_Groups_Oone__class_Oone(U_4813)),U_4814))
| ~ class_Rings_Olinordered__semidom(U_4813) ),
inference(variable_rename,[status(thm)],[f_1265_1]) ).
cnf(f_1265_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4815),U_4816))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4813),hAPP(hAPP(c_Power_Opower__class_Opower(U_4813),U_4814),U_4815)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4813),U_4814),U_4816)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4813),c_Groups_Oone__class_Oone(U_4813)),U_4814))
| ~ class_Rings_Olinordered__semidom(U_4813) ),
inference(clausify,[status(thm)],[f_1265_2]) ).
cnf(f_1265_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4813),hAPP(hAPP(c_Power_Opower__class_Opower(U_4813),U_4814),U_4815)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4813),U_4814),U_4816)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4815),U_4816))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4813),c_Groups_Oone__class_Oone(U_4813)),U_4814))
| ~ class_Rings_Olinordered__semidom(U_4813) ),
inference(clausify,[status(thm)],[f_1265_2]) ).
fof(f_1266_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_1266_2,plain,
! [U_4820,U_4819,U_4818,U_4817] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4819),U_4820))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4817),hAPP(hAPP(c_Power_Opower__class_Opower(U_4817),U_4818),U_4819)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4817),U_4818),U_4820)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4817),c_Groups_Oone__class_Oone(U_4817)),U_4818))
| ~ class_Rings_Olinordered__semidom(U_4817) ),
inference(variable_rename,[status(thm)],[f_1266_1]) ).
cnf(f_1266_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4819),U_4820))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4817),hAPP(hAPP(c_Power_Opower__class_Opower(U_4817),U_4818),U_4819)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4817),U_4818),U_4820)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4817),c_Groups_Oone__class_Oone(U_4817)),U_4818))
| ~ class_Rings_Olinordered__semidom(U_4817) ),
inference(clausify,[status(thm)],[f_1266_2]) ).
fof(f_1267_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_1267_2,plain,
! [U_4824,U_4823,U_4822,U_4821] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4821),hAPP(hAPP(c_Power_Opower__class_Opower(U_4821),U_4824),U_4822)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4821),U_4824),U_4823)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4821),c_Groups_Oone__class_Oone(U_4821)),U_4824))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4822),U_4823))
| ~ class_Rings_Olinordered__semidom(U_4821) ),
inference(variable_rename,[status(thm)],[f_1267_1]) ).
cnf(f_1267_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4821),hAPP(hAPP(c_Power_Opower__class_Opower(U_4821),U_4824),U_4822)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4821),U_4824),U_4823)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4821),c_Groups_Oone__class_Oone(U_4821)),U_4824))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4822),U_4823))
| ~ class_Rings_Olinordered__semidom(U_4821) ),
inference(clausify,[status(thm)],[f_1267_2]) ).
fof(f_1268_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_1268_2,plain,
! [U_4828,U_4827,U_4826,U_4825] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4825),hAPP(hAPP(c_Power_Opower__class_Opower(U_4825),U_4828),U_4826)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4825),U_4828),U_4827)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4825),c_Groups_Oone__class_Oone(U_4825)),U_4828))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4826),U_4827))
| ~ class_Rings_Olinordered__semidom(U_4825) ),
inference(variable_rename,[status(thm)],[f_1268_1]) ).
cnf(f_1268_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4825),hAPP(hAPP(c_Power_Opower__class_Opower(U_4825),U_4828),U_4826)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4825),U_4828),U_4827)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4825),c_Groups_Oone__class_Oone(U_4825)),U_4828))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4826),U_4827))
| ~ class_Rings_Olinordered__semidom(U_4825) ),
inference(clausify,[status(thm)],[f_1268_2]) ).
fof(f_1269_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_1269_2,plain,
! [U_4830,U_4829] :
( 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_4829),U_4830)))
| ~ 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_4829)) ),
inference(variable_rename,[status(thm)],[f_1269_1]) ).
cnf(f_1269_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_4829),U_4830)))
| ~ 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_4829)) ),
inference(clausify,[status(thm)],[f_1269_2]) ).
fof(f_1270_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_1270_2,plain,
! [U_4834,U_4833,U_4832,U_4831] :
( U_4832 = U_4834
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4833))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4831),c_Groups_Ozero__class_Ozero(U_4831)),U_4834))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4831),c_Groups_Ozero__class_Ozero(U_4831)),U_4832))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_4831),U_4832),U_4833) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4831),U_4834),U_4833)
| ~ class_Rings_Olinordered__semidom(U_4831) ),
inference(variable_rename,[status(thm)],[f_1270_1]) ).
cnf(f_1270_3,plain,
( U_4832 = U_4834
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4833))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4831),c_Groups_Ozero__class_Ozero(U_4831)),U_4834))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4831),c_Groups_Ozero__class_Ozero(U_4831)),U_4832))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_4831),U_4832),U_4833) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4831),U_4834),U_4833)
| ~ class_Rings_Olinordered__semidom(U_4831) ),
inference(clausify,[status(thm)],[f_1270_2]) ).
fof(f_1271_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_1271_2,plain,
! [U_4836,U_4835] :
( ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_4836,U_4835) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_4836),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4836),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4835))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4835),U_4836)) )
& ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_4836,U_4835) = 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_4835),U_4836)) ) ),
inference(variable_rename,[status(thm)],[f_1271_1]) ).
fof(f_1271_3,plain,
( ! [U_4840,U_4838] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_4840,U_4838) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_4840),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4840),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4838))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4838),U_4840)) )
& ! [U_4839,U_4837] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_4839,U_4837) = 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_4837),U_4839)) ) ),
inference(miniscope,[status(thm)],[f_1271_2]) ).
cnf(f_1271_4,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_4839,U_4837) = 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_4837),U_4839)) ),
inference(clausify,[status(thm)],[f_1271_3]) ).
cnf(f_1271_5,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_4840,U_4838) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_4840),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4840),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_4838))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4838),U_4840)) ),
inference(clausify,[status(thm)],[f_1271_3]) ).
fof(f_1272_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_1272_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_1272_1]) ).
fof(f_1273_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_1273_2,plain,
! [U_4842,U_4841] :
( 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_4841),U_4842)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4841)) ),
inference(variable_rename,[status(thm)],[f_1273_1]) ).
cnf(f_1273_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_4841),U_4842)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4841)) ),
inference(clausify,[status(thm)],[f_1273_2]) ).
fof(f_1274_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_1274_2,plain,
! [U_4848,U_4847,U_4846,U_4845,U_4844,U_4843] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_4843,U_4844,U_4845),U_4848),U_4846) = hAPP(hAPP(U_4845,U_4847),hAPP(hAPP(c_Finite__Set_Ofold(U_4843,U_4844,U_4845),U_4848),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4843,tc_HOL_Obool)),U_4846),hAPP(hAPP(c_Set_Oinsert(U_4843),U_4847),c_Orderings_Obot__class_Obot(tc_fun(U_4843,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_4843),U_4847),U_4846))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4843),U_4846))
| ~ c_Finite__Set_Ofun__left__comm(U_4843,U_4844,U_4845) ),
inference(variable_rename,[status(thm)],[f_1274_1]) ).
cnf(f_1274_3,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_4843,U_4844,U_4845),U_4848),U_4846) = hAPP(hAPP(U_4845,U_4847),hAPP(hAPP(c_Finite__Set_Ofold(U_4843,U_4844,U_4845),U_4848),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4843,tc_HOL_Obool)),U_4846),hAPP(hAPP(c_Set_Oinsert(U_4843),U_4847),c_Orderings_Obot__class_Obot(tc_fun(U_4843,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_4843),U_4847),U_4846))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4843),U_4846))
| ~ c_Finite__Set_Ofun__left__comm(U_4843,U_4844,U_4845) ),
inference(clausify,[status(thm)],[f_1274_2]) ).
fof(f_1275_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_1275_2,plain,
! [U_4854,U_4853,U_4852,U_4851,U_4850,U_4849] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_4849,U_4850,U_4851),U_4853),hAPP(hAPP(c_Set_Oinsert(U_4849),U_4854),U_4852)) = hAPP(hAPP(U_4851,U_4854),hAPP(hAPP(c_Finite__Set_Ofold(U_4849,U_4850,U_4851),U_4853),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4849,tc_HOL_Obool)),U_4852),hAPP(hAPP(c_Set_Oinsert(U_4849),U_4854),c_Orderings_Obot__class_Obot(tc_fun(U_4849,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4849),U_4852))
| ~ c_Finite__Set_Ofun__left__comm(U_4849,U_4850,U_4851) ),
inference(variable_rename,[status(thm)],[f_1275_1]) ).
cnf(f_1275_3,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_4849,U_4850,U_4851),U_4853),hAPP(hAPP(c_Set_Oinsert(U_4849),U_4854),U_4852)) = hAPP(hAPP(U_4851,U_4854),hAPP(hAPP(c_Finite__Set_Ofold(U_4849,U_4850,U_4851),U_4853),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4849,tc_HOL_Obool)),U_4852),hAPP(hAPP(c_Set_Oinsert(U_4849),U_4854),c_Orderings_Obot__class_Obot(tc_fun(U_4849,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4849),U_4852))
| ~ c_Finite__Set_Ofun__left__comm(U_4849,U_4850,U_4851) ),
inference(clausify,[status(thm)],[f_1275_2]) ).
fof(f_1276_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_1276_2,plain,
! [U_4856,U_4855] :
( 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_4855),U_4856)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4855)) ),
inference(variable_rename,[status(thm)],[f_1276_1]) ).
cnf(f_1276_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_4855),U_4856)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4855)) ),
inference(clausify,[status(thm)],[f_1276_2]) ).
fof(f_1277_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_1277_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_1277_1]) ).
fof(f_1278_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_1278_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_1278_1]) ).
fof(f_1279_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_1279_2,plain,
! [U_4862,U_4861,U_4860,U_4859,U_4858,U_4857] :
( hAPP(hAPP(U_4859,U_4860),hAPP(hAPP(U_4859,U_4861),U_4862)) = hAPP(hAPP(U_4859,U_4861),hAPP(hAPP(U_4859,U_4860),U_4862))
| ~ c_Finite__Set_Ofun__left__comm(U_4857,U_4858,U_4859) ),
inference(variable_rename,[status(thm)],[f_1279_1]) ).
fof(f_1279_3,plain,
! [U_4862,U_4861,U_4860,U_4859] :
( ! [U_4858,U_4857] : ~ c_Finite__Set_Ofun__left__comm(U_4857,U_4858,U_4859)
| hAPP(hAPP(U_4859,U_4860),hAPP(hAPP(U_4859,U_4861),U_4862)) = hAPP(hAPP(U_4859,U_4861),hAPP(hAPP(U_4859,U_4860),U_4862)) ),
inference(miniscope,[status(thm)],[f_1279_2]) ).
cnf(f_1279_4,plain,
( ~ c_Finite__Set_Ofun__left__comm(U_4857,U_4858,U_4859)
| hAPP(hAPP(U_4859,U_4860),hAPP(hAPP(U_4859,U_4861),U_4862)) = hAPP(hAPP(U_4859,U_4861),hAPP(hAPP(U_4859,U_4860),U_4862)) ),
inference(clausify,[status(thm)],[f_1279_3]) ).
fof(f_1280_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_1280_2,plain,
! [U_4868,U_4867,U_4866,U_4865,U_4864,U_4863] :
( hAPP(hAPP(U_4865,U_4867),hAPP(hAPP(c_Finite__Set_Ofold(U_4863,U_4864,U_4865),U_4868),U_4866)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4863,U_4864,U_4865),hAPP(hAPP(U_4865,U_4867),U_4868)),U_4866)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4863),U_4866))
| ~ c_Finite__Set_Ofun__left__comm(U_4863,U_4864,U_4865) ),
inference(variable_rename,[status(thm)],[f_1280_1]) ).
cnf(f_1280_3,plain,
( hAPP(hAPP(U_4865,U_4867),hAPP(hAPP(c_Finite__Set_Ofold(U_4863,U_4864,U_4865),U_4868),U_4866)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4863,U_4864,U_4865),hAPP(hAPP(U_4865,U_4867),U_4868)),U_4866)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4863),U_4866))
| ~ c_Finite__Set_Ofun__left__comm(U_4863,U_4864,U_4865) ),
inference(clausify,[status(thm)],[f_1280_2]) ).
fof(f_1281_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_1281_2,plain,
! [U_4874,U_4873,U_4872,U_4871,U_4870,U_4869] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_4869,U_4870,U_4871),U_4874),hAPP(hAPP(c_Set_Oinsert(U_4869),U_4873),U_4872)) = hAPP(hAPP(U_4871,U_4873),hAPP(hAPP(c_Finite__Set_Ofold(U_4869,U_4870,U_4871),U_4874),U_4872))
| hBOOL(hAPP(hAPP(c_member(U_4869),U_4873),U_4872))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4869),U_4872))
| ~ c_Finite__Set_Ofun__left__comm(U_4869,U_4870,U_4871) ),
inference(variable_rename,[status(thm)],[f_1281_1]) ).
cnf(f_1281_3,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_4869,U_4870,U_4871),U_4874),hAPP(hAPP(c_Set_Oinsert(U_4869),U_4873),U_4872)) = hAPP(hAPP(U_4871,U_4873),hAPP(hAPP(c_Finite__Set_Ofold(U_4869,U_4870,U_4871),U_4874),U_4872))
| hBOOL(hAPP(hAPP(c_member(U_4869),U_4873),U_4872))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4869),U_4872))
| ~ c_Finite__Set_Ofun__left__comm(U_4869,U_4870,U_4871) ),
inference(clausify,[status(thm)],[f_1281_2]) ).
fof(f_1282_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_1282_2,plain,
! [U_4880,U_4879,U_4878,U_4877,U_4876,U_4875] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_4875,U_4876,U_4877),U_4880),hAPP(hAPP(c_Set_Oinsert(U_4875),U_4879),U_4878)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4875,U_4876,U_4877),hAPP(hAPP(U_4877,U_4879),U_4880)),U_4878)
| hBOOL(hAPP(hAPP(c_member(U_4875),U_4879),U_4878))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4875),U_4878))
| ~ c_Finite__Set_Ofun__left__comm(U_4875,U_4876,U_4877) ),
inference(variable_rename,[status(thm)],[f_1282_1]) ).
cnf(f_1282_3,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_4875,U_4876,U_4877),U_4880),hAPP(hAPP(c_Set_Oinsert(U_4875),U_4879),U_4878)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4875,U_4876,U_4877),hAPP(hAPP(U_4877,U_4879),U_4880)),U_4878)
| hBOOL(hAPP(hAPP(c_member(U_4875),U_4879),U_4878))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4875),U_4878))
| ~ c_Finite__Set_Ofun__left__comm(U_4875,U_4876,U_4877) ),
inference(clausify,[status(thm)],[f_1282_2]) ).
fof(f_1283_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_1283_2,plain,
! [U_4886,U_4885,U_4884] :
( ! [U_4883] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4883),U_4884)),U_4885))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4883),U_4885))
| ? [U_4882] :
( ? [U_4881] :
( U_4883 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4881),U_4882)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4881),U_4886)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4882),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4884))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4885),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4886))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4884)) ),
inference(variable_rename,[status(thm)],[f_1283_1]) ).
fof(f_1283_3,plain,
! [U_4886,U_4885,U_4884] :
( ! [U_4883] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4883),U_4884)),U_4885))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4883),U_4885))
| ( ? [U_4881] :
( U_4883 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4881),sK102(U_4886,U_4885,U_4884,U_4883))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4881),U_4886)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK102(U_4886,U_4885,U_4884,U_4883)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4884))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4885),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4886))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4884)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_4882,sK102(U_4886,U_4885,U_4884,U_4883))],[f_1283_2]) ).
fof(f_1283_4,plain,
! [U_4886,U_4885,U_4884] :
( ! [U_4883] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4883),U_4884)),U_4885))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4883),U_4885))
| ( U_4883 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK103(U_4886,U_4885,U_4884,U_4883)),sK102(U_4886,U_4885,U_4884,U_4883))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK103(U_4886,U_4885,U_4884,U_4883)),U_4886))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK102(U_4886,U_4885,U_4884,U_4883)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4884))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4885),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4886))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4884)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_4881,sK103(U_4886,U_4885,U_4884,U_4883))],[f_1283_3]) ).
cnf(f_1283_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK102(U_4886,U_4885,U_4884,U_4883)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4884)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4883),U_4884)),U_4885))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4883),U_4885))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4885),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4886))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4884)) ),
inference(clausify,[status(thm)],[f_1283_4]) ).
cnf(f_1283_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK103(U_4886,U_4885,U_4884,U_4883)),U_4886))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4883),U_4884)),U_4885))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4883),U_4885))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4885),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4886))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4884)) ),
inference(clausify,[status(thm)],[f_1283_4]) ).
cnf(f_1283_7,plain,
( U_4883 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK103(U_4886,U_4885,U_4884,U_4883)),sK102(U_4886,U_4885,U_4884,U_4883))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4883),U_4884)),U_4885))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4883),U_4885))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4885),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4886))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4884)) ),
inference(clausify,[status(thm)],[f_1283_4]) ).
fof(f_1284_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_1284_2,plain,
! [U_4892,U_4891,U_4890] :
( ! [U_4889] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4891),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4889),U_4890)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4891),U_4889))
| ? [U_4888] :
( ? [U_4887] :
( U_4889 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4887),U_4888)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4887),U_4892)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4888),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4890))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4891),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4892))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4890)) ),
inference(variable_rename,[status(thm)],[f_1284_1]) ).
fof(f_1284_3,plain,
! [U_4892,U_4891,U_4890] :
( ! [U_4889] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4891),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4889),U_4890)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4891),U_4889))
| ( ? [U_4887] :
( U_4889 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4887),sK104(U_4892,U_4891,U_4890,U_4889))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4887),U_4892)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK104(U_4892,U_4891,U_4890,U_4889)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4890))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4891),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4892))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4890)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_4888,sK104(U_4892,U_4891,U_4890,U_4889))],[f_1284_2]) ).
fof(f_1284_4,plain,
! [U_4892,U_4891,U_4890] :
( ! [U_4889] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4891),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4889),U_4890)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4891),U_4889))
| ( U_4889 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK105(U_4892,U_4891,U_4890,U_4889)),sK104(U_4892,U_4891,U_4890,U_4889))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK105(U_4892,U_4891,U_4890,U_4889)),U_4892))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK104(U_4892,U_4891,U_4890,U_4889)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4890))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4891),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4892))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4890)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_4887,sK105(U_4892,U_4891,U_4890,U_4889))],[f_1284_3]) ).
cnf(f_1284_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK104(U_4892,U_4891,U_4890,U_4889)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4890)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4891),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4889),U_4890)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4891),U_4889))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4891),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4892))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4890)) ),
inference(clausify,[status(thm)],[f_1284_4]) ).
cnf(f_1284_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK105(U_4892,U_4891,U_4890,U_4889)),U_4892))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4891),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4889),U_4890)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4891),U_4889))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4891),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4892))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4890)) ),
inference(clausify,[status(thm)],[f_1284_4]) ).
cnf(f_1284_7,plain,
( U_4889 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK105(U_4892,U_4891,U_4890,U_4889)),sK104(U_4892,U_4891,U_4890,U_4889))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4891),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4889),U_4890)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4891),U_4889))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4891),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4892))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4890)) ),
inference(clausify,[status(thm)],[f_1284_4]) ).
fof(f_1285_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_1285_2,plain,
! [U_4898,U_4897,U_4896] :
( ! [U_4895] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4898),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4895),U_4896)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4898),U_4895))
| ? [U_4894] :
( ? [U_4893] :
( U_4895 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4893),U_4894)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4893),U_4897)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4894),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4896))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4896)) ),
inference(variable_rename,[status(thm)],[f_1285_1]) ).
fof(f_1285_3,plain,
! [U_4898,U_4897,U_4896] :
( ! [U_4895] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4898),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4895),U_4896)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4898),U_4895))
| ( ? [U_4893] :
( U_4895 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4893),sK106(U_4898,U_4897,U_4896,U_4895))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4893),U_4897)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK106(U_4898,U_4897,U_4896,U_4895)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4896))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4896)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_4894,sK106(U_4898,U_4897,U_4896,U_4895))],[f_1285_2]) ).
fof(f_1285_4,plain,
! [U_4898,U_4897,U_4896] :
( ! [U_4895] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4898),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4895),U_4896)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4898),U_4895))
| ( U_4895 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK107(U_4898,U_4897,U_4896,U_4895)),sK106(U_4898,U_4897,U_4896,U_4895))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK107(U_4898,U_4897,U_4896,U_4895)),U_4897))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK106(U_4898,U_4897,U_4896,U_4895)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4896))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4896)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_4893,sK107(U_4898,U_4897,U_4896,U_4895))],[f_1285_3]) ).
cnf(f_1285_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK106(U_4898,U_4897,U_4896,U_4895)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4896)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4898),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4895),U_4896)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4898),U_4895))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4896)) ),
inference(clausify,[status(thm)],[f_1285_4]) ).
cnf(f_1285_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK107(U_4898,U_4897,U_4896,U_4895)),U_4897))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4898),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4895),U_4896)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4898),U_4895))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4896)) ),
inference(clausify,[status(thm)],[f_1285_4]) ).
cnf(f_1285_7,plain,
( U_4895 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK107(U_4898,U_4897,U_4896,U_4895)),sK106(U_4898,U_4897,U_4896,U_4895))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4898),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4895),U_4896)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4898),U_4895))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4896)) ),
inference(clausify,[status(thm)],[f_1285_4]) ).
fof(f_1286_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_1286_2,plain,
! [U_4904,U_4903,U_4902] :
( ! [U_4901] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4901),U_4902)),U_4904))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4901),U_4904))
| ? [U_4900] :
( ? [U_4899] :
( U_4901 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4899),U_4900)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4899),U_4903)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4900),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4902))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4902)) ),
inference(variable_rename,[status(thm)],[f_1286_1]) ).
fof(f_1286_3,plain,
! [U_4904,U_4903,U_4902] :
( ! [U_4901] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4901),U_4902)),U_4904))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4901),U_4904))
| ( ? [U_4899] :
( U_4901 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4899),sK108(U_4904,U_4903,U_4902,U_4901))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4899),U_4903)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK108(U_4904,U_4903,U_4902,U_4901)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4902))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4902)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_4900,sK108(U_4904,U_4903,U_4902,U_4901))],[f_1286_2]) ).
fof(f_1286_4,plain,
! [U_4904,U_4903,U_4902] :
( ! [U_4901] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4901),U_4902)),U_4904))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4901),U_4904))
| ( U_4901 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK109(U_4904,U_4903,U_4902,U_4901)),sK108(U_4904,U_4903,U_4902,U_4901))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK109(U_4904,U_4903,U_4902,U_4901)),U_4903))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK108(U_4904,U_4903,U_4902,U_4901)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4902))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4902)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_4899,sK109(U_4904,U_4903,U_4902,U_4901))],[f_1286_3]) ).
cnf(f_1286_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK108(U_4904,U_4903,U_4902,U_4901)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4902)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4901),U_4902)),U_4904))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4901),U_4904))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4902)) ),
inference(clausify,[status(thm)],[f_1286_4]) ).
cnf(f_1286_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK109(U_4904,U_4903,U_4902,U_4901)),U_4903))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4901),U_4902)),U_4904))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4901),U_4904))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4902)) ),
inference(clausify,[status(thm)],[f_1286_4]) ).
cnf(f_1286_7,plain,
( U_4901 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK109(U_4904,U_4903,U_4902,U_4901)),sK108(U_4904,U_4903,U_4902,U_4901))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4901),U_4902)),U_4904))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4901),U_4904))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4902)) ),
inference(clausify,[status(thm)],[f_1286_4]) ).
fof(f_1287_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_1287_2,plain,
! [U_4910,U_4909,U_4908] :
( ! [U_4907] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4907),U_4908) != U_4909
| U_4907 = U_4909
| ? [U_4906] :
( ? [U_4905] :
( U_4907 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4905),U_4906)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4905),U_4910)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4906),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4908))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4909),U_4910))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4908)) ),
inference(variable_rename,[status(thm)],[f_1287_1]) ).
fof(f_1287_3,plain,
! [U_4910,U_4909,U_4908] :
( ! [U_4907] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4907),U_4908) != U_4909
| U_4907 = U_4909
| ( ? [U_4905] :
( U_4907 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4905),sK110(U_4910,U_4909,U_4908,U_4907))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4905),U_4910)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK110(U_4910,U_4909,U_4908,U_4907)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4908))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4909),U_4910))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4908)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_4906,sK110(U_4910,U_4909,U_4908,U_4907))],[f_1287_2]) ).
fof(f_1287_4,plain,
! [U_4910,U_4909,U_4908] :
( ! [U_4907] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4907),U_4908) != U_4909
| U_4907 = U_4909
| ( U_4907 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK111(U_4910,U_4909,U_4908,U_4907)),sK110(U_4910,U_4909,U_4908,U_4907))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK111(U_4910,U_4909,U_4908,U_4907)),U_4910))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK110(U_4910,U_4909,U_4908,U_4907)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4908))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4909),U_4910))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4908)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_4905,sK111(U_4910,U_4909,U_4908,U_4907))],[f_1287_3]) ).
cnf(f_1287_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK110(U_4910,U_4909,U_4908,U_4907)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4908)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4907),U_4908) != U_4909
| U_4907 = U_4909
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4909),U_4910))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4908)) ),
inference(clausify,[status(thm)],[f_1287_4]) ).
cnf(f_1287_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK111(U_4910,U_4909,U_4908,U_4907)),U_4910))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4907),U_4908) != U_4909
| U_4907 = U_4909
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4909),U_4910))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4908)) ),
inference(clausify,[status(thm)],[f_1287_4]) ).
cnf(f_1287_7,plain,
( U_4907 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK111(U_4910,U_4909,U_4908,U_4907)),sK110(U_4910,U_4909,U_4908,U_4907))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4907),U_4908) != U_4909
| U_4907 = U_4909
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4909),U_4910))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4908)) ),
inference(clausify,[status(thm)],[f_1287_4]) ).
fof(f_1288_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_1288_2,plain,
! [U_4916,U_4915,U_4914] :
( ! [U_4913] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4913),U_4914) != U_4915
| U_4913 = U_4915
| ? [U_4912] :
( ? [U_4911] :
( U_4913 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4911),U_4912)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4911),U_4916)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4912),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4914))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4915),U_4916))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4914)) ),
inference(variable_rename,[status(thm)],[f_1288_1]) ).
fof(f_1288_3,plain,
! [U_4916,U_4915,U_4914] :
( ! [U_4913] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4913),U_4914) != U_4915
| U_4913 = U_4915
| ( ? [U_4911] :
( U_4913 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4911),sK112(U_4916,U_4915,U_4914,U_4913))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4911),U_4916)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK112(U_4916,U_4915,U_4914,U_4913)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4914))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4915),U_4916))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4914)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_4912,sK112(U_4916,U_4915,U_4914,U_4913))],[f_1288_2]) ).
fof(f_1288_4,plain,
! [U_4916,U_4915,U_4914] :
( ! [U_4913] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4913),U_4914) != U_4915
| U_4913 = U_4915
| ( U_4913 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK113(U_4916,U_4915,U_4914,U_4913)),sK112(U_4916,U_4915,U_4914,U_4913))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK113(U_4916,U_4915,U_4914,U_4913)),U_4916))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK112(U_4916,U_4915,U_4914,U_4913)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4914))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4915),U_4916))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4914)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_4911,sK113(U_4916,U_4915,U_4914,U_4913))],[f_1288_3]) ).
cnf(f_1288_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK112(U_4916,U_4915,U_4914,U_4913)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4914)))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4913),U_4914) != U_4915
| U_4913 = U_4915
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4915),U_4916))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4914)) ),
inference(clausify,[status(thm)],[f_1288_4]) ).
cnf(f_1288_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK113(U_4916,U_4915,U_4914,U_4913)),U_4916))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4913),U_4914) != U_4915
| U_4913 = U_4915
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4915),U_4916))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4914)) ),
inference(clausify,[status(thm)],[f_1288_4]) ).
cnf(f_1288_7,plain,
( U_4913 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK113(U_4916,U_4915,U_4914,U_4913)),sK112(U_4916,U_4915,U_4914,U_4913))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4913),U_4914) != U_4915
| U_4913 = U_4915
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4915),U_4916))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4914)) ),
inference(clausify,[status(thm)],[f_1288_4]) ).
fof(f_1289_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_1289_2,plain,
! [U_4922,U_4921,U_4920] :
( ! [U_4919] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4921),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4919),U_4920)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4921),U_4919))
| ? [U_4918] :
( ? [U_4917] :
( U_4919 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4917),U_4918)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4917),U_4922)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4918),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4920))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4921),U_4922))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4920)) ),
inference(variable_rename,[status(thm)],[f_1289_1]) ).
fof(f_1289_3,plain,
! [U_4922,U_4921,U_4920] :
( ! [U_4919] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4921),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4919),U_4920)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4921),U_4919))
| ( ? [U_4917] :
( U_4919 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4917),sK114(U_4922,U_4921,U_4920,U_4919))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4917),U_4922)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK114(U_4922,U_4921,U_4920,U_4919)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4920))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4921),U_4922))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4920)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_4918,sK114(U_4922,U_4921,U_4920,U_4919))],[f_1289_2]) ).
fof(f_1289_4,plain,
! [U_4922,U_4921,U_4920] :
( ! [U_4919] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4921),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4919),U_4920)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4921),U_4919))
| ( U_4919 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK115(U_4922,U_4921,U_4920,U_4919)),sK114(U_4922,U_4921,U_4920,U_4919))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK115(U_4922,U_4921,U_4920,U_4919)),U_4922))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK114(U_4922,U_4921,U_4920,U_4919)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4920))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4921),U_4922))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4920)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_4917,sK115(U_4922,U_4921,U_4920,U_4919))],[f_1289_3]) ).
cnf(f_1289_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK114(U_4922,U_4921,U_4920,U_4919)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4920)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4921),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4919),U_4920)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4921),U_4919))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4921),U_4922))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4920)) ),
inference(clausify,[status(thm)],[f_1289_4]) ).
cnf(f_1289_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK115(U_4922,U_4921,U_4920,U_4919)),U_4922))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4921),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4919),U_4920)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4921),U_4919))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4921),U_4922))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4920)) ),
inference(clausify,[status(thm)],[f_1289_4]) ).
cnf(f_1289_7,plain,
( U_4919 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK115(U_4922,U_4921,U_4920,U_4919)),sK114(U_4922,U_4921,U_4920,U_4919))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4921),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4919),U_4920)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4921),U_4919))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4921),U_4922))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4920)) ),
inference(clausify,[status(thm)],[f_1289_4]) ).
fof(f_1290_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_1290_2,plain,
! [U_4927,U_4926,U_4925] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4926),U_4925) = U_4926
| ? [U_4924] :
( ? [U_4923] :
( U_4926 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4923),U_4924)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4923),U_4927)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4924),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4925))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4926),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4927))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4925)) ),
inference(variable_rename,[status(thm)],[f_1290_1]) ).
fof(f_1290_3,plain,
! [U_4927,U_4926,U_4925] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4926),U_4925) = U_4926
| ( ? [U_4923] :
( U_4926 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4923),sK116(U_4927,U_4926,U_4925))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4923),U_4927)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK116(U_4927,U_4926,U_4925)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4925))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4926),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4927))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4925)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_4924,sK116(U_4927,U_4926,U_4925))],[f_1290_2]) ).
fof(f_1290_4,plain,
! [U_4927,U_4926,U_4925] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4926),U_4925) = U_4926
| ( U_4926 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK117(U_4927,U_4926,U_4925)),sK116(U_4927,U_4926,U_4925))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK117(U_4927,U_4926,U_4925)),U_4927))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK116(U_4927,U_4926,U_4925)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4925))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4926),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4927))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4925)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_4923,sK117(U_4927,U_4926,U_4925))],[f_1290_3]) ).
cnf(f_1290_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK116(U_4927,U_4926,U_4925)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4925)))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4926),U_4925) = U_4926
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4926),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4927))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4925)) ),
inference(clausify,[status(thm)],[f_1290_4]) ).
cnf(f_1290_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK117(U_4927,U_4926,U_4925)),U_4927))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4926),U_4925) = U_4926
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4926),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4927))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4925)) ),
inference(clausify,[status(thm)],[f_1290_4]) ).
cnf(f_1290_7,plain,
( U_4926 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK117(U_4927,U_4926,U_4925)),sK116(U_4927,U_4926,U_4925))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4926),U_4925) = U_4926
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4926),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4927))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4925)) ),
inference(clausify,[status(thm)],[f_1290_4]) ).
fof(f_1291_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_1291_2,plain,
! [U_4932,U_4931,U_4930] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4931),U_4930) = U_4931
| ? [U_4929] :
( ? [U_4928] :
( U_4931 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4928),U_4929)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4928),U_4932)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4929),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4930))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4931),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4932))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4930)) ),
inference(variable_rename,[status(thm)],[f_1291_1]) ).
fof(f_1291_3,plain,
! [U_4932,U_4931,U_4930] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4931),U_4930) = U_4931
| ( ? [U_4928] :
( U_4931 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4928),sK118(U_4932,U_4931,U_4930))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4928),U_4932)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK118(U_4932,U_4931,U_4930)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4930))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4931),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4932))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4930)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_4929,sK118(U_4932,U_4931,U_4930))],[f_1291_2]) ).
fof(f_1291_4,plain,
! [U_4932,U_4931,U_4930] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4931),U_4930) = U_4931
| ( U_4931 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK119(U_4932,U_4931,U_4930)),sK118(U_4932,U_4931,U_4930))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK119(U_4932,U_4931,U_4930)),U_4932))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK118(U_4932,U_4931,U_4930)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4930))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4931),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4932))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4930)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_4928,sK119(U_4932,U_4931,U_4930))],[f_1291_3]) ).
cnf(f_1291_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK118(U_4932,U_4931,U_4930)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4930)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4931),U_4930) = U_4931
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4931),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4932))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4930)) ),
inference(clausify,[status(thm)],[f_1291_4]) ).
cnf(f_1291_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK119(U_4932,U_4931,U_4930)),U_4932))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4931),U_4930) = U_4931
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4931),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4932))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4930)) ),
inference(clausify,[status(thm)],[f_1291_4]) ).
cnf(f_1291_7,plain,
( U_4931 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK119(U_4932,U_4931,U_4930)),sK118(U_4932,U_4931,U_4930))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4931),U_4930) = U_4931
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4931),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4932))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4930)) ),
inference(clausify,[status(thm)],[f_1291_4]) ).
fof(f_1292_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_1292_2,plain,
! [U_4938,U_4937,U_4936] :
( ! [U_4935] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4935),U_4936)),U_4937))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4935),U_4937))
| ? [U_4934] :
( ? [U_4933] :
( U_4935 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4933),U_4934)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4933),U_4938)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4934),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4936))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4937),U_4938))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4936)) ),
inference(variable_rename,[status(thm)],[f_1292_1]) ).
fof(f_1292_3,plain,
! [U_4938,U_4937,U_4936] :
( ! [U_4935] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4935),U_4936)),U_4937))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4935),U_4937))
| ( ? [U_4933] :
( U_4935 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4933),sK120(U_4938,U_4937,U_4936,U_4935))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4933),U_4938)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK120(U_4938,U_4937,U_4936,U_4935)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4936))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4937),U_4938))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4936)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_4934,sK120(U_4938,U_4937,U_4936,U_4935))],[f_1292_2]) ).
fof(f_1292_4,plain,
! [U_4938,U_4937,U_4936] :
( ! [U_4935] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4935),U_4936)),U_4937))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4935),U_4937))
| ( U_4935 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK121(U_4938,U_4937,U_4936,U_4935)),sK120(U_4938,U_4937,U_4936,U_4935))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK121(U_4938,U_4937,U_4936,U_4935)),U_4938))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK120(U_4938,U_4937,U_4936,U_4935)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4936))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4937),U_4938))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4936)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_4933,sK121(U_4938,U_4937,U_4936,U_4935))],[f_1292_3]) ).
cnf(f_1292_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK120(U_4938,U_4937,U_4936,U_4935)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4936)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4935),U_4936)),U_4937))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4935),U_4937))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4937),U_4938))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4936)) ),
inference(clausify,[status(thm)],[f_1292_4]) ).
cnf(f_1292_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK121(U_4938,U_4937,U_4936,U_4935)),U_4938))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4935),U_4936)),U_4937))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4935),U_4937))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4937),U_4938))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4936)) ),
inference(clausify,[status(thm)],[f_1292_4]) ).
cnf(f_1292_7,plain,
( U_4935 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK121(U_4938,U_4937,U_4936,U_4935)),sK120(U_4938,U_4937,U_4936,U_4935))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4935),U_4936)),U_4937))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4935),U_4937))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4937),U_4938))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4936)) ),
inference(clausify,[status(thm)],[f_1292_4]) ).
fof(f_1293_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_1293_2,plain,
! [U_4944,U_4943,U_4942] :
( ! [U_4941] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4944),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4941),U_4942)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4944),U_4941))
| ? [U_4940] :
( ? [U_4939] :
( U_4941 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4939),U_4940)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4939),U_4943)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4940),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4942))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4942)) ),
inference(variable_rename,[status(thm)],[f_1293_1]) ).
fof(f_1293_3,plain,
! [U_4944,U_4943,U_4942] :
( ! [U_4941] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4944),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4941),U_4942)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4944),U_4941))
| ( ? [U_4939] :
( U_4941 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4939),sK122(U_4944,U_4943,U_4942,U_4941))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4939),U_4943)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK122(U_4944,U_4943,U_4942,U_4941)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4942))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4942)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_4940,sK122(U_4944,U_4943,U_4942,U_4941))],[f_1293_2]) ).
fof(f_1293_4,plain,
! [U_4944,U_4943,U_4942] :
( ! [U_4941] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4944),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4941),U_4942)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4944),U_4941))
| ( U_4941 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK123(U_4944,U_4943,U_4942,U_4941)),sK122(U_4944,U_4943,U_4942,U_4941))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK123(U_4944,U_4943,U_4942,U_4941)),U_4943))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK122(U_4944,U_4943,U_4942,U_4941)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4942))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4942)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(U_4939,sK123(U_4944,U_4943,U_4942,U_4941))],[f_1293_3]) ).
cnf(f_1293_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK122(U_4944,U_4943,U_4942,U_4941)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4942)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4944),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4941),U_4942)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4944),U_4941))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4942)) ),
inference(clausify,[status(thm)],[f_1293_4]) ).
cnf(f_1293_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK123(U_4944,U_4943,U_4942,U_4941)),U_4943))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4944),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4941),U_4942)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4944),U_4941))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4942)) ),
inference(clausify,[status(thm)],[f_1293_4]) ).
cnf(f_1293_7,plain,
( U_4941 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK123(U_4944,U_4943,U_4942,U_4941)),sK122(U_4944,U_4943,U_4942,U_4941))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4944),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4941),U_4942)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4944),U_4941))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4942)) ),
inference(clausify,[status(thm)],[f_1293_4]) ).
fof(f_1294_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_1294_2,plain,
! [U_4950,U_4949,U_4948] :
( ! [U_4947] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4947),U_4948)),U_4950))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4947),U_4950))
| ? [U_4946] :
( ? [U_4945] :
( U_4947 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4945),U_4946)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4945),U_4949)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4946),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4948))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4948)) ),
inference(variable_rename,[status(thm)],[f_1294_1]) ).
fof(f_1294_3,plain,
! [U_4950,U_4949,U_4948] :
( ! [U_4947] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4947),U_4948)),U_4950))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4947),U_4950))
| ( ? [U_4945] :
( U_4947 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4945),sK124(U_4950,U_4949,U_4948,U_4947))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_4945),U_4949)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK124(U_4950,U_4949,U_4948,U_4947)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4948))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4948)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(U_4946,sK124(U_4950,U_4949,U_4948,U_4947))],[f_1294_2]) ).
fof(f_1294_4,plain,
! [U_4950,U_4949,U_4948] :
( ! [U_4947] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4947),U_4948)),U_4950))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4947),U_4950))
| ( U_4947 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK125(U_4950,U_4949,U_4948,U_4947)),sK124(U_4950,U_4949,U_4948,U_4947))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK125(U_4950,U_4949,U_4948,U_4947)),U_4949))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK124(U_4950,U_4949,U_4948,U_4947)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4948))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4948)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(U_4945,sK125(U_4950,U_4949,U_4948,U_4947))],[f_1294_3]) ).
cnf(f_1294_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK124(U_4950,U_4949,U_4948,U_4947)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_4948)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4947),U_4948)),U_4950))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4947),U_4950))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4948)) ),
inference(clausify,[status(thm)],[f_1294_4]) ).
cnf(f_1294_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK125(U_4950,U_4949,U_4948,U_4947)),U_4949))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4947),U_4948)),U_4950))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4947),U_4950))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4948)) ),
inference(clausify,[status(thm)],[f_1294_4]) ).
cnf(f_1294_7,plain,
( U_4947 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK125(U_4950,U_4949,U_4948,U_4947)),sK124(U_4950,U_4949,U_4948,U_4947))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4947),U_4948)),U_4950))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4947),U_4950))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4948)) ),
inference(clausify,[status(thm)],[f_1294_4]) ).
fof(f_1295_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_1295_2,plain,
! [U_4952,U_4951] :
( ( c_Nat__Transfer_Otsub(U_4952,U_4951) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4951),U_4952)) )
& ( c_Nat__Transfer_Otsub(U_4952,U_4951) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4952),U_4951)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4951),U_4952)) ) ),
inference(variable_rename,[status(thm)],[f_1295_1]) ).
fof(f_1295_3,plain,
( ! [U_4956,U_4954] :
( c_Nat__Transfer_Otsub(U_4956,U_4954) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4954),U_4956)) )
& ! [U_4955,U_4953] :
( c_Nat__Transfer_Otsub(U_4955,U_4953) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4955),U_4953)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4953),U_4955)) ) ),
inference(miniscope,[status(thm)],[f_1295_2]) ).
cnf(f_1295_4,plain,
( c_Nat__Transfer_Otsub(U_4955,U_4953) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4955),U_4953)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4953),U_4955)) ),
inference(clausify,[status(thm)],[f_1295_3]) ).
cnf(f_1295_5,plain,
( c_Nat__Transfer_Otsub(U_4956,U_4954) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4954),U_4956)) ),
inference(clausify,[status(thm)],[f_1295_3]) ).
fof(f_1296_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_1296_2,plain,
! [U_4957] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4957)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_4957))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4957),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4957)),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_4957),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_1296_1]) ).
fof(f_1296_3,plain,
( ! [U_4959] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4959)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_4959))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4959),c_Int_OPls)) )
& ! [U_4958] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4958)),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_4958),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_1296_2]) ).
cnf(f_1296_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4958)),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_4958),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1296_3]) ).
cnf(f_1296_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4959)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_4959))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4959),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1296_3]) ).
fof(f_1297_1,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_Pls__def]) ).
cnf(f_1297_2,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1297_1]) ).
fof(f_1298_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_1298_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_1298_1]) ).
fof(f_1299_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_1299_2,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
inference(clausify,[status(thm)],[f_1299_1]) ).
fof(f_1300_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_1300_2,plain,
! [U_4960] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_4960) = U_4960,
inference(variable_rename,[status(thm)],[f_1300_1]) ).
cnf(f_1300_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_4960) = U_4960,
inference(clausify,[status(thm)],[f_1300_2]) ).
fof(f_1301_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_1301_2,plain,
! [U_4961] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4961),c_Int_OPls) = U_4961,
inference(variable_rename,[status(thm)],[f_1301_1]) ).
cnf(f_1301_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4961),c_Int_OPls) = U_4961,
inference(clausify,[status(thm)],[f_1301_2]) ).
fof(f_1302_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_1302_2,plain,
! [U_4962] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4962),c_Int_OPls) = U_4962,
inference(variable_rename,[status(thm)],[f_1302_1]) ).
cnf(f_1302_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4962),c_Int_OPls) = U_4962,
inference(clausify,[status(thm)],[f_1302_2]) ).
fof(f_1303_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_1303_2,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
inference(clausify,[status(thm)],[f_1303_1]) ).
fof(f_1304_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_1304_2,plain,
! [U_4963] :
( c_Groups_Ozero__class_Ozero(U_4963) = hAPP(c_Int_Onumber__class_Onumber__of(U_4963),c_Int_OPls)
| ~ class_Int_Onumber__ring(U_4963) ),
inference(variable_rename,[status(thm)],[f_1304_1]) ).
cnf(f_1304_3,plain,
( c_Groups_Ozero__class_Ozero(U_4963) = hAPP(c_Int_Onumber__class_Onumber__of(U_4963),c_Int_OPls)
| ~ class_Int_Onumber__ring(U_4963) ),
inference(clausify,[status(thm)],[f_1304_2]) ).
fof(f_1305_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_1305_2,plain,
! [U_4964] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_4964),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_4964)
| ~ class_Int_Onumber__ring(U_4964) ),
inference(variable_rename,[status(thm)],[f_1305_1]) ).
cnf(f_1305_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_4964),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_4964)
| ~ class_Int_Onumber__ring(U_4964) ),
inference(clausify,[status(thm)],[f_1305_2]) ).
fof(f_1306_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_1306_2,plain,
! [U_4966,U_4965] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4965),U_4966),hAPP(c_Int_Onumber__class_Onumber__of(U_4965),c_Int_OPls)) = U_4966
| ~ class_Int_Onumber__ring(U_4965) ),
inference(variable_rename,[status(thm)],[f_1306_1]) ).
cnf(f_1306_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4965),U_4966),hAPP(c_Int_Onumber__class_Onumber__of(U_4965),c_Int_OPls)) = U_4966
| ~ class_Int_Onumber__ring(U_4965) ),
inference(clausify,[status(thm)],[f_1306_2]) ).
fof(f_1307_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_1307_2,plain,
! [U_4968,U_4967] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4967),hAPP(c_Int_Onumber__class_Onumber__of(U_4967),c_Int_OPls)),U_4968) = U_4968
| ~ class_Int_Onumber__ring(U_4967) ),
inference(variable_rename,[status(thm)],[f_1307_1]) ).
cnf(f_1307_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4967),hAPP(c_Int_Onumber__class_Onumber__of(U_4967),c_Int_OPls)),U_4968) = U_4968
| ~ class_Int_Onumber__ring(U_4967) ),
inference(clausify,[status(thm)],[f_1307_2]) ).
fof(f_1308_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_1308_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_1308_1]) ).
fof(f_1309_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_1309_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_1309_1]) ).
fof(f_1310_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_1310_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_1310_1]) ).
fof(f_1311_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_1311_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_1311_1]) ).
fof(f_1312_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_1312_2,plain,
! [U_4969] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4969)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4969),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4969),c_Int_OPls))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4969) ) ),
inference(variable_rename,[status(thm)],[f_1312_1]) ).
fof(f_1312_3,plain,
( ! [U_4971] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4971)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4971),c_Int_OPls)) )
& ! [U_4970] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4970),c_Int_OPls))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4970) ) ),
inference(miniscope,[status(thm)],[f_1312_2]) ).
cnf(f_1312_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4970),c_Int_OPls))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4970) ),
inference(clausify,[status(thm)],[f_1312_3]) ).
cnf(f_1312_5,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4971)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4971),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1312_3]) ).
fof(f_1313_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_1313_2,plain,
! [U_4972] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4972) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4972),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4972),c_Int_OPls))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4972) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1313_1]) ).
fof(f_1313_3,plain,
( ! [U_4974] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4974) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4974),c_Int_OPls)) )
& ! [U_4973] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4973),c_Int_OPls))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4973) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1313_2]) ).
cnf(f_1313_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4973),c_Int_OPls))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4973) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1313_3]) ).
cnf(f_1313_5,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4974) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4974),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1313_3]) ).
fof(f_1314_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_1314_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_1314_1]) ).
fof(f_1315_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_1315_2,plain,
! [U_4976,U_4975] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4975)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4976)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4975),U_4976))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4976))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4975),U_4976)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4975),U_4976))
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4976))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4975),U_4976)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4975)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4976))) ) ),
inference(variable_rename,[status(thm)],[f_1315_1]) ).
fof(f_1315_3,plain,
( ! [U_4980,U_4978] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4978)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4980)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4978),U_4980))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4980))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4978),U_4980)) ) )
& ! [U_4979,U_4977] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4977),U_4979))
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4979))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4977),U_4979)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4977)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4979))) ) ),
inference(miniscope,[status(thm)],[f_1315_2]) ).
cnf(f_1315_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4979))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4977),U_4979))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4977)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4979))) ),
inference(clausify,[status(thm)],[f_1315_3]) ).
cnf(f_1315_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4977),U_4979))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4977)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4979))) ),
inference(clausify,[status(thm)],[f_1315_3]) ).
cnf(f_1315_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4978),U_4980))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4978),U_4980))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4978)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4980))) ),
inference(clausify,[status(thm)],[f_1315_3]) ).
cnf(f_1315_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4980))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4978),U_4980))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4978)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4980))) ),
inference(clausify,[status(thm)],[f_1315_3]) ).
fof(f_1316_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_1316_2,plain,
! [U_4982,U_4981] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4981)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4982)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4981),c_Int_OPls))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4981),U_4982)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4981),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4981),U_4982))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4981)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4982))) ) ),
inference(variable_rename,[status(thm)],[f_1316_1]) ).
fof(f_1316_3,plain,
( ! [U_4986,U_4984] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4984)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4986)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4984),c_Int_OPls))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4984),U_4986)) ) )
& ! [U_4985,U_4983] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4983),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4983),U_4985))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4983)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4985))) ) ),
inference(miniscope,[status(thm)],[f_1316_2]) ).
cnf(f_1316_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4983),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4983),U_4985))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4983)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4985))) ),
inference(clausify,[status(thm)],[f_1316_3]) ).
cnf(f_1316_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4984),U_4986))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4984)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4986))) ),
inference(clausify,[status(thm)],[f_1316_3]) ).
cnf(f_1316_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4984),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_4984)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4986))) ),
inference(clausify,[status(thm)],[f_1316_3]) ).
fof(f_1317_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_1317_2,plain,
! [U_4988,U_4987] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4987),hAPP(c_Int_Onumber__class_Onumber__of(U_4987),U_4988)),c_Groups_Ozero__class_Ozero(U_4987)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4988),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4988),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4987),hAPP(c_Int_Onumber__class_Onumber__of(U_4987),U_4988)),c_Groups_Ozero__class_Ozero(U_4987))) ) )
| ~ class_Rings_Olinordered__idom(U_4987)
| ~ class_Int_Onumber__ring(U_4987) ),
inference(variable_rename,[status(thm)],[f_1317_1]) ).
cnf(f_1317_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4988),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4987),hAPP(c_Int_Onumber__class_Onumber__of(U_4987),U_4988)),c_Groups_Ozero__class_Ozero(U_4987)))
| ~ class_Rings_Olinordered__idom(U_4987)
| ~ class_Int_Onumber__ring(U_4987) ),
inference(clausify,[status(thm)],[f_1317_2]) ).
cnf(f_1317_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4987),hAPP(c_Int_Onumber__class_Onumber__of(U_4987),U_4988)),c_Groups_Ozero__class_Ozero(U_4987)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4988),c_Int_OPls))
| ~ class_Rings_Olinordered__idom(U_4987)
| ~ class_Int_Onumber__ring(U_4987) ),
inference(clausify,[status(thm)],[f_1317_2]) ).
fof(f_1318_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_1318_2,plain,
! [U_4990,U_4989] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4989),c_Groups_Ozero__class_Ozero(U_4989)),hAPP(c_Int_Onumber__class_Onumber__of(U_4989),U_4990)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4990)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4990))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4989),c_Groups_Ozero__class_Ozero(U_4989)),hAPP(c_Int_Onumber__class_Onumber__of(U_4989),U_4990))) ) )
| ~ class_Rings_Olinordered__idom(U_4989)
| ~ class_Int_Onumber__ring(U_4989) ),
inference(variable_rename,[status(thm)],[f_1318_1]) ).
cnf(f_1318_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4990))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4989),c_Groups_Ozero__class_Ozero(U_4989)),hAPP(c_Int_Onumber__class_Onumber__of(U_4989),U_4990)))
| ~ class_Rings_Olinordered__idom(U_4989)
| ~ class_Int_Onumber__ring(U_4989) ),
inference(clausify,[status(thm)],[f_1318_2]) ).
cnf(f_1318_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4989),c_Groups_Ozero__class_Ozero(U_4989)),hAPP(c_Int_Onumber__class_Onumber__of(U_4989),U_4990)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4990))
| ~ class_Rings_Olinordered__idom(U_4989)
| ~ class_Int_Onumber__ring(U_4989) ),
inference(clausify,[status(thm)],[f_1318_2]) ).
fof(f_1319_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_1319_2,plain,
! [U_4992,U_4991] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4991),c_Groups_Ozero__class_Ozero(U_4991)),hAPP(c_Int_Onumber__class_Onumber__of(U_4991),U_4992)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4992)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4992))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4991),c_Groups_Ozero__class_Ozero(U_4991)),hAPP(c_Int_Onumber__class_Onumber__of(U_4991),U_4992))) ) )
| ~ class_Rings_Olinordered__idom(U_4991)
| ~ class_Int_Onumber__ring(U_4991) ),
inference(variable_rename,[status(thm)],[f_1319_1]) ).
cnf(f_1319_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4992))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4991),c_Groups_Ozero__class_Ozero(U_4991)),hAPP(c_Int_Onumber__class_Onumber__of(U_4991),U_4992)))
| ~ class_Rings_Olinordered__idom(U_4991)
| ~ class_Int_Onumber__ring(U_4991) ),
inference(clausify,[status(thm)],[f_1319_2]) ).
cnf(f_1319_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4991),c_Groups_Ozero__class_Ozero(U_4991)),hAPP(c_Int_Onumber__class_Onumber__of(U_4991),U_4992)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4992))
| ~ class_Rings_Olinordered__idom(U_4991)
| ~ class_Int_Onumber__ring(U_4991) ),
inference(clausify,[status(thm)],[f_1319_2]) ).
fof(f_1320_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_1320_2,plain,
! [U_4994,U_4993] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4993),hAPP(c_Int_Onumber__class_Onumber__of(U_4993),U_4994)),c_Groups_Ozero__class_Ozero(U_4993)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4994),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4994),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4993),hAPP(c_Int_Onumber__class_Onumber__of(U_4993),U_4994)),c_Groups_Ozero__class_Ozero(U_4993))) ) )
| ~ class_Rings_Olinordered__idom(U_4993)
| ~ class_Int_Onumber__ring(U_4993) ),
inference(variable_rename,[status(thm)],[f_1320_1]) ).
cnf(f_1320_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4994),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4993),hAPP(c_Int_Onumber__class_Onumber__of(U_4993),U_4994)),c_Groups_Ozero__class_Ozero(U_4993)))
| ~ class_Rings_Olinordered__idom(U_4993)
| ~ class_Int_Onumber__ring(U_4993) ),
inference(clausify,[status(thm)],[f_1320_2]) ).
cnf(f_1320_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4993),hAPP(c_Int_Onumber__class_Onumber__of(U_4993),U_4994)),c_Groups_Ozero__class_Ozero(U_4993)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4994),c_Int_OPls))
| ~ class_Rings_Olinordered__idom(U_4993)
| ~ class_Int_Onumber__ring(U_4993) ),
inference(clausify,[status(thm)],[f_1320_2]) ).
fof(f_1321_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_1321_2,plain,
! [U_4995] :
( ( 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_4995)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4995)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4995))
| ~ 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_4995))) ) ),
inference(variable_rename,[status(thm)],[f_1321_1]) ).
fof(f_1321_3,plain,
( ! [U_4997] :
( 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_4997)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4997)) )
& ! [U_4996] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4996))
| ~ 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_4996))) ) ),
inference(miniscope,[status(thm)],[f_1321_2]) ).
cnf(f_1321_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4996))
| ~ 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_4996))) ),
inference(clausify,[status(thm)],[f_1321_3]) ).
cnf(f_1321_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_4997)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4997)) ),
inference(clausify,[status(thm)],[f_1321_3]) ).
fof(f_1322_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_1322_2,plain,
! [U_4999,U_4998] :
( ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4998)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4999)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4998),U_4999))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4999),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4998)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4999)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4998)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4999),c_Int_OPls)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4998),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4998)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4999)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4999)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4998),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_1322_1]) ).
fof(f_1322_3,plain,
( ! [U_5003,U_5001] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5001)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5003)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5001),U_5003))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5003),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5001)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5003)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5001)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5003),c_Int_OPls)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5001),c_Int_OPls)) )
& ! [U_5002,U_5000] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5000)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5002)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5002)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5000),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_1322_2]) ).
cnf(f_1322_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5000)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5002)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5002)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5000),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1322_3]) ).
cnf(f_1322_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5001)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5003)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5001)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5003),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5001),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1322_3]) ).
cnf(f_1322_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5001)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5003)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5001),U_5003))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5003),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5001),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1322_3]) ).
fof(f_1323_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_1323_2,plain,
! [U_5005,U_5004] :
( 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_5004,U_5005)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5005))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5004)) ),
inference(variable_rename,[status(thm)],[f_1323_1]) ).
cnf(f_1323_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_5004,U_5005)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5005))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5004)) ),
inference(clausify,[status(thm)],[f_1323_2]) ).
fof(f_1324_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_1324_2,plain,
! [U_5007,U_5006] :
( c_Nat__Transfer_Otsub(U_5007,U_5006) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5007),U_5006)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5006),U_5007)) ),
inference(variable_rename,[status(thm)],[f_1324_1]) ).
cnf(f_1324_3,plain,
( c_Nat__Transfer_Otsub(U_5007,U_5006) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5007),U_5006)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5006),U_5007)) ),
inference(clausify,[status(thm)],[f_1324_2]) ).
fof(f_1325_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_1325_2,plain,
! [U_5009,U_5008] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5009)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5008)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5009),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_5008)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5008)) ),
inference(variable_rename,[status(thm)],[f_1325_1]) ).
cnf(f_1325_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5009)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5008)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5009),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_5008)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5008)) ),
inference(clausify,[status(thm)],[f_1325_2]) ).
fof(f_1326_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_1326_2,plain,
! [U_5011,U_5010] :
( ( ( c_Groups_Ozero__class_Ozero(U_5010) = hAPP(c_Int_Onumber__class_Onumber__of(U_5010),U_5011)
| ~ c_Int_Oiszero(U_5010,hAPP(c_Int_Onumber__class_Onumber__of(U_5010),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5011)))) )
& ( c_Int_Oiszero(U_5010,hAPP(c_Int_Onumber__class_Onumber__of(U_5010),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5011))))
| c_Groups_Ozero__class_Ozero(U_5010) != hAPP(c_Int_Onumber__class_Onumber__of(U_5010),U_5011) ) )
| ~ class_Int_Onumber__ring(U_5010) ),
inference(variable_rename,[status(thm)],[f_1326_1]) ).
cnf(f_1326_3,plain,
( c_Int_Oiszero(U_5010,hAPP(c_Int_Onumber__class_Onumber__of(U_5010),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5011))))
| c_Groups_Ozero__class_Ozero(U_5010) != hAPP(c_Int_Onumber__class_Onumber__of(U_5010),U_5011)
| ~ class_Int_Onumber__ring(U_5010) ),
inference(clausify,[status(thm)],[f_1326_2]) ).
cnf(f_1326_4,plain,
( c_Groups_Ozero__class_Ozero(U_5010) = hAPP(c_Int_Onumber__class_Onumber__of(U_5010),U_5011)
| ~ c_Int_Oiszero(U_5010,hAPP(c_Int_Onumber__class_Onumber__of(U_5010),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5011))))
| ~ class_Int_Onumber__ring(U_5010) ),
inference(clausify,[status(thm)],[f_1326_2]) ).
fof(f_1327_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_1327_2,plain,
! [U_5013,U_5012] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_5012),U_5013) = c_Groups_Ozero__class_Ozero(U_5012)
| ~ c_Int_Oiszero(U_5012,hAPP(c_Int_Onumber__class_Onumber__of(U_5012),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5013),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) )
& ( c_Int_Oiszero(U_5012,hAPP(c_Int_Onumber__class_Onumber__of(U_5012),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5013),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_5012),U_5013) != c_Groups_Ozero__class_Ozero(U_5012) ) )
| ~ class_Int_Onumber__ring(U_5012) ),
inference(variable_rename,[status(thm)],[f_1327_1]) ).
cnf(f_1327_3,plain,
( c_Int_Oiszero(U_5012,hAPP(c_Int_Onumber__class_Onumber__of(U_5012),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5013),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_5012),U_5013) != c_Groups_Ozero__class_Ozero(U_5012)
| ~ class_Int_Onumber__ring(U_5012) ),
inference(clausify,[status(thm)],[f_1327_2]) ).
cnf(f_1327_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_5012),U_5013) = c_Groups_Ozero__class_Ozero(U_5012)
| ~ c_Int_Oiszero(U_5012,hAPP(c_Int_Onumber__class_Onumber__of(U_5012),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5013),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| ~ class_Int_Onumber__ring(U_5012) ),
inference(clausify,[status(thm)],[f_1327_2]) ).
fof(f_1328_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_1328_2,plain,
! [U_5014] :
( ( 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_5014)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_5014))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5014),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_5014)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5014),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_1328_1]) ).
fof(f_1328_3,plain,
( ! [U_5016] :
( 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_5016)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_5016))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5016),c_Int_OPls)) )
& ! [U_5015] :
( 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_5015)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5015),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_1328_2]) ).
cnf(f_1328_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_5015)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5015),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1328_3]) ).
cnf(f_1328_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_5016)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_5016))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5016),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1328_3]) ).
fof(f_1329_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_1329_2,plain,
! [U_5017] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5017)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_5017))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5017),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5017)),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_5017),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_1329_1]) ).
fof(f_1329_3,plain,
( ! [U_5019] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5019)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_5019))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5019),c_Int_OPls)) )
& ! [U_5018] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5018)),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_5018),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_1329_2]) ).
cnf(f_1329_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5018)),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_5018),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1329_3]) ).
cnf(f_1329_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5019)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_5019))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5019),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1329_3]) ).
fof(f_1330_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_1330_2,plain,
! [U_5021,U_5020] :
( hBOOL(hAPP(hAPP(c_member(U_5020),hAPP(c_Int_Onumber__class_Onumber__of(U_5020),U_5021)),c_Nat_Osemiring__1__class_ONats(U_5020)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5021))
| ~ class_Int_Onumber__ring(U_5020) ),
inference(variable_rename,[status(thm)],[f_1330_1]) ).
cnf(f_1330_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_5020),hAPP(c_Int_Onumber__class_Onumber__of(U_5020),U_5021)),c_Nat_Osemiring__1__class_ONats(U_5020)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5021))
| ~ class_Int_Onumber__ring(U_5020) ),
inference(clausify,[status(thm)],[f_1330_2]) ).
fof(f_1331_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_1331_2,plain,
! [U_5023,U_5022] :
( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5022),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5023)) = c_Groups_Ozero__class_Ozero(U_5022)
| 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_5023))) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5022),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5023)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5022),U_5023)
| ~ 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_5023))) ) )
| ~ class_Int_Onumber__ring(U_5022) ),
inference(variable_rename,[status(thm)],[f_1331_1]) ).
cnf(f_1331_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5022),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5023)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5022),U_5023)
| ~ 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_5023)))
| ~ class_Int_Onumber__ring(U_5022) ),
inference(clausify,[status(thm)],[f_1331_2]) ).
cnf(f_1331_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5022),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5023)) = c_Groups_Ozero__class_Ozero(U_5022)
| 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_5023)))
| ~ class_Int_Onumber__ring(U_5022) ),
inference(clausify,[status(thm)],[f_1331_2]) ).
fof(f_1332_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_1332_2,plain,
! [U_5025,U_5024] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5024),hAPP(c_Int_Onumber__class_Onumber__of(U_5024),U_5025)),c_Groups_Oone__class_Oone(U_5024)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5024),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5025),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
| ~ class_Int_Onumber__ring(U_5024) ),
inference(variable_rename,[status(thm)],[f_1332_1]) ).
cnf(f_1332_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5024),hAPP(c_Int_Onumber__class_Onumber__of(U_5024),U_5025)),c_Groups_Oone__class_Oone(U_5024)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5024),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5025),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
| ~ class_Int_Onumber__ring(U_5024) ),
inference(clausify,[status(thm)],[f_1332_2]) ).
fof(f_1333_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_1333_2,plain,
! [U_5027,U_5026] : 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_5026))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5027))),
inference(variable_rename,[status(thm)],[f_1333_1]) ).
cnf(f_1333_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_5026))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5027))),
inference(clausify,[status(thm)],[f_1333_2]) ).
fof(f_1334_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_1334_2,plain,
! [U_5029,U_5028] : 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_5028)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5029))),
inference(variable_rename,[status(thm)],[f_1334_1]) ).
cnf(f_1334_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_5028)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5029))),
inference(clausify,[status(thm)],[f_1334_2]) ).
fof(f_1335_1,plain,
c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
inference(fof_nnf,[status(thm)],[fact_succ__Pls]) ).
cnf(f_1335_2,plain,
c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
inference(clausify,[status(thm)],[f_1335_1]) ).
fof(f_1336_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_1336_2,plain,
! [U_5031,U_5030] :
( ( c_Int_OBit1(U_5030) = c_Int_OBit1(U_5031)
| U_5030 != U_5031 )
& ( U_5030 = U_5031
| c_Int_OBit1(U_5030) != c_Int_OBit1(U_5031) ) ),
inference(variable_rename,[status(thm)],[f_1336_1]) ).
fof(f_1336_3,plain,
( ! [U_5035,U_5033] :
( c_Int_OBit1(U_5033) = c_Int_OBit1(U_5035)
| U_5033 != U_5035 )
& ! [U_5034,U_5032] :
( U_5032 = U_5034
| c_Int_OBit1(U_5032) != c_Int_OBit1(U_5034) ) ),
inference(miniscope,[status(thm)],[f_1336_2]) ).
cnf(f_1336_4,plain,
( U_5032 = U_5034
| c_Int_OBit1(U_5032) != c_Int_OBit1(U_5034) ),
inference(clausify,[status(thm)],[f_1336_3]) ).
cnf(f_1336_5,plain,
( c_Int_OBit1(U_5033) = c_Int_OBit1(U_5035)
| U_5033 != U_5035 ),
inference(clausify,[status(thm)],[f_1336_3]) ).
fof(f_1337_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_1337_2,plain,
! [U_5038,U_5037,U_5036] :
( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5036),U_5037) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5036),U_5038)
| U_5037 != U_5038 )
& ( U_5037 = U_5038
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5036),U_5037) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5036),U_5038) ) )
| ~ class_Nat_Osemiring__char__0(U_5036) ),
inference(variable_rename,[status(thm)],[f_1337_1]) ).
cnf(f_1337_3,plain,
( U_5037 = U_5038
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5036),U_5037) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5036),U_5038)
| ~ class_Nat_Osemiring__char__0(U_5036) ),
inference(clausify,[status(thm)],[f_1337_2]) ).
cnf(f_1337_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5036),U_5037) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5036),U_5038)
| U_5037 != U_5038
| ~ class_Nat_Osemiring__char__0(U_5036) ),
inference(clausify,[status(thm)],[f_1337_2]) ).
fof(f_1338_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_1338_2,plain,
! [U_5040,U_5039] :
( ~ c_Int_Oiszero(U_5039,hAPP(c_Int_Onumber__class_Onumber__of(U_5039),c_Int_OBit1(U_5040)))
| ~ class_Int_Oring__char__0(U_5039)
| ~ class_Int_Onumber__ring(U_5039) ),
inference(variable_rename,[status(thm)],[f_1338_1]) ).
cnf(f_1338_3,plain,
( ~ c_Int_Oiszero(U_5039,hAPP(c_Int_Onumber__class_Onumber__of(U_5039),c_Int_OBit1(U_5040)))
| ~ class_Int_Oring__char__0(U_5039)
| ~ class_Int_Onumber__ring(U_5039) ),
inference(clausify,[status(thm)],[f_1338_2]) ).
fof(f_1339_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_1339_2,plain,
! [U_5042,U_5041] :
( hBOOL(hAPP(hAPP(c_member(U_5041),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5041),U_5042)),c_Nat_Osemiring__1__class_ONats(U_5041)))
| ~ class_Rings_Osemiring__1(U_5041) ),
inference(variable_rename,[status(thm)],[f_1339_1]) ).
cnf(f_1339_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_5041),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5041),U_5042)),c_Nat_Osemiring__1__class_ONats(U_5041)))
| ~ class_Rings_Osemiring__1(U_5041) ),
inference(clausify,[status(thm)],[f_1339_2]) ).
fof(f_1340_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_1340_2,plain,
! [U_5044,U_5043] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5043)),c_Int_OBit1(U_5044)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5043),U_5044)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5043),U_5044))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5043)),c_Int_OBit1(U_5044))) ) ),
inference(variable_rename,[status(thm)],[f_1340_1]) ).
fof(f_1340_3,plain,
( ! [U_5048,U_5046] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5046)),c_Int_OBit1(U_5048)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5046),U_5048)) )
& ! [U_5047,U_5045] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5045),U_5047))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5045)),c_Int_OBit1(U_5047))) ) ),
inference(miniscope,[status(thm)],[f_1340_2]) ).
cnf(f_1340_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5045),U_5047))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5045)),c_Int_OBit1(U_5047))) ),
inference(clausify,[status(thm)],[f_1340_3]) ).
cnf(f_1340_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5046)),c_Int_OBit1(U_5048)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5046),U_5048)) ),
inference(clausify,[status(thm)],[f_1340_3]) ).
fof(f_1341_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_1341_2,plain,
! [U_5050,U_5049] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5049)),c_Int_OBit1(U_5050)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5049),U_5050)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5049),U_5050))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5049)),c_Int_OBit1(U_5050))) ) ),
inference(variable_rename,[status(thm)],[f_1341_1]) ).
fof(f_1341_3,plain,
( ! [U_5054,U_5052] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5052)),c_Int_OBit1(U_5054)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5052),U_5054)) )
& ! [U_5053,U_5051] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5051),U_5053))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5051)),c_Int_OBit1(U_5053))) ) ),
inference(miniscope,[status(thm)],[f_1341_2]) ).
cnf(f_1341_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5051),U_5053))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5051)),c_Int_OBit1(U_5053))) ),
inference(clausify,[status(thm)],[f_1341_3]) ).
cnf(f_1341_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5052)),c_Int_OBit1(U_5054)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5052),U_5054)) ),
inference(clausify,[status(thm)],[f_1341_3]) ).
fof(f_1342_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_1342_2,plain,
! [U_5056,U_5055] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5055)),c_Int_OBit1(U_5056)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5055),U_5056)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5055),U_5056))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5055)),c_Int_OBit1(U_5056))) ) ),
inference(variable_rename,[status(thm)],[f_1342_1]) ).
fof(f_1342_3,plain,
( ! [U_5060,U_5058] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5058)),c_Int_OBit1(U_5060)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5058),U_5060)) )
& ! [U_5059,U_5057] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5057),U_5059))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5057)),c_Int_OBit1(U_5059))) ) ),
inference(miniscope,[status(thm)],[f_1342_2]) ).
cnf(f_1342_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5057),U_5059))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5057)),c_Int_OBit1(U_5059))) ),
inference(clausify,[status(thm)],[f_1342_3]) ).
cnf(f_1342_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5058)),c_Int_OBit1(U_5060)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5058),U_5060)) ),
inference(clausify,[status(thm)],[f_1342_3]) ).
fof(f_1343_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_1343_2,plain,
! [U_5062,U_5061] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5061)),c_Int_OBit1(U_5062)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5061),U_5062)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5061),U_5062))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5061)),c_Int_OBit1(U_5062))) ) ),
inference(variable_rename,[status(thm)],[f_1343_1]) ).
fof(f_1343_3,plain,
( ! [U_5066,U_5064] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5064)),c_Int_OBit1(U_5066)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5064),U_5066)) )
& ! [U_5065,U_5063] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5063),U_5065))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5063)),c_Int_OBit1(U_5065))) ) ),
inference(miniscope,[status(thm)],[f_1343_2]) ).
cnf(f_1343_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5063),U_5065))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5063)),c_Int_OBit1(U_5065))) ),
inference(clausify,[status(thm)],[f_1343_3]) ).
cnf(f_1343_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5064)),c_Int_OBit1(U_5066)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5064),U_5066)) ),
inference(clausify,[status(thm)],[f_1343_3]) ).
fof(f_1344_1,plain,
! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_rel__simps_I46_J]) ).
fof(f_1344_2,plain,
! [U_5067] : c_Int_OBit1(U_5067) != c_Int_OPls,
inference(variable_rename,[status(thm)],[f_1344_1]) ).
cnf(f_1344_3,plain,
c_Int_OBit1(U_5067) != c_Int_OPls,
inference(clausify,[status(thm)],[f_1344_2]) ).
fof(f_1345_1,plain,
! [V_l] : c_Int_OPls != c_Int_OBit1(V_l),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I39_J]) ).
fof(f_1345_2,plain,
! [U_5068] : c_Int_OPls != c_Int_OBit1(U_5068),
inference(variable_rename,[status(thm)],[f_1345_1]) ).
cnf(f_1345_3,plain,
c_Int_OPls != c_Int_OBit1(U_5068),
inference(clausify,[status(thm)],[f_1345_2]) ).
fof(f_1346_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_1346_2,plain,
! [U_5069] :
( ~ c_Int_Oiszero(U_5069,hAPP(c_Int_Onumber__class_Onumber__of(U_5069),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_5069) ),
inference(variable_rename,[status(thm)],[f_1346_1]) ).
cnf(f_1346_3,plain,
( ~ c_Int_Oiszero(U_5069,hAPP(c_Int_Onumber__class_Onumber__of(U_5069),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_5069) ),
inference(clausify,[status(thm)],[f_1346_2]) ).
fof(f_1347_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_1347_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_1347_1]) ).
fof(f_1348_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_1348_2,plain,
! [U_5070] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_5070) = 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_5070)),
inference(variable_rename,[status(thm)],[f_1348_1]) ).
cnf(f_1348_3,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_5070) = 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_5070)),
inference(clausify,[status(thm)],[f_1348_2]) ).
fof(f_1349_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_1349_2,plain,
! [U_5072,U_5071] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5071),U_5072))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5071)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5072))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5071)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5072)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5071),U_5072)) ) ),
inference(variable_rename,[status(thm)],[f_1349_1]) ).
fof(f_1349_3,plain,
( ! [U_5076,U_5074] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5074),U_5076))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5074)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5076))) )
& ! [U_5075,U_5073] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5073)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5075)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5073),U_5075)) ) ),
inference(miniscope,[status(thm)],[f_1349_2]) ).
cnf(f_1349_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5073)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5075)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5073),U_5075)) ),
inference(clausify,[status(thm)],[f_1349_3]) ).
cnf(f_1349_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5074),U_5076))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5074)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5076))) ),
inference(clausify,[status(thm)],[f_1349_3]) ).
fof(f_1350_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_1350_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_1350_1]) ).
fof(f_1351_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_1351_2,plain,
! [U_5078,U_5077] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_5077),U_5078))
| ~ 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_5077)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5078))) )
& ( 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_5077)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5078)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_5077),U_5078)) ) ),
inference(variable_rename,[status(thm)],[f_1351_1]) ).
fof(f_1351_3,plain,
( ! [U_5082,U_5080] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_5080),U_5082))
| ~ 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_5080)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5082))) )
& ! [U_5081,U_5079] :
( 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_5079)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5081)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_5079),U_5081)) ) ),
inference(miniscope,[status(thm)],[f_1351_2]) ).
cnf(f_1351_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_5079)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5081)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_5079),U_5081)) ),
inference(clausify,[status(thm)],[f_1351_3]) ).
cnf(f_1351_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_5080),U_5082))
| ~ 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_5080)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5082))) ),
inference(clausify,[status(thm)],[f_1351_3]) ).
fof(f_1352_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_1352_2,plain,
! [U_5083] :
( c_Int_Oiszero(U_5083,c_Groups_Ozero__class_Ozero(U_5083))
| ~ class_Rings_Osemiring__1(U_5083) ),
inference(variable_rename,[status(thm)],[f_1352_1]) ).
cnf(f_1352_3,plain,
( c_Int_Oiszero(U_5083,c_Groups_Ozero__class_Ozero(U_5083))
| ~ class_Rings_Osemiring__1(U_5083) ),
inference(clausify,[status(thm)],[f_1352_2]) ).
fof(f_1353_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_1353_2,plain,
! [U_5085,U_5084] :
( ( ( c_Int_Oiszero(U_5084,U_5085)
| U_5085 != c_Groups_Ozero__class_Ozero(U_5084) )
& ( U_5085 = c_Groups_Ozero__class_Ozero(U_5084)
| ~ c_Int_Oiszero(U_5084,U_5085) ) )
| ~ class_Rings_Osemiring__1(U_5084) ),
inference(variable_rename,[status(thm)],[f_1353_1]) ).
cnf(f_1353_3,plain,
( U_5085 = c_Groups_Ozero__class_Ozero(U_5084)
| ~ c_Int_Oiszero(U_5084,U_5085)
| ~ class_Rings_Osemiring__1(U_5084) ),
inference(clausify,[status(thm)],[f_1353_2]) ).
cnf(f_1353_4,plain,
( c_Int_Oiszero(U_5084,U_5085)
| U_5085 != c_Groups_Ozero__class_Ozero(U_5084)
| ~ class_Rings_Osemiring__1(U_5084) ),
inference(clausify,[status(thm)],[f_1353_2]) ).
fof(f_1354_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_1354_2,plain,
! [U_5086] :
( ~ c_Int_Oiszero(U_5086,c_Groups_Oone__class_Oone(U_5086))
| ~ class_Rings_Osemiring__1(U_5086) ),
inference(variable_rename,[status(thm)],[f_1354_1]) ).
cnf(f_1354_3,plain,
( ~ c_Int_Oiszero(U_5086,c_Groups_Oone__class_Oone(U_5086))
| ~ class_Rings_Osemiring__1(U_5086) ),
inference(clausify,[status(thm)],[f_1354_2]) ).
fof(f_1355_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_1355_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_1355_1]) ).
fof(f_1356_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_1356_2,plain,
! [U_5087] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5087) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_5087 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_5087 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5087) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_1356_1]) ).
fof(f_1356_3,plain,
( ! [U_5089] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5089) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_5089 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_5088] :
( U_5088 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5088) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_1356_2]) ).
cnf(f_1356_4,plain,
( U_5088 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5088) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1356_3]) ).
cnf(f_1356_5,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5089) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_5089 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1356_3]) ).
fof(f_1357_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_1357_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_1357_1]) ).
fof(f_1358_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_1358_2,plain,
! [U_5090] : 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_5090))),
inference(variable_rename,[status(thm)],[f_1358_1]) ).
cnf(f_1358_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_5090))),
inference(clausify,[status(thm)],[f_1358_2]) ).
fof(f_1359_1,plain,
! [V_P_2] :
( ( ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
| ? [B_x] : ~ hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) )
& ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x)))
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__quantifiers_I1_J]) ).
fof(f_1359_2,plain,
! [U_5095] :
( ( ! [U_5094] :
( hBOOL(hAPP(U_5095,U_5094))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5094)) )
| ? [U_5093] : ~ hBOOL(hAPP(U_5095,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5093))) )
& ( ! [U_5092] : hBOOL(hAPP(U_5095,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5092)))
| ? [U_5091] :
( ~ hBOOL(hAPP(U_5095,U_5091))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5091)) ) ) ),
inference(variable_rename,[status(thm)],[f_1359_1]) ).
fof(f_1359_3,plain,
( ! [U_5097] :
( ! [U_5094] :
( hBOOL(hAPP(U_5097,U_5094))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5094)) )
| ? [U_5093] : ~ hBOOL(hAPP(U_5097,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5093))) )
& ! [U_5096] :
( ! [U_5092] : hBOOL(hAPP(U_5096,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5092)))
| ? [U_5091] :
( ~ hBOOL(hAPP(U_5096,U_5091))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5091)) ) ) ),
inference(miniscope,[status(thm)],[f_1359_2]) ).
fof(f_1359_4,plain,
( ! [U_5097] :
( ! [U_5094] :
( hBOOL(hAPP(U_5097,U_5094))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5094)) )
| ? [U_5093] : ~ hBOOL(hAPP(U_5097,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5093))) )
& ! [U_5096] :
( ! [U_5092] : hBOOL(hAPP(U_5096,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5092)))
| ( ~ hBOOL(hAPP(U_5096,sK126(U_5096)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK126(U_5096))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(U_5091,sK126(U_5096))],[f_1359_3]) ).
fof(f_1359_5,plain,
( ! [U_5097] :
( ! [U_5094] :
( hBOOL(hAPP(U_5097,U_5094))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5094)) )
| ~ hBOOL(hAPP(U_5097,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK127(U_5097)))) )
& ! [U_5096] :
( ! [U_5092] : hBOOL(hAPP(U_5096,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5092)))
| ( ~ hBOOL(hAPP(U_5096,sK126(U_5096)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK126(U_5096))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(U_5093,sK127(U_5097))],[f_1359_4]) ).
cnf(f_1359_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK126(U_5096)))
| hBOOL(hAPP(U_5096,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5092))) ),
inference(clausify,[status(thm)],[f_1359_5]) ).
cnf(f_1359_7,plain,
( ~ hBOOL(hAPP(U_5096,sK126(U_5096)))
| hBOOL(hAPP(U_5096,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5092))) ),
inference(clausify,[status(thm)],[f_1359_5]) ).
cnf(f_1359_8,plain,
( hBOOL(hAPP(U_5097,U_5094))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5094))
| ~ hBOOL(hAPP(U_5097,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK127(U_5097)))) ),
inference(clausify,[status(thm)],[f_1359_5]) ).
fof(f_1360_1,plain,
! [V_P_2] :
( ( ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
| ! [B_x] : ~ hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) )
& ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x)))
| ! [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__quantifiers_I2_J]) ).
fof(f_1360_2,plain,
! [U_5102] :
( ( ? [U_5101] :
( hBOOL(hAPP(U_5102,U_5101))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5101)) )
| ! [U_5100] : ~ hBOOL(hAPP(U_5102,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5100))) )
& ( ? [U_5099] : hBOOL(hAPP(U_5102,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5099)))
| ! [U_5098] :
( ~ hBOOL(hAPP(U_5102,U_5098))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5098)) ) ) ),
inference(variable_rename,[status(thm)],[f_1360_1]) ).
fof(f_1360_3,plain,
( ! [U_5104] :
( ? [U_5101] :
( hBOOL(hAPP(U_5104,U_5101))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5101)) )
| ! [U_5100] : ~ hBOOL(hAPP(U_5104,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5100))) )
& ! [U_5103] :
( ? [U_5099] : hBOOL(hAPP(U_5103,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5099)))
| ! [U_5098] :
( ~ hBOOL(hAPP(U_5103,U_5098))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5098)) ) ) ),
inference(miniscope,[status(thm)],[f_1360_2]) ).
fof(f_1360_4,plain,
( ! [U_5104] :
( ? [U_5101] :
( hBOOL(hAPP(U_5104,U_5101))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5101)) )
| ! [U_5100] : ~ hBOOL(hAPP(U_5104,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5100))) )
& ! [U_5103] :
( hBOOL(hAPP(U_5103,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK128(U_5103))))
| ! [U_5098] :
( ~ hBOOL(hAPP(U_5103,U_5098))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5098)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(U_5099,sK128(U_5103))],[f_1360_3]) ).
fof(f_1360_5,plain,
( ! [U_5104] :
( ( hBOOL(hAPP(U_5104,sK129(U_5104)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK129(U_5104))) )
| ! [U_5100] : ~ hBOOL(hAPP(U_5104,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5100))) )
& ! [U_5103] :
( hBOOL(hAPP(U_5103,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK128(U_5103))))
| ! [U_5098] :
( ~ hBOOL(hAPP(U_5103,U_5098))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5098)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(U_5101,sK129(U_5104))],[f_1360_4]) ).
cnf(f_1360_6,plain,
( hBOOL(hAPP(U_5103,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK128(U_5103))))
| ~ hBOOL(hAPP(U_5103,U_5098))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5098)) ),
inference(clausify,[status(thm)],[f_1360_5]) ).
cnf(f_1360_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK129(U_5104)))
| ~ hBOOL(hAPP(U_5104,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5100))) ),
inference(clausify,[status(thm)],[f_1360_5]) ).
cnf(f_1360_8,plain,
( hBOOL(hAPP(U_5104,sK129(U_5104)))
| ~ hBOOL(hAPP(U_5104,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5100))) ),
inference(clausify,[status(thm)],[f_1360_5]) ).
fof(f_1361_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_1361_2,plain,
! [U_5105] : 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_5105))),
inference(variable_rename,[status(thm)],[f_1361_1]) ).
cnf(f_1361_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_5105))),
inference(clausify,[status(thm)],[f_1361_2]) ).
fof(f_1362_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_1362_2,plain,
! [U_5106] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5106)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[f_1362_1]) ).
cnf(f_1362_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_5106)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_1362_2]) ).
fof(f_1363_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_1363_2,plain,
! [U_5108,U_5107] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5107)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5108)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5107),U_5108)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5107),U_5108))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5107)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5108))) ) ),
inference(variable_rename,[status(thm)],[f_1363_1]) ).
fof(f_1363_3,plain,
( ! [U_5112,U_5110] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5110),U_5112)) )
& ! [U_5111,U_5109] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5109),U_5111))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5109)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5111))) ) ),
inference(miniscope,[status(thm)],[f_1363_2]) ).
cnf(f_1363_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5109),U_5111))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5109)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5111))) ),
inference(clausify,[status(thm)],[f_1363_3]) ).
cnf(f_1363_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_5110)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5112)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5110),U_5112)) ),
inference(clausify,[status(thm)],[f_1363_3]) ).
fof(f_1364_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_1364_2,plain,
! [U_5114,U_5113] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5113)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5114)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5113),U_5114)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5113),U_5114))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5113)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5114))) ) ),
inference(variable_rename,[status(thm)],[f_1364_1]) ).
fof(f_1364_3,plain,
( ! [U_5118,U_5116] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5116),U_5118)) )
& ! [U_5117,U_5115] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5115),U_5117))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5115)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5117))) ) ),
inference(miniscope,[status(thm)],[f_1364_2]) ).
cnf(f_1364_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5115),U_5117))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5115)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5117))) ),
inference(clausify,[status(thm)],[f_1364_3]) ).
cnf(f_1364_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_5116)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5118)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5116),U_5118)) ),
inference(clausify,[status(thm)],[f_1364_3]) ).
fof(f_1365_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_1365_2,plain,
! [U_5119] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5119)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5119),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5119),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5119)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_1365_1]) ).
fof(f_1365_3,plain,
( ! [U_5121] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5121)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5121),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_5120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5120),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5120)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_1365_2]) ).
cnf(f_1365_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5120),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5120)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1365_3]) ).
cnf(f_1365_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5121)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5121),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1365_3]) ).
fof(f_1366_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_1366_2,plain,
! [U_5123,U_5122] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5122)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5123)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5122),U_5123)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5122),U_5123))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5122)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5123))) ) ),
inference(variable_rename,[status(thm)],[f_1366_1]) ).
fof(f_1366_3,plain,
( ! [U_5127,U_5125] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5125)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5127)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5125),U_5127)) )
& ! [U_5126,U_5124] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5124),U_5126))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5124)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5126))) ) ),
inference(miniscope,[status(thm)],[f_1366_2]) ).
cnf(f_1366_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5124),U_5126))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5124)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5126))) ),
inference(clausify,[status(thm)],[f_1366_3]) ).
cnf(f_1366_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_5125)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5127)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5125),U_5127)) ),
inference(clausify,[status(thm)],[f_1366_3]) ).
fof(f_1367_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_1367_2,plain,
! [U_5129,U_5128] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5128)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5129)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5128),U_5129)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5128),U_5129))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5128)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5129))) ) ),
inference(variable_rename,[status(thm)],[f_1367_1]) ).
fof(f_1367_3,plain,
( ! [U_5133,U_5131] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5131)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5133)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5131),U_5133)) )
& ! [U_5132,U_5130] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5130),U_5132))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5130)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5132))) ) ),
inference(miniscope,[status(thm)],[f_1367_2]) ).
cnf(f_1367_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5130),U_5132))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5130)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5132))) ),
inference(clausify,[status(thm)],[f_1367_3]) ).
cnf(f_1367_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_5131)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5133)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5131),U_5133)) ),
inference(clausify,[status(thm)],[f_1367_3]) ).
fof(f_1368_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_1368_2,plain,
! [U_5135,U_5134] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5134)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5135)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5134),U_5135)),
inference(variable_rename,[status(thm)],[f_1368_1]) ).
cnf(f_1368_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5134)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5135)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5134),U_5135)),
inference(clausify,[status(thm)],[f_1368_2]) ).
fof(f_1369_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_1369_2,plain,
! [U_5138,U_5137,U_5136] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5136)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5137)),U_5138)) = 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_5136),U_5137))),U_5138),
inference(variable_rename,[status(thm)],[f_1369_1]) ).
cnf(f_1369_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5136)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5137)),U_5138)) = 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_5136),U_5137))),U_5138),
inference(clausify,[status(thm)],[f_1369_2]) ).
fof(f_1370_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_1370_2,plain,
! [U_5140,U_5139] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5139)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5140)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5139),U_5140)),
inference(variable_rename,[status(thm)],[f_1370_1]) ).
cnf(f_1370_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5139)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5140)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5139),U_5140)),
inference(clausify,[status(thm)],[f_1370_2]) ).
fof(f_1371_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_1371_2,plain,
! [U_5144,U_5143] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5143),U_5144))
| ! [U_5142] : U_5144 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5143),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5142)) )
& ( ? [U_5141] : U_5144 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5143),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5141))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5143),U_5144)) ) ),
inference(variable_rename,[status(thm)],[f_1371_1]) ).
fof(f_1371_3,plain,
( ! [U_5148,U_5146] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5146),U_5148))
| ! [U_5142] : U_5148 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5146),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5142)) )
& ! [U_5147,U_5145] :
( ? [U_5141] : U_5147 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5145),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5141))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5145),U_5147)) ) ),
inference(miniscope,[status(thm)],[f_1371_2]) ).
fof(f_1371_4,plain,
( ! [U_5148,U_5146] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5146),U_5148))
| ! [U_5142] : U_5148 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5146),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5142)) )
& ! [U_5147,U_5145] :
( U_5147 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5145),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK130(U_5147,U_5145)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5145),U_5147)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(U_5141,sK130(U_5147,U_5145))],[f_1371_3]) ).
cnf(f_1371_5,plain,
( U_5147 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5145),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK130(U_5147,U_5145)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5145),U_5147)) ),
inference(clausify,[status(thm)],[f_1371_4]) ).
cnf(f_1371_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5146),U_5148))
| U_5148 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5146),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5142)) ),
inference(clausify,[status(thm)],[f_1371_4]) ).
fof(f_1372_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_1372_2,plain,
! [U_5149] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5149)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5149)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5149))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5149))) ) ),
inference(variable_rename,[status(thm)],[f_1372_1]) ).
fof(f_1372_3,plain,
( ! [U_5151] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5151)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5151)) )
& ! [U_5150] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5150))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5150))) ) ),
inference(miniscope,[status(thm)],[f_1372_2]) ).
cnf(f_1372_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5150))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5150))) ),
inference(clausify,[status(thm)],[f_1372_3]) ).
cnf(f_1372_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5151)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5151)) ),
inference(clausify,[status(thm)],[f_1372_3]) ).
fof(f_1373_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_1373_2,plain,
! [U_5152] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5152)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5152),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5152),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5152)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_1373_1]) ).
fof(f_1373_3,plain,
( ! [U_5154] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5154)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5154),c_Int_OPls)) )
& ! [U_5153] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5153),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5153)),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_1373_2]) ).
cnf(f_1373_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5153),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5153)),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1373_3]) ).
cnf(f_1373_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5154)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5154),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1373_3]) ).
fof(f_1374_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_1374_2,plain,
! [U_5156,U_5155] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5155),c_Groups_Ozero__class_Ozero(U_5155)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5155),U_5156)))
| ~ class_Rings_Olinordered__semidom(U_5155) ),
inference(variable_rename,[status(thm)],[f_1374_1]) ).
cnf(f_1374_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5155),c_Groups_Ozero__class_Ozero(U_5155)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5155),U_5156)))
| ~ class_Rings_Olinordered__semidom(U_5155) ),
inference(clausify,[status(thm)],[f_1374_2]) ).
fof(f_1375_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_1375_2,plain,
! [U_5158,U_5157] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5157),c_Groups_Ozero__class_Ozero(U_5157)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5157),U_5158)))
| ~ class_Rings_Olinordered__semidom(U_5157) ),
inference(variable_rename,[status(thm)],[f_1375_1]) ).
cnf(f_1375_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5157),c_Groups_Ozero__class_Ozero(U_5157)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5157),U_5158)))
| ~ class_Rings_Olinordered__semidom(U_5157) ),
inference(clausify,[status(thm)],[f_1375_2]) ).
fof(f_1376_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_1376_2,plain,
! [U_5160,U_5159] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5159)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5160)
| U_5160 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5159 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( U_5160 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_5159 = 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_5159)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5160) ) ),
inference(variable_rename,[status(thm)],[f_1376_1]) ).
fof(f_1376_3,plain,
( ! [U_5164,U_5162] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5162)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5164)
| U_5164 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5162 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_5163,U_5161] :
( ( U_5163 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_5161 = 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_5161)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5163) ) ),
inference(miniscope,[status(thm)],[f_1376_2]) ).
cnf(f_1376_4,plain,
( U_5161 = 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_5161)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5163) ),
inference(clausify,[status(thm)],[f_1376_3]) ).
cnf(f_1376_5,plain,
( U_5163 = 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_5161)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5163) ),
inference(clausify,[status(thm)],[f_1376_3]) ).
cnf(f_1376_6,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5162)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5164)
| U_5164 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5162 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1376_3]) ).
fof(f_1377_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_1377_2,plain,
! [U_5166,U_5165] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5165),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5165),U_5166)),c_Groups_Ozero__class_Ozero(U_5165)))
| ~ class_Rings_Olinordered__semidom(U_5165) ),
inference(variable_rename,[status(thm)],[f_1377_1]) ).
cnf(f_1377_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5165),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5165),U_5166)),c_Groups_Ozero__class_Ozero(U_5165)))
| ~ class_Rings_Olinordered__semidom(U_5165) ),
inference(clausify,[status(thm)],[f_1377_2]) ).
fof(f_1378_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_1378_2,plain,
! [U_5167] : c_Int_OBit1(U_5167) = 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_5167)),U_5167),
inference(variable_rename,[status(thm)],[f_1378_1]) ).
cnf(f_1378_3,plain,
c_Int_OBit1(U_5167) = 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_5167)),U_5167),
inference(clausify,[status(thm)],[f_1378_2]) ).
fof(f_1379_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_1379_2,plain,
! [U_5169,U_5168] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5168)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5169)))),
inference(variable_rename,[status(thm)],[f_1379_1]) ).
cnf(f_1379_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_5168)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5169)))),
inference(clausify,[status(thm)],[f_1379_2]) ).
fof(f_1380_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_1380_2,plain,
! [U_5170] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5170),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_5170)
| ~ class_Rings_Osemiring__1(U_5170) ),
inference(variable_rename,[status(thm)],[f_1380_1]) ).
cnf(f_1380_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5170),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_5170)
| ~ class_Rings_Osemiring__1(U_5170) ),
inference(clausify,[status(thm)],[f_1380_2]) ).
fof(f_1381_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_1381_2,plain,
! [U_5173,U_5172,U_5171] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5172),U_5173))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5171),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5171),U_5172)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5171),U_5173)))
| ~ class_Rings_Olinordered__semidom(U_5171) ),
inference(variable_rename,[status(thm)],[f_1381_1]) ).
cnf(f_1381_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5172),U_5173))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5171),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5171),U_5172)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5171),U_5173)))
| ~ class_Rings_Olinordered__semidom(U_5171) ),
inference(clausify,[status(thm)],[f_1381_2]) ).
fof(f_1382_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_1382_2,plain,
! [U_5176,U_5175,U_5174] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5174),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5174),U_5175)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5174),U_5176)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5175),U_5176))
| ~ class_Rings_Olinordered__semidom(U_5174) ),
inference(variable_rename,[status(thm)],[f_1382_1]) ).
cnf(f_1382_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5174),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5174),U_5175)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5174),U_5176)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5175),U_5176))
| ~ class_Rings_Olinordered__semidom(U_5174) ),
inference(clausify,[status(thm)],[f_1382_2]) ).
fof(f_1383_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_1383_2,plain,
! [U_5179,U_5178,U_5177] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5177),U_5178)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5177),U_5179)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5178),U_5179)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5178),U_5179))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5177),U_5178)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5177),U_5179))) ) )
| ~ class_Rings_Olinordered__semidom(U_5177) ),
inference(variable_rename,[status(thm)],[f_1383_1]) ).
cnf(f_1383_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5178),U_5179))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5177),U_5178)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5177),U_5179)))
| ~ class_Rings_Olinordered__semidom(U_5177) ),
inference(clausify,[status(thm)],[f_1383_2]) ).
cnf(f_1383_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5177),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5177),U_5178)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5177),U_5179)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5178),U_5179))
| ~ class_Rings_Olinordered__semidom(U_5177) ),
inference(clausify,[status(thm)],[f_1383_2]) ).
fof(f_1384_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_1384_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_1384_1]) ).
fof(f_1385_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_1385_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_1385_1]) ).
fof(f_1386_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_1386_2,plain,
! [U_5182,U_5181,U_5180] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5180),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5180),U_5181)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5180),U_5182)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5181),U_5182)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5181),U_5182))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5180),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5180),U_5181)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5180),U_5182))) ) )
| ~ class_Rings_Olinordered__semidom(U_5180) ),
inference(variable_rename,[status(thm)],[f_1386_1]) ).
cnf(f_1386_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5181),U_5182))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5180),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5180),U_5181)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5180),U_5182)))
| ~ class_Rings_Olinordered__semidom(U_5180) ),
inference(clausify,[status(thm)],[f_1386_2]) ).
cnf(f_1386_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5180),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5180),U_5181)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5180),U_5182)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5181),U_5182))
| ~ class_Rings_Olinordered__semidom(U_5180) ),
inference(clausify,[status(thm)],[f_1386_2]) ).
fof(f_1387_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_1387_2,plain,
! [U_5185,U_5184,U_5183] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5183),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5184),U_5185)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5183),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5183),U_5184)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5183),U_5185))
| ~ class_Rings_Osemiring__1(U_5183) ),
inference(variable_rename,[status(thm)],[f_1387_1]) ).
cnf(f_1387_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5183),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5184),U_5185)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5183),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5183),U_5184)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5183),U_5185))
| ~ class_Rings_Osemiring__1(U_5183) ),
inference(clausify,[status(thm)],[f_1387_2]) ).
fof(f_1388_1,plain,
! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x,
inference(fof_nnf,[status(thm)],[fact_succ__pred]) ).
fof(f_1388_2,plain,
! [U_5186] : c_Int_Osucc(c_Int_Opred(U_5186)) = U_5186,
inference(variable_rename,[status(thm)],[f_1388_1]) ).
cnf(f_1388_3,plain,
c_Int_Osucc(c_Int_Opred(U_5186)) = U_5186,
inference(clausify,[status(thm)],[f_1388_2]) ).
fof(f_1389_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_1389_2,plain,
! [U_5187] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5187),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_5187)
| ~ class_Rings_Osemiring__1(U_5187) ),
inference(variable_rename,[status(thm)],[f_1389_1]) ).
cnf(f_1389_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5187),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_5187)
| ~ class_Rings_Osemiring__1(U_5187) ),
inference(clausify,[status(thm)],[f_1389_2]) ).
fof(f_1390_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_1390_2,plain,
! [U_5188] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_5188)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5188))),
inference(variable_rename,[status(thm)],[f_1390_1]) ).
cnf(f_1390_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_5188)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5188))),
inference(clausify,[status(thm)],[f_1390_2]) ).
fof(f_1391_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_1391_2,plain,
! [U_5190,U_5189] :
( hBOOL(hAPP(hAPP(c_member(U_5189),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5189),U_5190)),c_Int_Oring__1__class_OInts(U_5189)))
| ~ class_Rings_Oring__1(U_5189) ),
inference(variable_rename,[status(thm)],[f_1391_1]) ).
cnf(f_1391_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_5189),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5189),U_5190)),c_Int_Oring__1__class_OInts(U_5189)))
| ~ class_Rings_Oring__1(U_5189) ),
inference(clausify,[status(thm)],[f_1391_2]) ).
fof(f_1392_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_1392_2,plain,
! [U_5193,U_5192,U_5191] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5191),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5192),U_5193)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5191),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5191),U_5192)),U_5193)
| ~ class_Rings_Osemiring__1(U_5191) ),
inference(variable_rename,[status(thm)],[f_1392_1]) ).
cnf(f_1392_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5191),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5192),U_5193)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5191),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5191),U_5192)),U_5193)
| ~ class_Rings_Osemiring__1(U_5191) ),
inference(clausify,[status(thm)],[f_1392_2]) ).
fof(f_1393_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_1393_2,plain,
! [U_5195,U_5194] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5194),U_5195)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5194)),U_5195),
inference(variable_rename,[status(thm)],[f_1393_1]) ).
cnf(f_1393_3,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5194),U_5195)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5194)),U_5195),
inference(clausify,[status(thm)],[f_1393_2]) ).
fof(f_1394_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_1394_2,plain,
! [U_5197,U_5196] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5196)),U_5197) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5196),U_5197)),
inference(variable_rename,[status(thm)],[f_1394_1]) ).
cnf(f_1394_3,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5196)),U_5197) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5196),U_5197)),
inference(clausify,[status(thm)],[f_1394_2]) ).
fof(f_1395_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_1395_2,plain,
! [U_5199,U_5198] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5198)),U_5199) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5198),U_5199)),
inference(variable_rename,[status(thm)],[f_1395_1]) ).
cnf(f_1395_3,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5198)),U_5199) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5198),U_5199)),
inference(clausify,[status(thm)],[f_1395_2]) ).
fof(f_1396_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_1396_2,plain,
! [U_5201,U_5200] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5200),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5201)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5200),U_5201)),
inference(variable_rename,[status(thm)],[f_1396_1]) ).
cnf(f_1396_3,plain,
c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5200),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5201)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5200),U_5201)),
inference(clausify,[status(thm)],[f_1396_2]) ).
fof(f_1397_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_1397_2,plain,
! [U_5202] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_5202))
| ~ 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_5202))) )
& ( 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_5202)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_5202)) ) ),
inference(variable_rename,[status(thm)],[f_1397_1]) ).
fof(f_1397_3,plain,
( ! [U_5204] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_5204))
| ~ 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_5204))) )
& ! [U_5203] :
( 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_5203)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_5203)) ) ),
inference(miniscope,[status(thm)],[f_1397_2]) ).
cnf(f_1397_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_5203)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_5203)) ),
inference(clausify,[status(thm)],[f_1397_3]) ).
cnf(f_1397_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_5204))
| ~ 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_5204))) ),
inference(clausify,[status(thm)],[f_1397_3]) ).
fof(f_1398_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_1398_2,plain,
! [U_5205] :
( c_Fun_Oinj__on(tc_Nat_Onat,U_5205,c_Nat_Osemiring__1__class_Oof__nat(U_5205),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| ~ class_Nat_Osemiring__char__0(U_5205) ),
inference(variable_rename,[status(thm)],[f_1398_1]) ).
cnf(f_1398_3,plain,
( c_Fun_Oinj__on(tc_Nat_Onat,U_5205,c_Nat_Osemiring__1__class_Oof__nat(U_5205),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| ~ class_Nat_Osemiring__char__0(U_5205) ),
inference(clausify,[status(thm)],[f_1398_2]) ).
fof(f_1399_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_1399_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_1399_1]) ).
fof(f_1400_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_1400_2,plain,
! [U_5207,U_5206] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_5206),c_Int_OBit1(U_5207)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5206),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5206),c_Groups_Oone__class_Oone(U_5206)),hAPP(c_Int_Onumber__class_Onumber__of(U_5206),U_5207))),hAPP(c_Int_Onumber__class_Onumber__of(U_5206),U_5207))
| ~ class_Int_Onumber__ring(U_5206) ),
inference(variable_rename,[status(thm)],[f_1400_1]) ).
cnf(f_1400_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_5206),c_Int_OBit1(U_5207)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5206),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5206),c_Groups_Oone__class_Oone(U_5206)),hAPP(c_Int_Onumber__class_Onumber__of(U_5206),U_5207))),hAPP(c_Int_Onumber__class_Onumber__of(U_5206),U_5207))
| ~ class_Int_Onumber__ring(U_5206) ),
inference(clausify,[status(thm)],[f_1400_2]) ).
fof(f_1401_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_1401_2,plain,
! [U_5208] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5208)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_5208 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_5208 = 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_5208)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_1401_1]) ).
fof(f_1401_3,plain,
( ! [U_5210] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5210)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_5210 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_5209] :
( U_5209 = 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_5209)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_1401_2]) ).
cnf(f_1401_4,plain,
( U_5209 = 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_5209)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1401_3]) ).
cnf(f_1401_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_5210)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_5210 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1401_3]) ).
fof(f_1402_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_1402_2,plain,
! [U_5211] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_5211),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_5211)
| ~ class_Int_Onumber__ring(U_5211) ),
inference(variable_rename,[status(thm)],[f_1402_1]) ).
cnf(f_1402_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_5211),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_5211)
| ~ class_Int_Onumber__ring(U_5211) ),
inference(clausify,[status(thm)],[f_1402_2]) ).
fof(f_1403_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_1403_2,plain,
! [U_5212] :
( c_Groups_Oone__class_Oone(U_5212) = hAPP(c_Int_Onumber__class_Onumber__of(U_5212),c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(U_5212) ),
inference(variable_rename,[status(thm)],[f_1403_1]) ).
cnf(f_1403_3,plain,
( c_Groups_Oone__class_Oone(U_5212) = hAPP(c_Int_Onumber__class_Onumber__of(U_5212),c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(U_5212) ),
inference(clausify,[status(thm)],[f_1403_2]) ).
fof(f_1404_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_1404_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_1404_1]) ).
fof(f_1405_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_1405_2,plain,
! [U_5216,U_5215] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5215),U_5216))
| ! [U_5214] : U_5216 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5215),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_5214))) )
& ( ? [U_5213] : U_5216 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5215),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_5213)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5215),U_5216)) ) ),
inference(variable_rename,[status(thm)],[f_1405_1]) ).
fof(f_1405_3,plain,
( ! [U_5220,U_5218] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5218),U_5220))
| ! [U_5214] : U_5220 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5218),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_5214))) )
& ! [U_5219,U_5217] :
( ? [U_5213] : U_5219 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5217),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_5213)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5217),U_5219)) ) ),
inference(miniscope,[status(thm)],[f_1405_2]) ).
fof(f_1405_4,plain,
( ! [U_5220,U_5218] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5218),U_5220))
| ! [U_5214] : U_5220 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5218),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_5214))) )
& ! [U_5219,U_5217] :
( U_5219 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5217),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK131(U_5219,U_5217))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5217),U_5219)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(U_5213,sK131(U_5219,U_5217))],[f_1405_3]) ).
cnf(f_1405_5,plain,
( U_5219 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5217),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK131(U_5219,U_5217))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5217),U_5219)) ),
inference(clausify,[status(thm)],[f_1405_4]) ).
cnf(f_1405_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5218),U_5220))
| U_5220 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5218),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_5214))) ),
inference(clausify,[status(thm)],[f_1405_4]) ).
fof(f_1406_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_1406_2,plain,
! [U_5221] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5221)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5221),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5221),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5221)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_1406_1]) ).
fof(f_1406_3,plain,
( ! [U_5223] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5223)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5223),c_Int_OPls)) )
& ! [U_5222] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5222),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5222)),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_1406_2]) ).
cnf(f_1406_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5222),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5222)),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1406_3]) ).
cnf(f_1406_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5223)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5223),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1406_3]) ).
fof(f_1407_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_1407_2,plain,
! [U_5224] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5224)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5224)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5224))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5224))) ) ),
inference(variable_rename,[status(thm)],[f_1407_1]) ).
fof(f_1407_3,plain,
( ! [U_5226] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5226)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5226)) )
& ! [U_5225] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5225))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5225))) ) ),
inference(miniscope,[status(thm)],[f_1407_2]) ).
cnf(f_1407_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5225))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5225))) ),
inference(clausify,[status(thm)],[f_1407_3]) ).
cnf(f_1407_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5226)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5226)) ),
inference(clausify,[status(thm)],[f_1407_3]) ).
fof(f_1408_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_1408_2,plain,
! [U_5228,U_5227] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5227)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5228))))
| U_5228 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5227 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( U_5228 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_5227 = 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_5227)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5228)))) ) ),
inference(variable_rename,[status(thm)],[f_1408_1]) ).
fof(f_1408_3,plain,
( ! [U_5232,U_5230] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5230)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5232))))
| U_5232 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5230 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_5231,U_5229] :
( ( U_5231 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_5229 = 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_5229)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5231)))) ) ),
inference(miniscope,[status(thm)],[f_1408_2]) ).
cnf(f_1408_4,plain,
( U_5229 = 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_5229)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5231)))) ),
inference(clausify,[status(thm)],[f_1408_3]) ).
cnf(f_1408_5,plain,
( U_5231 = 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_5229)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5231)))) ),
inference(clausify,[status(thm)],[f_1408_3]) ).
cnf(f_1408_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_5230)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5232))))
| U_5232 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5230 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1408_3]) ).
fof(f_1409_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_1409_2,plain,
! [U_5233] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_5233)) = 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_5233)),
inference(variable_rename,[status(thm)],[f_1409_1]) ).
cnf(f_1409_3,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_5233)) = 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_5233)),
inference(clausify,[status(thm)],[f_1409_2]) ).
fof(f_1410_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_1410_2,plain,
! [U_5234] : 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_5234))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[f_1410_1]) ).
cnf(f_1410_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_5234))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_1410_2]) ).
fof(f_1411_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_1411_2,plain,
! [U_5236,U_5235] :
( ( ( c_Groups_Oone__class_Oone(U_5235) = hAPP(c_Int_Onumber__class_Onumber__of(U_5235),U_5236)
| ~ c_Int_Oiszero(U_5235,hAPP(c_Int_Onumber__class_Onumber__of(U_5235),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_5236)))) )
& ( c_Int_Oiszero(U_5235,hAPP(c_Int_Onumber__class_Onumber__of(U_5235),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_5236))))
| c_Groups_Oone__class_Oone(U_5235) != hAPP(c_Int_Onumber__class_Onumber__of(U_5235),U_5236) ) )
| ~ class_Int_Onumber__ring(U_5235) ),
inference(variable_rename,[status(thm)],[f_1411_1]) ).
cnf(f_1411_3,plain,
( c_Int_Oiszero(U_5235,hAPP(c_Int_Onumber__class_Onumber__of(U_5235),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_5236))))
| c_Groups_Oone__class_Oone(U_5235) != hAPP(c_Int_Onumber__class_Onumber__of(U_5235),U_5236)
| ~ class_Int_Onumber__ring(U_5235) ),
inference(clausify,[status(thm)],[f_1411_2]) ).
cnf(f_1411_4,plain,
( c_Groups_Oone__class_Oone(U_5235) = hAPP(c_Int_Onumber__class_Onumber__of(U_5235),U_5236)
| ~ c_Int_Oiszero(U_5235,hAPP(c_Int_Onumber__class_Onumber__of(U_5235),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_5236))))
| ~ class_Int_Onumber__ring(U_5235) ),
inference(clausify,[status(thm)],[f_1411_2]) ).
fof(f_1412_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_1412_2,plain,
! [U_5238,U_5237] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_5237),U_5238) = c_Groups_Oone__class_Oone(U_5237)
| ~ c_Int_Oiszero(U_5237,hAPP(c_Int_Onumber__class_Onumber__of(U_5237),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5238),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) )
& ( c_Int_Oiszero(U_5237,hAPP(c_Int_Onumber__class_Onumber__of(U_5237),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5238),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_5237),U_5238) != c_Groups_Oone__class_Oone(U_5237) ) )
| ~ class_Int_Onumber__ring(U_5237) ),
inference(variable_rename,[status(thm)],[f_1412_1]) ).
cnf(f_1412_3,plain,
( c_Int_Oiszero(U_5237,hAPP(c_Int_Onumber__class_Onumber__of(U_5237),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5238),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_5237),U_5238) != c_Groups_Oone__class_Oone(U_5237)
| ~ class_Int_Onumber__ring(U_5237) ),
inference(clausify,[status(thm)],[f_1412_2]) ).
cnf(f_1412_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_5237),U_5238) = c_Groups_Oone__class_Oone(U_5237)
| ~ c_Int_Oiszero(U_5237,hAPP(c_Int_Onumber__class_Onumber__of(U_5237),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5238),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
| ~ class_Int_Onumber__ring(U_5237) ),
inference(clausify,[status(thm)],[f_1412_2]) ).
fof(f_1413_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_1413_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_1413_1]) ).
fof(f_1414_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_1414_2,plain,
! [U_5240,U_5239] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5240)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5239)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5240),U_5239))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5239),U_5240)) ),
inference(variable_rename,[status(thm)],[f_1414_1]) ).
cnf(f_1414_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5240)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5239)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5240),U_5239))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5239),U_5240)) ),
inference(clausify,[status(thm)],[f_1414_2]) ).
fof(f_1415_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_1415_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_1415_1]) ).
fof(f_1416_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_1416_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_1416_1]) ).
fof(f_1417_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_1417_2,plain,
! [U_5242,U_5241] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5241),hAPP(c_Nat_OSuc,U_5242)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5241),c_Groups_Oone__class_Oone(U_5241)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5241),U_5242))
| ~ class_Rings_Osemiring__1(U_5241) ),
inference(variable_rename,[status(thm)],[f_1417_1]) ).
cnf(f_1417_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5241),hAPP(c_Nat_OSuc,U_5242)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5241),c_Groups_Oone__class_Oone(U_5241)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5241),U_5242))
| ~ class_Rings_Osemiring__1(U_5241) ),
inference(clausify,[status(thm)],[f_1417_2]) ).
fof(f_1418_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_1418_2,plain,
! [U_5245,U_5244,U_5243] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5243),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5245),U_5244)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5243),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5243),U_5245)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5243),U_5244))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5244),U_5245))
| ~ class_Rings_Oring__1(U_5243) ),
inference(variable_rename,[status(thm)],[f_1418_1]) ).
cnf(f_1418_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5243),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5245),U_5244)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5243),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5243),U_5245)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5243),U_5244))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5244),U_5245))
| ~ class_Rings_Oring__1(U_5243) ),
inference(clausify,[status(thm)],[f_1418_2]) ).
fof(f_1419_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_1419_2,plain,
! [U_5246] : c_Int_Osucc(U_5246) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5246),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(variable_rename,[status(thm)],[f_1419_1]) ).
cnf(f_1419_3,plain,
c_Int_Osucc(U_5246) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5246),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_1419_2]) ).
fof(f_1420_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_1420_2,plain,
! [U_5247] :
( c_Int_Oiszero(U_5247,hAPP(c_Int_Onumber__class_Onumber__of(U_5247),c_Int_OPls))
| ~ class_Int_Onumber__ring(U_5247) ),
inference(variable_rename,[status(thm)],[f_1420_1]) ).
cnf(f_1420_3,plain,
( c_Int_Oiszero(U_5247,hAPP(c_Int_Onumber__class_Onumber__of(U_5247),c_Int_OPls))
| ~ class_Int_Onumber__ring(U_5247) ),
inference(clausify,[status(thm)],[f_1420_2]) ).
fof(f_1421_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_1421_2,plain,
! [U_5248] :
( hBOOL(hAPP(hAPP(c_member(U_5248),c_Groups_Ozero__class_Ozero(U_5248)),c_Nat_Osemiring__1__class_ONats(U_5248)))
| ~ class_Rings_Osemiring__1(U_5248) ),
inference(variable_rename,[status(thm)],[f_1421_1]) ).
cnf(f_1421_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_5248),c_Groups_Ozero__class_Ozero(U_5248)),c_Nat_Osemiring__1__class_ONats(U_5248)))
| ~ class_Rings_Osemiring__1(U_5248) ),
inference(clausify,[status(thm)],[f_1421_2]) ).
fof(f_1422_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_1422_2,plain,
! [U_5251,U_5250,U_5249] :
( hBOOL(hAPP(hAPP(c_member(U_5249),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5249),U_5250),U_5251)),c_Nat_Osemiring__1__class_ONats(U_5249)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5249),U_5251),c_Nat_Osemiring__1__class_ONats(U_5249)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5249),U_5250),c_Nat_Osemiring__1__class_ONats(U_5249)))
| ~ class_Rings_Osemiring__1(U_5249) ),
inference(variable_rename,[status(thm)],[f_1422_1]) ).
cnf(f_1422_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_5249),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5249),U_5250),U_5251)),c_Nat_Osemiring__1__class_ONats(U_5249)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5249),U_5251),c_Nat_Osemiring__1__class_ONats(U_5249)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5249),U_5250),c_Nat_Osemiring__1__class_ONats(U_5249)))
| ~ class_Rings_Osemiring__1(U_5249) ),
inference(clausify,[status(thm)],[f_1422_2]) ).
fof(f_1423_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_1423_2,plain,
! [U_5252] :
( hBOOL(hAPP(hAPP(c_member(U_5252),c_Groups_Oone__class_Oone(U_5252)),c_Nat_Osemiring__1__class_ONats(U_5252)))
| ~ class_Rings_Osemiring__1(U_5252) ),
inference(variable_rename,[status(thm)],[f_1423_1]) ).
cnf(f_1423_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_5252),c_Groups_Oone__class_Oone(U_5252)),c_Nat_Osemiring__1__class_ONats(U_5252)))
| ~ class_Rings_Osemiring__1(U_5252) ),
inference(clausify,[status(thm)],[f_1423_2]) ).
fof(f_1424_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_1424_2,plain,
! [U_5253] :
( ( 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_5253)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5253)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5253))
| ~ 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_5253))) ) ),
inference(variable_rename,[status(thm)],[f_1424_1]) ).
fof(f_1424_3,plain,
( ! [U_5255] :
( 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_5255)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5255)) )
& ! [U_5254] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5254))
| ~ 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_5254))) ) ),
inference(miniscope,[status(thm)],[f_1424_2]) ).
cnf(f_1424_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5254))
| ~ 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_5254))) ),
inference(clausify,[status(thm)],[f_1424_3]) ).
cnf(f_1424_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_5255)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5255)) ),
inference(clausify,[status(thm)],[f_1424_3]) ).
fof(f_1425_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_1425_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_1425_1]) ).
fof(f_1426_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_1426_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_1426_1]) ).
fof(f_1427_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_1427_2,plain,
! [U_5256] : ~ 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_5256))))),
inference(variable_rename,[status(thm)],[f_1427_1]) ).
cnf(f_1427_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_5256))))),
inference(clausify,[status(thm)],[f_1427_2]) ).
fof(f_1428_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_1428_2,plain,
! [U_5257] : 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_5257)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[f_1428_1]) ).
cnf(f_1428_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_5257)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_1428_2]) ).
fof(f_1429_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_1429_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_1429_1]) ).
fof(f_1430_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_1430_2,plain,
! [U_5258] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5258))) = 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_5258),
inference(variable_rename,[status(thm)],[f_1430_1]) ).
cnf(f_1430_3,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5258))) = 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_5258),
inference(clausify,[status(thm)],[f_1430_2]) ).
fof(f_1431_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_1431_2,plain,
! [U_5260,U_5259] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),c_Groups_Ozero__class_Ozero(U_5259)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5259),U_5260)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5260)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5260))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),c_Groups_Ozero__class_Ozero(U_5259)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5259),U_5260))) ) )
| ~ class_Rings_Olinordered__semidom(U_5259) ),
inference(variable_rename,[status(thm)],[f_1431_1]) ).
cnf(f_1431_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5260))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),c_Groups_Ozero__class_Ozero(U_5259)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5259),U_5260)))
| ~ class_Rings_Olinordered__semidom(U_5259) ),
inference(clausify,[status(thm)],[f_1431_2]) ).
cnf(f_1431_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5259),c_Groups_Ozero__class_Ozero(U_5259)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5259),U_5260)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5260))
| ~ class_Rings_Olinordered__semidom(U_5259) ),
inference(clausify,[status(thm)],[f_1431_2]) ).
fof(f_1432_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_1432_2,plain,
! [U_5262,U_5261] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5261),c_Groups_Oone__class_Oone(U_5261)),hAPP(c_Int_Onumber__class_Onumber__of(U_5261),U_5262)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5262)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5262))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5261),c_Groups_Oone__class_Oone(U_5261)),hAPP(c_Int_Onumber__class_Onumber__of(U_5261),U_5262))) ) )
| ~ class_Rings_Olinordered__idom(U_5261)
| ~ class_Int_Onumber__ring(U_5261) ),
inference(variable_rename,[status(thm)],[f_1432_1]) ).
cnf(f_1432_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5262))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5261),c_Groups_Oone__class_Oone(U_5261)),hAPP(c_Int_Onumber__class_Onumber__of(U_5261),U_5262)))
| ~ class_Rings_Olinordered__idom(U_5261)
| ~ class_Int_Onumber__ring(U_5261) ),
inference(clausify,[status(thm)],[f_1432_2]) ).
cnf(f_1432_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5261),c_Groups_Oone__class_Oone(U_5261)),hAPP(c_Int_Onumber__class_Onumber__of(U_5261),U_5262)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5262))
| ~ class_Rings_Olinordered__idom(U_5261)
| ~ class_Int_Onumber__ring(U_5261) ),
inference(clausify,[status(thm)],[f_1432_2]) ).
fof(f_1433_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_1433_2,plain,
! [U_5264,U_5263] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),hAPP(c_Int_Onumber__class_Onumber__of(U_5263),U_5264)),c_Groups_Oone__class_Oone(U_5263)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5264),c_Int_OBit1(c_Int_OPls))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5264),c_Int_OBit1(c_Int_OPls)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),hAPP(c_Int_Onumber__class_Onumber__of(U_5263),U_5264)),c_Groups_Oone__class_Oone(U_5263))) ) )
| ~ class_Rings_Olinordered__idom(U_5263)
| ~ class_Int_Onumber__ring(U_5263) ),
inference(variable_rename,[status(thm)],[f_1433_1]) ).
cnf(f_1433_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5264),c_Int_OBit1(c_Int_OPls)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),hAPP(c_Int_Onumber__class_Onumber__of(U_5263),U_5264)),c_Groups_Oone__class_Oone(U_5263)))
| ~ class_Rings_Olinordered__idom(U_5263)
| ~ class_Int_Onumber__ring(U_5263) ),
inference(clausify,[status(thm)],[f_1433_2]) ).
cnf(f_1433_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),hAPP(c_Int_Onumber__class_Onumber__of(U_5263),U_5264)),c_Groups_Oone__class_Oone(U_5263)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5264),c_Int_OBit1(c_Int_OPls)))
| ~ class_Rings_Olinordered__idom(U_5263)
| ~ class_Int_Onumber__ring(U_5263) ),
inference(clausify,[status(thm)],[f_1433_2]) ).
fof(f_1434_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_1434_2,plain,
! [U_5266,U_5265] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5265),hAPP(c_Int_Onumber__class_Onumber__of(U_5265),U_5266)),c_Groups_Oone__class_Oone(U_5265)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5266),c_Int_OBit1(c_Int_OPls))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5266),c_Int_OBit1(c_Int_OPls)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5265),hAPP(c_Int_Onumber__class_Onumber__of(U_5265),U_5266)),c_Groups_Oone__class_Oone(U_5265))) ) )
| ~ class_Rings_Olinordered__idom(U_5265)
| ~ class_Int_Onumber__ring(U_5265) ),
inference(variable_rename,[status(thm)],[f_1434_1]) ).
cnf(f_1434_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5266),c_Int_OBit1(c_Int_OPls)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5265),hAPP(c_Int_Onumber__class_Onumber__of(U_5265),U_5266)),c_Groups_Oone__class_Oone(U_5265)))
| ~ class_Rings_Olinordered__idom(U_5265)
| ~ class_Int_Onumber__ring(U_5265) ),
inference(clausify,[status(thm)],[f_1434_2]) ).
cnf(f_1434_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5265),hAPP(c_Int_Onumber__class_Onumber__of(U_5265),U_5266)),c_Groups_Oone__class_Oone(U_5265)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5266),c_Int_OBit1(c_Int_OPls)))
| ~ class_Rings_Olinordered__idom(U_5265)
| ~ class_Int_Onumber__ring(U_5265) ),
inference(clausify,[status(thm)],[f_1434_2]) ).
fof(f_1435_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_1435_2,plain,
! [U_5268,U_5267] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5267),c_Groups_Oone__class_Oone(U_5267)),hAPP(c_Int_Onumber__class_Onumber__of(U_5267),U_5268)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5268)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5268))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5267),c_Groups_Oone__class_Oone(U_5267)),hAPP(c_Int_Onumber__class_Onumber__of(U_5267),U_5268))) ) )
| ~ class_Rings_Olinordered__idom(U_5267)
| ~ class_Int_Onumber__ring(U_5267) ),
inference(variable_rename,[status(thm)],[f_1435_1]) ).
cnf(f_1435_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5268))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5267),c_Groups_Oone__class_Oone(U_5267)),hAPP(c_Int_Onumber__class_Onumber__of(U_5267),U_5268)))
| ~ class_Rings_Olinordered__idom(U_5267)
| ~ class_Int_Onumber__ring(U_5267) ),
inference(clausify,[status(thm)],[f_1435_2]) ).
cnf(f_1435_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5267),c_Groups_Oone__class_Oone(U_5267)),hAPP(c_Int_Onumber__class_Onumber__of(U_5267),U_5268)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5268))
| ~ class_Rings_Olinordered__idom(U_5267)
| ~ class_Int_Onumber__ring(U_5267) ),
inference(clausify,[status(thm)],[f_1435_2]) ).
fof(f_1436_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_1436_2,plain,
! [U_5270,U_5269] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_5269),c_Int_Osucc(U_5270)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5269),c_Groups_Oone__class_Oone(U_5269)),hAPP(c_Int_Onumber__class_Onumber__of(U_5269),U_5270))
| ~ class_Int_Onumber__ring(U_5269) ),
inference(variable_rename,[status(thm)],[f_1436_1]) ).
cnf(f_1436_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_5269),c_Int_Osucc(U_5270)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5269),c_Groups_Oone__class_Oone(U_5269)),hAPP(c_Int_Onumber__class_Onumber__of(U_5269),U_5270))
| ~ class_Int_Onumber__ring(U_5269) ),
inference(clausify,[status(thm)],[f_1436_2]) ).
fof(f_1437_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_1437_2,plain,
! [U_5272,U_5271] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5271),hAPP(c_Int_Onumber__class_Onumber__of(U_5271),U_5272)),c_Groups_Oone__class_Oone(U_5271)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5271),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5272),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_5271) ),
inference(variable_rename,[status(thm)],[f_1437_1]) ).
cnf(f_1437_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5271),hAPP(c_Int_Onumber__class_Onumber__of(U_5271),U_5272)),c_Groups_Oone__class_Oone(U_5271)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5271),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5272),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_5271) ),
inference(clausify,[status(thm)],[f_1437_2]) ).
fof(f_1438_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_1438_2,plain,
! [U_5274,U_5273] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5273),c_Groups_Oone__class_Oone(U_5273)),hAPP(c_Int_Onumber__class_Onumber__of(U_5273),U_5274)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5273),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5274))
| ~ class_Int_Onumber__ring(U_5273) ),
inference(variable_rename,[status(thm)],[f_1438_1]) ).
cnf(f_1438_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5273),c_Groups_Oone__class_Oone(U_5273)),hAPP(c_Int_Onumber__class_Onumber__of(U_5273),U_5274)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5273),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5274))
| ~ class_Int_Onumber__ring(U_5273) ),
inference(clausify,[status(thm)],[f_1438_2]) ).
fof(f_1439_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_1439_2,plain,
! [U_5276,U_5275] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5276)),U_5275) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5276),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5275),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_5275)) ),
inference(variable_rename,[status(thm)],[f_1439_1]) ).
cnf(f_1439_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5276)),U_5275) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5276),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5275),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_5275)) ),
inference(clausify,[status(thm)],[f_1439_2]) ).
fof(f_1440_1,plain,
! [V_y_2,V_x_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2))))
| ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) )
| ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) ) )
& ( ( ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) ) )
| ~ hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2)))) ) ),
inference(fof_nnf,[status(thm)],[fact_zdiff__int__split]) ).
fof(f_1440_2,plain,
! [U_5279,U_5278,U_5277] :
( ( hBOOL(hAPP(U_5277,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5278),U_5279))))
| ( ~ hBOOL(hAPP(U_5277,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5278),U_5279)) )
| ( ~ hBOOL(hAPP(U_5277,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5278)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5279))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5279),U_5278)) ) )
& ( ( ( hBOOL(hAPP(U_5277,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5278),U_5279)) )
& ( hBOOL(hAPP(U_5277,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5278)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5279))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5279),U_5278)) ) )
| ~ hBOOL(hAPP(U_5277,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5278),U_5279)))) ) ),
inference(variable_rename,[status(thm)],[f_1440_1]) ).
fof(f_1440_3,plain,
( ! [U_5285,U_5283,U_5281] :
( hBOOL(hAPP(U_5281,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5283),U_5285))))
| ( ~ hBOOL(hAPP(U_5281,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5283),U_5285)) )
| ( ~ hBOOL(hAPP(U_5281,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5283)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5285))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5285),U_5283)) ) )
& ! [U_5284,U_5282,U_5280] :
( ( ( hBOOL(hAPP(U_5280,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5282),U_5284)) )
& ( hBOOL(hAPP(U_5280,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5282)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5284))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5284),U_5282)) ) )
| ~ hBOOL(hAPP(U_5280,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5282),U_5284)))) ) ),
inference(miniscope,[status(thm)],[f_1440_2]) ).
cnf(f_1440_4,plain,
( hBOOL(hAPP(U_5280,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5282)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5284))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5284),U_5282))
| ~ hBOOL(hAPP(U_5280,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5282),U_5284)))) ),
inference(clausify,[status(thm)],[f_1440_3]) ).
cnf(f_1440_5,plain,
( hBOOL(hAPP(U_5280,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5282),U_5284))
| ~ hBOOL(hAPP(U_5280,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5282),U_5284)))) ),
inference(clausify,[status(thm)],[f_1440_3]) ).
cnf(f_1440_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5283),U_5285))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5285),U_5283))
| hBOOL(hAPP(U_5281,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5283),U_5285)))) ),
inference(clausify,[status(thm)],[f_1440_3]) ).
cnf(f_1440_7,plain,
( ~ hBOOL(hAPP(U_5281,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5285),U_5283))
| hBOOL(hAPP(U_5281,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5283),U_5285)))) ),
inference(clausify,[status(thm)],[f_1440_3]) ).
cnf(f_1440_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5283),U_5285))
| ~ hBOOL(hAPP(U_5281,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5283)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5285))))
| hBOOL(hAPP(U_5281,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5283),U_5285)))) ),
inference(clausify,[status(thm)],[f_1440_3]) ).
cnf(f_1440_9,plain,
( ~ hBOOL(hAPP(U_5281,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_5281,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5283)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5285))))
| hBOOL(hAPP(U_5281,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5283),U_5285)))) ),
inference(clausify,[status(thm)],[f_1440_3]) ).
fof(f_1441_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_1441_2,plain,
! [U_5288,U_5287,U_5286] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_5286),U_5287) = hAPP(c_Int_Onumber__class_Onumber__of(U_5286),U_5288)
| ~ c_Int_Oiszero(U_5286,hAPP(c_Int_Onumber__class_Onumber__of(U_5286),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5287),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5288)))) )
& ( c_Int_Oiszero(U_5286,hAPP(c_Int_Onumber__class_Onumber__of(U_5286),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5287),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5288))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_5286),U_5287) != hAPP(c_Int_Onumber__class_Onumber__of(U_5286),U_5288) ) )
| ~ class_Int_Onumber__ring(U_5286) ),
inference(variable_rename,[status(thm)],[f_1441_1]) ).
cnf(f_1441_3,plain,
( c_Int_Oiszero(U_5286,hAPP(c_Int_Onumber__class_Onumber__of(U_5286),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5287),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5288))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_5286),U_5287) != hAPP(c_Int_Onumber__class_Onumber__of(U_5286),U_5288)
| ~ class_Int_Onumber__ring(U_5286) ),
inference(clausify,[status(thm)],[f_1441_2]) ).
cnf(f_1441_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_5286),U_5287) = hAPP(c_Int_Onumber__class_Onumber__of(U_5286),U_5288)
| ~ c_Int_Oiszero(U_5286,hAPP(c_Int_Onumber__class_Onumber__of(U_5286),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5287),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5288))))
| ~ class_Int_Onumber__ring(U_5286) ),
inference(clausify,[status(thm)],[f_1441_2]) ).
fof(f_1442_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_1442_2,plain,
! [U_5290,U_5289] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5289),c_Groups_Oone__class_Oone(U_5289)),hAPP(c_Int_Onumber__class_Onumber__of(U_5289),U_5290)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5289),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_5290)))
| ~ class_Int_Onumber__ring(U_5289) ),
inference(variable_rename,[status(thm)],[f_1442_1]) ).
cnf(f_1442_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5289),c_Groups_Oone__class_Oone(U_5289)),hAPP(c_Int_Onumber__class_Onumber__of(U_5289),U_5290)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5289),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_5290)))
| ~ class_Int_Onumber__ring(U_5289) ),
inference(clausify,[status(thm)],[f_1442_2]) ).
fof(f_1443_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_1443_2,plain,
! [U_5292,U_5291] :
( ( 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_5291)),U_5292)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_5291))),U_5292)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5291))) )
& ( 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_5291)),U_5292)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_5292)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5291))) ) ),
inference(variable_rename,[status(thm)],[f_1443_1]) ).
fof(f_1443_3,plain,
( ! [U_5296,U_5294] :
( 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_5294)),U_5296)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_5294))),U_5296)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5294))) )
& ! [U_5295,U_5293] :
( 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_5293)),U_5295)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_5295)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5293))) ) ),
inference(miniscope,[status(thm)],[f_1443_2]) ).
cnf(f_1443_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_5293)),U_5295)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_5295)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5293))) ),
inference(clausify,[status(thm)],[f_1443_3]) ).
cnf(f_1443_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_5294)),U_5296)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_5294))),U_5296)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5294))) ),
inference(clausify,[status(thm)],[f_1443_3]) ).
fof(f_1444_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_1444_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_1444_1]) ).
fof(f_1445_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_1445_2,plain,
! [U_5299,U_5298,U_5297] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5297),c_Groups_Ozero__class_Ozero(U_5297)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5297),hAPP(hAPP(c_Power_Opower__class_Opower(U_5297),U_5298),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_5297),U_5299),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ( U_5299 = c_Groups_Ozero__class_Ozero(U_5297)
& U_5298 = c_Groups_Ozero__class_Ozero(U_5297) ) )
& ( U_5299 != c_Groups_Ozero__class_Ozero(U_5297)
| U_5298 != c_Groups_Ozero__class_Ozero(U_5297)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5297),c_Groups_Ozero__class_Ozero(U_5297)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5297),hAPP(hAPP(c_Power_Opower__class_Opower(U_5297),U_5298),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_5297),U_5299),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ) )
| ~ class_Rings_Olinordered__idom(U_5297) ),
inference(variable_rename,[status(thm)],[f_1445_1]) ).
cnf(f_1445_3,plain,
( U_5299 != c_Groups_Ozero__class_Ozero(U_5297)
| U_5298 != c_Groups_Ozero__class_Ozero(U_5297)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5297),c_Groups_Ozero__class_Ozero(U_5297)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5297),hAPP(hAPP(c_Power_Opower__class_Opower(U_5297),U_5298),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_5297),U_5299),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ class_Rings_Olinordered__idom(U_5297) ),
inference(clausify,[status(thm)],[f_1445_2]) ).
cnf(f_1445_4,plain,
( U_5298 = c_Groups_Ozero__class_Ozero(U_5297)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5297),c_Groups_Ozero__class_Ozero(U_5297)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5297),hAPP(hAPP(c_Power_Opower__class_Opower(U_5297),U_5298),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_5297),U_5299),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ class_Rings_Olinordered__idom(U_5297) ),
inference(clausify,[status(thm)],[f_1445_2]) ).
cnf(f_1445_5,plain,
( U_5299 = c_Groups_Ozero__class_Ozero(U_5297)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5297),c_Groups_Ozero__class_Ozero(U_5297)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5297),hAPP(hAPP(c_Power_Opower__class_Opower(U_5297),U_5298),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_5297),U_5299),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ class_Rings_Olinordered__idom(U_5297) ),
inference(clausify,[status(thm)],[f_1445_2]) ).
fof(f_1446_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_1446_2,plain,
! [U_5302,U_5301,U_5300] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5300),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5300),hAPP(hAPP(c_Power_Opower__class_Opower(U_5300),U_5301),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_5300),U_5302),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_5300)))
| ~ class_Rings_Olinordered__idom(U_5300) ),
inference(variable_rename,[status(thm)],[f_1446_1]) ).
cnf(f_1446_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5300),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5300),hAPP(hAPP(c_Power_Opower__class_Opower(U_5300),U_5301),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_5300),U_5302),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_5300)))
| ~ class_Rings_Olinordered__idom(U_5300) ),
inference(clausify,[status(thm)],[f_1446_2]) ).
fof(f_1447_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_1447_2,plain,
! [U_5305,U_5304,U_5303] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5303),c_Groups_Ozero__class_Ozero(U_5303)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5303),hAPP(hAPP(c_Power_Opower__class_Opower(U_5303),U_5304),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_5303),U_5305),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ class_Rings_Olinordered__idom(U_5303) ),
inference(variable_rename,[status(thm)],[f_1447_1]) ).
cnf(f_1447_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5303),c_Groups_Ozero__class_Ozero(U_5303)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5303),hAPP(hAPP(c_Power_Opower__class_Opower(U_5303),U_5304),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_5303),U_5305),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ class_Rings_Olinordered__idom(U_5303) ),
inference(clausify,[status(thm)],[f_1447_2]) ).
fof(f_1448_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_1448_2,plain,
! [U_5308,U_5307,U_5306] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5306),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5306),hAPP(hAPP(c_Power_Opower__class_Opower(U_5306),U_5307),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_5306),U_5308),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_5306)))
| U_5308 != c_Groups_Ozero__class_Ozero(U_5306)
| U_5307 != c_Groups_Ozero__class_Ozero(U_5306) )
& ( ( U_5308 = c_Groups_Ozero__class_Ozero(U_5306)
& U_5307 = c_Groups_Ozero__class_Ozero(U_5306) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5306),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5306),hAPP(hAPP(c_Power_Opower__class_Opower(U_5306),U_5307),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_5306),U_5308),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_5306))) ) )
| ~ class_Rings_Olinordered__idom(U_5306) ),
inference(variable_rename,[status(thm)],[f_1448_1]) ).
cnf(f_1448_3,plain,
( U_5307 = c_Groups_Ozero__class_Ozero(U_5306)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5306),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5306),hAPP(hAPP(c_Power_Opower__class_Opower(U_5306),U_5307),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_5306),U_5308),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_5306)))
| ~ class_Rings_Olinordered__idom(U_5306) ),
inference(clausify,[status(thm)],[f_1448_2]) ).
cnf(f_1448_4,plain,
( U_5308 = c_Groups_Ozero__class_Ozero(U_5306)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5306),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5306),hAPP(hAPP(c_Power_Opower__class_Opower(U_5306),U_5307),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_5306),U_5308),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_5306)))
| ~ class_Rings_Olinordered__idom(U_5306) ),
inference(clausify,[status(thm)],[f_1448_2]) ).
cnf(f_1448_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5306),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5306),hAPP(hAPP(c_Power_Opower__class_Opower(U_5306),U_5307),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_5306),U_5308),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_5306)))
| U_5308 != c_Groups_Ozero__class_Ozero(U_5306)
| U_5307 != c_Groups_Ozero__class_Ozero(U_5306)
| ~ class_Rings_Olinordered__idom(U_5306) ),
inference(clausify,[status(thm)],[f_1448_2]) ).
fof(f_1449_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_1449_2,plain,
! [U_5310,U_5309] :
( ( U_5309 = U_5310
| hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5309) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5310) )
& ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5309) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5310)
| U_5309 != U_5310 ) ),
inference(variable_rename,[status(thm)],[f_1449_1]) ).
fof(f_1449_3,plain,
( ! [U_5314,U_5312] :
( U_5312 = U_5314
| hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5312) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5314) )
& ! [U_5313,U_5311] :
( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5311) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5313)
| U_5311 != U_5313 ) ),
inference(miniscope,[status(thm)],[f_1449_2]) ).
cnf(f_1449_4,plain,
( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5311) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5313)
| U_5311 != U_5313 ),
inference(clausify,[status(thm)],[f_1449_3]) ).
cnf(f_1449_5,plain,
( U_5312 = U_5314
| hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5312) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5314) ),
inference(clausify,[status(thm)],[f_1449_3]) ).
fof(f_1450_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_1450_2,plain,
! [U_5316,U_5315] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5315) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5316)
| U_5315 != U_5316 )
& ( U_5315 = U_5316
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5315) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5316) ) ),
inference(variable_rename,[status(thm)],[f_1450_1]) ).
fof(f_1450_3,plain,
( ! [U_5320,U_5318] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5318) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5320)
| U_5318 != U_5320 )
& ! [U_5319,U_5317] :
( U_5317 = U_5319
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5317) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5319) ) ),
inference(miniscope,[status(thm)],[f_1450_2]) ).
cnf(f_1450_4,plain,
( U_5317 = U_5319
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5317) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5319) ),
inference(clausify,[status(thm)],[f_1450_3]) ).
cnf(f_1450_5,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5318) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5320)
| U_5318 != U_5320 ),
inference(clausify,[status(thm)],[f_1450_3]) ).
fof(f_1451_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_1451_2,plain,
! [U_5322,U_5321] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_5321),U_5322))
| ~ 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_5321)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5322))) )
& ( 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_5321)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5322)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_5321),U_5322)) ) ),
inference(variable_rename,[status(thm)],[f_1451_1]) ).
fof(f_1451_3,plain,
( ! [U_5326,U_5324] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_5324),U_5326))
| ~ 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_5324)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5326))) )
& ! [U_5325,U_5323] :
( 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_5323)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5325)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_5323),U_5325)) ) ),
inference(miniscope,[status(thm)],[f_1451_2]) ).
cnf(f_1451_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_5323)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5325)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_5323),U_5325)) ),
inference(clausify,[status(thm)],[f_1451_3]) ).
cnf(f_1451_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_5324),U_5326))
| ~ 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_5324)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_5326))) ),
inference(clausify,[status(thm)],[f_1451_3]) ).
fof(f_1452_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_1452_2,plain,
! [U_5328,U_5327] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5327) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5328)
| U_5327 != U_5328 )
& ( U_5327 = U_5328
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5327) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5328) ) ),
inference(variable_rename,[status(thm)],[f_1452_1]) ).
fof(f_1452_3,plain,
( ! [U_5332,U_5330] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5330) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5332)
| U_5330 != U_5332 )
& ! [U_5331,U_5329] :
( U_5329 = U_5331
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5329) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5331) ) ),
inference(miniscope,[status(thm)],[f_1452_2]) ).
cnf(f_1452_4,plain,
( U_5329 = U_5331
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5329) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5331) ),
inference(clausify,[status(thm)],[f_1452_3]) ).
cnf(f_1452_5,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5330) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5332)
| U_5330 != U_5332 ),
inference(clausify,[status(thm)],[f_1452_3]) ).
fof(f_1453_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_1453_2,plain,
! [U_5333] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5333))),
inference(variable_rename,[status(thm)],[f_1453_1]) ).
cnf(f_1453_3,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5333))),
inference(clausify,[status(thm)],[f_1453_2]) ).
fof(f_1454_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_1454_2,plain,
! [U_5334] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5334))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5334))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5334)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5334)))) ) ),
inference(variable_rename,[status(thm)],[f_1454_1]) ).
fof(f_1454_3,plain,
( ! [U_5336] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5336))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5336))) )
& ! [U_5335] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5335)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5335)))) ) ),
inference(miniscope,[status(thm)],[f_1454_2]) ).
cnf(f_1454_4,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5335)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5335)))) ),
inference(clausify,[status(thm)],[f_1454_3]) ).
cnf(f_1454_5,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5336))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5336))) ),
inference(clausify,[status(thm)],[f_1454_3]) ).
fof(f_1455_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_1455_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_1455_1]) ).
fof(f_1456_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_1456_2,plain,
! [U_5338,U_5337] :
( ( c_Int_OBit0(U_5337) = c_Int_OBit0(U_5338)
| U_5337 != U_5338 )
& ( U_5337 = U_5338
| c_Int_OBit0(U_5337) != c_Int_OBit0(U_5338) ) ),
inference(variable_rename,[status(thm)],[f_1456_1]) ).
fof(f_1456_3,plain,
( ! [U_5342,U_5340] :
( c_Int_OBit0(U_5340) = c_Int_OBit0(U_5342)
| U_5340 != U_5342 )
& ! [U_5341,U_5339] :
( U_5339 = U_5341
| c_Int_OBit0(U_5339) != c_Int_OBit0(U_5341) ) ),
inference(miniscope,[status(thm)],[f_1456_2]) ).
cnf(f_1456_4,plain,
( U_5339 = U_5341
| c_Int_OBit0(U_5339) != c_Int_OBit0(U_5341) ),
inference(clausify,[status(thm)],[f_1456_3]) ).
cnf(f_1456_5,plain,
( c_Int_OBit0(U_5340) = c_Int_OBit0(U_5342)
| U_5340 != U_5342 ),
inference(clausify,[status(thm)],[f_1456_3]) ).
fof(f_1457_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_1457_2,plain,
! [U_5344,U_5343] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5343)),c_Int_OBit0(U_5344)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5343),U_5344)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5343),U_5344))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5343)),c_Int_OBit0(U_5344))) ) ),
inference(variable_rename,[status(thm)],[f_1457_1]) ).
fof(f_1457_3,plain,
( ! [U_5348,U_5346] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5346)),c_Int_OBit0(U_5348)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5346),U_5348)) )
& ! [U_5347,U_5345] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5345),U_5347))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5345)),c_Int_OBit0(U_5347))) ) ),
inference(miniscope,[status(thm)],[f_1457_2]) ).
cnf(f_1457_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5345),U_5347))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5345)),c_Int_OBit0(U_5347))) ),
inference(clausify,[status(thm)],[f_1457_3]) ).
cnf(f_1457_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5346)),c_Int_OBit0(U_5348)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5346),U_5348)) ),
inference(clausify,[status(thm)],[f_1457_3]) ).
fof(f_1458_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_1458_2,plain,
! [U_5350,U_5349] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5349)),c_Int_OBit0(U_5350)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5349),U_5350)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5349),U_5350))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5349)),c_Int_OBit0(U_5350))) ) ),
inference(variable_rename,[status(thm)],[f_1458_1]) ).
fof(f_1458_3,plain,
( ! [U_5354,U_5352] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5352)),c_Int_OBit0(U_5354)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5352),U_5354)) )
& ! [U_5353,U_5351] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5351),U_5353))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5351)),c_Int_OBit0(U_5353))) ) ),
inference(miniscope,[status(thm)],[f_1458_2]) ).
cnf(f_1458_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5351),U_5353))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5351)),c_Int_OBit0(U_5353))) ),
inference(clausify,[status(thm)],[f_1458_3]) ).
cnf(f_1458_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5352)),c_Int_OBit0(U_5354)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5352),U_5354)) ),
inference(clausify,[status(thm)],[f_1458_3]) ).
fof(f_1459_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_1459_2,plain,
! [U_5356,U_5355] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5355)),c_Int_OBit0(U_5356)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5355),U_5356)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5355),U_5356))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5355)),c_Int_OBit0(U_5356))) ) ),
inference(variable_rename,[status(thm)],[f_1459_1]) ).
fof(f_1459_3,plain,
( ! [U_5360,U_5358] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5358)),c_Int_OBit0(U_5360)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5358),U_5360)) )
& ! [U_5359,U_5357] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5357),U_5359))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5357)),c_Int_OBit0(U_5359))) ) ),
inference(miniscope,[status(thm)],[f_1459_2]) ).
cnf(f_1459_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5357),U_5359))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5357)),c_Int_OBit0(U_5359))) ),
inference(clausify,[status(thm)],[f_1459_3]) ).
cnf(f_1459_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5358)),c_Int_OBit0(U_5360)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5358),U_5360)) ),
inference(clausify,[status(thm)],[f_1459_3]) ).
fof(f_1460_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_1460_2,plain,
! [U_5362,U_5361] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5361)),c_Int_OBit0(U_5362)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5361),U_5362)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5361),U_5362))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5361)),c_Int_OBit0(U_5362))) ) ),
inference(variable_rename,[status(thm)],[f_1460_1]) ).
fof(f_1460_3,plain,
( ! [U_5366,U_5364] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5364)),c_Int_OBit0(U_5366)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5364),U_5366)) )
& ! [U_5365,U_5363] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5363),U_5365))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5363)),c_Int_OBit0(U_5365))) ) ),
inference(miniscope,[status(thm)],[f_1460_2]) ).
cnf(f_1460_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5363),U_5365))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5363)),c_Int_OBit0(U_5365))) ),
inference(clausify,[status(thm)],[f_1460_3]) ).
cnf(f_1460_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5364)),c_Int_OBit0(U_5366)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5364),U_5366)) ),
inference(clausify,[status(thm)],[f_1460_3]) ).
fof(f_1461_1,plain,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_Bit0__Pls]) ).
cnf(f_1461_2,plain,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
inference(clausify,[status(thm)],[f_1461_1]) ).
fof(f_1462_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_1462_2,plain,
! [U_5367] :
( ( c_Int_OPls = c_Int_OBit0(U_5367)
| c_Int_OPls != U_5367 )
& ( c_Int_OPls = U_5367
| c_Int_OPls != c_Int_OBit0(U_5367) ) ),
inference(variable_rename,[status(thm)],[f_1462_1]) ).
fof(f_1462_3,plain,
( ! [U_5369] :
( c_Int_OPls = c_Int_OBit0(U_5369)
| c_Int_OPls != U_5369 )
& ! [U_5368] :
( c_Int_OPls = U_5368
| c_Int_OPls != c_Int_OBit0(U_5368) ) ),
inference(miniscope,[status(thm)],[f_1462_2]) ).
cnf(f_1462_4,plain,
( c_Int_OPls = U_5368
| c_Int_OPls != c_Int_OBit0(U_5368) ),
inference(clausify,[status(thm)],[f_1462_3]) ).
cnf(f_1462_5,plain,
( c_Int_OPls = c_Int_OBit0(U_5369)
| c_Int_OPls != U_5369 ),
inference(clausify,[status(thm)],[f_1462_3]) ).
fof(f_1463_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_1463_2,plain,
! [U_5370] :
( ( c_Int_OBit0(U_5370) = c_Int_OPls
| U_5370 != c_Int_OPls )
& ( U_5370 = c_Int_OPls
| c_Int_OBit0(U_5370) != c_Int_OPls ) ),
inference(variable_rename,[status(thm)],[f_1463_1]) ).
fof(f_1463_3,plain,
( ! [U_5372] :
( c_Int_OBit0(U_5372) = c_Int_OPls
| U_5372 != c_Int_OPls )
& ! [U_5371] :
( U_5371 = c_Int_OPls
| c_Int_OBit0(U_5371) != c_Int_OPls ) ),
inference(miniscope,[status(thm)],[f_1463_2]) ).
cnf(f_1463_4,plain,
( U_5371 = c_Int_OPls
| c_Int_OBit0(U_5371) != c_Int_OPls ),
inference(clausify,[status(thm)],[f_1463_3]) ).
cnf(f_1463_5,plain,
( c_Int_OBit0(U_5372) = c_Int_OPls
| U_5372 != c_Int_OPls ),
inference(clausify,[status(thm)],[f_1463_3]) ).
fof(f_1464_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_1464_2,plain,
! [U_5374,U_5373] : c_Int_OBit0(U_5373) != c_Int_OBit1(U_5374),
inference(variable_rename,[status(thm)],[f_1464_1]) ).
cnf(f_1464_3,plain,
c_Int_OBit0(U_5373) != c_Int_OBit1(U_5374),
inference(clausify,[status(thm)],[f_1464_2]) ).
fof(f_1465_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_1465_2,plain,
! [U_5376,U_5375] : c_Int_OBit1(U_5375) != c_Int_OBit0(U_5376),
inference(variable_rename,[status(thm)],[f_1465_1]) ).
cnf(f_1465_3,plain,
c_Int_OBit1(U_5375) != c_Int_OBit0(U_5376),
inference(clausify,[status(thm)],[f_1465_2]) ).
fof(f_1466_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_1466_2,plain,
! [U_5377] : c_Int_OBit0(U_5377) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5377),U_5377),
inference(variable_rename,[status(thm)],[f_1466_1]) ).
cnf(f_1466_3,plain,
c_Int_OBit0(U_5377) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5377),U_5377),
inference(clausify,[status(thm)],[f_1466_2]) ).
fof(f_1467_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_1467_2,plain,
! [U_5379,U_5378] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_5378)),c_Int_OBit0(U_5379)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5378),U_5379)),
inference(variable_rename,[status(thm)],[f_1467_1]) ).
cnf(f_1467_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_5378)),c_Int_OBit0(U_5379)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5378),U_5379)),
inference(clausify,[status(thm)],[f_1467_2]) ).
fof(f_1468_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_1468_2,plain,
! [U_5381,U_5380] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_5380)),c_Int_OBit0(U_5381)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5380),U_5381)),
inference(variable_rename,[status(thm)],[f_1468_1]) ).
cnf(f_1468_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_5380)),c_Int_OBit0(U_5381)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5380),U_5381)),
inference(clausify,[status(thm)],[f_1468_2]) ).
fof(f_1469_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_1469_2,plain,
! [U_5382] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_5382)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5382)),
inference(variable_rename,[status(thm)],[f_1469_1]) ).
cnf(f_1469_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_5382)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5382)),
inference(clausify,[status(thm)],[f_1469_2]) ).
fof(f_1470_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_1470_2,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_1470_1]) ).
fof(f_1471_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_1471_2,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_1471_1]) ).
fof(f_1472_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_1472_2,plain,
! [U_5383] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5383)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5383),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5383),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5383)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_1472_1]) ).
fof(f_1472_3,plain,
( ! [U_5385] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5385)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5385),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_5384] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5384),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5384)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_1472_2]) ).
cnf(f_1472_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5384),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5384)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
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_OBit0(U_5385)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5385),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
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_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_1473_2,plain,
! [U_5386] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5386)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5386),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5386),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5386)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_1473_1]) ).
fof(f_1473_3,plain,
( ! [U_5388] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5388)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5388),c_Int_OPls)) )
& ! [U_5387] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5387),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5387)),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_1473_2]) ).
cnf(f_1473_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5387),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5387)),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_OBit0(U_5388)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5388),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1473_3]) ).
fof(f_1474_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_1474_2,plain,
! [U_5389] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5389)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5389)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5389))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5389))) ) ),
inference(variable_rename,[status(thm)],[f_1474_1]) ).
fof(f_1474_3,plain,
( ! [U_5391] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5391)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5391)) )
& ! [U_5390] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5390))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5390))) ) ),
inference(miniscope,[status(thm)],[f_1474_2]) ).
cnf(f_1474_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5390))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5390))) ),
inference(clausify,[status(thm)],[f_1474_3]) ).
cnf(f_1474_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5391)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5391)) ),
inference(clausify,[status(thm)],[f_1474_3]) ).
fof(f_1475_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_1475_2,plain,
! [U_5393,U_5392] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5392)),c_Int_OBit1(U_5393)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5392),U_5393)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5392),U_5393))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5392)),c_Int_OBit1(U_5393))) ) ),
inference(variable_rename,[status(thm)],[f_1475_1]) ).
fof(f_1475_3,plain,
( ! [U_5397,U_5395] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5395)),c_Int_OBit1(U_5397)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5395),U_5397)) )
& ! [U_5396,U_5394] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5394),U_5396))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5394)),c_Int_OBit1(U_5396))) ) ),
inference(miniscope,[status(thm)],[f_1475_2]) ).
cnf(f_1475_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5394),U_5396))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5394)),c_Int_OBit1(U_5396))) ),
inference(clausify,[status(thm)],[f_1475_3]) ).
cnf(f_1475_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5395)),c_Int_OBit1(U_5397)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5395),U_5397)) ),
inference(clausify,[status(thm)],[f_1475_3]) ).
fof(f_1476_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_1476_2,plain,
! [U_5399,U_5398] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5398)),c_Int_OBit1(U_5399)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5398),U_5399)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5398),U_5399))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5398)),c_Int_OBit1(U_5399))) ) ),
inference(variable_rename,[status(thm)],[f_1476_1]) ).
fof(f_1476_3,plain,
( ! [U_5403,U_5401] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5401)),c_Int_OBit1(U_5403)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5401),U_5403)) )
& ! [U_5402,U_5400] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5400),U_5402))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5400)),c_Int_OBit1(U_5402))) ) ),
inference(miniscope,[status(thm)],[f_1476_2]) ).
cnf(f_1476_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5400),U_5402))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5400)),c_Int_OBit1(U_5402))) ),
inference(clausify,[status(thm)],[f_1476_3]) ).
cnf(f_1476_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5401)),c_Int_OBit1(U_5403)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5401),U_5403)) ),
inference(clausify,[status(thm)],[f_1476_3]) ).
fof(f_1477_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_1477_2,plain,
! [U_5404] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5404)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5404),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5404),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5404)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_1477_1]) ).
fof(f_1477_3,plain,
( ! [U_5406] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5406)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5406),c_Int_OPls)) )
& ! [U_5405] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5405),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5405)),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_1477_2]) ).
cnf(f_1477_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5405),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5405)),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1477_3]) ).
cnf(f_1477_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5406)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5406),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1477_3]) ).
fof(f_1478_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_1478_2,plain,
! [U_5407] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5407)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5407)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5407))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5407))) ) ),
inference(variable_rename,[status(thm)],[f_1478_1]) ).
fof(f_1478_3,plain,
( ! [U_5409] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5409)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5409)) )
& ! [U_5408] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5408))) ) ),
inference(miniscope,[status(thm)],[f_1478_2]) ).
cnf(f_1478_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5408))) ),
inference(clausify,[status(thm)],[f_1478_3]) ).
cnf(f_1478_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5409)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5409)) ),
inference(clausify,[status(thm)],[f_1478_3]) ).
fof(f_1479_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_1479_2,plain,
! [U_5411,U_5410] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5410)),c_Int_OBit0(U_5411)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5410),U_5411)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5410),U_5411))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5410)),c_Int_OBit0(U_5411))) ) ),
inference(variable_rename,[status(thm)],[f_1479_1]) ).
fof(f_1479_3,plain,
( ! [U_5415,U_5413] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5413)),c_Int_OBit0(U_5415)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5413),U_5415)) )
& ! [U_5414,U_5412] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5412),U_5414))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5412)),c_Int_OBit0(U_5414))) ) ),
inference(miniscope,[status(thm)],[f_1479_2]) ).
cnf(f_1479_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5412),U_5414))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5412)),c_Int_OBit0(U_5414))) ),
inference(clausify,[status(thm)],[f_1479_3]) ).
cnf(f_1479_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5413)),c_Int_OBit0(U_5415)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5413),U_5415)) ),
inference(clausify,[status(thm)],[f_1479_3]) ).
fof(f_1480_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_1480_2,plain,
! [U_5417,U_5416] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5416)),c_Int_OBit0(U_5417)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5416),U_5417)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5416),U_5417))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5416)),c_Int_OBit0(U_5417))) ) ),
inference(variable_rename,[status(thm)],[f_1480_1]) ).
fof(f_1480_3,plain,
( ! [U_5421,U_5419] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5419)),c_Int_OBit0(U_5421)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5419),U_5421)) )
& ! [U_5420,U_5418] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5418),U_5420))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5418)),c_Int_OBit0(U_5420))) ) ),
inference(miniscope,[status(thm)],[f_1480_2]) ).
cnf(f_1480_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5418),U_5420))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5418)),c_Int_OBit0(U_5420))) ),
inference(clausify,[status(thm)],[f_1480_3]) ).
cnf(f_1480_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5419)),c_Int_OBit0(U_5421)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5419),U_5421)) ),
inference(clausify,[status(thm)],[f_1480_3]) ).
fof(f_1481_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_1481_2,plain,
! [U_5423,U_5422] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_5422)),c_Int_OBit0(U_5423)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5422),U_5423)),
inference(variable_rename,[status(thm)],[f_1481_1]) ).
cnf(f_1481_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_5422)),c_Int_OBit0(U_5423)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5422),U_5423)),
inference(clausify,[status(thm)],[f_1481_2]) ).
fof(f_1482_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_1482_2,plain,
! [U_5425,U_5424] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_5424)),c_Int_OBit1(U_5425)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5424),U_5425)),
inference(variable_rename,[status(thm)],[f_1482_1]) ).
cnf(f_1482_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_5424)),c_Int_OBit1(U_5425)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5424),U_5425)),
inference(clausify,[status(thm)],[f_1482_2]) ).
fof(f_1483_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_1483_2,plain,
! [U_5426] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5426)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_5426)),
inference(variable_rename,[status(thm)],[f_1483_1]) ).
cnf(f_1483_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5426)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_5426)),
inference(clausify,[status(thm)],[f_1483_2]) ).
fof(f_1484_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_1484_2,plain,
! [U_5428,U_5427] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_5427)),c_Int_OBit0(U_5428)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5427),U_5428)),
inference(variable_rename,[status(thm)],[f_1484_1]) ).
cnf(f_1484_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_5427)),c_Int_OBit0(U_5428)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5427),U_5428)),
inference(clausify,[status(thm)],[f_1484_2]) ).
fof(f_1485_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_1485_2,plain,
! [U_5430,U_5429] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_5429)),c_Int_OBit1(U_5430)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5429),U_5430)),
inference(variable_rename,[status(thm)],[f_1485_1]) ).
cnf(f_1485_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_5429)),c_Int_OBit1(U_5430)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5429),U_5430)),
inference(clausify,[status(thm)],[f_1485_2]) ).
fof(f_1486_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_1486_2,plain,
! [U_5431] : c_Int_Opred(c_Int_OBit0(U_5431)) = c_Int_OBit1(c_Int_Opred(U_5431)),
inference(variable_rename,[status(thm)],[f_1486_1]) ).
cnf(f_1486_3,plain,
c_Int_Opred(c_Int_OBit0(U_5431)) = c_Int_OBit1(c_Int_Opred(U_5431)),
inference(clausify,[status(thm)],[f_1486_2]) ).
fof(f_1487_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_1487_2,plain,
! [U_5432] : c_Int_Opred(c_Int_OBit1(U_5432)) = c_Int_OBit0(U_5432),
inference(variable_rename,[status(thm)],[f_1487_1]) ).
cnf(f_1487_3,plain,
c_Int_Opred(c_Int_OBit1(U_5432)) = c_Int_OBit0(U_5432),
inference(clausify,[status(thm)],[f_1487_2]) ).
fof(f_1488_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_1488_2,plain,
! [U_5434,U_5433] :
( ( ( c_Int_Oiszero(U_5433,hAPP(c_Int_Onumber__class_Onumber__of(U_5433),c_Int_OBit0(U_5434)))
| ~ c_Int_Oiszero(U_5433,hAPP(c_Int_Onumber__class_Onumber__of(U_5433),U_5434)) )
& ( c_Int_Oiszero(U_5433,hAPP(c_Int_Onumber__class_Onumber__of(U_5433),U_5434))
| ~ c_Int_Oiszero(U_5433,hAPP(c_Int_Onumber__class_Onumber__of(U_5433),c_Int_OBit0(U_5434))) ) )
| ~ class_Int_Oring__char__0(U_5433)
| ~ class_Int_Onumber__ring(U_5433) ),
inference(variable_rename,[status(thm)],[f_1488_1]) ).
cnf(f_1488_3,plain,
( c_Int_Oiszero(U_5433,hAPP(c_Int_Onumber__class_Onumber__of(U_5433),U_5434))
| ~ c_Int_Oiszero(U_5433,hAPP(c_Int_Onumber__class_Onumber__of(U_5433),c_Int_OBit0(U_5434)))
| ~ class_Int_Oring__char__0(U_5433)
| ~ class_Int_Onumber__ring(U_5433) ),
inference(clausify,[status(thm)],[f_1488_2]) ).
cnf(f_1488_4,plain,
( c_Int_Oiszero(U_5433,hAPP(c_Int_Onumber__class_Onumber__of(U_5433),c_Int_OBit0(U_5434)))
| ~ c_Int_Oiszero(U_5433,hAPP(c_Int_Onumber__class_Onumber__of(U_5433),U_5434))
| ~ class_Int_Oring__char__0(U_5433)
| ~ class_Int_Onumber__ring(U_5433) ),
inference(clausify,[status(thm)],[f_1488_2]) ).
fof(f_1489_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_1489_2,plain,
! [U_5435] : c_Int_Osucc(c_Int_OBit0(U_5435)) = c_Int_OBit1(U_5435),
inference(variable_rename,[status(thm)],[f_1489_1]) ).
cnf(f_1489_3,plain,
c_Int_Osucc(c_Int_OBit0(U_5435)) = c_Int_OBit1(U_5435),
inference(clausify,[status(thm)],[f_1489_2]) ).
fof(f_1490_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_1490_2,plain,
! [U_5436] : c_Int_Osucc(c_Int_OBit1(U_5436)) = c_Int_OBit0(c_Int_Osucc(U_5436)),
inference(variable_rename,[status(thm)],[f_1490_1]) ).
cnf(f_1490_3,plain,
c_Int_Osucc(c_Int_OBit1(U_5436)) = c_Int_OBit0(c_Int_Osucc(U_5436)),
inference(clausify,[status(thm)],[f_1490_2]) ).
fof(f_1491_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_1491_2,plain,
! [U_5437] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5437))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5437)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5437))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5437)) ) ),
inference(variable_rename,[status(thm)],[f_1491_1]) ).
fof(f_1491_3,plain,
( ! [U_5439] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5439))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5439)) )
& ! [U_5438] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5438))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5438)) ) ),
inference(miniscope,[status(thm)],[f_1491_2]) ).
cnf(f_1491_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5438))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5438)) ),
inference(clausify,[status(thm)],[f_1491_3]) ).
cnf(f_1491_5,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5439))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5439)) ),
inference(clausify,[status(thm)],[f_1491_3]) ).
fof(f_1492_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_1492_2,plain,
! [U_5440] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5440))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5440),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5440),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5440)) ) ),
inference(variable_rename,[status(thm)],[f_1492_1]) ).
fof(f_1492_3,plain,
( ! [U_5442] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5442))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5442),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_5441] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5441),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5441)) ) ),
inference(miniscope,[status(thm)],[f_1492_2]) ).
cnf(f_1492_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5441),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5441)) ),
inference(clausify,[status(thm)],[f_1492_3]) ).
cnf(f_1492_5,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5442))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5442),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1492_3]) ).
fof(f_1493_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_1493_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_1493_1]) ).
fof(f_1494_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_1494_2,plain,
! [U_5443] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5443))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5443))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5443)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5443)))) ) ),
inference(variable_rename,[status(thm)],[f_1494_1]) ).
fof(f_1494_3,plain,
( ! [U_5445] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5445))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5445))) )
& ! [U_5444] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5444)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5444)))) ) ),
inference(miniscope,[status(thm)],[f_1494_2]) ).
cnf(f_1494_4,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5444)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5444)))) ),
inference(clausify,[status(thm)],[f_1494_3]) ).
cnf(f_1494_5,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5445))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5445))) ),
inference(clausify,[status(thm)],[f_1494_3]) ).
fof(f_1495_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_1495_2,plain,
! [U_5446] : 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_5446))))),
inference(variable_rename,[status(thm)],[f_1495_1]) ).
cnf(f_1495_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_5446))))),
inference(clausify,[status(thm)],[f_1495_2]) ).
fof(f_1496_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_1496_2,plain,
! [U_5448,U_5447] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_5447),c_Int_OBit0(U_5448)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5447),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5447),c_Groups_Ozero__class_Ozero(U_5447)),hAPP(c_Int_Onumber__class_Onumber__of(U_5447),U_5448))),hAPP(c_Int_Onumber__class_Onumber__of(U_5447),U_5448))
| ~ class_Int_Onumber__ring(U_5447) ),
inference(variable_rename,[status(thm)],[f_1496_1]) ).
cnf(f_1496_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_5447),c_Int_OBit0(U_5448)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5447),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5447),c_Groups_Ozero__class_Ozero(U_5447)),hAPP(c_Int_Onumber__class_Onumber__of(U_5447),U_5448))),hAPP(c_Int_Onumber__class_Onumber__of(U_5447),U_5448))
| ~ class_Int_Onumber__ring(U_5447) ),
inference(clausify,[status(thm)],[f_1496_2]) ).
fof(f_1497_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_1497_2,plain,
! [U_5450,U_5449] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5449)),c_Int_OBit1(U_5450)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5449),U_5450)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5449),U_5450))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5449)),c_Int_OBit1(U_5450))) ) ),
inference(variable_rename,[status(thm)],[f_1497_1]) ).
fof(f_1497_3,plain,
( ! [U_5454,U_5452] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5452)),c_Int_OBit1(U_5454)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5452),U_5454)) )
& ! [U_5453,U_5451] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5451),U_5453))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5451)),c_Int_OBit1(U_5453))) ) ),
inference(miniscope,[status(thm)],[f_1497_2]) ).
cnf(f_1497_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5451),U_5453))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5451)),c_Int_OBit1(U_5453))) ),
inference(clausify,[status(thm)],[f_1497_3]) ).
cnf(f_1497_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5452)),c_Int_OBit1(U_5454)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5452),U_5454)) ),
inference(clausify,[status(thm)],[f_1497_3]) ).
fof(f_1498_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_1498_2,plain,
! [U_5456,U_5455] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5455)),c_Int_OBit1(U_5456)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5455),U_5456)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5455),U_5456))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5455)),c_Int_OBit1(U_5456))) ) ),
inference(variable_rename,[status(thm)],[f_1498_1]) ).
fof(f_1498_3,plain,
( ! [U_5460,U_5458] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5458)),c_Int_OBit1(U_5460)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5458),U_5460)) )
& ! [U_5459,U_5457] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5457),U_5459))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5457)),c_Int_OBit1(U_5459))) ) ),
inference(miniscope,[status(thm)],[f_1498_2]) ).
cnf(f_1498_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5457),U_5459))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5457)),c_Int_OBit1(U_5459))) ),
inference(clausify,[status(thm)],[f_1498_3]) ).
cnf(f_1498_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5458)),c_Int_OBit1(U_5460)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5458),U_5460)) ),
inference(clausify,[status(thm)],[f_1498_3]) ).
fof(f_1499_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_1499_2,plain,
! [U_5462,U_5461] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5461)),c_Int_OBit0(U_5462)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5461),U_5462)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5461),U_5462))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5461)),c_Int_OBit0(U_5462))) ) ),
inference(variable_rename,[status(thm)],[f_1499_1]) ).
fof(f_1499_3,plain,
( ! [U_5466,U_5464] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5464)),c_Int_OBit0(U_5466)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5464),U_5466)) )
& ! [U_5465,U_5463] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5463),U_5465))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5463)),c_Int_OBit0(U_5465))) ) ),
inference(miniscope,[status(thm)],[f_1499_2]) ).
cnf(f_1499_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5463),U_5465))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5463)),c_Int_OBit0(U_5465))) ),
inference(clausify,[status(thm)],[f_1499_3]) ).
cnf(f_1499_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5464)),c_Int_OBit0(U_5466)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5464),U_5466)) ),
inference(clausify,[status(thm)],[f_1499_3]) ).
fof(f_1500_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_1500_2,plain,
! [U_5468,U_5467] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5467)),c_Int_OBit0(U_5468)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5467),U_5468)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5467),U_5468))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5467)),c_Int_OBit0(U_5468))) ) ),
inference(variable_rename,[status(thm)],[f_1500_1]) ).
fof(f_1500_3,plain,
( ! [U_5472,U_5470] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5470)),c_Int_OBit0(U_5472)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5470),U_5472)) )
& ! [U_5471,U_5469] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5469),U_5471))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5469)),c_Int_OBit0(U_5471))) ) ),
inference(miniscope,[status(thm)],[f_1500_2]) ).
cnf(f_1500_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5469),U_5471))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5469)),c_Int_OBit0(U_5471))) ),
inference(clausify,[status(thm)],[f_1500_3]) ).
cnf(f_1500_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5470)),c_Int_OBit0(U_5472)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5470),U_5472)) ),
inference(clausify,[status(thm)],[f_1500_3]) ).
fof(f_1501_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_1501_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_1501_1]) ).
fof(f_1502_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_1502_2,plain,
! [U_5474,U_5473] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_5473)),c_Int_OBit1(U_5474)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_5473)),U_5474)),
inference(variable_rename,[status(thm)],[f_1502_1]) ).
cnf(f_1502_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_5473)),c_Int_OBit1(U_5474)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_5473)),U_5474)),
inference(clausify,[status(thm)],[f_1502_2]) ).
fof(f_1503_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_1503_2,plain,
! [U_5476,U_5475] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_5475)),c_Int_OBit1(U_5476)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5475),c_Int_Osucc(U_5476))),
inference(variable_rename,[status(thm)],[f_1503_1]) ).
cnf(f_1503_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_5475)),c_Int_OBit1(U_5476)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5475),c_Int_Osucc(U_5476))),
inference(clausify,[status(thm)],[f_1503_2]) ).
fof(f_1504_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_1504_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_1504_1]) ).
fof(f_1505_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_1505_2,plain,
! [U_5477] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5477) = 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_5477))) ),
inference(variable_rename,[status(thm)],[f_1505_1]) ).
cnf(f_1505_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5477) = 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_5477))) ),
inference(clausify,[status(thm)],[f_1505_2]) ).
fof(f_1506_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_1506_2,plain,
! [U_5478] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5478)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5478)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5478))) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5478)) = 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_5478))) ) ),
inference(variable_rename,[status(thm)],[f_1506_1]) ).
fof(f_1506_3,plain,
( ! [U_5480] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5480)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5480)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5480))) )
& ! [U_5479] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5479)) = 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_5479))) ) ),
inference(miniscope,[status(thm)],[f_1506_2]) ).
cnf(f_1506_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5479)) = 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_5479))) ),
inference(clausify,[status(thm)],[f_1506_3]) ).
cnf(f_1506_5,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5480)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5480)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5480))) ),
inference(clausify,[status(thm)],[f_1506_3]) ).
fof(f_1507_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_1507_2,plain,
! [U_5481] :
( ( 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_5481))))
& 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_5481)))) )
| ~ 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_5481))) ),
inference(variable_rename,[status(thm)],[f_1507_1]) ).
cnf(f_1507_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_5481))))
| ~ 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_5481))) ),
inference(clausify,[status(thm)],[f_1507_2]) ).
cnf(f_1507_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_5481))))
| ~ 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_5481))) ),
inference(clausify,[status(thm)],[f_1507_2]) ).
fof(f_1508_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_1508_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_1508_1]) ).
fof(f_1509_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_1509_2,plain,
! [U_5483,U_5482] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5482) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5483)
| ( ( ( U_5482 != U_5483
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5483))) )
| ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5482) != 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_5483))) ) )
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5482))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5483)),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_5482))) ) )
& ( ( ( ( ( U_5482 = U_5483
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5483))) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5482) = 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_5483))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5482))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5483)),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_5482))) ) )
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5482) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5483) ) ),
inference(variable_rename,[status(thm)],[f_1509_1]) ).
fof(f_1509_3,plain,
( ! [U_5487,U_5485] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5485) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5487)
| ( ( ( U_5485 != U_5487
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5487))) )
| ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5485) != 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_5487))) ) )
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5485))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5487)),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_5485))) ) )
& ! [U_5486,U_5484] :
( ( ( ( ( U_5484 = U_5486
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5486))) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5484) = 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_5486))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5484))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5486)),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_5484))) ) )
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5484) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5486) ) ),
inference(miniscope,[status(thm)],[f_1509_2]) ).
cnf(f_1509_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_5486)),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_5484)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5484) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5486) ),
inference(clausify,[status(thm)],[f_1509_3]) ).
cnf(f_1509_5,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5484) = 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_5486)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5484)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5484) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5486) ),
inference(clausify,[status(thm)],[f_1509_3]) ).
cnf(f_1509_6,plain,
( U_5484 = U_5486
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5486)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5484)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5484) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5486) ),
inference(clausify,[status(thm)],[f_1509_3]) ).
cnf(f_1509_7,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5485)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5485)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5485) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5487) ),
inference(clausify,[status(thm)],[f_1509_3]) ).
cnf(f_1509_8,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5487)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5487)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5485)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5485) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5487) ),
inference(clausify,[status(thm)],[f_1509_3]) ).
cnf(f_1509_9,plain,
( U_5485 != U_5487
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5487)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5485)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5485) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5487) ),
inference(clausify,[status(thm)],[f_1509_3]) ).
cnf(f_1509_10,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5487)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5485) != 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_5485)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5485) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5487) ),
inference(clausify,[status(thm)],[f_1509_3]) ).
cnf(f_1509_11,plain,
( U_5485 != U_5487
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5485) != 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_5485)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5485) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5487) ),
inference(clausify,[status(thm)],[f_1509_3]) ).
cnf(f_1509_12,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5485)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5487)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5485) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5487) ),
inference(clausify,[status(thm)],[f_1509_3]) ).
cnf(f_1509_13,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5487)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5487)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5487)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5485) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5487) ),
inference(clausify,[status(thm)],[f_1509_3]) ).
cnf(f_1509_14,plain,
( U_5485 != U_5487
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5487)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5487)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5485) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5487) ),
inference(clausify,[status(thm)],[f_1509_3]) ).
cnf(f_1509_15,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5487)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5485) != 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_5487)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5485) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5487) ),
inference(clausify,[status(thm)],[f_1509_3]) ).
cnf(f_1509_16,plain,
( U_5485 != U_5487
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5485) != 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_5487)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5485) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5487) ),
inference(clausify,[status(thm)],[f_1509_3]) ).
fof(f_1510_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_1510_2,plain,
! [U_5490,U_5489,U_5488] :
( ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5488)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5489)),U_5490)) = 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_5488),U_5489))),U_5490)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5489))) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5488)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5489)),U_5490)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5488)),U_5490)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5489))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5488))) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5488)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5489)),U_5490)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5489)),U_5490)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5488))) ) ),
inference(variable_rename,[status(thm)],[f_1510_1]) ).
fof(f_1510_3,plain,
( ! [U_5496,U_5494,U_5492] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5492)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5494)),U_5496)) = 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_5492),U_5494))),U_5496)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5494))) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5492)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5494)),U_5496)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5492)),U_5496)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5494))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5492))) )
& ! [U_5495,U_5493,U_5491] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5491)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5493)),U_5495)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5493)),U_5495)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5491))) ) ),
inference(miniscope,[status(thm)],[f_1510_2]) ).
cnf(f_1510_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5491)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5493)),U_5495)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5493)),U_5495)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5491))) ),
inference(clausify,[status(thm)],[f_1510_3]) ).
cnf(f_1510_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5492)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5494)),U_5496)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5492)),U_5496)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5494)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5492))) ),
inference(clausify,[status(thm)],[f_1510_3]) ).
cnf(f_1510_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5492)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5494)),U_5496)) = 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_5492),U_5494))),U_5496)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5494)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5492))) ),
inference(clausify,[status(thm)],[f_1510_3]) ).
fof(f_1511_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_1511_2,plain,
! [U_5497] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5497),c_Groups_Oone__class_Oone(U_5497)),c_Groups_Oone__class_Oone(U_5497)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5497),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_5497) ),
inference(variable_rename,[status(thm)],[f_1511_1]) ).
cnf(f_1511_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5497),c_Groups_Oone__class_Oone(U_5497)),c_Groups_Oone__class_Oone(U_5497)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5497),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_5497) ),
inference(clausify,[status(thm)],[f_1511_2]) ).
fof(f_1512_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_1512_2,plain,
! [U_5499,U_5498] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5498),U_5499),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_5498)
| U_5499 != c_Groups_Ozero__class_Ozero(U_5498) )
& ( U_5499 = c_Groups_Ozero__class_Ozero(U_5498)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_5498),U_5499),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_5498) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(U_5498) ),
inference(variable_rename,[status(thm)],[f_1512_1]) ).
cnf(f_1512_3,plain,
( U_5499 = c_Groups_Ozero__class_Ozero(U_5498)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_5498),U_5499),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_5498)
| ~ class_Rings_Oring__1__no__zero__divisors(U_5498) ),
inference(clausify,[status(thm)],[f_1512_2]) ).
cnf(f_1512_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5498),U_5499),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_5498)
| U_5499 != c_Groups_Ozero__class_Ozero(U_5498)
| ~ class_Rings_Oring__1__no__zero__divisors(U_5498) ),
inference(clausify,[status(thm)],[f_1512_2]) ).
fof(f_1513_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_1513_2,plain,
! [U_5500] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5500),c_Groups_Ozero__class_Ozero(U_5500)),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_5500)
| ~ class_Rings_Osemiring__1(U_5500) ),
inference(variable_rename,[status(thm)],[f_1513_1]) ).
cnf(f_1513_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5500),c_Groups_Ozero__class_Ozero(U_5500)),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_5500)
| ~ class_Rings_Osemiring__1(U_5500) ),
inference(clausify,[status(thm)],[f_1513_2]) ).
fof(f_1514_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_1514_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_1514_1]) ).
fof(f_1515_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_1515_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_1515_1]) ).
fof(f_1516_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_1516_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_1516_1]) ).
fof(f_1517_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_1517_2,plain,
! [U_5501] : 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_5501) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5501)),
inference(variable_rename,[status(thm)],[f_1517_1]) ).
cnf(f_1517_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_5501) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5501)),
inference(clausify,[status(thm)],[f_1517_2]) ).
fof(f_1518_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_1518_2,plain,
! [U_5502] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5502),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_5502)),
inference(variable_rename,[status(thm)],[f_1518_1]) ).
cnf(f_1518_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5502),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_5502)),
inference(clausify,[status(thm)],[f_1518_2]) ).
fof(f_1519_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_1519_2,plain,
! [U_5503] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5503),c_Groups_Oone__class_Oone(U_5503)),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_5503)
| ~ class_Rings_Osemiring__1(U_5503) ),
inference(variable_rename,[status(thm)],[f_1519_1]) ).
cnf(f_1519_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5503),c_Groups_Oone__class_Oone(U_5503)),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_5503)
| ~ class_Rings_Osemiring__1(U_5503) ),
inference(clausify,[status(thm)],[f_1519_2]) ).
fof(f_1520_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_1520_2,plain,
! [U_5505,U_5504] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5504),hAPP(c_Groups_Ouminus__class_Ouminus(U_5504),U_5505)),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_5504),U_5505),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Oring__1(U_5504) ),
inference(variable_rename,[status(thm)],[f_1520_1]) ).
cnf(f_1520_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5504),hAPP(c_Groups_Ouminus__class_Ouminus(U_5504),U_5505)),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_5504),U_5505),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Oring__1(U_5504) ),
inference(clausify,[status(thm)],[f_1520_2]) ).
fof(f_1521_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_1521_2,plain,
! [U_5506] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5506))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5506) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5506) = 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_5506)))) ) ),
inference(variable_rename,[status(thm)],[f_1521_1]) ).
fof(f_1521_3,plain,
( ! [U_5508] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5508))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5508) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_5507] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5507) = 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_5507)))) ) ),
inference(miniscope,[status(thm)],[f_1521_2]) ).
cnf(f_1521_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5507) = 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_5507)))) ),
inference(clausify,[status(thm)],[f_1521_3]) ).
cnf(f_1521_5,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5508))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5508) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1521_3]) ).
fof(f_1522_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_1522_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_1522_1]) ).
fof(f_1523_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_1523_2,plain,
! [U_5510,U_5509] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5509),c_Groups_Ozero__class_Ozero(U_5509)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5509),U_5510),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_5509) ),
inference(variable_rename,[status(thm)],[f_1523_1]) ).
cnf(f_1523_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5509),c_Groups_Ozero__class_Ozero(U_5509)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5509),U_5510),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_5509) ),
inference(clausify,[status(thm)],[f_1523_2]) ).
fof(f_1524_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_1524_2,plain,
! [U_5513,U_5512,U_5511] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5511),U_5512),U_5513))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5511),c_Groups_Ozero__class_Ozero(U_5511)),U_5513))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5511),hAPP(hAPP(c_Power_Opower__class_Opower(U_5511),U_5512),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_5511),U_5513),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__semidom(U_5511) ),
inference(variable_rename,[status(thm)],[f_1524_1]) ).
cnf(f_1524_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5511),U_5512),U_5513))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5511),c_Groups_Ozero__class_Ozero(U_5511)),U_5513))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5511),hAPP(hAPP(c_Power_Opower__class_Opower(U_5511),U_5512),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_5511),U_5513),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__semidom(U_5511) ),
inference(clausify,[status(thm)],[f_1524_2]) ).
fof(f_1525_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_1525_2,plain,
! [U_5516,U_5515,U_5514] :
( U_5515 = U_5516
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5514),c_Groups_Ozero__class_Ozero(U_5514)),U_5516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5514),c_Groups_Ozero__class_Ozero(U_5514)),U_5515))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_5514),U_5515),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_5514),U_5516),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__semidom(U_5514) ),
inference(variable_rename,[status(thm)],[f_1525_1]) ).
cnf(f_1525_3,plain,
( U_5515 = U_5516
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5514),c_Groups_Ozero__class_Ozero(U_5514)),U_5516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5514),c_Groups_Ozero__class_Ozero(U_5514)),U_5515))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_5514),U_5515),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_5514),U_5516),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__semidom(U_5514) ),
inference(clausify,[status(thm)],[f_1525_2]) ).
fof(f_1526_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_1526_2,plain,
! [U_5518,U_5517] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5517),c_Groups_Ozero__class_Ozero(U_5517)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5517),U_5518),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| U_5518 = c_Groups_Ozero__class_Ozero(U_5517) )
& ( U_5518 != c_Groups_Ozero__class_Ozero(U_5517)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5517),c_Groups_Ozero__class_Ozero(U_5517)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5517),U_5518),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
| ~ class_Rings_Olinordered__idom(U_5517) ),
inference(variable_rename,[status(thm)],[f_1526_1]) ).
cnf(f_1526_3,plain,
( U_5518 != c_Groups_Ozero__class_Ozero(U_5517)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5517),c_Groups_Ozero__class_Ozero(U_5517)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5517),U_5518),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_5517) ),
inference(clausify,[status(thm)],[f_1526_2]) ).
cnf(f_1526_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5517),c_Groups_Ozero__class_Ozero(U_5517)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5517),U_5518),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| U_5518 = c_Groups_Ozero__class_Ozero(U_5517)
| ~ class_Rings_Olinordered__idom(U_5517) ),
inference(clausify,[status(thm)],[f_1526_2]) ).
fof(f_1527_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_1527_2,plain,
! [U_5520,U_5519] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),hAPP(hAPP(c_Power_Opower__class_Opower(U_5519),U_5520),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_5519)))
| ~ class_Rings_Olinordered__idom(U_5519) ),
inference(variable_rename,[status(thm)],[f_1527_1]) ).
cnf(f_1527_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5519),hAPP(hAPP(c_Power_Opower__class_Opower(U_5519),U_5520),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_5519)))
| ~ class_Rings_Olinordered__idom(U_5519) ),
inference(clausify,[status(thm)],[f_1527_2]) ).
fof(f_1528_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_1528_2,plain,
! [U_5523,U_5522,U_5521] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5521),hAPP(hAPP(c_Power_Opower__class_Opower(U_5521),U_5522),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_5521),U_5523),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_5521)
| U_5523 != c_Groups_Ozero__class_Ozero(U_5521)
| U_5522 != c_Groups_Ozero__class_Ozero(U_5521) )
& ( ( U_5523 = c_Groups_Ozero__class_Ozero(U_5521)
& U_5522 = c_Groups_Ozero__class_Ozero(U_5521) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5521),hAPP(hAPP(c_Power_Opower__class_Opower(U_5521),U_5522),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_5521),U_5523),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_5521) ) )
| ~ class_Rings_Olinordered__idom(U_5521) ),
inference(variable_rename,[status(thm)],[f_1528_1]) ).
cnf(f_1528_3,plain,
( U_5522 = c_Groups_Ozero__class_Ozero(U_5521)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5521),hAPP(hAPP(c_Power_Opower__class_Opower(U_5521),U_5522),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_5521),U_5523),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_5521)
| ~ class_Rings_Olinordered__idom(U_5521) ),
inference(clausify,[status(thm)],[f_1528_2]) ).
cnf(f_1528_4,plain,
( U_5523 = c_Groups_Ozero__class_Ozero(U_5521)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5521),hAPP(hAPP(c_Power_Opower__class_Opower(U_5521),U_5522),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_5521),U_5523),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_5521)
| ~ class_Rings_Olinordered__idom(U_5521) ),
inference(clausify,[status(thm)],[f_1528_2]) ).
cnf(f_1528_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5521),hAPP(hAPP(c_Power_Opower__class_Opower(U_5521),U_5522),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_5521),U_5523),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_5521)
| U_5523 != c_Groups_Ozero__class_Ozero(U_5521)
| U_5522 != c_Groups_Ozero__class_Ozero(U_5521)
| ~ class_Rings_Olinordered__idom(U_5521) ),
inference(clausify,[status(thm)],[f_1528_2]) ).
fof(f_1529_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_1529_2,plain,
! [U_5524] :
( U_5524 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_5524 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5524),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_1529_1]) ).
cnf(f_1529_3,plain,
( U_5524 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_5524 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5524),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(clausify,[status(thm)],[f_1529_2]) ).
fof(f_1530_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_1530_2,plain,
! [U_5526,U_5525] :
( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5525),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5526)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5525),U_5526)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5526))) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5525),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5526)) = c_Groups_Ozero__class_Ozero(U_5525)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5526))) ) )
| ~ class_Int_Onumber__ring(U_5525) ),
inference(variable_rename,[status(thm)],[f_1530_1]) ).
cnf(f_1530_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5525),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5526)) = c_Groups_Ozero__class_Ozero(U_5525)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5526)))
| ~ class_Int_Onumber__ring(U_5525) ),
inference(clausify,[status(thm)],[f_1530_2]) ).
cnf(f_1530_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5525),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5526)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5525),U_5526)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5526)))
| ~ class_Int_Onumber__ring(U_5525) ),
inference(clausify,[status(thm)],[f_1530_2]) ).
fof(f_1531_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_1531_2,plain,
! [U_5528,U_5527] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5527),U_5528),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_5527)
| ( U_5528 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5527),c_Groups_Oone__class_Oone(U_5527))
& U_5528 != c_Groups_Oone__class_Oone(U_5527) ) )
& ( U_5528 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5527),c_Groups_Oone__class_Oone(U_5527))
| U_5528 = c_Groups_Oone__class_Oone(U_5527)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_5527),U_5528),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_5527) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(U_5527) ),
inference(variable_rename,[status(thm)],[f_1531_1]) ).
cnf(f_1531_3,plain,
( U_5528 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5527),c_Groups_Oone__class_Oone(U_5527))
| U_5528 = c_Groups_Oone__class_Oone(U_5527)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_5527),U_5528),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_5527)
| ~ class_Rings_Oring__1__no__zero__divisors(U_5527) ),
inference(clausify,[status(thm)],[f_1531_2]) ).
cnf(f_1531_4,plain,
( U_5528 != c_Groups_Oone__class_Oone(U_5527)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_5527),U_5528),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_5527)
| ~ class_Rings_Oring__1__no__zero__divisors(U_5527) ),
inference(clausify,[status(thm)],[f_1531_2]) ).
cnf(f_1531_5,plain,
( U_5528 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5527),c_Groups_Oone__class_Oone(U_5527))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_5527),U_5528),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_5527)
| ~ class_Rings_Oring__1__no__zero__divisors(U_5527) ),
inference(clausify,[status(thm)],[f_1531_2]) ).
fof(f_1532_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_1532_2,plain,
! [U_5529] :
( ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5529)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_5529))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5529))) )
& ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5529)) = 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_5529))) ) ),
inference(variable_rename,[status(thm)],[f_1532_1]) ).
fof(f_1532_3,plain,
( ! [U_5531] :
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5531)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_5531))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5531))) )
& ! [U_5530] :
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5530)) = 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_5530))) ) ),
inference(miniscope,[status(thm)],[f_1532_2]) ).
cnf(f_1532_4,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5530)) = 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_5530))) ),
inference(clausify,[status(thm)],[f_1532_3]) ).
cnf(f_1532_5,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5531)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_5531))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5531))) ),
inference(clausify,[status(thm)],[f_1532_3]) ).
fof(f_1533_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_1533_2,plain,
! [U_5534,U_5533,U_5532] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5532),U_5533),U_5534))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5532),c_Groups_Ozero__class_Ozero(U_5532)),U_5534))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5532),hAPP(hAPP(c_Power_Opower__class_Opower(U_5532),U_5533),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_5532),U_5534),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__semidom(U_5532) ),
inference(variable_rename,[status(thm)],[f_1533_1]) ).
cnf(f_1533_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5532),U_5533),U_5534))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5532),c_Groups_Ozero__class_Ozero(U_5532)),U_5534))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5532),hAPP(hAPP(c_Power_Opower__class_Opower(U_5532),U_5533),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_5532),U_5534),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__semidom(U_5532) ),
inference(clausify,[status(thm)],[f_1533_2]) ).
fof(f_1534_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_1534_2,plain,
! [U_5536,U_5535] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5535),hAPP(c_Groups_Ouminus__class_Ouminus(U_5535),c_Groups_Oone__class_Oone(U_5535))),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_5536))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5535),c_Groups_Oone__class_Oone(U_5535))
| ~ class_Rings_Oring__1(U_5535) ),
inference(variable_rename,[status(thm)],[f_1534_1]) ).
cnf(f_1534_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5535),hAPP(c_Groups_Ouminus__class_Ouminus(U_5535),c_Groups_Oone__class_Oone(U_5535))),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_5536))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5535),c_Groups_Oone__class_Oone(U_5535))
| ~ class_Rings_Oring__1(U_5535) ),
inference(clausify,[status(thm)],[f_1534_2]) ).
fof(f_1535_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_1535_2,plain,
! [U_5539,U_5538,U_5537] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5537),hAPP(hAPP(c_Power_Opower__class_Opower(U_5537),U_5538),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_5539)))),c_Groups_Ozero__class_Ozero(U_5537)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5537),U_5538),c_Groups_Ozero__class_Ozero(U_5537)))
| ~ class_Rings_Olinordered__idom(U_5537) ),
inference(variable_rename,[status(thm)],[f_1535_1]) ).
cnf(f_1535_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5537),hAPP(hAPP(c_Power_Opower__class_Opower(U_5537),U_5538),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_5539)))),c_Groups_Ozero__class_Ozero(U_5537)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5537),U_5538),c_Groups_Ozero__class_Ozero(U_5537)))
| ~ class_Rings_Olinordered__idom(U_5537) ),
inference(clausify,[status(thm)],[f_1535_2]) ).
fof(f_1536_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_1536_2,plain,
! [U_5542,U_5541,U_5540] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5540),c_Groups_Ozero__class_Ozero(U_5540)),U_5541))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5540),c_Groups_Ozero__class_Ozero(U_5540)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5540),U_5541),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_5542)))))
| ~ class_Rings_Olinordered__idom(U_5540) ),
inference(variable_rename,[status(thm)],[f_1536_1]) ).
cnf(f_1536_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5540),c_Groups_Ozero__class_Ozero(U_5540)),U_5541))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5540),c_Groups_Ozero__class_Ozero(U_5540)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5540),U_5541),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_5542)))))
| ~ class_Rings_Olinordered__idom(U_5540) ),
inference(clausify,[status(thm)],[f_1536_2]) ).
fof(f_1537_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_1537_2,plain,
! [U_5545,U_5544,U_5543] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5543),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5543),U_5544),U_5545)),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_5543),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5543),hAPP(hAPP(c_Power_Opower__class_Opower(U_5543),U_5544),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_5543),U_5545),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_5543),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5543),hAPP(c_Int_Onumber__class_Onumber__of(U_5543),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5544)),U_5545))
| ~ class_Int_Onumber__ring(U_5543) ),
inference(variable_rename,[status(thm)],[f_1537_1]) ).
cnf(f_1537_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5543),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5543),U_5544),U_5545)),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_5543),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5543),hAPP(hAPP(c_Power_Opower__class_Opower(U_5543),U_5544),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_5543),U_5545),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_5543),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5543),hAPP(c_Int_Onumber__class_Onumber__of(U_5543),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5544)),U_5545))
| ~ class_Int_Onumber__ring(U_5543) ),
inference(clausify,[status(thm)],[f_1537_2]) ).
fof(f_1538_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_1538_2,plain,
! [U_5547,U_5546] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5546),hAPP(c_Groups_Ouminus__class_Ouminus(U_5546),c_Groups_Oone__class_Oone(U_5546))),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_5547)) = c_Groups_Oone__class_Oone(U_5546)
| ~ class_Rings_Oring__1(U_5546) ),
inference(variable_rename,[status(thm)],[f_1538_1]) ).
cnf(f_1538_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5546),hAPP(c_Groups_Ouminus__class_Ouminus(U_5546),c_Groups_Oone__class_Oone(U_5546))),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_5547)) = c_Groups_Oone__class_Oone(U_5546)
| ~ class_Rings_Oring__1(U_5546) ),
inference(clausify,[status(thm)],[f_1538_2]) ).
fof(f_1539_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_1539_2,plain,
! [U_5550,U_5549,U_5548] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5548),c_Groups_Ozero__class_Ozero(U_5548)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5548),U_5549),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_5550))))
| ~ class_Rings_Olinordered__idom(U_5548) ),
inference(variable_rename,[status(thm)],[f_1539_1]) ).
cnf(f_1539_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5548),c_Groups_Ozero__class_Ozero(U_5548)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5548),U_5549),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_5550))))
| ~ class_Rings_Olinordered__idom(U_5548) ),
inference(clausify,[status(thm)],[f_1539_2]) ).
fof(f_1540_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_1540_2,plain,
! [U_5552,U_5551] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5551)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5552)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5551),U_5552)),
inference(variable_rename,[status(thm)],[f_1540_1]) ).
cnf(f_1540_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5551)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5552)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5551),U_5552)),
inference(clausify,[status(thm)],[f_1540_2]) ).
fof(f_1541_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_1541_2,plain,
! [U_5554,U_5553] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5553)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5554)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5553),U_5554)),
inference(variable_rename,[status(thm)],[f_1541_1]) ).
cnf(f_1541_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5553)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5554)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5553),U_5554)),
inference(clausify,[status(thm)],[f_1541_2]) ).
fof(f_1542_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_1542_2,plain,
! [U_5556,U_5555] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5555),U_5556)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5555)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5556)),
inference(variable_rename,[status(thm)],[f_1542_1]) ).
cnf(f_1542_3,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5555),U_5556)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5555)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5556)),
inference(clausify,[status(thm)],[f_1542_2]) ).
fof(f_1543_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_1543_2,plain,
! [U_5559,U_5558,U_5557] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5557),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5558),U_5559)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5557),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5557),U_5558)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5557),U_5559))
| ~ class_Rings_Osemiring__1(U_5557) ),
inference(variable_rename,[status(thm)],[f_1543_1]) ).
cnf(f_1543_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5557),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5558),U_5559)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5557),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5557),U_5558)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5557),U_5559))
| ~ class_Rings_Osemiring__1(U_5557) ),
inference(clausify,[status(thm)],[f_1543_2]) ).
fof(f_1544_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_1544_2,plain,
! [U_5563,U_5562,U_5561,U_5560] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5560),hAPP(c_Int_Onumber__class_Onumber__of(U_5560),U_5561)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5560),hAPP(c_Int_Onumber__class_Onumber__of(U_5560),U_5562)),U_5563)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5560),hAPP(c_Int_Onumber__class_Onumber__of(U_5560),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5561),U_5562))),U_5563)
| ~ class_Int_Onumber__ring(U_5560) ),
inference(variable_rename,[status(thm)],[f_1544_1]) ).
cnf(f_1544_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5560),hAPP(c_Int_Onumber__class_Onumber__of(U_5560),U_5561)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5560),hAPP(c_Int_Onumber__class_Onumber__of(U_5560),U_5562)),U_5563)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5560),hAPP(c_Int_Onumber__class_Onumber__of(U_5560),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5561),U_5562))),U_5563)
| ~ class_Int_Onumber__ring(U_5560) ),
inference(clausify,[status(thm)],[f_1544_2]) ).
fof(f_1545_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_1545_2,plain,
! [U_5566,U_5565,U_5564] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5564),hAPP(c_Int_Onumber__class_Onumber__of(U_5564),U_5565)),hAPP(c_Int_Onumber__class_Onumber__of(U_5564),U_5566)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5564),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5565),U_5566))
| ~ class_Int_Onumber__ring(U_5564) ),
inference(variable_rename,[status(thm)],[f_1545_1]) ).
cnf(f_1545_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5564),hAPP(c_Int_Onumber__class_Onumber__of(U_5564),U_5565)),hAPP(c_Int_Onumber__class_Onumber__of(U_5564),U_5566)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5564),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5565),U_5566))
| ~ class_Int_Onumber__ring(U_5564) ),
inference(clausify,[status(thm)],[f_1545_2]) ).
fof(f_1546_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_1546_2,plain,
! [U_5569,U_5568,U_5567] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_5567),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5568),U_5569)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5567),hAPP(c_Int_Onumber__class_Onumber__of(U_5567),U_5568)),hAPP(c_Int_Onumber__class_Onumber__of(U_5567),U_5569))
| ~ class_Int_Onumber__ring(U_5567) ),
inference(variable_rename,[status(thm)],[f_1546_1]) ).
cnf(f_1546_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_5567),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5568),U_5569)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5567),hAPP(c_Int_Onumber__class_Onumber__of(U_5567),U_5568)),hAPP(c_Int_Onumber__class_Onumber__of(U_5567),U_5569))
| ~ class_Int_Onumber__ring(U_5567) ),
inference(clausify,[status(thm)],[f_1546_2]) ).
fof(f_1547_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_1547_2,plain,
! [U_5574,U_5573,U_5572,U_5571,U_5570] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5570),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5570),U_5571),U_5572)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5570),U_5573),U_5574)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5570),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5570),U_5571),U_5573)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5570),U_5572),U_5574))
| ~ class_Rings_Ocomm__semiring__1(U_5570) ),
inference(variable_rename,[status(thm)],[f_1547_1]) ).
cnf(f_1547_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5570),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5570),U_5571),U_5572)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5570),U_5573),U_5574)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5570),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5570),U_5571),U_5573)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5570),U_5572),U_5574))
| ~ class_Rings_Ocomm__semiring__1(U_5570) ),
inference(clausify,[status(thm)],[f_1547_2]) ).
fof(f_1548_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_1548_2,plain,
! [U_5579,U_5578,U_5577,U_5576,U_5575] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5575),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5575),U_5576),U_5577)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5575),U_5578),U_5579)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5575),U_5578),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5575),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5575),U_5576),U_5577)),U_5579))
| ~ class_Rings_Ocomm__semiring__1(U_5575) ),
inference(variable_rename,[status(thm)],[f_1548_1]) ).
cnf(f_1548_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5575),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5575),U_5576),U_5577)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5575),U_5578),U_5579)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5575),U_5578),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5575),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5575),U_5576),U_5577)),U_5579))
| ~ class_Rings_Ocomm__semiring__1(U_5575) ),
inference(clausify,[status(thm)],[f_1548_2]) ).
fof(f_1549_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_1549_2,plain,
! [U_5584,U_5583,U_5582,U_5581,U_5580] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5580),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5580),U_5581),U_5582)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5580),U_5583),U_5584)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5580),U_5581),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5580),U_5582),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5580),U_5583),U_5584)))
| ~ class_Rings_Ocomm__semiring__1(U_5580) ),
inference(variable_rename,[status(thm)],[f_1549_1]) ).
cnf(f_1549_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5580),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5580),U_5581),U_5582)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5580),U_5583),U_5584)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5580),U_5581),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5580),U_5582),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5580),U_5583),U_5584)))
| ~ class_Rings_Ocomm__semiring__1(U_5580) ),
inference(clausify,[status(thm)],[f_1549_2]) ).
fof(f_1550_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_1550_2,plain,
! [U_5588,U_5587,U_5586,U_5585] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5585),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5585),U_5586),U_5587)),U_5588) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5585),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5585),U_5586),U_5588)),U_5587)
| ~ class_Rings_Ocomm__semiring__1(U_5585) ),
inference(variable_rename,[status(thm)],[f_1550_1]) ).
cnf(f_1550_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5585),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5585),U_5586),U_5587)),U_5588) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5585),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5585),U_5586),U_5588)),U_5587)
| ~ class_Rings_Ocomm__semiring__1(U_5585) ),
inference(clausify,[status(thm)],[f_1550_2]) ).
fof(f_1551_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_1551_2,plain,
! [U_5592,U_5591,U_5590,U_5589] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5589),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5589),U_5590),U_5591)),U_5592) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5589),U_5590),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5589),U_5591),U_5592))
| ~ class_Rings_Ocomm__semiring__1(U_5589) ),
inference(variable_rename,[status(thm)],[f_1551_1]) ).
cnf(f_1551_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5589),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5589),U_5590),U_5591)),U_5592) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5589),U_5590),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5589),U_5591),U_5592))
| ~ class_Rings_Ocomm__semiring__1(U_5589) ),
inference(clausify,[status(thm)],[f_1551_2]) ).
fof(f_1552_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_1552_2,plain,
! [U_5596,U_5595,U_5594,U_5593] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5593),U_5594),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5593),U_5595),U_5596)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5593),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5593),U_5594),U_5595)),U_5596)
| ~ class_Rings_Ocomm__semiring__1(U_5593) ),
inference(variable_rename,[status(thm)],[f_1552_1]) ).
cnf(f_1552_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5593),U_5594),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5593),U_5595),U_5596)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5593),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5593),U_5594),U_5595)),U_5596)
| ~ class_Rings_Ocomm__semiring__1(U_5593) ),
inference(clausify,[status(thm)],[f_1552_2]) ).
fof(f_1553_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_1553_2,plain,
! [U_5600,U_5599,U_5598,U_5597] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5597),U_5598),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5597),U_5599),U_5600)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5597),U_5599),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5597),U_5598),U_5600))
| ~ class_Rings_Ocomm__semiring__1(U_5597) ),
inference(variable_rename,[status(thm)],[f_1553_1]) ).
cnf(f_1553_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5597),U_5598),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5597),U_5599),U_5600)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5597),U_5599),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5597),U_5598),U_5600))
| ~ class_Rings_Ocomm__semiring__1(U_5597) ),
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),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_1554_2,plain,
! [U_5603,U_5602,U_5601] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5601),U_5602),U_5603) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5601),U_5603),U_5602)
| ~ class_Rings_Ocomm__semiring__1(U_5601) ),
inference(variable_rename,[status(thm)],[f_1554_1]) ).
cnf(f_1554_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5601),U_5602),U_5603) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5601),U_5603),U_5602)
| ~ class_Rings_Ocomm__semiring__1(U_5601) ),
inference(clausify,[status(thm)],[f_1554_2]) ).
fof(f_1555_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_1555_2,plain,
! [U_5606,U_5605,U_5604] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5604),U_5605)),U_5606) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5605),U_5606)),
inference(variable_rename,[status(thm)],[f_1555_1]) ).
cnf(f_1555_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5604),U_5605)),U_5606) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5605),U_5606)),
inference(clausify,[status(thm)],[f_1555_2]) ).
fof(f_1556_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_1556_2,plain,
! [U_5608,U_5607] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5607),U_5608) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5608),U_5607),
inference(variable_rename,[status(thm)],[f_1556_1]) ).
cnf(f_1556_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5607),U_5608) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5608),U_5607),
inference(clausify,[status(thm)],[f_1556_2]) ).
fof(f_1557_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_1557_2,plain,
! [U_5612,U_5611,U_5610,U_5609] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5609),U_5610),U_5611)),U_5612) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5609),U_5610),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5609),U_5611),U_5612))
| ~ class_Groups_Oab__semigroup__mult(U_5609) ),
inference(variable_rename,[status(thm)],[f_1557_1]) ).
cnf(f_1557_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5609),U_5610),U_5611)),U_5612) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5609),U_5610),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5609),U_5611),U_5612))
| ~ class_Groups_Oab__semigroup__mult(U_5609) ),
inference(clausify,[status(thm)],[f_1557_2]) ).
fof(f_1558_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_1558_2,plain,
! [U_5615,U_5614,U_5613] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5613),U_5614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5613),U_5614),U_5615)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5613),U_5614),U_5615)
| ~ class_Lattices_Oab__semigroup__idem__mult(U_5613) ),
inference(variable_rename,[status(thm)],[f_1558_1]) ).
cnf(f_1558_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5613),U_5614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5613),U_5614),U_5615)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5613),U_5614),U_5615)
| ~ class_Lattices_Oab__semigroup__idem__mult(U_5613) ),
inference(clausify,[status(thm)],[f_1558_2]) ).
fof(f_1559_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_1559_2,plain,
! [U_5617,U_5616] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5616),U_5617),U_5617) = U_5617
| ~ class_Lattices_Oab__semigroup__idem__mult(U_5616) ),
inference(variable_rename,[status(thm)],[f_1559_1]) ).
cnf(f_1559_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5616),U_5617),U_5617) = U_5617
| ~ class_Lattices_Oab__semigroup__idem__mult(U_5616) ),
inference(clausify,[status(thm)],[f_1559_2]) ).
fof(f_1560_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_1560_2,plain,
! [U_5619,U_5618] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5618),U_5619),U_5619) = U_5619
| ~ class_Lattices_Oab__semigroup__idem__mult(U_5618) ),
inference(variable_rename,[status(thm)],[f_1560_1]) ).
cnf(f_1560_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5618),U_5619),U_5619) = U_5619
| ~ class_Lattices_Oab__semigroup__idem__mult(U_5618) ),
inference(clausify,[status(thm)],[f_1560_2]) ).
fof(f_1561_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_1561_2,plain,
! [U_5621,U_5620] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5620),c_Groups_Ozero__class_Ozero(U_5620)),U_5621) = c_Groups_Ozero__class_Ozero(U_5620)
| ~ class_Rings_Omult__zero(U_5620) ),
inference(variable_rename,[status(thm)],[f_1561_1]) ).
cnf(f_1561_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5620),c_Groups_Ozero__class_Ozero(U_5620)),U_5621) = c_Groups_Ozero__class_Ozero(U_5620)
| ~ class_Rings_Omult__zero(U_5620) ),
inference(clausify,[status(thm)],[f_1561_2]) ).
fof(f_1562_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_1562_2,plain,
! [U_5623,U_5622] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5622),U_5623),c_Groups_Ozero__class_Ozero(U_5622)) = c_Groups_Ozero__class_Ozero(U_5622)
| ~ class_Rings_Omult__zero(U_5622) ),
inference(variable_rename,[status(thm)],[f_1562_1]) ).
cnf(f_1562_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5622),U_5623),c_Groups_Ozero__class_Ozero(U_5622)) = c_Groups_Ozero__class_Ozero(U_5622)
| ~ class_Rings_Omult__zero(U_5622) ),
inference(clausify,[status(thm)],[f_1562_2]) ).
fof(f_1563_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_1563_2,plain,
! [U_5626,U_5625,U_5624] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5624),U_5625),U_5626) = c_Groups_Ozero__class_Ozero(U_5624)
| ( U_5626 != c_Groups_Ozero__class_Ozero(U_5624)
& U_5625 != c_Groups_Ozero__class_Ozero(U_5624) ) )
& ( U_5626 = c_Groups_Ozero__class_Ozero(U_5624)
| U_5625 = c_Groups_Ozero__class_Ozero(U_5624)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5624),U_5625),U_5626) != c_Groups_Ozero__class_Ozero(U_5624) ) )
| ~ class_Rings_Oring__no__zero__divisors(U_5624) ),
inference(variable_rename,[status(thm)],[f_1563_1]) ).
cnf(f_1563_3,plain,
( U_5626 = c_Groups_Ozero__class_Ozero(U_5624)
| U_5625 = c_Groups_Ozero__class_Ozero(U_5624)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5624),U_5625),U_5626) != c_Groups_Ozero__class_Ozero(U_5624)
| ~ class_Rings_Oring__no__zero__divisors(U_5624) ),
inference(clausify,[status(thm)],[f_1563_2]) ).
cnf(f_1563_4,plain,
( U_5625 != c_Groups_Ozero__class_Ozero(U_5624)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5624),U_5625),U_5626) = c_Groups_Ozero__class_Ozero(U_5624)
| ~ class_Rings_Oring__no__zero__divisors(U_5624) ),
inference(clausify,[status(thm)],[f_1563_2]) ).
cnf(f_1563_5,plain,
( U_5626 != c_Groups_Ozero__class_Ozero(U_5624)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5624),U_5625),U_5626) = c_Groups_Ozero__class_Ozero(U_5624)
| ~ class_Rings_Oring__no__zero__divisors(U_5624) ),
inference(clausify,[status(thm)],[f_1563_2]) ).
fof(f_1564_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_1564_2,plain,
! [U_5629,U_5628,U_5627] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5627),U_5628),U_5629) != c_Groups_Ozero__class_Ozero(U_5627)
| U_5629 = c_Groups_Ozero__class_Ozero(U_5627)
| U_5628 = c_Groups_Ozero__class_Ozero(U_5627)
| ~ class_Rings_Ono__zero__divisors(U_5627) ),
inference(variable_rename,[status(thm)],[f_1564_1]) ).
cnf(f_1564_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5627),U_5628),U_5629) != c_Groups_Ozero__class_Ozero(U_5627)
| U_5629 = c_Groups_Ozero__class_Ozero(U_5627)
| U_5628 = c_Groups_Ozero__class_Ozero(U_5627)
| ~ class_Rings_Ono__zero__divisors(U_5627) ),
inference(clausify,[status(thm)],[f_1564_2]) ).
fof(f_1565_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_1565_2,plain,
! [U_5632,U_5631,U_5630] :
( U_5632 = c_Groups_Ozero__class_Ozero(U_5630)
| U_5631 = c_Groups_Ozero__class_Ozero(U_5630)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5630),U_5631),U_5632) != c_Groups_Ozero__class_Ozero(U_5630)
| ~ class_Rings_Ono__zero__divisors(U_5630) ),
inference(variable_rename,[status(thm)],[f_1565_1]) ).
cnf(f_1565_3,plain,
( U_5632 = c_Groups_Ozero__class_Ozero(U_5630)
| U_5631 = c_Groups_Ozero__class_Ozero(U_5630)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5630),U_5631),U_5632) != c_Groups_Ozero__class_Ozero(U_5630)
| ~ class_Rings_Ono__zero__divisors(U_5630) ),
inference(clausify,[status(thm)],[f_1565_2]) ).
fof(f_1566_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_1566_2,plain,
! [U_5634,U_5633] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5633),U_5634),c_Groups_Ozero__class_Ozero(U_5633)) = c_Groups_Ozero__class_Ozero(U_5633)
| ~ class_Rings_Ocomm__semiring__1(U_5633) ),
inference(variable_rename,[status(thm)],[f_1566_1]) ).
cnf(f_1566_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5633),U_5634),c_Groups_Ozero__class_Ozero(U_5633)) = c_Groups_Ozero__class_Ozero(U_5633)
| ~ class_Rings_Ocomm__semiring__1(U_5633) ),
inference(clausify,[status(thm)],[f_1566_2]) ).
fof(f_1567_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_1567_2,plain,
! [U_5636,U_5635] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5635),c_Groups_Ozero__class_Ozero(U_5635)),U_5636) = c_Groups_Ozero__class_Ozero(U_5635)
| ~ class_Rings_Ocomm__semiring__1(U_5635) ),
inference(variable_rename,[status(thm)],[f_1567_1]) ).
cnf(f_1567_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5635),c_Groups_Ozero__class_Ozero(U_5635)),U_5636) = c_Groups_Ozero__class_Ozero(U_5635)
| ~ class_Rings_Ocomm__semiring__1(U_5635) ),
inference(clausify,[status(thm)],[f_1567_2]) ).
fof(f_1568_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_1568_2,plain,
! [U_5641,U_5640,U_5639,U_5638,U_5637] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5637),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5637),U_5638),U_5639)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5637),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5637),U_5640),U_5639)),U_5641)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5637),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5637),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5637),U_5638),U_5640)),U_5639)),U_5641)
| ~ class_Rings_Osemiring(U_5637) ),
inference(variable_rename,[status(thm)],[f_1568_1]) ).
cnf(f_1568_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5637),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5637),U_5638),U_5639)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5637),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5637),U_5640),U_5639)),U_5641)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5637),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5637),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5637),U_5638),U_5640)),U_5639)),U_5641)
| ~ class_Rings_Osemiring(U_5637) ),
inference(clausify,[status(thm)],[f_1568_2]) ).
fof(f_1569_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_1569_2,plain,
! [U_5645,U_5644,U_5643,U_5642] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5642),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5642),U_5643),U_5644)),U_5645) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5642),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5642),U_5643),U_5645)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5642),U_5644),U_5645))
| ~ class_Rings_Ocomm__semiring(U_5642) ),
inference(variable_rename,[status(thm)],[f_1569_1]) ).
cnf(f_1569_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5642),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5642),U_5643),U_5644)),U_5645) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5642),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5642),U_5643),U_5645)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5642),U_5644),U_5645))
| ~ class_Rings_Ocomm__semiring(U_5642) ),
inference(clausify,[status(thm)],[f_1569_2]) ).
fof(f_1570_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_1570_2,plain,
! [U_5649,U_5648,U_5647,U_5646] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5646),U_5647),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5646),U_5648),U_5649)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5646),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5646),U_5647),U_5648)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5646),U_5647),U_5649))
| ~ class_Rings_Ocomm__semiring__1(U_5646) ),
inference(variable_rename,[status(thm)],[f_1570_1]) ).
cnf(f_1570_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5646),U_5647),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5646),U_5648),U_5649)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5646),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5646),U_5647),U_5648)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5646),U_5647),U_5649))
| ~ class_Rings_Ocomm__semiring__1(U_5646) ),
inference(clausify,[status(thm)],[f_1570_2]) ).
fof(f_1571_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( ( ( ( V_c_2 != V_d_2
& V_a_2 != V_b_2 )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2))
| V_c_2 = V_d_2
| V_a_2 = V_b_2 ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) ),
inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq]) ).
fof(f_1571_2,plain,
! [U_5654,U_5653,U_5652,U_5651,U_5650] :
( ( ( ( U_5653 != U_5654
& U_5651 != U_5652 )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5650),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5650),U_5651),U_5653)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5650),U_5652),U_5654)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5650),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5650),U_5651),U_5654)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5650),U_5652),U_5653)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5650),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5650),U_5651),U_5653)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5650),U_5652),U_5654)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5650),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5650),U_5651),U_5654)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5650),U_5652),U_5653))
| U_5653 = U_5654
| U_5651 = U_5652 ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_5650) ),
inference(variable_rename,[status(thm)],[f_1571_1]) ).
cnf(f_1571_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5650),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5650),U_5651),U_5653)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5650),U_5652),U_5654)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5650),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5650),U_5651),U_5654)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5650),U_5652),U_5653))
| U_5653 = U_5654
| U_5651 = U_5652
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_5650) ),
inference(clausify,[status(thm)],[f_1571_2]) ).
cnf(f_1571_4,plain,
( U_5651 != U_5652
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5650),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5650),U_5651),U_5653)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5650),U_5652),U_5654)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5650),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5650),U_5651),U_5654)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5650),U_5652),U_5653))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_5650) ),
inference(clausify,[status(thm)],[f_1571_2]) ).
cnf(f_1571_5,plain,
( U_5653 != U_5654
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5650),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5650),U_5651),U_5653)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5650),U_5652),U_5654)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5650),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5650),U_5651),U_5654)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5650),U_5652),U_5653))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_5650) ),
inference(clausify,[status(thm)],[f_1571_2]) ).
fof(f_1572_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_1572_2,plain,
! [U_5658,U_5657,U_5656,U_5655] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5655),U_5656),U_5657)),U_5658) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5655),U_5656),U_5658)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5655),U_5657),U_5658))
| ~ class_Rings_Ocomm__semiring__1(U_5655) ),
inference(variable_rename,[status(thm)],[f_1572_1]) ).
cnf(f_1572_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5655),U_5656),U_5657)),U_5658) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5655),U_5656),U_5658)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5655),U_5657),U_5658))
| ~ class_Rings_Ocomm__semiring__1(U_5655) ),
inference(clausify,[status(thm)],[f_1572_2]) ).
fof(f_1573_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_1573_2,plain,
! [U_5662,U_5661,U_5660,U_5659] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5659),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5659),U_5660),U_5661)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5659),U_5662),U_5661)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5659),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5659),U_5660),U_5662)),U_5661)
| ~ class_Rings_Ocomm__semiring__1(U_5659) ),
inference(variable_rename,[status(thm)],[f_1573_1]) ).
cnf(f_1573_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5659),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5659),U_5660),U_5661)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5659),U_5662),U_5661)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5659),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5659),U_5660),U_5662)),U_5661)
| ~ class_Rings_Ocomm__semiring__1(U_5659) ),
inference(clausify,[status(thm)],[f_1573_2]) ).
fof(f_1574_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_1574_2,plain,
! [U_5667,U_5666,U_5665,U_5664,U_5663] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5663),U_5664),U_5665)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5663),U_5666),U_5667)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5663),U_5664),U_5667)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5663),U_5666),U_5665))
| ( U_5665 != U_5667
& U_5664 != U_5666 ) )
& ( U_5665 = U_5667
| U_5664 = U_5666
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5663),U_5664),U_5665)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5663),U_5666),U_5667)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5663),U_5664),U_5667)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5663),U_5666),U_5665)) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_5663) ),
inference(variable_rename,[status(thm)],[f_1574_1]) ).
cnf(f_1574_3,plain,
( U_5665 = U_5667
| U_5664 = U_5666
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5663),U_5664),U_5665)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5663),U_5666),U_5667)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5663),U_5664),U_5667)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5663),U_5666),U_5665))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_5663) ),
inference(clausify,[status(thm)],[f_1574_2]) ).
cnf(f_1574_4,plain,
( U_5664 != U_5666
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5663),U_5664),U_5665)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5663),U_5666),U_5667)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5663),U_5664),U_5667)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5663),U_5666),U_5665))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_5663) ),
inference(clausify,[status(thm)],[f_1574_2]) ).
cnf(f_1574_5,plain,
( U_5665 != U_5667
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5663),U_5664),U_5665)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5663),U_5666),U_5667)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5663),U_5664),U_5667)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5663),U_5666),U_5665))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_5663) ),
inference(clausify,[status(thm)],[f_1574_2]) ).
fof(f_1575_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_1575_2,plain,
! [U_5669,U_5668] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5668),U_5669),c_Groups_Oone__class_Oone(U_5668)) = U_5669
| ~ class_Rings_Ocomm__semiring__1(U_5668) ),
inference(variable_rename,[status(thm)],[f_1575_1]) ).
cnf(f_1575_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5668),U_5669),c_Groups_Oone__class_Oone(U_5668)) = U_5669
| ~ class_Rings_Ocomm__semiring__1(U_5668) ),
inference(clausify,[status(thm)],[f_1575_2]) ).
fof(f_1576_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_1576_2,plain,
! [U_5671,U_5670] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5670),c_Groups_Oone__class_Oone(U_5670)),U_5671) = U_5671
| ~ class_Rings_Ocomm__semiring__1(U_5670) ),
inference(variable_rename,[status(thm)],[f_1576_1]) ).
cnf(f_1576_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5670),c_Groups_Oone__class_Oone(U_5670)),U_5671) = U_5671
| ~ class_Rings_Ocomm__semiring__1(U_5670) ),
inference(clausify,[status(thm)],[f_1576_2]) ).
fof(f_1577_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_1577_2,plain,
! [U_5673,U_5672] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5672),U_5673),c_Groups_Oone__class_Oone(U_5672)) = U_5673
| ~ class_Groups_Ocomm__monoid__mult(U_5672) ),
inference(variable_rename,[status(thm)],[f_1577_1]) ).
cnf(f_1577_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5672),U_5673),c_Groups_Oone__class_Oone(U_5672)) = U_5673
| ~ class_Groups_Ocomm__monoid__mult(U_5672) ),
inference(clausify,[status(thm)],[f_1577_2]) ).
fof(f_1578_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_1578_2,plain,
! [U_5675,U_5674] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5674),U_5675),c_Groups_Oone__class_Oone(U_5674)) = U_5675
| ~ class_Groups_Omonoid__mult(U_5674) ),
inference(variable_rename,[status(thm)],[f_1578_1]) ).
cnf(f_1578_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5674),U_5675),c_Groups_Oone__class_Oone(U_5674)) = U_5675
| ~ class_Groups_Omonoid__mult(U_5674) ),
inference(clausify,[status(thm)],[f_1578_2]) ).
fof(f_1579_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_1579_2,plain,
! [U_5677,U_5676] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5676),c_Groups_Oone__class_Oone(U_5676)),U_5677) = U_5677
| ~ class_Groups_Ocomm__monoid__mult(U_5676) ),
inference(variable_rename,[status(thm)],[f_1579_1]) ).
cnf(f_1579_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5676),c_Groups_Oone__class_Oone(U_5676)),U_5677) = U_5677
| ~ class_Groups_Ocomm__monoid__mult(U_5676) ),
inference(clausify,[status(thm)],[f_1579_2]) ).
fof(f_1580_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_1580_2,plain,
! [U_5679,U_5678] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5678),c_Groups_Oone__class_Oone(U_5678)),U_5679) = U_5679
| ~ class_Groups_Omonoid__mult(U_5678) ),
inference(variable_rename,[status(thm)],[f_1580_1]) ).
cnf(f_1580_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5678),c_Groups_Oone__class_Oone(U_5678)),U_5679) = U_5679
| ~ class_Groups_Omonoid__mult(U_5678) ),
inference(clausify,[status(thm)],[f_1580_2]) ).
fof(f_1581_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_1581_2,plain,
! [U_5682,U_5681,U_5680] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5680),U_5681) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5682),U_5681)
| ( U_5681 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_5680 != U_5682 ) )
& ( U_5681 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5680 = U_5682
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5680),U_5681) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5682),U_5681) ) ),
inference(variable_rename,[status(thm)],[f_1581_1]) ).
fof(f_1581_3,plain,
( ! [U_5688,U_5686,U_5684] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5684),U_5686) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5688),U_5686)
| ( U_5686 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_5684 != U_5688 ) )
& ! [U_5687,U_5685,U_5683] :
( U_5685 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5683 = U_5687
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5683),U_5685) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5687),U_5685) ) ),
inference(miniscope,[status(thm)],[f_1581_2]) ).
cnf(f_1581_4,plain,
( U_5685 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5683 = U_5687
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5683),U_5685) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5687),U_5685) ),
inference(clausify,[status(thm)],[f_1581_3]) ).
cnf(f_1581_5,plain,
( U_5684 != U_5688
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5684),U_5686) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5688),U_5686) ),
inference(clausify,[status(thm)],[f_1581_3]) ).
cnf(f_1581_6,plain,
( U_5686 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5684),U_5686) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5688),U_5686) ),
inference(clausify,[status(thm)],[f_1581_3]) ).
fof(f_1582_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_1582_2,plain,
! [U_5691,U_5690,U_5689] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5689),U_5690) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5689),U_5691)
| ( U_5689 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_5690 != U_5691 ) )
& ( U_5689 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5690 = U_5691
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5689),U_5690) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5689),U_5691) ) ),
inference(variable_rename,[status(thm)],[f_1582_1]) ).
fof(f_1582_3,plain,
( ! [U_5697,U_5695,U_5693] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5693),U_5695) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5693),U_5697)
| ( U_5693 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_5695 != U_5697 ) )
& ! [U_5696,U_5694,U_5692] :
( U_5692 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5694 = U_5696
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5692),U_5694) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5692),U_5696) ) ),
inference(miniscope,[status(thm)],[f_1582_2]) ).
cnf(f_1582_4,plain,
( U_5692 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5694 = U_5696
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5692),U_5694) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5692),U_5696) ),
inference(clausify,[status(thm)],[f_1582_3]) ).
cnf(f_1582_5,plain,
( U_5695 != U_5697
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5693),U_5695) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5693),U_5697) ),
inference(clausify,[status(thm)],[f_1582_3]) ).
cnf(f_1582_6,plain,
( U_5693 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5693),U_5695) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5693),U_5697) ),
inference(clausify,[status(thm)],[f_1582_3]) ).
fof(f_1583_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_1583_2,plain,
! [U_5699,U_5698] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5698),U_5699) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( U_5699 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_5698 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_5699 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5698 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5698),U_5699) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1583_1]) ).
fof(f_1583_3,plain,
( ! [U_5703,U_5701] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5701),U_5703) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( U_5703 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_5701 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_5702,U_5700] :
( U_5702 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5700 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5700),U_5702) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1583_2]) ).
cnf(f_1583_4,plain,
( U_5702 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5700 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5700),U_5702) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1583_3]) ).
cnf(f_1583_5,plain,
( U_5701 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5701),U_5703) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1583_3]) ).
cnf(f_1583_6,plain,
( U_5703 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5701),U_5703) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1583_3]) ).
fof(f_1584_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_1584_2,plain,
! [U_5704] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5704),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1584_1]) ).
cnf(f_1584_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5704),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1584_2]) ).
fof(f_1585_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_1585_2,plain,
! [U_5705] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5705) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1585_1]) ).
cnf(f_1585_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5705) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1585_2]) ).
fof(f_1586_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_1586_2,plain,
! [U_5708,U_5707,U_5706] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_5706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5706),U_5707),U_5708)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5706),U_5707),hAPP(c_Groups_Ouminus__class_Ouminus(U_5706),U_5708))
| ~ class_Rings_Oring(U_5706) ),
inference(variable_rename,[status(thm)],[f_1586_1]) ).
cnf(f_1586_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_5706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5706),U_5707),U_5708)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5706),U_5707),hAPP(c_Groups_Ouminus__class_Ouminus(U_5706),U_5708))
| ~ class_Rings_Oring(U_5706) ),
inference(clausify,[status(thm)],[f_1586_2]) ).
fof(f_1587_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_1587_2,plain,
! [U_5711,U_5710,U_5709] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_5709),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5709),U_5710),U_5711)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5709),hAPP(c_Groups_Ouminus__class_Ouminus(U_5709),U_5710)),U_5711)
| ~ class_Rings_Oring(U_5709) ),
inference(variable_rename,[status(thm)],[f_1587_1]) ).
cnf(f_1587_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_5709),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5709),U_5710),U_5711)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5709),hAPP(c_Groups_Ouminus__class_Ouminus(U_5709),U_5710)),U_5711)
| ~ class_Rings_Oring(U_5709) ),
inference(clausify,[status(thm)],[f_1587_2]) ).
fof(f_1588_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_1588_2,plain,
! [U_5714,U_5713,U_5712] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5712),hAPP(c_Groups_Ouminus__class_Ouminus(U_5712),U_5713)),U_5714) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5712),U_5713),hAPP(c_Groups_Ouminus__class_Ouminus(U_5712),U_5714))
| ~ class_Rings_Oring(U_5712) ),
inference(variable_rename,[status(thm)],[f_1588_1]) ).
cnf(f_1588_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5712),hAPP(c_Groups_Ouminus__class_Ouminus(U_5712),U_5713)),U_5714) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5712),U_5713),hAPP(c_Groups_Ouminus__class_Ouminus(U_5712),U_5714))
| ~ class_Rings_Oring(U_5712) ),
inference(clausify,[status(thm)],[f_1588_2]) ).
fof(f_1589_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_1589_2,plain,
! [U_5717,U_5716,U_5715] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5715),hAPP(c_Groups_Ouminus__class_Ouminus(U_5715),U_5716)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5715),U_5717)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5715),U_5716),U_5717)
| ~ class_Rings_Oring(U_5715) ),
inference(variable_rename,[status(thm)],[f_1589_1]) ).
cnf(f_1589_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5715),hAPP(c_Groups_Ouminus__class_Ouminus(U_5715),U_5716)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5715),U_5717)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5715),U_5716),U_5717)
| ~ class_Rings_Oring(U_5715) ),
inference(clausify,[status(thm)],[f_1589_2]) ).
fof(f_1590_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_1590_2,plain,
! [U_5720,U_5719,U_5718] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5718),U_5719),U_5719) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5718),U_5720),U_5720)
| ( U_5719 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5718),U_5720)
& U_5719 != U_5720 ) )
& ( U_5719 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5718),U_5720)
| U_5719 = U_5720
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5718),U_5719),U_5719) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5718),U_5720),U_5720) ) )
| ~ class_Rings_Oidom(U_5718) ),
inference(variable_rename,[status(thm)],[f_1590_1]) ).
cnf(f_1590_3,plain,
( U_5719 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5718),U_5720)
| U_5719 = U_5720
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5718),U_5719),U_5719) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5718),U_5720),U_5720)
| ~ class_Rings_Oidom(U_5718) ),
inference(clausify,[status(thm)],[f_1590_2]) ).
cnf(f_1590_4,plain,
( U_5719 != U_5720
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5718),U_5719),U_5719) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5718),U_5720),U_5720)
| ~ class_Rings_Oidom(U_5718) ),
inference(clausify,[status(thm)],[f_1590_2]) ).
cnf(f_1590_5,plain,
( U_5719 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5718),U_5720)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5718),U_5719),U_5719) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5718),U_5720),U_5720)
| ~ class_Rings_Oidom(U_5718) ),
inference(clausify,[status(thm)],[f_1590_2]) ).
fof(f_1591_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_1591_2,plain,
! [U_5723,U_5722,U_5721] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5721)),U_5722) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5721)),U_5723)
| U_5722 != U_5723 )
& ( U_5722 = U_5723
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5721)),U_5722) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5721)),U_5723) ) ),
inference(variable_rename,[status(thm)],[f_1591_1]) ).
fof(f_1591_3,plain,
( ! [U_5729,U_5727] :
( ! [U_5725] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5725)),U_5727) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5725)),U_5729)
| U_5727 != U_5729 )
& ! [U_5728,U_5726] :
( ! [U_5724] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5724)),U_5726) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5724)),U_5728)
| U_5726 = U_5728 ) ),
inference(miniscope,[status(thm)],[f_1591_2]) ).
cnf(f_1591_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5724)),U_5726) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5724)),U_5728)
| U_5726 = U_5728 ),
inference(clausify,[status(thm)],[f_1591_3]) ).
cnf(f_1591_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5725)),U_5727) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5725)),U_5729)
| U_5727 != U_5729 ),
inference(clausify,[status(thm)],[f_1591_3]) ).
fof(f_1592_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_1592_2,plain,
! [U_5732,U_5731,U_5730] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5730),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5731),U_5732)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5730),U_5731)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5730),U_5732)),
inference(variable_rename,[status(thm)],[f_1592_1]) ).
cnf(f_1592_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5730),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5731),U_5732)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5730),U_5731)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5730),U_5732)),
inference(clausify,[status(thm)],[f_1592_2]) ).
fof(f_1593_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_1593_2,plain,
! [U_5735,U_5734,U_5733] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5733),U_5734)),U_5735) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5733),U_5735)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5734),U_5735)),
inference(variable_rename,[status(thm)],[f_1593_1]) ).
cnf(f_1593_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5733),U_5734)),U_5735) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5733),U_5735)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5734),U_5735)),
inference(clausify,[status(thm)],[f_1593_2]) ).
fof(f_1594_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_1594_2,plain,
! [U_5739,U_5738,U_5737,U_5736] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5736),U_5737),U_5738)),U_5739) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5736),hAPP(hAPP(c_Power_Opower__class_Opower(U_5736),U_5737),U_5739)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5736),U_5738),U_5739))
| ~ class_Groups_Ocomm__monoid__mult(U_5736) ),
inference(variable_rename,[status(thm)],[f_1594_1]) ).
cnf(f_1594_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5736),U_5737),U_5738)),U_5739) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5736),hAPP(hAPP(c_Power_Opower__class_Opower(U_5736),U_5737),U_5739)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5736),U_5738),U_5739))
| ~ class_Groups_Ocomm__monoid__mult(U_5736) ),
inference(clausify,[status(thm)],[f_1594_2]) ).
fof(f_1595_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_1595_2,plain,
! [U_5742,U_5741,U_5740] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5740),hAPP(hAPP(c_Power_Opower__class_Opower(U_5740),U_5741),U_5742)),U_5741) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5740),U_5741),hAPP(hAPP(c_Power_Opower__class_Opower(U_5740),U_5741),U_5742))
| ~ class_Groups_Omonoid__mult(U_5740) ),
inference(variable_rename,[status(thm)],[f_1595_1]) ).
cnf(f_1595_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5740),hAPP(hAPP(c_Power_Opower__class_Opower(U_5740),U_5741),U_5742)),U_5741) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5740),U_5741),hAPP(hAPP(c_Power_Opower__class_Opower(U_5740),U_5741),U_5742))
| ~ class_Groups_Omonoid__mult(U_5740) ),
inference(clausify,[status(thm)],[f_1595_2]) ).
fof(f_1596_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_1596_2,plain,
! [U_5746,U_5745,U_5744,U_5743] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5743),U_5744),U_5745)),U_5746) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5743),hAPP(hAPP(c_Power_Opower__class_Opower(U_5743),U_5744),U_5746)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5743),U_5745),U_5746))
| ~ class_Rings_Ocomm__semiring__1(U_5743) ),
inference(variable_rename,[status(thm)],[f_1596_1]) ).
cnf(f_1596_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5743),U_5744),U_5745)),U_5746) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5743),hAPP(hAPP(c_Power_Opower__class_Opower(U_5743),U_5744),U_5746)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5743),U_5745),U_5746))
| ~ class_Rings_Ocomm__semiring__1(U_5743) ),
inference(clausify,[status(thm)],[f_1596_2]) ).
fof(f_1597_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_1597_2,plain,
! [U_5747] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5747),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5747),U_5747))),
inference(variable_rename,[status(thm)],[f_1597_1]) ).
cnf(f_1597_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5747),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5747),U_5747))),
inference(clausify,[status(thm)],[f_1597_2]) ).
fof(f_1598_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_1598_2,plain,
! [U_5748] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5748),U_5748)))),
inference(variable_rename,[status(thm)],[f_1598_1]) ).
cnf(f_1598_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5748),U_5748)))),
inference(clausify,[status(thm)],[f_1598_2]) ).
fof(f_1599_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_1599_2,plain,
! [U_5751,U_5750,U_5749] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5749),U_5751)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5750),U_5751)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5749),U_5750)) ),
inference(variable_rename,[status(thm)],[f_1599_1]) ).
cnf(f_1599_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_5749),U_5751)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5750),U_5751)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5749),U_5750)) ),
inference(clausify,[status(thm)],[f_1599_2]) ).
fof(f_1600_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_1600_2,plain,
! [U_5754,U_5753,U_5752] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5754),U_5752)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5754),U_5753)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5752),U_5753)) ),
inference(variable_rename,[status(thm)],[f_1600_1]) ).
cnf(f_1600_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_5754),U_5752)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5754),U_5753)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5752),U_5753)) ),
inference(clausify,[status(thm)],[f_1600_2]) ).
fof(f_1601_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_1601_2,plain,
! [U_5758,U_5757,U_5756,U_5755] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5755),U_5757)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5756),U_5758)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5757),U_5758))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5755),U_5756)) ),
inference(variable_rename,[status(thm)],[f_1601_1]) ).
cnf(f_1601_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_5755),U_5757)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5756),U_5758)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5757),U_5758))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5755),U_5756)) ),
inference(clausify,[status(thm)],[f_1601_2]) ).
fof(f_1602_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_1602_2,plain,
! [U_5759] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_5759) = c_Int_OPls,
inference(variable_rename,[status(thm)],[f_1602_1]) ).
cnf(f_1602_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_5759) = c_Int_OPls,
inference(clausify,[status(thm)],[f_1602_2]) ).
fof(f_1603_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_1603_2,plain,
! [U_5762,U_5761,U_5760] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5760),U_5761)),U_5762) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5760),U_5762)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5761),U_5762)),
inference(variable_rename,[status(thm)],[f_1603_1]) ).
cnf(f_1603_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5760),U_5761)),U_5762) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5760),U_5762)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5761),U_5762)),
inference(clausify,[status(thm)],[f_1603_2]) ).
fof(f_1604_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_1604_2,plain,
! [U_5765,U_5764,U_5763] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5763),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5764),U_5765)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5763),U_5764)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5763),U_5765)),
inference(variable_rename,[status(thm)],[f_1604_1]) ).
cnf(f_1604_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5763),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5764),U_5765)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5763),U_5764)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5763),U_5765)),
inference(clausify,[status(thm)],[f_1604_2]) ).
fof(f_1605_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_1605_2,plain,
! [U_5769,U_5768,U_5767,U_5766] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5766),U_5767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5768),U_5769)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5766),hAPP(hAPP(c_Power_Opower__class_Opower(U_5766),U_5767),U_5768)),U_5769)
| ~ class_Groups_Omonoid__mult(U_5766) ),
inference(variable_rename,[status(thm)],[f_1605_1]) ).
cnf(f_1605_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5766),U_5767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5768),U_5769)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5766),hAPP(hAPP(c_Power_Opower__class_Opower(U_5766),U_5767),U_5768)),U_5769)
| ~ class_Groups_Omonoid__mult(U_5766) ),
inference(clausify,[status(thm)],[f_1605_2]) ).
fof(f_1606_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_1606_2,plain,
! [U_5773,U_5772,U_5771,U_5770] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5770),hAPP(hAPP(c_Power_Opower__class_Opower(U_5770),U_5771),U_5772)),U_5773) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5770),U_5771),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5772),U_5773))
| ~ class_Rings_Ocomm__semiring__1(U_5770) ),
inference(variable_rename,[status(thm)],[f_1606_1]) ).
cnf(f_1606_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5770),hAPP(hAPP(c_Power_Opower__class_Opower(U_5770),U_5771),U_5772)),U_5773) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5770),U_5771),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5772),U_5773))
| ~ class_Rings_Ocomm__semiring__1(U_5770) ),
inference(clausify,[status(thm)],[f_1606_2]) ).
fof(f_1607_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_1607_2,plain,
! [U_5775,U_5774] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5774)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5775)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5774),U_5775)),
inference(variable_rename,[status(thm)],[f_1607_1]) ).
cnf(f_1607_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5774)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5775)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5774),U_5775)),
inference(clausify,[status(thm)],[f_1607_2]) ).
fof(f_1608_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_1608_2,plain,
! [U_5777,U_5776] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_5776)),U_5777) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5776),U_5777)),
inference(variable_rename,[status(thm)],[f_1608_1]) ).
cnf(f_1608_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_5776)),U_5777) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5776),U_5777)),
inference(clausify,[status(thm)],[f_1608_2]) ).
fof(f_1609_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_1609_2,plain,
! [U_5780,U_5779,U_5778] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5778),U_5779)),U_5780) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5778),U_5780)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5779),U_5780)),
inference(variable_rename,[status(thm)],[f_1609_1]) ).
cnf(f_1609_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5778),U_5779)),U_5780) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5778),U_5780)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5779),U_5780)),
inference(clausify,[status(thm)],[f_1609_2]) ).
fof(f_1610_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_1610_2,plain,
! [U_5783,U_5782,U_5781] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5781),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5782),U_5783)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5781),U_5782)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5781),U_5783)),
inference(variable_rename,[status(thm)],[f_1610_1]) ).
cnf(f_1610_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5781),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5782),U_5783)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5781),U_5782)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5781),U_5783)),
inference(clausify,[status(thm)],[f_1610_2]) ).
fof(f_1611_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_1611_2,plain,
! [U_5784] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5784),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_5784,
inference(variable_rename,[status(thm)],[f_1611_1]) ).
cnf(f_1611_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5784),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_5784,
inference(clausify,[status(thm)],[f_1611_2]) ).
fof(f_1612_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_1612_2,plain,
! [U_5785] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_5785) = U_5785,
inference(variable_rename,[status(thm)],[f_1612_1]) ).
cnf(f_1612_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_5785) = U_5785,
inference(clausify,[status(thm)],[f_1612_2]) ).
fof(f_1613_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_1613_2,plain,
! [U_5788,U_5787,U_5786] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5786),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5787),U_5788)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5786),U_5787)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5786),U_5788)),
inference(variable_rename,[status(thm)],[f_1613_1]) ).
cnf(f_1613_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5786),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5787),U_5788)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5786),U_5787)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5786),U_5788)),
inference(clausify,[status(thm)],[f_1613_2]) ).
fof(f_1614_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_1614_2,plain,
! [U_5791,U_5790,U_5789] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5789),U_5790)),U_5791) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5789),U_5791)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5790),U_5791)),
inference(variable_rename,[status(thm)],[f_1614_1]) ).
cnf(f_1614_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5789),U_5790)),U_5791) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5789),U_5791)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5790),U_5791)),
inference(clausify,[status(thm)],[f_1614_2]) ).
fof(f_1615_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_1615_2,plain,
! [U_5793,U_5792] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5792)),U_5793) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5792),U_5793)),
inference(variable_rename,[status(thm)],[f_1615_1]) ).
cnf(f_1615_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5792)),U_5793) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5792),U_5793)),
inference(clausify,[status(thm)],[f_1615_2]) ).
fof(f_1616_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_1616_2,plain,
! [U_5795,U_5794] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5794),U_5795) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_5795 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_5794 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( U_5795 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_5794 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5794),U_5795) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1616_1]) ).
fof(f_1616_3,plain,
( ! [U_5799,U_5797] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5797),U_5799) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_5799 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_5797 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_5798,U_5796] :
( ( U_5798 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_5796 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5796),U_5798) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1616_2]) ).
cnf(f_1616_4,plain,
( U_5796 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5796),U_5798) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1616_3]) ).
cnf(f_1616_5,plain,
( U_5798 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5796),U_5798) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1616_3]) ).
cnf(f_1616_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5797),U_5799) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_5799 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_5797 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1616_3]) ).
fof(f_1617_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_1617_2,plain,
! [U_5800] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5800),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_5800,
inference(variable_rename,[status(thm)],[f_1617_1]) ).
cnf(f_1617_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5800),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_5800,
inference(clausify,[status(thm)],[f_1617_2]) ).
fof(f_1618_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_1618_2,plain,
! [U_5802,U_5801] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5801),U_5802)
| U_5802 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_5801 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( U_5802 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_5801 = 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_5801),U_5802) ) ),
inference(variable_rename,[status(thm)],[f_1618_1]) ).
fof(f_1618_3,plain,
( ! [U_5806,U_5804] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5804),U_5806)
| U_5806 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_5804 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_5805,U_5803] :
( ( U_5805 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_5803 = 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_5803),U_5805) ) ),
inference(miniscope,[status(thm)],[f_1618_2]) ).
cnf(f_1618_4,plain,
( U_5803 = 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_5803),U_5805) ),
inference(clausify,[status(thm)],[f_1618_3]) ).
cnf(f_1618_5,plain,
( U_5805 = 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_5803),U_5805) ),
inference(clausify,[status(thm)],[f_1618_3]) ).
cnf(f_1618_6,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5804),U_5806)
| U_5806 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_5804 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1618_3]) ).
fof(f_1619_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_1619_2,plain,
! [U_5807] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_5807) = U_5807,
inference(variable_rename,[status(thm)],[f_1619_1]) ).
cnf(f_1619_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_5807) = U_5807,
inference(clausify,[status(thm)],[f_1619_2]) ).
fof(f_1620_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_1620_2,plain,
! [U_5810,U_5809,U_5808] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5808),U_5809)),U_5810) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5808),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5809),U_5810)),
inference(variable_rename,[status(thm)],[f_1620_1]) ).
cnf(f_1620_3,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5808),U_5809)),U_5810) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5808),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5809),U_5810)),
inference(clausify,[status(thm)],[f_1620_2]) ).
fof(f_1621_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_1621_2,plain,
! [U_5813,U_5812,U_5811] :
( c_Groups_Osgn__class_Osgn(U_5811,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5811),U_5812),U_5813)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5811),c_Groups_Osgn__class_Osgn(U_5811,U_5812)),c_Groups_Osgn__class_Osgn(U_5811,U_5813))
| ~ class_Rings_Olinordered__idom(U_5811) ),
inference(variable_rename,[status(thm)],[f_1621_1]) ).
cnf(f_1621_3,plain,
( c_Groups_Osgn__class_Osgn(U_5811,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5811),U_5812),U_5813)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5811),c_Groups_Osgn__class_Osgn(U_5811,U_5812)),c_Groups_Osgn__class_Osgn(U_5811,U_5813))
| ~ class_Rings_Olinordered__idom(U_5811) ),
inference(clausify,[status(thm)],[f_1621_2]) ).
fof(f_1622_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_1622_2,plain,
! [U_5814] :
( c_Finite__Set_Ofun__left__comm(U_5814,U_5814,c_Groups_Otimes__class_Otimes(U_5814))
| ~ class_Groups_Oab__semigroup__mult(U_5814) ),
inference(variable_rename,[status(thm)],[f_1622_1]) ).
cnf(f_1622_3,plain,
( c_Finite__Set_Ofun__left__comm(U_5814,U_5814,c_Groups_Otimes__class_Otimes(U_5814))
| ~ class_Groups_Oab__semigroup__mult(U_5814) ),
inference(clausify,[status(thm)],[f_1622_2]) ).
fof(f_1623_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_1623_2,plain,
! [U_5816,U_5815] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5815)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5816)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5815),U_5816))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5815),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5815)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5816)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5815),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_1623_1]) ).
fof(f_1623_3,plain,
( ! [U_5820,U_5818] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5818)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5820)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5818),U_5820))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5818),c_Int_OPls)) )
& ! [U_5819,U_5817] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5817)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5819)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5817),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_1623_2]) ).
cnf(f_1623_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5817)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5819)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5817),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1623_3]) ).
cnf(f_1623_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5818)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5820)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5818),U_5820))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5818),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1623_3]) ).
fof(f_1624_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_1624_2,plain,
! [U_5823,U_5822,U_5821] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5821)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5822)),U_5823)) = 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_5821),U_5822))),U_5823)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5821),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5821)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5822)),U_5823)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5821),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_1624_1]) ).
fof(f_1624_3,plain,
( ! [U_5829,U_5827,U_5825] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5825)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5827)),U_5829)) = 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_5825),U_5827))),U_5829)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5825),c_Int_OPls)) )
& ! [U_5828,U_5826,U_5824] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5824)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5826)),U_5828)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5824),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_1624_2]) ).
cnf(f_1624_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5824)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5826)),U_5828)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5824),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1624_3]) ).
cnf(f_1624_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5825)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5827)),U_5829)) = 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_5825),U_5827))),U_5829)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5825),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1624_3]) ).
fof(f_1625_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_1625_2,plain,
! [U_5832,U_5831,U_5830] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5830),U_5831),U_5832)),c_Groups_Ozero__class_Ozero(U_5830)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),c_Groups_Ozero__class_Ozero(U_5830)),U_5832))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),U_5831),c_Groups_Ozero__class_Ozero(U_5830))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),U_5832),c_Groups_Ozero__class_Ozero(U_5830)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),c_Groups_Ozero__class_Ozero(U_5830)),U_5831)) ) )
| ~ class_Rings_Oordered__cancel__semiring(U_5830) ),
inference(variable_rename,[status(thm)],[f_1625_1]) ).
cnf(f_1625_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),U_5832),c_Groups_Ozero__class_Ozero(U_5830)))
| ~ 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(hAPP(c_Groups_Otimes__class_Otimes(U_5830),U_5831),U_5832)),c_Groups_Ozero__class_Ozero(U_5830)))
| ~ class_Rings_Oordered__cancel__semiring(U_5830) ),
inference(clausify,[status(thm)],[f_1625_2]) ).
cnf(f_1625_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),c_Groups_Ozero__class_Ozero(U_5830)),U_5832))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),U_5831),c_Groups_Ozero__class_Ozero(U_5830)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5830),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5830),U_5831),U_5832)),c_Groups_Ozero__class_Ozero(U_5830)))
| ~ class_Rings_Oordered__cancel__semiring(U_5830) ),
inference(clausify,[status(thm)],[f_1625_2]) ).
fof(f_1626_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_1626_2,plain,
! [U_5835,U_5834,U_5833] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5833),c_Groups_Ozero__class_Ozero(U_5833)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5833),U_5834),U_5835)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5833),U_5835),c_Groups_Ozero__class_Ozero(U_5833)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5833),U_5834),c_Groups_Ozero__class_Ozero(U_5833))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5833),c_Groups_Ozero__class_Ozero(U_5833)),U_5835))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5833),c_Groups_Ozero__class_Ozero(U_5833)),U_5834)) ) )
| ~ class_Rings_Oordered__ring(U_5833) ),
inference(variable_rename,[status(thm)],[f_1626_1]) ).
cnf(f_1626_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5833),c_Groups_Ozero__class_Ozero(U_5833)),U_5835))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5833),c_Groups_Ozero__class_Ozero(U_5833)),U_5834))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5833),c_Groups_Ozero__class_Ozero(U_5833)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5833),U_5834),U_5835)))
| ~ class_Rings_Oordered__ring(U_5833) ),
inference(clausify,[status(thm)],[f_1626_2]) ).
cnf(f_1626_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5833),U_5835),c_Groups_Ozero__class_Ozero(U_5833)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5833),U_5834),c_Groups_Ozero__class_Ozero(U_5833)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5833),c_Groups_Ozero__class_Ozero(U_5833)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5833),U_5834),U_5835)))
| ~ class_Rings_Oordered__ring(U_5833) ),
inference(clausify,[status(thm)],[f_1626_2]) ).
fof(f_1627_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_1627_2,plain,
! [U_5840,U_5839,U_5838,U_5837,U_5836] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5836),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5836),U_5837),U_5839)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5836),U_5838),U_5840)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5836),c_Groups_Ozero__class_Ozero(U_5836)),U_5839))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5836),c_Groups_Ozero__class_Ozero(U_5836)),U_5838))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5836),U_5839),U_5840))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5836),U_5837),U_5838))
| ~ class_Rings_Oordered__semiring(U_5836) ),
inference(variable_rename,[status(thm)],[f_1627_1]) ).
cnf(f_1627_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5836),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5836),U_5837),U_5839)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5836),U_5838),U_5840)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5836),c_Groups_Ozero__class_Ozero(U_5836)),U_5839))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5836),c_Groups_Ozero__class_Ozero(U_5836)),U_5838))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5836),U_5839),U_5840))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5836),U_5837),U_5838))
| ~ class_Rings_Oordered__semiring(U_5836) ),
inference(clausify,[status(thm)],[f_1627_2]) ).
fof(f_1628_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_1628_2,plain,
! [U_5845,U_5844,U_5843,U_5842,U_5841] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5841),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5841),U_5842),U_5844)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5841),U_5843),U_5845)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5841),c_Groups_Ozero__class_Ozero(U_5841)),U_5844))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5841),c_Groups_Ozero__class_Ozero(U_5841)),U_5842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5841),U_5844),U_5845))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5841),U_5842),U_5843))
| ~ class_Rings_Oordered__semiring(U_5841) ),
inference(variable_rename,[status(thm)],[f_1628_1]) ).
cnf(f_1628_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5841),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5841),U_5842),U_5844)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5841),U_5843),U_5845)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5841),c_Groups_Ozero__class_Ozero(U_5841)),U_5844))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5841),c_Groups_Ozero__class_Ozero(U_5841)),U_5842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5841),U_5844),U_5845))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5841),U_5842),U_5843))
| ~ class_Rings_Oordered__semiring(U_5841) ),
inference(clausify,[status(thm)],[f_1628_2]) ).
fof(f_1629_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_1629_2,plain,
! [U_5849,U_5848,U_5847,U_5846] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5846),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5846),U_5849),U_5848)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5846),U_5849),U_5847)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5846),U_5849),c_Groups_Ozero__class_Ozero(U_5846)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5846),U_5847),U_5848))
| ~ class_Rings_Oordered__ring(U_5846) ),
inference(variable_rename,[status(thm)],[f_1629_1]) ).
cnf(f_1629_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5846),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5846),U_5849),U_5848)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5846),U_5849),U_5847)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5846),U_5849),c_Groups_Ozero__class_Ozero(U_5846)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5846),U_5847),U_5848))
| ~ class_Rings_Oordered__ring(U_5846) ),
inference(clausify,[status(thm)],[f_1629_2]) ).
fof(f_1630_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_1630_2,plain,
! [U_5853,U_5852,U_5851,U_5850] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5850),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5850),U_5852),U_5853)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5850),U_5851),U_5853)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5850),U_5853),c_Groups_Ozero__class_Ozero(U_5850)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5850),U_5851),U_5852))
| ~ class_Rings_Oordered__ring(U_5850) ),
inference(variable_rename,[status(thm)],[f_1630_1]) ).
cnf(f_1630_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5850),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5850),U_5852),U_5853)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5850),U_5851),U_5853)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5850),U_5853),c_Groups_Ozero__class_Ozero(U_5850)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5850),U_5851),U_5852))
| ~ class_Rings_Oordered__ring(U_5850) ),
inference(clausify,[status(thm)],[f_1630_2]) ).
fof(f_1631_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_1631_2,plain,
! [U_5857,U_5856,U_5855,U_5854] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5854),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5854),U_5857),U_5855)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5854),U_5857),U_5856)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5854),c_Groups_Ozero__class_Ozero(U_5854)),U_5857))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5854),U_5855),U_5856))
| ~ class_Rings_Oordered__comm__semiring(U_5854) ),
inference(variable_rename,[status(thm)],[f_1631_1]) ).
cnf(f_1631_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5854),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5854),U_5857),U_5855)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5854),U_5857),U_5856)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5854),c_Groups_Ozero__class_Ozero(U_5854)),U_5857))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5854),U_5855),U_5856))
| ~ class_Rings_Oordered__comm__semiring(U_5854) ),
inference(clausify,[status(thm)],[f_1631_2]) ).
fof(f_1632_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_1632_2,plain,
! [U_5861,U_5860,U_5859,U_5858] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5858),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5858),U_5861),U_5859)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5858),U_5861),U_5860)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5858),c_Groups_Ozero__class_Ozero(U_5858)),U_5861))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5858),U_5859),U_5860))
| ~ class_Rings_Oordered__semiring(U_5858) ),
inference(variable_rename,[status(thm)],[f_1632_1]) ).
cnf(f_1632_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5858),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5858),U_5861),U_5859)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5858),U_5861),U_5860)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5858),c_Groups_Ozero__class_Ozero(U_5858)),U_5861))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5858),U_5859),U_5860))
| ~ class_Rings_Oordered__semiring(U_5858) ),
inference(clausify,[status(thm)],[f_1632_2]) ).
fof(f_1633_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_1633_2,plain,
! [U_5865,U_5864,U_5863,U_5862] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5862),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5862),U_5863),U_5865)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5862),U_5864),U_5865)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5862),c_Groups_Ozero__class_Ozero(U_5862)),U_5865))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5862),U_5863),U_5864))
| ~ class_Rings_Oordered__semiring(U_5862) ),
inference(variable_rename,[status(thm)],[f_1633_1]) ).
cnf(f_1633_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5862),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5862),U_5863),U_5865)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5862),U_5864),U_5865)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5862),c_Groups_Ozero__class_Ozero(U_5862)),U_5865))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5862),U_5863),U_5864))
| ~ class_Rings_Oordered__semiring(U_5862) ),
inference(clausify,[status(thm)],[f_1633_2]) ).
fof(f_1634_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_1634_2,plain,
! [U_5868,U_5867,U_5866] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5866),c_Groups_Ozero__class_Ozero(U_5866)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5866),U_5867),U_5868)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5866),U_5868),c_Groups_Ozero__class_Ozero(U_5866)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5866),U_5867),c_Groups_Ozero__class_Ozero(U_5866)))
| ~ class_Rings_Oordered__ring(U_5866) ),
inference(variable_rename,[status(thm)],[f_1634_1]) ).
cnf(f_1634_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5866),c_Groups_Ozero__class_Ozero(U_5866)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5866),U_5867),U_5868)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5866),U_5868),c_Groups_Ozero__class_Ozero(U_5866)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5866),U_5867),c_Groups_Ozero__class_Ozero(U_5866)))
| ~ class_Rings_Oordered__ring(U_5866) ),
inference(clausify,[status(thm)],[f_1634_2]) ).
fof(f_1635_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_1635_2,plain,
! [U_5871,U_5870,U_5869] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5869),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5869),U_5870),U_5871)),c_Groups_Ozero__class_Ozero(U_5869)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5869),c_Groups_Ozero__class_Ozero(U_5869)),U_5871))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5869),U_5870),c_Groups_Ozero__class_Ozero(U_5869)))
| ~ class_Rings_Oordered__cancel__semiring(U_5869) ),
inference(variable_rename,[status(thm)],[f_1635_1]) ).
cnf(f_1635_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5869),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5869),U_5870),U_5871)),c_Groups_Ozero__class_Ozero(U_5869)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5869),c_Groups_Ozero__class_Ozero(U_5869)),U_5871))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5869),U_5870),c_Groups_Ozero__class_Ozero(U_5869)))
| ~ class_Rings_Oordered__cancel__semiring(U_5869) ),
inference(clausify,[status(thm)],[f_1635_2]) ).
fof(f_1636_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_1636_2,plain,
! [U_5874,U_5873,U_5872] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5872),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5872),U_5874),U_5873)),c_Groups_Ozero__class_Ozero(U_5872)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5872),U_5874),c_Groups_Ozero__class_Ozero(U_5872)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5872),c_Groups_Ozero__class_Ozero(U_5872)),U_5873))
| ~ class_Rings_Oordered__cancel__semiring(U_5872) ),
inference(variable_rename,[status(thm)],[f_1636_1]) ).
cnf(f_1636_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5872),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5872),U_5874),U_5873)),c_Groups_Ozero__class_Ozero(U_5872)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5872),U_5874),c_Groups_Ozero__class_Ozero(U_5872)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5872),c_Groups_Ozero__class_Ozero(U_5872)),U_5873))
| ~ class_Rings_Oordered__cancel__semiring(U_5872) ),
inference(clausify,[status(thm)],[f_1636_2]) ).
fof(f_1637_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_1637_2,plain,
! [U_5877,U_5876,U_5875] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5875),U_5876),U_5877)),c_Groups_Ozero__class_Ozero(U_5875)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5875),U_5877),c_Groups_Ozero__class_Ozero(U_5875)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5875),c_Groups_Ozero__class_Ozero(U_5875)),U_5876))
| ~ class_Rings_Oordered__cancel__semiring(U_5875) ),
inference(variable_rename,[status(thm)],[f_1637_1]) ).
cnf(f_1637_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5875),U_5876),U_5877)),c_Groups_Ozero__class_Ozero(U_5875)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5875),U_5877),c_Groups_Ozero__class_Ozero(U_5875)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5875),c_Groups_Ozero__class_Ozero(U_5875)),U_5876))
| ~ class_Rings_Oordered__cancel__semiring(U_5875) ),
inference(clausify,[status(thm)],[f_1637_2]) ).
fof(f_1638_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_1638_2,plain,
! [U_5880,U_5879,U_5878] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5878),c_Groups_Ozero__class_Ozero(U_5878)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5878),U_5879),U_5880)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5878),c_Groups_Ozero__class_Ozero(U_5878)),U_5880))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5878),c_Groups_Ozero__class_Ozero(U_5878)),U_5879))
| ~ class_Rings_Oordered__cancel__semiring(U_5878) ),
inference(variable_rename,[status(thm)],[f_1638_1]) ).
cnf(f_1638_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5878),c_Groups_Ozero__class_Ozero(U_5878)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5878),U_5879),U_5880)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5878),c_Groups_Ozero__class_Ozero(U_5878)),U_5880))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5878),c_Groups_Ozero__class_Ozero(U_5878)),U_5879))
| ~ class_Rings_Oordered__cancel__semiring(U_5878) ),
inference(clausify,[status(thm)],[f_1638_2]) ).
fof(f_1639_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_1639_2,plain,
! [U_5883,U_5882,U_5881] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5881),U_5882),U_5883)),c_Groups_Ozero__class_Ozero(U_5881)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),c_Groups_Ozero__class_Ozero(U_5881)),U_5883))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),U_5882),c_Groups_Ozero__class_Ozero(U_5881))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),U_5883),c_Groups_Ozero__class_Ozero(U_5881)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),c_Groups_Ozero__class_Ozero(U_5881)),U_5882)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),c_Groups_Ozero__class_Ozero(U_5881)),U_5883))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),U_5882),c_Groups_Ozero__class_Ozero(U_5881))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),U_5883),c_Groups_Ozero__class_Ozero(U_5881)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),c_Groups_Ozero__class_Ozero(U_5881)),U_5882)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5881),U_5882),U_5883)),c_Groups_Ozero__class_Ozero(U_5881))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_5881) ),
inference(variable_rename,[status(thm)],[f_1639_1]) ).
cnf(f_1639_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),U_5882),c_Groups_Ozero__class_Ozero(U_5881)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),c_Groups_Ozero__class_Ozero(U_5881)),U_5882))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5881),U_5882),U_5883)),c_Groups_Ozero__class_Ozero(U_5881)))
| ~ class_Rings_Olinordered__ring__strict(U_5881) ),
inference(clausify,[status(thm)],[f_1639_2]) ).
cnf(f_1639_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),c_Groups_Ozero__class_Ozero(U_5881)),U_5883))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),c_Groups_Ozero__class_Ozero(U_5881)),U_5882))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5881),U_5882),U_5883)),c_Groups_Ozero__class_Ozero(U_5881)))
| ~ class_Rings_Olinordered__ring__strict(U_5881) ),
inference(clausify,[status(thm)],[f_1639_2]) ).
cnf(f_1639_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),U_5882),c_Groups_Ozero__class_Ozero(U_5881)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),U_5883),c_Groups_Ozero__class_Ozero(U_5881)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5881),U_5882),U_5883)),c_Groups_Ozero__class_Ozero(U_5881)))
| ~ class_Rings_Olinordered__ring__strict(U_5881) ),
inference(clausify,[status(thm)],[f_1639_2]) ).
cnf(f_1639_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),c_Groups_Ozero__class_Ozero(U_5881)),U_5883))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),U_5883),c_Groups_Ozero__class_Ozero(U_5881)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5881),U_5882),U_5883)),c_Groups_Ozero__class_Ozero(U_5881)))
| ~ class_Rings_Olinordered__ring__strict(U_5881) ),
inference(clausify,[status(thm)],[f_1639_2]) ).
cnf(f_1639_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),U_5883),c_Groups_Ozero__class_Ozero(U_5881)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),c_Groups_Ozero__class_Ozero(U_5881)),U_5882))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5881),U_5882),U_5883)),c_Groups_Ozero__class_Ozero(U_5881)))
| ~ class_Rings_Olinordered__ring__strict(U_5881) ),
inference(clausify,[status(thm)],[f_1639_2]) ).
cnf(f_1639_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),c_Groups_Ozero__class_Ozero(U_5881)),U_5883))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),U_5882),c_Groups_Ozero__class_Ozero(U_5881)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5881),U_5882),U_5883)),c_Groups_Ozero__class_Ozero(U_5881)))
| ~ class_Rings_Olinordered__ring__strict(U_5881) ),
inference(clausify,[status(thm)],[f_1639_2]) ).
fof(f_1640_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_1640_2,plain,
! [U_5886,U_5885,U_5884] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),c_Groups_Ozero__class_Ozero(U_5884)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5884),U_5885),U_5886)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),U_5886),c_Groups_Ozero__class_Ozero(U_5884)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),U_5885),c_Groups_Ozero__class_Ozero(U_5884))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),c_Groups_Ozero__class_Ozero(U_5884)),U_5886))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),c_Groups_Ozero__class_Ozero(U_5884)),U_5885)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),U_5886),c_Groups_Ozero__class_Ozero(U_5884)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),U_5885),c_Groups_Ozero__class_Ozero(U_5884))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),c_Groups_Ozero__class_Ozero(U_5884)),U_5886))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),c_Groups_Ozero__class_Ozero(U_5884)),U_5885)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),c_Groups_Ozero__class_Ozero(U_5884)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5884),U_5885),U_5886))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_5884) ),
inference(variable_rename,[status(thm)],[f_1640_1]) ).
cnf(f_1640_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),U_5885),c_Groups_Ozero__class_Ozero(U_5884)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),c_Groups_Ozero__class_Ozero(U_5884)),U_5885))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),c_Groups_Ozero__class_Ozero(U_5884)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5884),U_5885),U_5886)))
| ~ class_Rings_Olinordered__ring__strict(U_5884) ),
inference(clausify,[status(thm)],[f_1640_2]) ).
cnf(f_1640_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),U_5886),c_Groups_Ozero__class_Ozero(U_5884)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),c_Groups_Ozero__class_Ozero(U_5884)),U_5885))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),c_Groups_Ozero__class_Ozero(U_5884)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5884),U_5885),U_5886)))
| ~ class_Rings_Olinordered__ring__strict(U_5884) ),
inference(clausify,[status(thm)],[f_1640_2]) ).
cnf(f_1640_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),U_5885),c_Groups_Ozero__class_Ozero(U_5884)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),c_Groups_Ozero__class_Ozero(U_5884)),U_5886))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),c_Groups_Ozero__class_Ozero(U_5884)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5884),U_5885),U_5886)))
| ~ class_Rings_Olinordered__ring__strict(U_5884) ),
inference(clausify,[status(thm)],[f_1640_2]) ).
cnf(f_1640_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),U_5886),c_Groups_Ozero__class_Ozero(U_5884)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),c_Groups_Ozero__class_Ozero(U_5884)),U_5886))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),c_Groups_Ozero__class_Ozero(U_5884)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5884),U_5885),U_5886)))
| ~ class_Rings_Olinordered__ring__strict(U_5884) ),
inference(clausify,[status(thm)],[f_1640_2]) ).
cnf(f_1640_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),c_Groups_Ozero__class_Ozero(U_5884)),U_5886))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),c_Groups_Ozero__class_Ozero(U_5884)),U_5885))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),c_Groups_Ozero__class_Ozero(U_5884)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5884),U_5885),U_5886)))
| ~ class_Rings_Olinordered__ring__strict(U_5884) ),
inference(clausify,[status(thm)],[f_1640_2]) ).
cnf(f_1640_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),U_5886),c_Groups_Ozero__class_Ozero(U_5884)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),U_5885),c_Groups_Ozero__class_Ozero(U_5884)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5884),c_Groups_Ozero__class_Ozero(U_5884)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5884),U_5885),U_5886)))
| ~ class_Rings_Olinordered__ring__strict(U_5884) ),
inference(clausify,[status(thm)],[f_1640_2]) ).
fof(f_1641_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_1641_2,plain,
! [U_5888,U_5887] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5887),c_Groups_Ozero__class_Ozero(U_5887)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5887),U_5888),U_5888)))
| ~ class_Rings_Olinordered__ring(U_5887) ),
inference(variable_rename,[status(thm)],[f_1641_1]) ).
cnf(f_1641_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5887),c_Groups_Ozero__class_Ozero(U_5887)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5887),U_5888),U_5888)))
| ~ class_Rings_Olinordered__ring(U_5887) ),
inference(clausify,[status(thm)],[f_1641_2]) ).
fof(f_1642_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_1642_2,plain,
! [U_5890,U_5889] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5889),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5889),U_5890),U_5890)),c_Groups_Ozero__class_Ozero(U_5889)))
| ~ class_Rings_Olinordered__ring(U_5889) ),
inference(variable_rename,[status(thm)],[f_1642_1]) ).
cnf(f_1642_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5889),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5889),U_5890),U_5890)),c_Groups_Ozero__class_Ozero(U_5889)))
| ~ class_Rings_Olinordered__ring(U_5889) ),
inference(clausify,[status(thm)],[f_1642_2]) ).
fof(f_1643_1,plain,
! [V_b_2,V_c_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj]) ).
fof(f_1643_2,plain,
! [U_5894,U_5893,U_5892,U_5891] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5891),U_5892),U_5893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5891),U_5894),U_5893)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),U_5894),U_5892))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),U_5893),c_Groups_Ozero__class_Ozero(U_5891))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),U_5892),U_5894))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),c_Groups_Ozero__class_Ozero(U_5891)),U_5893)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),U_5894),U_5892))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),U_5893),c_Groups_Ozero__class_Ozero(U_5891))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),U_5892),U_5894))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),c_Groups_Ozero__class_Ozero(U_5891)),U_5893)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5891),U_5892),U_5893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5891),U_5894),U_5893))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_5891) ),
inference(variable_rename,[status(thm)],[f_1643_1]) ).
cnf(f_1643_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),U_5893),c_Groups_Ozero__class_Ozero(U_5891)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),c_Groups_Ozero__class_Ozero(U_5891)),U_5893))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5891),U_5892),U_5893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5891),U_5894),U_5893)))
| ~ class_Rings_Olinordered__ring__strict(U_5891) ),
inference(clausify,[status(thm)],[f_1643_2]) ).
cnf(f_1643_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),U_5894),U_5892))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),c_Groups_Ozero__class_Ozero(U_5891)),U_5893))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5891),U_5892),U_5893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5891),U_5894),U_5893)))
| ~ class_Rings_Olinordered__ring__strict(U_5891) ),
inference(clausify,[status(thm)],[f_1643_2]) ).
cnf(f_1643_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),U_5893),c_Groups_Ozero__class_Ozero(U_5891)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),U_5892),U_5894))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5891),U_5892),U_5893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5891),U_5894),U_5893)))
| ~ class_Rings_Olinordered__ring__strict(U_5891) ),
inference(clausify,[status(thm)],[f_1643_2]) ).
cnf(f_1643_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),U_5894),U_5892))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),U_5892),U_5894))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5891),U_5892),U_5893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5891),U_5894),U_5893)))
| ~ class_Rings_Olinordered__ring__strict(U_5891) ),
inference(clausify,[status(thm)],[f_1643_2]) ).
cnf(f_1643_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),U_5892),U_5894))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),c_Groups_Ozero__class_Ozero(U_5891)),U_5893))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5891),U_5892),U_5893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5891),U_5894),U_5893)))
| ~ class_Rings_Olinordered__ring__strict(U_5891) ),
inference(clausify,[status(thm)],[f_1643_2]) ).
cnf(f_1643_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),U_5894),U_5892))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),U_5893),c_Groups_Ozero__class_Ozero(U_5891)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5891),U_5892),U_5893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5891),U_5894),U_5893)))
| ~ class_Rings_Olinordered__ring__strict(U_5891) ),
inference(clausify,[status(thm)],[f_1643_2]) ).
fof(f_1644_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj]) ).
fof(f_1644_2,plain,
! [U_5898,U_5897,U_5896,U_5895] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5895),U_5896),U_5897)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5895),U_5896),U_5898)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),U_5898),U_5897))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),U_5896),c_Groups_Ozero__class_Ozero(U_5895))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),U_5897),U_5898))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),c_Groups_Ozero__class_Ozero(U_5895)),U_5896)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),U_5898),U_5897))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),U_5896),c_Groups_Ozero__class_Ozero(U_5895))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),U_5897),U_5898))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),c_Groups_Ozero__class_Ozero(U_5895)),U_5896)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5895),U_5896),U_5897)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5895),U_5896),U_5898))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_5895) ),
inference(variable_rename,[status(thm)],[f_1644_1]) ).
cnf(f_1644_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),U_5896),c_Groups_Ozero__class_Ozero(U_5895)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),c_Groups_Ozero__class_Ozero(U_5895)),U_5896))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5895),U_5896),U_5897)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5895),U_5896),U_5898)))
| ~ class_Rings_Olinordered__ring__strict(U_5895) ),
inference(clausify,[status(thm)],[f_1644_2]) ).
cnf(f_1644_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),U_5898),U_5897))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),c_Groups_Ozero__class_Ozero(U_5895)),U_5896))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5895),U_5896),U_5897)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5895),U_5896),U_5898)))
| ~ class_Rings_Olinordered__ring__strict(U_5895) ),
inference(clausify,[status(thm)],[f_1644_2]) ).
cnf(f_1644_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),U_5896),c_Groups_Ozero__class_Ozero(U_5895)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),U_5897),U_5898))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5895),U_5896),U_5897)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5895),U_5896),U_5898)))
| ~ class_Rings_Olinordered__ring__strict(U_5895) ),
inference(clausify,[status(thm)],[f_1644_2]) ).
cnf(f_1644_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),U_5898),U_5897))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),U_5897),U_5898))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5895),U_5896),U_5897)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5895),U_5896),U_5898)))
| ~ class_Rings_Olinordered__ring__strict(U_5895) ),
inference(clausify,[status(thm)],[f_1644_2]) ).
cnf(f_1644_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),U_5897),U_5898))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),c_Groups_Ozero__class_Ozero(U_5895)),U_5896))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5895),U_5896),U_5897)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5895),U_5896),U_5898)))
| ~ class_Rings_Olinordered__ring__strict(U_5895) ),
inference(clausify,[status(thm)],[f_1644_2]) ).
cnf(f_1644_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),U_5898),U_5897))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),U_5896),c_Groups_Ozero__class_Ozero(U_5895)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5895),U_5896),U_5897)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5895),U_5896),U_5898)))
| ~ class_Rings_Olinordered__ring__strict(U_5895) ),
inference(clausify,[status(thm)],[f_1644_2]) ).
fof(f_1645_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos]) ).
fof(f_1645_2,plain,
! [U_5902,U_5901,U_5900,U_5899] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5899),U_5900),U_5901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5899),U_5900),U_5902)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5899),U_5901),U_5902)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5899),U_5901),U_5902))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5899),U_5900),U_5901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5899),U_5900),U_5902))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5899),c_Groups_Ozero__class_Ozero(U_5899)),U_5900))
| ~ class_Rings_Olinordered__ring__strict(U_5899) ),
inference(variable_rename,[status(thm)],[f_1645_1]) ).
cnf(f_1645_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5899),U_5901),U_5902))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5899),U_5900),U_5901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5899),U_5900),U_5902)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5899),c_Groups_Ozero__class_Ozero(U_5899)),U_5900))
| ~ class_Rings_Olinordered__ring__strict(U_5899) ),
inference(clausify,[status(thm)],[f_1645_2]) ).
cnf(f_1645_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5899),U_5900),U_5901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5899),U_5900),U_5902)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5899),U_5901),U_5902))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5899),c_Groups_Ozero__class_Ozero(U_5899)),U_5900))
| ~ class_Rings_Olinordered__ring__strict(U_5899) ),
inference(clausify,[status(thm)],[f_1645_2]) ).
fof(f_1646_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_1646_2,plain,
! [U_5905,U_5904,U_5903] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5903),c_Groups_Ozero__class_Ozero(U_5903)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5903),U_5904),U_5905)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5903),c_Groups_Ozero__class_Ozero(U_5903)),U_5905))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5903),c_Groups_Ozero__class_Ozero(U_5903)),U_5904))
| ~ class_Rings_Olinordered__semiring__strict(U_5903) ),
inference(variable_rename,[status(thm)],[f_1646_1]) ).
cnf(f_1646_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5903),c_Groups_Ozero__class_Ozero(U_5903)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5903),U_5904),U_5905)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5903),c_Groups_Ozero__class_Ozero(U_5903)),U_5905))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5903),c_Groups_Ozero__class_Ozero(U_5903)),U_5904))
| ~ class_Rings_Olinordered__semiring__strict(U_5903) ),
inference(clausify,[status(thm)],[f_1646_2]) ).
fof(f_1647_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_1647_2,plain,
! [U_5908,U_5907,U_5906] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5906),U_5907),U_5908)),c_Groups_Ozero__class_Ozero(U_5906)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5906),U_5908),c_Groups_Ozero__class_Ozero(U_5906)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5906),c_Groups_Ozero__class_Ozero(U_5906)),U_5907))
| ~ class_Rings_Olinordered__semiring__strict(U_5906) ),
inference(variable_rename,[status(thm)],[f_1647_1]) ).
cnf(f_1647_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5906),U_5907),U_5908)),c_Groups_Ozero__class_Ozero(U_5906)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5906),U_5908),c_Groups_Ozero__class_Ozero(U_5906)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5906),c_Groups_Ozero__class_Ozero(U_5906)),U_5907))
| ~ class_Rings_Olinordered__semiring__strict(U_5906) ),
inference(clausify,[status(thm)],[f_1647_2]) ).
fof(f_1648_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_1648_2,plain,
! [U_5911,U_5910,U_5909] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5909),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5909),U_5911),U_5910)),c_Groups_Ozero__class_Ozero(U_5909)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5909),U_5911),c_Groups_Ozero__class_Ozero(U_5909)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5909),c_Groups_Ozero__class_Ozero(U_5909)),U_5910))
| ~ class_Rings_Olinordered__semiring__strict(U_5909) ),
inference(variable_rename,[status(thm)],[f_1648_1]) ).
cnf(f_1648_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5909),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5909),U_5911),U_5910)),c_Groups_Ozero__class_Ozero(U_5909)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5909),U_5911),c_Groups_Ozero__class_Ozero(U_5909)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5909),c_Groups_Ozero__class_Ozero(U_5909)),U_5910))
| ~ class_Rings_Olinordered__semiring__strict(U_5909) ),
inference(clausify,[status(thm)],[f_1648_2]) ).
fof(f_1649_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_1649_2,plain,
! [U_5914,U_5913,U_5912] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5912),c_Groups_Ozero__class_Ozero(U_5912)),U_5914))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5912),c_Groups_Ozero__class_Ozero(U_5912)),U_5913))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5912),c_Groups_Ozero__class_Ozero(U_5912)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5912),U_5913),U_5914)))
| ~ class_Rings_Olinordered__semiring__strict(U_5912) ),
inference(variable_rename,[status(thm)],[f_1649_1]) ).
cnf(f_1649_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5912),c_Groups_Ozero__class_Ozero(U_5912)),U_5914))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5912),c_Groups_Ozero__class_Ozero(U_5912)),U_5913))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5912),c_Groups_Ozero__class_Ozero(U_5912)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5912),U_5913),U_5914)))
| ~ class_Rings_Olinordered__semiring__strict(U_5912) ),
inference(clausify,[status(thm)],[f_1649_2]) ).
fof(f_1650_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_1650_2,plain,
! [U_5917,U_5916,U_5915] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5915),c_Groups_Ozero__class_Ozero(U_5915)),U_5916))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5915),c_Groups_Ozero__class_Ozero(U_5915)),U_5917))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5915),c_Groups_Ozero__class_Ozero(U_5915)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5915),U_5916),U_5917)))
| ~ class_Rings_Olinordered__semiring__strict(U_5915) ),
inference(variable_rename,[status(thm)],[f_1650_1]) ).
cnf(f_1650_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5915),c_Groups_Ozero__class_Ozero(U_5915)),U_5916))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5915),c_Groups_Ozero__class_Ozero(U_5915)),U_5917))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5915),c_Groups_Ozero__class_Ozero(U_5915)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5915),U_5916),U_5917)))
| ~ class_Rings_Olinordered__semiring__strict(U_5915) ),
inference(clausify,[status(thm)],[f_1650_2]) ).
fof(f_1651_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg]) ).
fof(f_1651_2,plain,
! [U_5921,U_5920,U_5919,U_5918] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5918),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5918),U_5919),U_5920)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5918),U_5919),U_5921)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5918),U_5921),U_5920)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5918),U_5921),U_5920))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5918),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5918),U_5919),U_5920)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5918),U_5919),U_5921))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5918),U_5919),c_Groups_Ozero__class_Ozero(U_5918)))
| ~ class_Rings_Olinordered__ring__strict(U_5918) ),
inference(variable_rename,[status(thm)],[f_1651_1]) ).
cnf(f_1651_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5918),U_5921),U_5920))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5918),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5918),U_5919),U_5920)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5918),U_5919),U_5921)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5918),U_5919),c_Groups_Ozero__class_Ozero(U_5918)))
| ~ class_Rings_Olinordered__ring__strict(U_5918) ),
inference(clausify,[status(thm)],[f_1651_2]) ).
cnf(f_1651_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5918),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5918),U_5919),U_5920)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5918),U_5919),U_5921)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5918),U_5921),U_5920))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5918),U_5919),c_Groups_Ozero__class_Ozero(U_5918)))
| ~ class_Rings_Olinordered__ring__strict(U_5918) ),
inference(clausify,[status(thm)],[f_1651_2]) ).
fof(f_1652_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_1652_2,plain,
! [U_5924,U_5923,U_5922] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5922),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5922),U_5923),U_5924)),c_Groups_Ozero__class_Ozero(U_5922)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5922),c_Groups_Ozero__class_Ozero(U_5922)),U_5924))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5922),U_5923),c_Groups_Ozero__class_Ozero(U_5922)))
| ~ class_Rings_Olinordered__semiring__strict(U_5922) ),
inference(variable_rename,[status(thm)],[f_1652_1]) ).
cnf(f_1652_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5922),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5922),U_5923),U_5924)),c_Groups_Ozero__class_Ozero(U_5922)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5922),c_Groups_Ozero__class_Ozero(U_5922)),U_5924))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5922),U_5923),c_Groups_Ozero__class_Ozero(U_5922)))
| ~ class_Rings_Olinordered__semiring__strict(U_5922) ),
inference(clausify,[status(thm)],[f_1652_2]) ).
fof(f_1653_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_1653_2,plain,
! [U_5927,U_5926,U_5925] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5925),c_Groups_Ozero__class_Ozero(U_5925)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5925),U_5926),U_5927)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5925),U_5927),c_Groups_Ozero__class_Ozero(U_5925)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5925),U_5926),c_Groups_Ozero__class_Ozero(U_5925)))
| ~ class_Rings_Olinordered__ring__strict(U_5925) ),
inference(variable_rename,[status(thm)],[f_1653_1]) ).
cnf(f_1653_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5925),c_Groups_Ozero__class_Ozero(U_5925)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5925),U_5926),U_5927)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5925),U_5927),c_Groups_Ozero__class_Ozero(U_5925)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5925),U_5926),c_Groups_Ozero__class_Ozero(U_5925)))
| ~ class_Rings_Olinordered__ring__strict(U_5925) ),
inference(clausify,[status(thm)],[f_1653_2]) ).
fof(f_1654_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_1654_2,plain,
! [U_5931,U_5930,U_5929,U_5928] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5928),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5928),U_5929),U_5931)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5928),U_5930),U_5931)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5928),c_Groups_Ozero__class_Ozero(U_5928)),U_5931))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5928),U_5929),U_5930))
| ~ class_Rings_Olinordered__semiring__strict(U_5928) ),
inference(variable_rename,[status(thm)],[f_1654_1]) ).
cnf(f_1654_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5928),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5928),U_5929),U_5931)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5928),U_5930),U_5931)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5928),c_Groups_Ozero__class_Ozero(U_5928)),U_5931))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5928),U_5929),U_5930))
| ~ class_Rings_Olinordered__semiring__strict(U_5928) ),
inference(clausify,[status(thm)],[f_1654_2]) ).
fof(f_1655_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_1655_2,plain,
! [U_5935,U_5934,U_5933,U_5932] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5932),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5932),U_5935),U_5933)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5932),U_5935),U_5934)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5932),c_Groups_Ozero__class_Ozero(U_5932)),U_5935))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5932),U_5933),U_5934))
| ~ class_Rings_Olinordered__semiring__strict(U_5932) ),
inference(variable_rename,[status(thm)],[f_1655_1]) ).
cnf(f_1655_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5932),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5932),U_5935),U_5933)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5932),U_5935),U_5934)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5932),c_Groups_Ozero__class_Ozero(U_5932)),U_5935))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5932),U_5933),U_5934))
| ~ class_Rings_Olinordered__semiring__strict(U_5932) ),
inference(clausify,[status(thm)],[f_1655_2]) ).
fof(f_1656_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_1656_2,plain,
! [U_5939,U_5938,U_5937,U_5936] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5936),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5936),U_5939),U_5937)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5936),U_5939),U_5938)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5936),c_Groups_Ozero__class_Ozero(U_5936)),U_5939))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5936),U_5937),U_5938))
| ~ class_Rings_Olinordered__comm__semiring__strict(U_5936) ),
inference(variable_rename,[status(thm)],[f_1656_1]) ).
cnf(f_1656_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5936),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5936),U_5939),U_5937)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5936),U_5939),U_5938)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5936),c_Groups_Ozero__class_Ozero(U_5936)),U_5939))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5936),U_5937),U_5938))
| ~ class_Rings_Olinordered__comm__semiring__strict(U_5936) ),
inference(clausify,[status(thm)],[f_1656_2]) ).
fof(f_1657_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_1657_2,plain,
! [U_5943,U_5942,U_5941,U_5940] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5940),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5940),U_5942),U_5943)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5940),U_5941),U_5943)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5940),U_5943),c_Groups_Ozero__class_Ozero(U_5940)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5940),U_5941),U_5942))
| ~ class_Rings_Olinordered__ring__strict(U_5940) ),
inference(variable_rename,[status(thm)],[f_1657_1]) ).
cnf(f_1657_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5940),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5940),U_5942),U_5943)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5940),U_5941),U_5943)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5940),U_5943),c_Groups_Ozero__class_Ozero(U_5940)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5940),U_5941),U_5942))
| ~ class_Rings_Olinordered__ring__strict(U_5940) ),
inference(clausify,[status(thm)],[f_1657_2]) ).
fof(f_1658_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_1658_2,plain,
! [U_5947,U_5946,U_5945,U_5944] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5944),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5944),U_5947),U_5946)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5944),U_5947),U_5945)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5944),U_5947),c_Groups_Ozero__class_Ozero(U_5944)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5944),U_5945),U_5946))
| ~ class_Rings_Olinordered__ring__strict(U_5944) ),
inference(variable_rename,[status(thm)],[f_1658_1]) ).
cnf(f_1658_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5944),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5944),U_5947),U_5946)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5944),U_5947),U_5945)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5944),U_5947),c_Groups_Ozero__class_Ozero(U_5944)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5944),U_5945),U_5946))
| ~ class_Rings_Olinordered__ring__strict(U_5944) ),
inference(clausify,[status(thm)],[f_1658_2]) ).
fof(f_1659_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_1659_2,plain,
! [U_5950,U_5949,U_5948] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5948),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5948),U_5949),U_5949)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5948),U_5950),U_5950)) = c_Groups_Ozero__class_Ozero(U_5948)
| U_5950 != c_Groups_Ozero__class_Ozero(U_5948)
| U_5949 != c_Groups_Ozero__class_Ozero(U_5948) )
& ( ( U_5950 = c_Groups_Ozero__class_Ozero(U_5948)
& U_5949 = c_Groups_Ozero__class_Ozero(U_5948) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5948),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5948),U_5949),U_5949)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5948),U_5950),U_5950)) != c_Groups_Ozero__class_Ozero(U_5948) ) )
| ~ class_Rings_Olinordered__ring__strict(U_5948) ),
inference(variable_rename,[status(thm)],[f_1659_1]) ).
cnf(f_1659_3,plain,
( U_5949 = c_Groups_Ozero__class_Ozero(U_5948)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5948),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5948),U_5949),U_5949)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5948),U_5950),U_5950)) != c_Groups_Ozero__class_Ozero(U_5948)
| ~ class_Rings_Olinordered__ring__strict(U_5948) ),
inference(clausify,[status(thm)],[f_1659_2]) ).
cnf(f_1659_4,plain,
( U_5950 = c_Groups_Ozero__class_Ozero(U_5948)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5948),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5948),U_5949),U_5949)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5948),U_5950),U_5950)) != c_Groups_Ozero__class_Ozero(U_5948)
| ~ class_Rings_Olinordered__ring__strict(U_5948) ),
inference(clausify,[status(thm)],[f_1659_2]) ).
cnf(f_1659_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5948),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5948),U_5949),U_5949)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5948),U_5950),U_5950)) = c_Groups_Ozero__class_Ozero(U_5948)
| U_5950 != c_Groups_Ozero__class_Ozero(U_5948)
| U_5949 != c_Groups_Ozero__class_Ozero(U_5948)
| ~ class_Rings_Olinordered__ring__strict(U_5948) ),
inference(clausify,[status(thm)],[f_1659_2]) ).
fof(f_1660_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_1660_2,plain,
! [U_5956,U_5955,U_5954,U_5953,U_5952,U_5951] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5951),U_5953),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5951),U_5952),U_5955)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5951),U_5954),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5951),U_5952),U_5956))
| U_5955 = U_5956
| U_5953 != U_5954
| U_5952 = c_Groups_Ozero__class_Ozero(U_5951)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_5951) ),
inference(variable_rename,[status(thm)],[f_1660_1]) ).
cnf(f_1660_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5951),U_5953),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5951),U_5952),U_5955)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5951),U_5954),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5951),U_5952),U_5956))
| U_5955 = U_5956
| U_5953 != U_5954
| U_5952 = c_Groups_Ozero__class_Ozero(U_5951)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_5951) ),
inference(clausify,[status(thm)],[f_1660_2]) ).
fof(f_1661_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_1661_2,plain,
! [U_5959,U_5958,U_5957] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5957),c_Groups_Oone__class_Oone(U_5957)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5957),U_5958),U_5959)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5957),c_Groups_Oone__class_Oone(U_5957)),U_5959))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5957),c_Groups_Oone__class_Oone(U_5957)),U_5958))
| ~ class_Rings_Olinordered__semidom(U_5957) ),
inference(variable_rename,[status(thm)],[f_1661_1]) ).
cnf(f_1661_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5957),c_Groups_Oone__class_Oone(U_5957)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5957),U_5958),U_5959)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5957),c_Groups_Oone__class_Oone(U_5957)),U_5959))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5957),c_Groups_Oone__class_Oone(U_5957)),U_5958))
| ~ class_Rings_Olinordered__semidom(U_5957) ),
inference(clausify,[status(thm)],[f_1661_2]) ).
fof(f_1662_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2) != V_d_2 )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2) = V_d_2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2) ) )
| ~ class_Rings_Oring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__add__iff1]) ).
fof(f_1662_2,plain,
! [U_5965,U_5964,U_5963,U_5962,U_5961,U_5960] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5960),U_5961),U_5962)),U_5963) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5960),U_5964),U_5962)),U_5965)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5960),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5960),U_5961),U_5964)),U_5962)),U_5963) != U_5965 )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5960),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5960),U_5961),U_5964)),U_5962)),U_5963) = U_5965
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5960),U_5961),U_5962)),U_5963) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5960),U_5964),U_5962)),U_5965) ) )
| ~ class_Rings_Oring(U_5960) ),
inference(variable_rename,[status(thm)],[f_1662_1]) ).
cnf(f_1662_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5960),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5960),U_5961),U_5964)),U_5962)),U_5963) = U_5965
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5960),U_5961),U_5962)),U_5963) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5960),U_5964),U_5962)),U_5965)
| ~ class_Rings_Oring(U_5960) ),
inference(clausify,[status(thm)],[f_1662_2]) ).
cnf(f_1662_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5960),U_5961),U_5962)),U_5963) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5960),U_5964),U_5962)),U_5965)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5960),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5960),U_5961),U_5964)),U_5962)),U_5963) != U_5965
| ~ class_Rings_Oring(U_5960) ),
inference(clausify,[status(thm)],[f_1662_2]) ).
fof(f_1663_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
| V_c_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2) )
& ( V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2) ) )
| ~ class_Rings_Oring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__add__iff2]) ).
fof(f_1663_2,plain,
! [U_5971,U_5970,U_5969,U_5968,U_5967,U_5966] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5966),U_5967),U_5968)),U_5969) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5966),U_5970),U_5968)),U_5971)
| U_5969 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5966),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5966),U_5970),U_5967)),U_5968)),U_5971) )
& ( U_5969 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5966),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5966),U_5970),U_5967)),U_5968)),U_5971)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5966),U_5967),U_5968)),U_5969) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5966),U_5970),U_5968)),U_5971) ) )
| ~ class_Rings_Oring(U_5966) ),
inference(variable_rename,[status(thm)],[f_1663_1]) ).
cnf(f_1663_3,plain,
( U_5969 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5966),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5966),U_5970),U_5967)),U_5968)),U_5971)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5966),U_5967),U_5968)),U_5969) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5966),U_5970),U_5968)),U_5971)
| ~ class_Rings_Oring(U_5966) ),
inference(clausify,[status(thm)],[f_1663_2]) ).
cnf(f_1663_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5966),U_5967),U_5968)),U_5969) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5966),U_5970),U_5968)),U_5971)
| U_5969 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5966),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5966),U_5970),U_5967)),U_5968)),U_5971)
| ~ class_Rings_Oring(U_5966) ),
inference(clausify,[status(thm)],[f_1663_2]) ).
fof(f_1664_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_1664_2,plain,
! [U_5975,U_5974,U_5973,U_5972] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5972),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5972),U_5973),U_5974)),hAPP(c_Int_Onumber__class_Onumber__of(U_5972),U_5975)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5972),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5972),U_5973),hAPP(c_Int_Onumber__class_Onumber__of(U_5972),U_5975))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5972),U_5974),hAPP(c_Int_Onumber__class_Onumber__of(U_5972),U_5975)))
| ~ class_Rings_Osemiring(U_5972)
| ~ class_Int_Onumber(U_5972) ),
inference(variable_rename,[status(thm)],[f_1664_1]) ).
cnf(f_1664_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5972),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5972),U_5973),U_5974)),hAPP(c_Int_Onumber__class_Onumber__of(U_5972),U_5975)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5972),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5972),U_5973),hAPP(c_Int_Onumber__class_Onumber__of(U_5972),U_5975))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5972),U_5974),hAPP(c_Int_Onumber__class_Onumber__of(U_5972),U_5975)))
| ~ class_Rings_Osemiring(U_5972)
| ~ class_Int_Onumber(U_5972) ),
inference(clausify,[status(thm)],[f_1664_2]) ).
fof(f_1665_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_1665_2,plain,
! [U_5979,U_5978,U_5977,U_5976] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5976),hAPP(c_Int_Onumber__class_Onumber__of(U_5976),U_5977)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5976),U_5978),U_5979)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5976),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5976),hAPP(c_Int_Onumber__class_Onumber__of(U_5976),U_5977)),U_5978)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5976),hAPP(c_Int_Onumber__class_Onumber__of(U_5976),U_5977)),U_5979))
| ~ class_Rings_Osemiring(U_5976)
| ~ class_Int_Onumber(U_5976) ),
inference(variable_rename,[status(thm)],[f_1665_1]) ).
cnf(f_1665_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5976),hAPP(c_Int_Onumber__class_Onumber__of(U_5976),U_5977)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5976),U_5978),U_5979)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5976),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5976),hAPP(c_Int_Onumber__class_Onumber__of(U_5976),U_5977)),U_5978)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5976),hAPP(c_Int_Onumber__class_Onumber__of(U_5976),U_5977)),U_5979))
| ~ class_Rings_Osemiring(U_5976)
| ~ class_Int_Onumber(U_5976) ),
inference(clausify,[status(thm)],[f_1665_2]) ).
fof(f_1666_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_1666_2,plain,
! [U_5982,U_5981,U_5980] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5980),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5980),U_5981),U_5982)),U_5982) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5980),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5980),U_5981),c_Groups_Oone__class_Oone(U_5980))),U_5982)
| ~ class_Rings_Ocomm__semiring__1(U_5980) ),
inference(variable_rename,[status(thm)],[f_1666_1]) ).
cnf(f_1666_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5980),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5980),U_5981),U_5982)),U_5982) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5980),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5980),U_5981),c_Groups_Oone__class_Oone(U_5980))),U_5982)
| ~ class_Rings_Ocomm__semiring__1(U_5980) ),
inference(clausify,[status(thm)],[f_1666_2]) ).
fof(f_1667_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_1667_2,plain,
! [U_5985,U_5984,U_5983] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5983),U_5984),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5983),U_5985),U_5984)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5983),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5983),U_5985),c_Groups_Oone__class_Oone(U_5983))),U_5984)
| ~ class_Rings_Ocomm__semiring__1(U_5983) ),
inference(variable_rename,[status(thm)],[f_1667_1]) ).
cnf(f_1667_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5983),U_5984),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5983),U_5985),U_5984)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5983),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5983),U_5985),c_Groups_Oone__class_Oone(U_5983))),U_5984)
| ~ class_Rings_Ocomm__semiring__1(U_5983) ),
inference(clausify,[status(thm)],[f_1667_2]) ).
fof(f_1668_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_1668_2,plain,
! [U_5987,U_5986] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5986),U_5987),U_5987) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5986),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5986),c_Groups_Oone__class_Oone(U_5986)),c_Groups_Oone__class_Oone(U_5986))),U_5987)
| ~ class_Rings_Ocomm__semiring__1(U_5986) ),
inference(variable_rename,[status(thm)],[f_1668_1]) ).
cnf(f_1668_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5986),U_5987),U_5987) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5986),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5986),c_Groups_Oone__class_Oone(U_5986)),c_Groups_Oone__class_Oone(U_5986))),U_5987)
| ~ class_Rings_Ocomm__semiring__1(U_5986) ),
inference(clausify,[status(thm)],[f_1668_2]) ).
fof(f_1669_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_1669_2,plain,
! [U_5991,U_5990,U_5989,U_5988] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5988),hAPP(c_Int_Onumber__class_Onumber__of(U_5988),U_5989)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5988),U_5990),U_5991)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5988),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5988),hAPP(c_Int_Onumber__class_Onumber__of(U_5988),U_5989)),U_5990)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5988),hAPP(c_Int_Onumber__class_Onumber__of(U_5988),U_5989)),U_5991))
| ~ class_Rings_Oring(U_5988)
| ~ class_Int_Onumber(U_5988) ),
inference(variable_rename,[status(thm)],[f_1669_1]) ).
cnf(f_1669_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5988),hAPP(c_Int_Onumber__class_Onumber__of(U_5988),U_5989)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5988),U_5990),U_5991)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5988),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5988),hAPP(c_Int_Onumber__class_Onumber__of(U_5988),U_5989)),U_5990)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5988),hAPP(c_Int_Onumber__class_Onumber__of(U_5988),U_5989)),U_5991))
| ~ class_Rings_Oring(U_5988)
| ~ class_Int_Onumber(U_5988) ),
inference(clausify,[status(thm)],[f_1669_2]) ).
fof(f_1670_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_1670_2,plain,
! [U_5995,U_5994,U_5993,U_5992] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5992),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5992),U_5993),U_5994)),hAPP(c_Int_Onumber__class_Onumber__of(U_5992),U_5995)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5992),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5992),U_5993),hAPP(c_Int_Onumber__class_Onumber__of(U_5992),U_5995))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5992),U_5994),hAPP(c_Int_Onumber__class_Onumber__of(U_5992),U_5995)))
| ~ class_Rings_Oring(U_5992)
| ~ class_Int_Onumber(U_5992) ),
inference(variable_rename,[status(thm)],[f_1670_1]) ).
cnf(f_1670_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5992),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5992),U_5993),U_5994)),hAPP(c_Int_Onumber__class_Onumber__of(U_5992),U_5995)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5992),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5992),U_5993),hAPP(c_Int_Onumber__class_Onumber__of(U_5992),U_5995))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5992),U_5994),hAPP(c_Int_Onumber__class_Onumber__of(U_5992),U_5995)))
| ~ class_Rings_Oring(U_5992)
| ~ class_Int_Onumber(U_5992) ),
inference(clausify,[status(thm)],[f_1670_2]) ).
fof(f_1671_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_1671_2,plain,
! [U_5997,U_5996] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_5996),U_5997) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5996),hAPP(c_Groups_Ouminus__class_Ouminus(U_5996),c_Groups_Oone__class_Oone(U_5996))),U_5997)
| ~ class_Rings_Ocomm__ring__1(U_5996) ),
inference(variable_rename,[status(thm)],[f_1671_1]) ).
cnf(f_1671_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_5996),U_5997) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5996),hAPP(c_Groups_Ouminus__class_Ouminus(U_5996),c_Groups_Oone__class_Oone(U_5996))),U_5997)
| ~ class_Rings_Ocomm__ring__1(U_5996) ),
inference(clausify,[status(thm)],[f_1671_2]) ).
fof(f_1672_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_1672_2,plain,
! [U_5999,U_5998] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5998),U_5999),U_5999) = c_Groups_Oone__class_Oone(U_5998)
| ( U_5999 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5998),c_Groups_Oone__class_Oone(U_5998))
& U_5999 != c_Groups_Oone__class_Oone(U_5998) ) )
& ( U_5999 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5998),c_Groups_Oone__class_Oone(U_5998))
| U_5999 = c_Groups_Oone__class_Oone(U_5998)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5998),U_5999),U_5999) != c_Groups_Oone__class_Oone(U_5998) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(U_5998) ),
inference(variable_rename,[status(thm)],[f_1672_1]) ).
cnf(f_1672_3,plain,
( U_5999 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5998),c_Groups_Oone__class_Oone(U_5998))
| U_5999 = c_Groups_Oone__class_Oone(U_5998)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5998),U_5999),U_5999) != c_Groups_Oone__class_Oone(U_5998)
| ~ class_Rings_Oring__1__no__zero__divisors(U_5998) ),
inference(clausify,[status(thm)],[f_1672_2]) ).
cnf(f_1672_4,plain,
( U_5999 != c_Groups_Oone__class_Oone(U_5998)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5998),U_5999),U_5999) = c_Groups_Oone__class_Oone(U_5998)
| ~ class_Rings_Oring__1__no__zero__divisors(U_5998) ),
inference(clausify,[status(thm)],[f_1672_2]) ).
cnf(f_1672_5,plain,
( U_5999 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5998),c_Groups_Oone__class_Oone(U_5998))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5998),U_5999),U_5999) = c_Groups_Oone__class_Oone(U_5998)
| ~ class_Rings_Oring__1__no__zero__divisors(U_5998) ),
inference(clausify,[status(thm)],[f_1672_2]) ).
fof(f_1673_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_1673_2,plain,
! [U_6001,U_6000] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6000),U_6001) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6001 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6000 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( ( U_6001 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_6000 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6000),U_6001) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_1673_1]) ).
fof(f_1673_3,plain,
( ! [U_6005,U_6003] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6003),U_6005) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6005 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6003 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ! [U_6004,U_6002] :
( ( U_6004 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_6002 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6002),U_6004) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_1673_2]) ).
cnf(f_1673_4,plain,
( U_6002 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6002),U_6004) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_1673_3]) ).
cnf(f_1673_5,plain,
( U_6004 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6002),U_6004) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_1673_3]) ).
cnf(f_1673_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6003),U_6005) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6005 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6003 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_1673_3]) ).
fof(f_1674_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_1674_2,plain,
! [U_6007,U_6006] :
( ( 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_6006),U_6007)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6007))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6006)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6007))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6006)) )
| ~ 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_6006),U_6007))) ) ),
inference(variable_rename,[status(thm)],[f_1674_1]) ).
fof(f_1674_3,plain,
( ! [U_6011,U_6009] :
( 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_6009),U_6011)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6011))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6009)) )
& ! [U_6010,U_6008] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6010))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6008)) )
| ~ 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_6008),U_6010))) ) ),
inference(miniscope,[status(thm)],[f_1674_2]) ).
cnf(f_1674_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6008))
| ~ 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_6008),U_6010))) ),
inference(clausify,[status(thm)],[f_1674_3]) ).
cnf(f_1674_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6010))
| ~ 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_6008),U_6010))) ),
inference(clausify,[status(thm)],[f_1674_3]) ).
cnf(f_1674_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_6009),U_6011)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6011))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6009)) ),
inference(clausify,[status(thm)],[f_1674_3]) ).
fof(f_1675_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_1675_2,plain,
! [U_6014,U_6013,U_6012] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6012),U_6013)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6012),U_6014)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6013),U_6014))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6012)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6013),U_6014))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6012)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6012),U_6013)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6012),U_6014))) ) ),
inference(variable_rename,[status(thm)],[f_1675_1]) ).
fof(f_1675_3,plain,
( ! [U_6020,U_6018,U_6016] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6016),U_6018)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6016),U_6020)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6018),U_6020))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6016)) )
& ! [U_6019,U_6017,U_6015] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6017),U_6019))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6015)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6015),U_6017)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6015),U_6019))) ) ),
inference(miniscope,[status(thm)],[f_1675_2]) ).
cnf(f_1675_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6015))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6015),U_6017)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6015),U_6019))) ),
inference(clausify,[status(thm)],[f_1675_3]) ).
cnf(f_1675_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6017),U_6019))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6015),U_6017)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6015),U_6019))) ),
inference(clausify,[status(thm)],[f_1675_3]) ).
cnf(f_1675_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6016),U_6018)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6016),U_6020)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6018),U_6020))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6016)) ),
inference(clausify,[status(thm)],[f_1675_3]) ).
fof(f_1676_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_1676_2,plain,
! [U_6023,U_6022,U_6021] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6021),U_6022)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6023),U_6022)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6021),U_6023))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6022)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6021),U_6023))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6022)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6021),U_6022)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6023),U_6022))) ) ),
inference(variable_rename,[status(thm)],[f_1676_1]) ).
fof(f_1676_3,plain,
( ! [U_6029,U_6027,U_6025] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6025),U_6027)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6029),U_6027)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6025),U_6029))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6027)) )
& ! [U_6028,U_6026,U_6024] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6024),U_6028))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6026)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6024),U_6026)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6028),U_6026))) ) ),
inference(miniscope,[status(thm)],[f_1676_2]) ).
cnf(f_1676_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6026))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6024),U_6026)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6028),U_6026))) ),
inference(clausify,[status(thm)],[f_1676_3]) ).
cnf(f_1676_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6024),U_6028))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6024),U_6026)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6028),U_6026))) ),
inference(clausify,[status(thm)],[f_1676_3]) ).
cnf(f_1676_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6025),U_6027)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6029),U_6027)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6025),U_6029))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6027)) ),
inference(clausify,[status(thm)],[f_1676_3]) ).
fof(f_1677_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_1677_2,plain,
! [U_6032,U_6031,U_6030] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6030),U_6032)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6031),U_6032)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6032))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6030),U_6031)) ),
inference(variable_rename,[status(thm)],[f_1677_1]) ).
cnf(f_1677_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6030),U_6032)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6031),U_6032)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6032))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6030),U_6031)) ),
inference(clausify,[status(thm)],[f_1677_2]) ).
fof(f_1678_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_1678_2,plain,
! [U_6035,U_6034,U_6033] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6035),U_6033)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6035),U_6034)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6035))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6033),U_6034)) ),
inference(variable_rename,[status(thm)],[f_1678_1]) ).
cnf(f_1678_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6035),U_6033)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6035),U_6034)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6035))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6033),U_6034)) ),
inference(clausify,[status(thm)],[f_1678_2]) ).
fof(f_1679_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_1679_2,plain,
! [U_6038,U_6037,U_6036] :
( ( 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_6036)),U_6037)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6036)),U_6038)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6037),U_6038)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6037),U_6038))
| ~ 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_6036)),U_6037)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6036)),U_6038))) ) ),
inference(variable_rename,[status(thm)],[f_1679_1]) ).
fof(f_1679_3,plain,
( ! [U_6044,U_6042] :
( ! [U_6040] : 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_6040)),U_6042)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6040)),U_6044)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6042),U_6044)) )
& ! [U_6043,U_6041] :
( ! [U_6039] : ~ 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_6039)),U_6041)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6039)),U_6043)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6041),U_6043)) ) ),
inference(miniscope,[status(thm)],[f_1679_2]) ).
cnf(f_1679_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_6039)),U_6041)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6039)),U_6043)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6041),U_6043)) ),
inference(clausify,[status(thm)],[f_1679_3]) ).
cnf(f_1679_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_6040)),U_6042)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6040)),U_6044)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6042),U_6044)) ),
inference(clausify,[status(thm)],[f_1679_3]) ).
fof(f_1680_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_1680_2,plain,
! [U_6047,U_6046,U_6045] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6045),U_6046),hAPP(c_Nat_OSuc,U_6047)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6045),hAPP(hAPP(c_Power_Opower__class_Opower(U_6045),U_6046),U_6047)),U_6046)
| ~ class_Groups_Omonoid__mult(U_6045) ),
inference(variable_rename,[status(thm)],[f_1680_1]) ).
cnf(f_1680_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6045),U_6046),hAPP(c_Nat_OSuc,U_6047)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6045),hAPP(hAPP(c_Power_Opower__class_Opower(U_6045),U_6046),U_6047)),U_6046)
| ~ class_Groups_Omonoid__mult(U_6045) ),
inference(clausify,[status(thm)],[f_1680_2]) ).
fof(f_1681_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_1681_2,plain,
! [U_6050,U_6049,U_6048] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6048),U_6049),hAPP(c_Nat_OSuc,U_6050)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6048),U_6049),hAPP(hAPP(c_Power_Opower__class_Opower(U_6048),U_6049),U_6050))
| ~ class_Power_Opower(U_6048) ),
inference(variable_rename,[status(thm)],[f_1681_1]) ).
cnf(f_1681_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6048),U_6049),hAPP(c_Nat_OSuc,U_6050)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6048),U_6049),hAPP(hAPP(c_Power_Opower__class_Opower(U_6048),U_6049),U_6050))
| ~ class_Power_Opower(U_6048) ),
inference(clausify,[status(thm)],[f_1681_2]) ).
fof(f_1682_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_1682_2,plain,
! [U_6053,U_6052,U_6051] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6051),U_6052),hAPP(c_Nat_OSuc,U_6053)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6051),U_6052),hAPP(hAPP(c_Power_Opower__class_Opower(U_6051),U_6052),U_6053))
| ~ class_Rings_Ocomm__semiring__1(U_6051) ),
inference(variable_rename,[status(thm)],[f_1682_1]) ).
cnf(f_1682_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6051),U_6052),hAPP(c_Nat_OSuc,U_6053)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6051),U_6052),hAPP(hAPP(c_Power_Opower__class_Opower(U_6051),U_6052),U_6053))
| ~ class_Rings_Ocomm__semiring__1(U_6051) ),
inference(clausify,[status(thm)],[f_1682_2]) ).
fof(f_1683_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_1683_2,plain,
! [U_6056,U_6055,U_6054] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6054),U_6055),hAPP(hAPP(c_Power_Opower__class_Opower(U_6054),U_6055),U_6056)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6054),U_6055),hAPP(c_Nat_OSuc,U_6056))
| ~ class_Rings_Ocomm__semiring__1(U_6054) ),
inference(variable_rename,[status(thm)],[f_1683_1]) ).
cnf(f_1683_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6054),U_6055),hAPP(hAPP(c_Power_Opower__class_Opower(U_6054),U_6055),U_6056)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6054),U_6055),hAPP(c_Nat_OSuc,U_6056))
| ~ class_Rings_Ocomm__semiring__1(U_6054) ),
inference(clausify,[status(thm)],[f_1683_2]) ).
fof(f_1684_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_1684_2,plain,
! [U_6059,U_6058,U_6057] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6057),hAPP(hAPP(c_Power_Opower__class_Opower(U_6057),U_6058),U_6059)),U_6058) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6057),U_6058),hAPP(c_Nat_OSuc,U_6059))
| ~ class_Rings_Ocomm__semiring__1(U_6057) ),
inference(variable_rename,[status(thm)],[f_1684_1]) ).
cnf(f_1684_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6057),hAPP(hAPP(c_Power_Opower__class_Opower(U_6057),U_6058),U_6059)),U_6058) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6057),U_6058),hAPP(c_Nat_OSuc,U_6059))
| ~ class_Rings_Ocomm__semiring__1(U_6057) ),
inference(clausify,[status(thm)],[f_1684_2]) ).
fof(f_1685_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_1685_2,plain,
! [U_6061,U_6060] :
( 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_6060),U_6061)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6061))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6060)) ),
inference(variable_rename,[status(thm)],[f_1685_1]) ).
cnf(f_1685_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_6060),U_6061)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6061))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6060)) ),
inference(clausify,[status(thm)],[f_1685_2]) ).
fof(f_1686_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_1686_2,plain,
! [U_6063,U_6062] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6062),hAPP(c_Nat_OSuc,U_6063)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6062),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6062),U_6063)),
inference(variable_rename,[status(thm)],[f_1686_1]) ).
cnf(f_1686_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6062),hAPP(c_Nat_OSuc,U_6063)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6062),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6062),U_6063)),
inference(clausify,[status(thm)],[f_1686_2]) ).
fof(f_1687_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_1687_2,plain,
! [U_6065,U_6064] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6064)),U_6065) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6065),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6064),U_6065)),
inference(variable_rename,[status(thm)],[f_1687_1]) ).
cnf(f_1687_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6064)),U_6065) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6065),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6064),U_6065)),
inference(clausify,[status(thm)],[f_1687_2]) ).
fof(f_1688_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_1688_2,plain,
! [U_6068,U_6067,U_6066] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6068),U_6066)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6068),U_6067)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6068))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6066),U_6067)) ),
inference(variable_rename,[status(thm)],[f_1688_1]) ).
cnf(f_1688_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6068),U_6066)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6068),U_6067)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6068))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6066),U_6067)) ),
inference(clausify,[status(thm)],[f_1688_2]) ).
fof(f_1689_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_1689_2,plain,
! [U_6072,U_6071,U_6070,U_6069] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6069),U_6070),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6071),U_6072)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6069),hAPP(hAPP(c_Power_Opower__class_Opower(U_6069),U_6070),U_6071)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6069),U_6070),U_6072))
| ~ class_Groups_Omonoid__mult(U_6069) ),
inference(variable_rename,[status(thm)],[f_1689_1]) ).
cnf(f_1689_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6069),U_6070),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6071),U_6072)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6069),hAPP(hAPP(c_Power_Opower__class_Opower(U_6069),U_6070),U_6071)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6069),U_6070),U_6072))
| ~ class_Groups_Omonoid__mult(U_6069) ),
inference(clausify,[status(thm)],[f_1689_2]) ).
fof(f_1690_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_1690_2,plain,
! [U_6076,U_6075,U_6074,U_6073] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6073),hAPP(hAPP(c_Power_Opower__class_Opower(U_6073),U_6074),U_6075)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6073),U_6074),U_6076)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6073),U_6074),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6075),U_6076))
| ~ class_Rings_Ocomm__semiring__1(U_6073) ),
inference(variable_rename,[status(thm)],[f_1690_1]) ).
cnf(f_1690_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6073),hAPP(hAPP(c_Power_Opower__class_Opower(U_6073),U_6074),U_6075)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6073),U_6074),U_6076)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6073),U_6074),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6075),U_6076))
| ~ class_Rings_Ocomm__semiring__1(U_6073) ),
inference(clausify,[status(thm)],[f_1690_2]) ).
fof(f_1691_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_1691_2,plain,
! [U_6079,U_6078,U_6077] :
( ( 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_6077)),U_6078)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6077)),U_6079)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6078),U_6079)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6078),U_6079))
| ~ 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_6077)),U_6078)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6077)),U_6079))) ) ),
inference(variable_rename,[status(thm)],[f_1691_1]) ).
fof(f_1691_3,plain,
( ! [U_6085,U_6083] :
( ! [U_6081] : 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_6081)),U_6083)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6081)),U_6085)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6083),U_6085)) )
& ! [U_6084,U_6082] :
( ! [U_6080] : ~ 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_6080)),U_6082)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6080)),U_6084)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6082),U_6084)) ) ),
inference(miniscope,[status(thm)],[f_1691_2]) ).
cnf(f_1691_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_6080)),U_6082)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6080)),U_6084)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6082),U_6084)) ),
inference(clausify,[status(thm)],[f_1691_3]) ).
cnf(f_1691_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_6081)),U_6083)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6081)),U_6085)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6083),U_6085)) ),
inference(clausify,[status(thm)],[f_1691_3]) ).
fof(f_1692_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_1692_2,plain,
! [U_6087,U_6086] :
( U_6086 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6087 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_6086 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6086),U_6087) ),
inference(variable_rename,[status(thm)],[f_1692_1]) ).
cnf(f_1692_3,plain,
( U_6086 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6087 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_6086 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6086),U_6087) ),
inference(clausify,[status(thm)],[f_1692_2]) ).
fof(f_1693_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_1693_2,plain,
! [U_6090,U_6089,U_6088] :
( hBOOL(hAPP(hAPP(c_member(U_6088),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6088),U_6089),U_6090)),c_Int_Oring__1__class_OInts(U_6088)))
| ~ hBOOL(hAPP(hAPP(c_member(U_6088),U_6090),c_Int_Oring__1__class_OInts(U_6088)))
| ~ hBOOL(hAPP(hAPP(c_member(U_6088),U_6089),c_Int_Oring__1__class_OInts(U_6088)))
| ~ class_Rings_Oring__1(U_6088) ),
inference(variable_rename,[status(thm)],[f_1693_1]) ).
cnf(f_1693_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_6088),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6088),U_6089),U_6090)),c_Int_Oring__1__class_OInts(U_6088)))
| ~ hBOOL(hAPP(hAPP(c_member(U_6088),U_6090),c_Int_Oring__1__class_OInts(U_6088)))
| ~ hBOOL(hAPP(hAPP(c_member(U_6088),U_6089),c_Int_Oring__1__class_OInts(U_6088)))
| ~ class_Rings_Oring__1(U_6088) ),
inference(clausify,[status(thm)],[f_1693_2]) ).
fof(f_1694_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_1694_2,plain,
! [U_6093,U_6092,U_6091] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6091),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6092),U_6093)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6091),U_6092)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6091),U_6093)),
inference(variable_rename,[status(thm)],[f_1694_1]) ).
cnf(f_1694_3,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6091),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6092),U_6093)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6091),U_6092)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6091),U_6093)),
inference(clausify,[status(thm)],[f_1694_2]) ).
fof(f_1695_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_1695_2,plain,
! [U_6096,U_6095,U_6094] :
( hBOOL(hAPP(hAPP(c_member(U_6094),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6094),U_6095),U_6096)),c_Nat_Osemiring__1__class_ONats(U_6094)))
| ~ hBOOL(hAPP(hAPP(c_member(U_6094),U_6096),c_Nat_Osemiring__1__class_ONats(U_6094)))
| ~ hBOOL(hAPP(hAPP(c_member(U_6094),U_6095),c_Nat_Osemiring__1__class_ONats(U_6094)))
| ~ class_Rings_Osemiring__1(U_6094) ),
inference(variable_rename,[status(thm)],[f_1695_1]) ).
cnf(f_1695_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_6094),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6094),U_6095),U_6096)),c_Nat_Osemiring__1__class_ONats(U_6094)))
| ~ hBOOL(hAPP(hAPP(c_member(U_6094),U_6096),c_Nat_Osemiring__1__class_ONats(U_6094)))
| ~ hBOOL(hAPP(hAPP(c_member(U_6094),U_6095),c_Nat_Osemiring__1__class_ONats(U_6094)))
| ~ class_Rings_Osemiring__1(U_6094) ),
inference(clausify,[status(thm)],[f_1695_2]) ).
fof(f_1696_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_1696_2,plain,
! [U_6099,U_6098,U_6097] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6097),U_6098),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_6099)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6097),hAPP(hAPP(c_Power_Opower__class_Opower(U_6097),U_6098),U_6099)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6097),U_6098),U_6099))
| ~ class_Rings_Ocomm__semiring__1(U_6097) ),
inference(variable_rename,[status(thm)],[f_1696_1]) ).
cnf(f_1696_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6097),U_6098),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_6099)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6097),hAPP(hAPP(c_Power_Opower__class_Opower(U_6097),U_6098),U_6099)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6097),U_6098),U_6099))
| ~ class_Rings_Ocomm__semiring__1(U_6097) ),
inference(clausify,[status(thm)],[f_1696_2]) ).
fof(f_1697_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_1697_2,plain,
! [U_6103,U_6102,U_6101,U_6100] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6100),U_6102),U_6103))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6100),c_Groups_Ozero__class_Ozero(U_6100)),U_6101))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6100),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6100),U_6101),U_6102)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6100),U_6101),U_6103)))
| ~ class_Rings_Olinordered__semiring__strict(U_6100) ),
inference(variable_rename,[status(thm)],[f_1697_1]) ).
cnf(f_1697_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6100),U_6102),U_6103))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6100),c_Groups_Ozero__class_Ozero(U_6100)),U_6101))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6100),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6100),U_6101),U_6102)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6100),U_6101),U_6103)))
| ~ class_Rings_Olinordered__semiring__strict(U_6100) ),
inference(clausify,[status(thm)],[f_1697_2]) ).
fof(f_1698_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_1698_2,plain,
! [U_6107,U_6106,U_6105,U_6104] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6104),U_6105),U_6107))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6104),c_Groups_Ozero__class_Ozero(U_6104)),U_6106))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6104),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6104),U_6105),U_6106)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6104),U_6107),U_6106)))
| ~ class_Rings_Olinordered__semiring__strict(U_6104) ),
inference(variable_rename,[status(thm)],[f_1698_1]) ).
cnf(f_1698_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6104),U_6105),U_6107))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6104),c_Groups_Ozero__class_Ozero(U_6104)),U_6106))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6104),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6104),U_6105),U_6106)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6104),U_6107),U_6106)))
| ~ class_Rings_Olinordered__semiring__strict(U_6104) ),
inference(clausify,[status(thm)],[f_1698_2]) ).
fof(f_1699_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_1699_2,plain,
! [U_6111,U_6110,U_6109,U_6108] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6108),U_6110),U_6111))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6108),c_Groups_Ozero__class_Ozero(U_6108)),U_6109))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6108),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6108),U_6109),U_6110)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6108),U_6109),U_6111)))
| ~ class_Rings_Olinordered__semiring__strict(U_6108) ),
inference(variable_rename,[status(thm)],[f_1699_1]) ).
cnf(f_1699_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6108),U_6110),U_6111))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6108),c_Groups_Ozero__class_Ozero(U_6108)),U_6109))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6108),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6108),U_6109),U_6110)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6108),U_6109),U_6111)))
| ~ class_Rings_Olinordered__semiring__strict(U_6108) ),
inference(clausify,[status(thm)],[f_1699_2]) ).
fof(f_1700_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_1700_2,plain,
! [U_6115,U_6114,U_6113,U_6112] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6112),U_6114),U_6115))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6112),c_Groups_Ozero__class_Ozero(U_6112)),U_6113))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6112),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6112),U_6113),U_6114)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6112),U_6113),U_6115)))
| ~ class_Rings_Olinordered__semiring(U_6112) ),
inference(variable_rename,[status(thm)],[f_1700_1]) ).
cnf(f_1700_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6112),U_6114),U_6115))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6112),c_Groups_Ozero__class_Ozero(U_6112)),U_6113))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6112),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6112),U_6113),U_6114)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6112),U_6113),U_6115)))
| ~ class_Rings_Olinordered__semiring(U_6112) ),
inference(clausify,[status(thm)],[f_1700_2]) ).
fof(f_1701_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_1701_2,plain,
! [U_6119,U_6118,U_6117,U_6116] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6116),U_6117),U_6119))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6116),c_Groups_Ozero__class_Ozero(U_6116)),U_6118))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6116),U_6117),U_6118)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6116),U_6119),U_6118)))
| ~ class_Rings_Olinordered__semiring__strict(U_6116) ),
inference(variable_rename,[status(thm)],[f_1701_1]) ).
cnf(f_1701_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6116),U_6117),U_6119))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6116),c_Groups_Ozero__class_Ozero(U_6116)),U_6118))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6116),U_6117),U_6118)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6116),U_6119),U_6118)))
| ~ class_Rings_Olinordered__semiring__strict(U_6116) ),
inference(clausify,[status(thm)],[f_1701_2]) ).
fof(f_1702_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_1702_2,plain,
! [U_6123,U_6122,U_6121,U_6120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6120),U_6121),U_6123))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6120),c_Groups_Ozero__class_Ozero(U_6120)),U_6122))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6120),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6120),U_6121),U_6122)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6120),U_6123),U_6122)))
| ~ class_Rings_Olinordered__semiring(U_6120) ),
inference(variable_rename,[status(thm)],[f_1702_1]) ).
cnf(f_1702_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6120),U_6121),U_6123))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6120),c_Groups_Ozero__class_Ozero(U_6120)),U_6122))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6120),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6120),U_6121),U_6122)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6120),U_6123),U_6122)))
| ~ class_Rings_Olinordered__semiring(U_6120) ),
inference(clausify,[status(thm)],[f_1702_2]) ).
fof(f_1703_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_1703_2,plain,
! [U_6128,U_6127,U_6126,U_6125,U_6124] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6124),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6124),U_6125),U_6127)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6124),U_6126),U_6128)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6124),c_Groups_Ozero__class_Ozero(U_6124)),U_6127))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6124),c_Groups_Ozero__class_Ozero(U_6124)),U_6125))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6124),U_6127),U_6128))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6124),U_6125),U_6126))
| ~ class_Rings_Olinordered__semiring__strict(U_6124) ),
inference(variable_rename,[status(thm)],[f_1703_1]) ).
cnf(f_1703_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6124),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6124),U_6125),U_6127)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6124),U_6126),U_6128)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6124),c_Groups_Ozero__class_Ozero(U_6124)),U_6127))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6124),c_Groups_Ozero__class_Ozero(U_6124)),U_6125))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6124),U_6127),U_6128))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6124),U_6125),U_6126))
| ~ class_Rings_Olinordered__semiring__strict(U_6124) ),
inference(clausify,[status(thm)],[f_1703_2]) ).
fof(f_1704_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_1704_2,plain,
! [U_6133,U_6132,U_6131,U_6130,U_6129] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6129),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6129),U_6130),U_6132)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6129),U_6131),U_6133)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6129),c_Groups_Ozero__class_Ozero(U_6129)),U_6132))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6129),c_Groups_Ozero__class_Ozero(U_6129)),U_6130))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6129),U_6132),U_6133))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6129),U_6130),U_6131))
| ~ class_Rings_Olinordered__semiring__strict(U_6129) ),
inference(variable_rename,[status(thm)],[f_1704_1]) ).
cnf(f_1704_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6129),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6129),U_6130),U_6132)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6129),U_6131),U_6133)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6129),c_Groups_Ozero__class_Ozero(U_6129)),U_6132))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6129),c_Groups_Ozero__class_Ozero(U_6129)),U_6130))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6129),U_6132),U_6133))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6129),U_6130),U_6131))
| ~ class_Rings_Olinordered__semiring__strict(U_6129) ),
inference(clausify,[status(thm)],[f_1704_2]) ).
fof(f_1705_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_1705_2,plain,
! [U_6138,U_6137,U_6136,U_6135,U_6134] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6134),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6134),U_6135),U_6137)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6134),U_6136),U_6138)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6134),c_Groups_Ozero__class_Ozero(U_6134)),U_6137))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6134),c_Groups_Ozero__class_Ozero(U_6134)),U_6135))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6134),U_6137),U_6138))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6134),U_6135),U_6136))
| ~ class_Rings_Olinordered__semiring__strict(U_6134) ),
inference(variable_rename,[status(thm)],[f_1705_1]) ).
cnf(f_1705_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6134),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6134),U_6135),U_6137)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6134),U_6136),U_6138)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6134),c_Groups_Ozero__class_Ozero(U_6134)),U_6137))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6134),c_Groups_Ozero__class_Ozero(U_6134)),U_6135))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6134),U_6137),U_6138))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6134),U_6135),U_6136))
| ~ class_Rings_Olinordered__semiring__strict(U_6134) ),
inference(clausify,[status(thm)],[f_1705_2]) ).
fof(f_1706_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_1706_2,plain,
! [U_6143,U_6142,U_6141,U_6140,U_6139] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6139),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6139),U_6140),U_6142)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6139),U_6141),U_6143)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6139),c_Groups_Ozero__class_Ozero(U_6139)),U_6142))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6139),c_Groups_Ozero__class_Ozero(U_6139)),U_6141))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6139),U_6142),U_6143))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6139),U_6140),U_6141))
| ~ class_Rings_Olinordered__semiring__strict(U_6139) ),
inference(variable_rename,[status(thm)],[f_1706_1]) ).
cnf(f_1706_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6139),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6139),U_6140),U_6142)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6139),U_6141),U_6143)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6139),c_Groups_Ozero__class_Ozero(U_6139)),U_6142))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6139),c_Groups_Ozero__class_Ozero(U_6139)),U_6141))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6139),U_6142),U_6143))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6139),U_6140),U_6141))
| ~ class_Rings_Olinordered__semiring__strict(U_6139) ),
inference(clausify,[status(thm)],[f_1706_2]) ).
fof(f_1707_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg]) ).
fof(f_1707_2,plain,
! [U_6147,U_6146,U_6145,U_6144] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6144),U_6145),U_6146)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6144),U_6145),U_6147)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6144),U_6147),U_6146)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6144),U_6147),U_6146))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6144),U_6145),U_6146)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6144),U_6145),U_6147))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6144),U_6145),c_Groups_Ozero__class_Ozero(U_6144)))
| ~ class_Rings_Olinordered__ring__strict(U_6144) ),
inference(variable_rename,[status(thm)],[f_1707_1]) ).
cnf(f_1707_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6144),U_6147),U_6146))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6144),U_6145),U_6146)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6144),U_6145),U_6147)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6144),U_6145),c_Groups_Ozero__class_Ozero(U_6144)))
| ~ class_Rings_Olinordered__ring__strict(U_6144) ),
inference(clausify,[status(thm)],[f_1707_2]) ).
cnf(f_1707_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6144),U_6145),U_6146)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6144),U_6145),U_6147)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6144),U_6147),U_6146))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6144),U_6145),c_Groups_Ozero__class_Ozero(U_6144)))
| ~ class_Rings_Olinordered__ring__strict(U_6144) ),
inference(clausify,[status(thm)],[f_1707_2]) ).
fof(f_1708_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos]) ).
fof(f_1708_2,plain,
! [U_6151,U_6150,U_6149,U_6148] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6148),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6148),U_6149),U_6150)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6148),U_6149),U_6151)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6148),U_6150),U_6151)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6148),U_6150),U_6151))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6148),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6148),U_6149),U_6150)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6148),U_6149),U_6151))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6148),c_Groups_Ozero__class_Ozero(U_6148)),U_6149))
| ~ class_Rings_Olinordered__ring__strict(U_6148) ),
inference(variable_rename,[status(thm)],[f_1708_1]) ).
cnf(f_1708_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6148),U_6150),U_6151))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6148),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6148),U_6149),U_6150)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6148),U_6149),U_6151)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6148),c_Groups_Ozero__class_Ozero(U_6148)),U_6149))
| ~ class_Rings_Olinordered__ring__strict(U_6148) ),
inference(clausify,[status(thm)],[f_1708_2]) ).
cnf(f_1708_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6148),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6148),U_6149),U_6150)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6148),U_6149),U_6151)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6148),U_6150),U_6151))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6148),c_Groups_Ozero__class_Ozero(U_6148)),U_6149))
| ~ class_Rings_Olinordered__ring__strict(U_6148) ),
inference(clausify,[status(thm)],[f_1708_2]) ).
fof(f_1709_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_1709_2,plain,
! [U_6154,U_6153,U_6152] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6152),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6152),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6152),U_6153),U_6153)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6152),U_6154),U_6154))),c_Groups_Ozero__class_Ozero(U_6152)))
| U_6154 != c_Groups_Ozero__class_Ozero(U_6152)
| U_6153 != c_Groups_Ozero__class_Ozero(U_6152) )
& ( ( U_6154 = c_Groups_Ozero__class_Ozero(U_6152)
& U_6153 = c_Groups_Ozero__class_Ozero(U_6152) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6152),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6152),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6152),U_6153),U_6153)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6152),U_6154),U_6154))),c_Groups_Ozero__class_Ozero(U_6152))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_6152) ),
inference(variable_rename,[status(thm)],[f_1709_1]) ).
cnf(f_1709_3,plain,
( U_6153 = c_Groups_Ozero__class_Ozero(U_6152)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6152),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6152),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6152),U_6153),U_6153)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6152),U_6154),U_6154))),c_Groups_Ozero__class_Ozero(U_6152)))
| ~ class_Rings_Olinordered__ring__strict(U_6152) ),
inference(clausify,[status(thm)],[f_1709_2]) ).
cnf(f_1709_4,plain,
( U_6154 = c_Groups_Ozero__class_Ozero(U_6152)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6152),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6152),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6152),U_6153),U_6153)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6152),U_6154),U_6154))),c_Groups_Ozero__class_Ozero(U_6152)))
| ~ class_Rings_Olinordered__ring__strict(U_6152) ),
inference(clausify,[status(thm)],[f_1709_2]) ).
cnf(f_1709_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6152),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6152),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6152),U_6153),U_6153)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6152),U_6154),U_6154))),c_Groups_Ozero__class_Ozero(U_6152)))
| U_6154 != c_Groups_Ozero__class_Ozero(U_6152)
| U_6153 != c_Groups_Ozero__class_Ozero(U_6152)
| ~ class_Rings_Olinordered__ring__strict(U_6152) ),
inference(clausify,[status(thm)],[f_1709_2]) ).
fof(f_1710_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_1710_2,plain,
! [U_6157,U_6156,U_6155] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6155),c_Groups_Ozero__class_Ozero(U_6155)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6155),U_6156),U_6156)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6155),U_6157),U_6157))))
| ~ class_Rings_Olinordered__ring(U_6155) ),
inference(variable_rename,[status(thm)],[f_1710_1]) ).
cnf(f_1710_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6155),c_Groups_Ozero__class_Ozero(U_6155)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6155),U_6156),U_6156)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6155),U_6157),U_6157))))
| ~ class_Rings_Olinordered__ring(U_6155) ),
inference(clausify,[status(thm)],[f_1710_2]) ).
fof(f_1711_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_1711_2,plain,
! [U_6160,U_6159,U_6158] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6158),c_Groups_Ozero__class_Ozero(U_6158)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6158),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6158),U_6159),U_6159)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6158),U_6160),U_6160))))
| ( U_6160 = c_Groups_Ozero__class_Ozero(U_6158)
& U_6159 = c_Groups_Ozero__class_Ozero(U_6158) ) )
& ( U_6160 != c_Groups_Ozero__class_Ozero(U_6158)
| U_6159 != c_Groups_Ozero__class_Ozero(U_6158)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6158),c_Groups_Ozero__class_Ozero(U_6158)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6158),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6158),U_6159),U_6159)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6158),U_6160),U_6160)))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_6158) ),
inference(variable_rename,[status(thm)],[f_1711_1]) ).
cnf(f_1711_3,plain,
( U_6160 != c_Groups_Ozero__class_Ozero(U_6158)
| U_6159 != c_Groups_Ozero__class_Ozero(U_6158)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6158),c_Groups_Ozero__class_Ozero(U_6158)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6158),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6158),U_6159),U_6159)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6158),U_6160),U_6160))))
| ~ class_Rings_Olinordered__ring__strict(U_6158) ),
inference(clausify,[status(thm)],[f_1711_2]) ).
cnf(f_1711_4,plain,
( U_6159 = c_Groups_Ozero__class_Ozero(U_6158)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6158),c_Groups_Ozero__class_Ozero(U_6158)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6158),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6158),U_6159),U_6159)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6158),U_6160),U_6160))))
| ~ class_Rings_Olinordered__ring__strict(U_6158) ),
inference(clausify,[status(thm)],[f_1711_2]) ).
cnf(f_1711_5,plain,
( U_6160 = c_Groups_Ozero__class_Ozero(U_6158)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6158),c_Groups_Ozero__class_Ozero(U_6158)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6158),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6158),U_6159),U_6159)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6158),U_6160),U_6160))))
| ~ class_Rings_Olinordered__ring__strict(U_6158) ),
inference(clausify,[status(thm)],[f_1711_2]) ).
fof(f_1712_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_1712_2,plain,
! [U_6163,U_6162,U_6161] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6161),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6161),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6161),U_6162),U_6162)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6161),U_6163),U_6163))),c_Groups_Ozero__class_Ozero(U_6161)))
| ~ class_Rings_Olinordered__ring(U_6161) ),
inference(variable_rename,[status(thm)],[f_1712_1]) ).
cnf(f_1712_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6161),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6161),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6161),U_6162),U_6162)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6161),U_6163),U_6163))),c_Groups_Ozero__class_Ozero(U_6161)))
| ~ class_Rings_Olinordered__ring(U_6161) ),
inference(clausify,[status(thm)],[f_1712_2]) ).
fof(f_1713_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_1713_2,plain,
! [U_6166,U_6165,U_6164] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6164),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6164),U_6166),U_6165)),U_6165))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6164),U_6166),c_Groups_Oone__class_Oone(U_6164)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6164),c_Groups_Ozero__class_Ozero(U_6164)),U_6166))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6164),c_Groups_Ozero__class_Ozero(U_6164)),U_6165))
| ~ class_Rings_Olinordered__idom(U_6164) ),
inference(variable_rename,[status(thm)],[f_1713_1]) ).
cnf(f_1713_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6164),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6164),U_6166),U_6165)),U_6165))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6164),U_6166),c_Groups_Oone__class_Oone(U_6164)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6164),c_Groups_Ozero__class_Ozero(U_6164)),U_6166))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6164),c_Groups_Ozero__class_Ozero(U_6164)),U_6165))
| ~ class_Rings_Olinordered__idom(U_6164) ),
inference(clausify,[status(thm)],[f_1713_2]) ).
fof(f_1714_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_1714_2,plain,
! [U_6169,U_6168,U_6167] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6167),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6167),U_6168),U_6169)),U_6168))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6167),U_6169),c_Groups_Oone__class_Oone(U_6167)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6167),c_Groups_Ozero__class_Ozero(U_6167)),U_6169))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6167),c_Groups_Ozero__class_Ozero(U_6167)),U_6168))
| ~ class_Rings_Olinordered__idom(U_6167) ),
inference(variable_rename,[status(thm)],[f_1714_1]) ).
cnf(f_1714_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6167),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6167),U_6168),U_6169)),U_6168))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6167),U_6169),c_Groups_Oone__class_Oone(U_6167)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6167),c_Groups_Ozero__class_Ozero(U_6167)),U_6169))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6167),c_Groups_Ozero__class_Ozero(U_6167)),U_6168))
| ~ class_Rings_Olinordered__idom(U_6167) ),
inference(clausify,[status(thm)],[f_1714_2]) ).
fof(f_1715_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_1715_2,plain,
! [U_6172,U_6171,U_6170] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6170),U_6171),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_6172))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6170),U_6171),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6170),hAPP(hAPP(c_Power_Opower__class_Opower(U_6170),U_6171),U_6172)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6170),U_6171),U_6172)))
| ~ class_Rings_Ocomm__semiring__1(U_6170) ),
inference(variable_rename,[status(thm)],[f_1715_1]) ).
cnf(f_1715_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6170),U_6171),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_6172))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6170),U_6171),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6170),hAPP(hAPP(c_Power_Opower__class_Opower(U_6170),U_6171),U_6172)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6170),U_6171),U_6172)))
| ~ class_Rings_Ocomm__semiring__1(U_6170) ),
inference(clausify,[status(thm)],[f_1715_2]) ).
fof(f_1716_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_1716_2,plain,
! [U_6175,U_6174,U_6173] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6173),U_6174),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_6175))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6173),U_6174),hAPP(hAPP(c_Power_Opower__class_Opower(U_6173),hAPP(hAPP(c_Power_Opower__class_Opower(U_6173),U_6174),U_6175)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Groups_Omonoid__mult(U_6173) ),
inference(variable_rename,[status(thm)],[f_1716_1]) ).
cnf(f_1716_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6173),U_6174),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_6175))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6173),U_6174),hAPP(hAPP(c_Power_Opower__class_Opower(U_6173),hAPP(hAPP(c_Power_Opower__class_Opower(U_6173),U_6174),U_6175)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Groups_Omonoid__mult(U_6173) ),
inference(clausify,[status(thm)],[f_1716_2]) ).
fof(f_1717_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) ) )
| ~ class_Rings_Oordered__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__add__iff1]) ).
fof(f_1717_2,plain,
! [U_6181,U_6180,U_6179,U_6178,U_6177,U_6176] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6176),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6176),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6176),U_6177),U_6178)),U_6179)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6176),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6176),U_6180),U_6178)),U_6181)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6176),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6176),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6176),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6176),U_6177),U_6180)),U_6178)),U_6179)),U_6181)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6176),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6176),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6176),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6176),U_6177),U_6180)),U_6178)),U_6179)),U_6181))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6176),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6176),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6176),U_6177),U_6178)),U_6179)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6176),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6176),U_6180),U_6178)),U_6181))) ) )
| ~ class_Rings_Oordered__ring(U_6176) ),
inference(variable_rename,[status(thm)],[f_1717_1]) ).
cnf(f_1717_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6176),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6176),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6176),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6176),U_6177),U_6180)),U_6178)),U_6179)),U_6181))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6176),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6176),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6176),U_6177),U_6178)),U_6179)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6176),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6176),U_6180),U_6178)),U_6181)))
| ~ class_Rings_Oordered__ring(U_6176) ),
inference(clausify,[status(thm)],[f_1717_2]) ).
cnf(f_1717_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6176),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6176),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6176),U_6177),U_6178)),U_6179)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6176),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6176),U_6180),U_6178)),U_6181)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6176),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6176),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6176),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6176),U_6177),U_6180)),U_6178)),U_6179)),U_6181))
| ~ class_Rings_Oordered__ring(U_6176) ),
inference(clausify,[status(thm)],[f_1717_2]) ).
fof(f_1718_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) ) )
| ~ class_Rings_Oordered__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__add__iff2]) ).
fof(f_1718_2,plain,
! [U_6187,U_6186,U_6185,U_6184,U_6183,U_6182] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6182),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6182),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6182),U_6183),U_6184)),U_6185)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6182),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6182),U_6186),U_6184)),U_6187)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6182),U_6185),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6182),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6182),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6182),U_6186),U_6183)),U_6184)),U_6187))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6182),U_6185),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6182),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6182),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6182),U_6186),U_6183)),U_6184)),U_6187)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6182),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6182),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6182),U_6183),U_6184)),U_6185)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6182),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6182),U_6186),U_6184)),U_6187))) ) )
| ~ class_Rings_Oordered__ring(U_6182) ),
inference(variable_rename,[status(thm)],[f_1718_1]) ).
cnf(f_1718_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6182),U_6185),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6182),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6182),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6182),U_6186),U_6183)),U_6184)),U_6187)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6182),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6182),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6182),U_6183),U_6184)),U_6185)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6182),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6182),U_6186),U_6184)),U_6187)))
| ~ class_Rings_Oordered__ring(U_6182) ),
inference(clausify,[status(thm)],[f_1718_2]) ).
cnf(f_1718_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6182),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6182),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6182),U_6183),U_6184)),U_6185)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6182),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6182),U_6186),U_6184)),U_6187)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6182),U_6185),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6182),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6182),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6182),U_6186),U_6183)),U_6184)),U_6187)))
| ~ class_Rings_Oordered__ring(U_6182) ),
inference(clausify,[status(thm)],[f_1718_2]) ).
fof(f_1719_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) ) )
| ~ class_Rings_Oordered__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__add__iff1]) ).
fof(f_1719_2,plain,
! [U_6193,U_6192,U_6191,U_6190,U_6189,U_6188] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6188),U_6189),U_6190)),U_6191)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6188),U_6192),U_6190)),U_6193)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6188),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6188),U_6189),U_6192)),U_6190)),U_6191)),U_6193)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6188),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6188),U_6189),U_6192)),U_6190)),U_6191)),U_6193))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6188),U_6189),U_6190)),U_6191)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6188),U_6192),U_6190)),U_6193))) ) )
| ~ class_Rings_Oordered__ring(U_6188) ),
inference(variable_rename,[status(thm)],[f_1719_1]) ).
cnf(f_1719_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6188),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6188),U_6189),U_6192)),U_6190)),U_6191)),U_6193))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6188),U_6189),U_6190)),U_6191)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6188),U_6192),U_6190)),U_6193)))
| ~ class_Rings_Oordered__ring(U_6188) ),
inference(clausify,[status(thm)],[f_1719_2]) ).
cnf(f_1719_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6188),U_6189),U_6190)),U_6191)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6188),U_6192),U_6190)),U_6193)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6188),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6188),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6188),U_6189),U_6192)),U_6190)),U_6191)),U_6193))
| ~ class_Rings_Oordered__ring(U_6188) ),
inference(clausify,[status(thm)],[f_1719_2]) ).
fof(f_1720_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) ) )
| ~ class_Rings_Oordered__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__add__iff2]) ).
fof(f_1720_2,plain,
! [U_6199,U_6198,U_6197,U_6196,U_6195,U_6194] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6194),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6194),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6194),U_6195),U_6196)),U_6197)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6194),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6194),U_6198),U_6196)),U_6199)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6194),U_6197),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6194),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6194),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6194),U_6198),U_6195)),U_6196)),U_6199))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6194),U_6197),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6194),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6194),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6194),U_6198),U_6195)),U_6196)),U_6199)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6194),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6194),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6194),U_6195),U_6196)),U_6197)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6194),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6194),U_6198),U_6196)),U_6199))) ) )
| ~ class_Rings_Oordered__ring(U_6194) ),
inference(variable_rename,[status(thm)],[f_1720_1]) ).
cnf(f_1720_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6194),U_6197),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6194),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6194),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6194),U_6198),U_6195)),U_6196)),U_6199)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6194),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6194),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6194),U_6195),U_6196)),U_6197)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6194),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6194),U_6198),U_6196)),U_6199)))
| ~ class_Rings_Oordered__ring(U_6194) ),
inference(clausify,[status(thm)],[f_1720_2]) ).
cnf(f_1720_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6194),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6194),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6194),U_6195),U_6196)),U_6197)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6194),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6194),U_6198),U_6196)),U_6199)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6194),U_6197),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6194),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6194),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6194),U_6198),U_6195)),U_6196)),U_6199)))
| ~ class_Rings_Oordered__ring(U_6194) ),
inference(clausify,[status(thm)],[f_1720_2]) ).
fof(f_1721_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_1721_2,plain,
! [U_6202,U_6201,U_6200] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6200),c_Groups_Oone__class_Oone(U_6200)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6200),U_6201),hAPP(hAPP(c_Power_Opower__class_Opower(U_6200),U_6201),U_6202))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6200),c_Groups_Oone__class_Oone(U_6200)),U_6201))
| ~ class_Rings_Olinordered__semidom(U_6200) ),
inference(variable_rename,[status(thm)],[f_1721_1]) ).
cnf(f_1721_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6200),c_Groups_Oone__class_Oone(U_6200)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6200),U_6201),hAPP(hAPP(c_Power_Opower__class_Opower(U_6200),U_6201),U_6202))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6200),c_Groups_Oone__class_Oone(U_6200)),U_6201))
| ~ class_Rings_Olinordered__semidom(U_6200) ),
inference(clausify,[status(thm)],[f_1721_2]) ).
fof(f_1722_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_1722_2,plain,
! [U_6205,U_6204,U_6203] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6203),hAPP(hAPP(c_Power_Opower__class_Opower(U_6203),U_6204),U_6205)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6203),U_6204),hAPP(hAPP(c_Power_Opower__class_Opower(U_6203),U_6204),U_6205))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6203),c_Groups_Oone__class_Oone(U_6203)),U_6204))
| ~ class_Rings_Olinordered__semidom(U_6203) ),
inference(variable_rename,[status(thm)],[f_1722_1]) ).
cnf(f_1722_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6203),hAPP(hAPP(c_Power_Opower__class_Opower(U_6203),U_6204),U_6205)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6203),U_6204),hAPP(hAPP(c_Power_Opower__class_Opower(U_6203),U_6204),U_6205))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6203),c_Groups_Oone__class_Oone(U_6203)),U_6204))
| ~ class_Rings_Olinordered__semidom(U_6203) ),
inference(clausify,[status(thm)],[f_1722_2]) ).
fof(f_1723_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_1723_2,plain,
! [U_6207,U_6206] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6206),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6207),U_6206)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6207))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6206)) ),
inference(variable_rename,[status(thm)],[f_1723_1]) ).
cnf(f_1723_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6206),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6207),U_6206)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6207))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6206)) ),
inference(clausify,[status(thm)],[f_1723_2]) ).
fof(f_1724_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_1724_2,plain,
! [U_6209,U_6208] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6208),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6208),U_6209)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6209))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6208)) ),
inference(variable_rename,[status(thm)],[f_1724_1]) ).
cnf(f_1724_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6208),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6208),U_6209)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6209))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6208)) ),
inference(clausify,[status(thm)],[f_1724_2]) ).
fof(f_1725_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_1725_2,plain,
! [U_6211,U_6210] :
( 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_6211),U_6210)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6211))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6210)) ),
inference(variable_rename,[status(thm)],[f_1725_1]) ).
cnf(f_1725_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_6211),U_6210)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6211))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6210)) ),
inference(clausify,[status(thm)],[f_1725_2]) ).
fof(f_1726_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_1726_2,plain,
! [U_6214,U_6213,U_6212] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6212),hAPP(c_Groups_Ouminus__class_Ouminus(U_6212),U_6213)),U_6214) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6212),hAPP(hAPP(c_Power_Opower__class_Opower(U_6212),hAPP(c_Groups_Ouminus__class_Ouminus(U_6212),c_Groups_Oone__class_Oone(U_6212))),U_6214)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6212),U_6213),U_6214))
| ~ class_Rings_Oring__1(U_6212) ),
inference(variable_rename,[status(thm)],[f_1726_1]) ).
cnf(f_1726_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6212),hAPP(c_Groups_Ouminus__class_Ouminus(U_6212),U_6213)),U_6214) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6212),hAPP(hAPP(c_Power_Opower__class_Opower(U_6212),hAPP(c_Groups_Ouminus__class_Ouminus(U_6212),c_Groups_Oone__class_Oone(U_6212))),U_6214)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6212),U_6213),U_6214))
| ~ class_Rings_Oring__1(U_6212) ),
inference(clausify,[status(thm)],[f_1726_2]) ).
fof(f_1727_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_1727_2,plain,
! [U_6216,U_6215] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6215),U_6216),hAPP(c_Int_Onumber__class_Onumber__of(U_6215),c_Int_OBit1(c_Int_OPls))) = U_6216
| ~ class_Int_Onumber__ring(U_6215) ),
inference(variable_rename,[status(thm)],[f_1727_1]) ).
cnf(f_1727_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6215),U_6216),hAPP(c_Int_Onumber__class_Onumber__of(U_6215),c_Int_OBit1(c_Int_OPls))) = U_6216
| ~ class_Int_Onumber__ring(U_6215) ),
inference(clausify,[status(thm)],[f_1727_2]) ).
fof(f_1728_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_1728_2,plain,
! [U_6218,U_6217] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6217),hAPP(c_Int_Onumber__class_Onumber__of(U_6217),c_Int_OBit1(c_Int_OPls))),U_6218) = U_6218
| ~ class_Int_Onumber__ring(U_6217) ),
inference(variable_rename,[status(thm)],[f_1728_1]) ).
cnf(f_1728_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6217),hAPP(c_Int_Onumber__class_Onumber__of(U_6217),c_Int_OBit1(c_Int_OPls))),U_6218) = U_6218
| ~ class_Int_Onumber__ring(U_6217) ),
inference(clausify,[status(thm)],[f_1728_2]) ).
fof(f_1729_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_1729_2,plain,
! [U_6220,U_6219] :
( ( 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_6219),U_6220)))
| ~ 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_6220))
| ~ 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_6219)) )
& ( ( 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_6220))
& 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_6219)) )
| ~ 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_6219),U_6220))) ) ),
inference(variable_rename,[status(thm)],[f_1729_1]) ).
fof(f_1729_3,plain,
( ! [U_6224,U_6222] :
( 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_6222),U_6224)))
| ~ 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_6224))
| ~ 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_6222)) )
& ! [U_6223,U_6221] :
( ( 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_6223))
& 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_6221)) )
| ~ 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_6221),U_6223))) ) ),
inference(miniscope,[status(thm)],[f_1729_2]) ).
cnf(f_1729_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_6221))
| ~ 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_6221),U_6223))) ),
inference(clausify,[status(thm)],[f_1729_3]) ).
cnf(f_1729_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_6223))
| ~ 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_6221),U_6223))) ),
inference(clausify,[status(thm)],[f_1729_3]) ).
cnf(f_1729_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_6222),U_6224)))
| ~ 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_6224))
| ~ 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_6222)) ),
inference(clausify,[status(thm)],[f_1729_3]) ).
fof(f_1730_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_1730_2,plain,
! [U_6227,U_6226,U_6225] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6225),U_6226)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6227),U_6226)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6225),U_6227))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6226)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6225),U_6227))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6226))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6225),U_6226)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6227),U_6226))) ) ),
inference(variable_rename,[status(thm)],[f_1730_1]) ).
fof(f_1730_3,plain,
( ! [U_6233,U_6231,U_6229] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6229),U_6231)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6233),U_6231)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6229),U_6233))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6231)) ) )
& ! [U_6232,U_6230,U_6228] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6228),U_6232))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6230))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6228),U_6230)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6232),U_6230))) ) ),
inference(miniscope,[status(thm)],[f_1730_2]) ).
cnf(f_1730_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6228),U_6232))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6230))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6228),U_6230)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6232),U_6230))) ),
inference(clausify,[status(thm)],[f_1730_3]) ).
cnf(f_1730_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6231))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6229),U_6231)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6233),U_6231))) ),
inference(clausify,[status(thm)],[f_1730_3]) ).
cnf(f_1730_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6229),U_6233))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6229),U_6231)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6233),U_6231))) ),
inference(clausify,[status(thm)],[f_1730_3]) ).
fof(f_1731_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_1731_2,plain,
! [U_6236,U_6235,U_6234] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6234),U_6235)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6234),U_6236)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6235),U_6236))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6234)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6235),U_6236))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6234))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6234),U_6235)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6234),U_6236))) ) ),
inference(variable_rename,[status(thm)],[f_1731_1]) ).
fof(f_1731_3,plain,
( ! [U_6242,U_6240,U_6238] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6238),U_6240)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6238),U_6242)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6240),U_6242))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6238)) ) )
& ! [U_6241,U_6239,U_6237] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6239),U_6241))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6237))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6237),U_6239)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6237),U_6241))) ) ),
inference(miniscope,[status(thm)],[f_1731_2]) ).
cnf(f_1731_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6239),U_6241))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6237))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6237),U_6239)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6237),U_6241))) ),
inference(clausify,[status(thm)],[f_1731_3]) ).
cnf(f_1731_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6238))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6238),U_6240)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6238),U_6242))) ),
inference(clausify,[status(thm)],[f_1731_3]) ).
cnf(f_1731_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6240),U_6242))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6238),U_6240)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6238),U_6242))) ),
inference(clausify,[status(thm)],[f_1731_3]) ).
fof(f_1732_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_1732_2,plain,
! [U_6245,U_6244,U_6243] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6243),hAPP(c_Groups_Ouminus__class_Ouminus(U_6243),hAPP(c_Int_Onumber__class_Onumber__of(U_6243),U_6244))),U_6245) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6243),hAPP(c_Int_Onumber__class_Onumber__of(U_6243),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6244))),U_6245)
| ~ class_Int_Onumber__ring(U_6243) ),
inference(variable_rename,[status(thm)],[f_1732_1]) ).
cnf(f_1732_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6243),hAPP(c_Groups_Ouminus__class_Ouminus(U_6243),hAPP(c_Int_Onumber__class_Onumber__of(U_6243),U_6244))),U_6245) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6243),hAPP(c_Int_Onumber__class_Onumber__of(U_6243),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6244))),U_6245)
| ~ class_Int_Onumber__ring(U_6243) ),
inference(clausify,[status(thm)],[f_1732_2]) ).
fof(f_1733_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_1733_2,plain,
! [U_6247,U_6246] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6246),U_6247) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_6247 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_6246 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( ( U_6247 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& U_6246 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6246),U_6247) != 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_6246)) ),
inference(variable_rename,[status(thm)],[f_1733_1]) ).
cnf(f_1733_3,plain,
( U_6246 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6246),U_6247) != 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_6246)) ),
inference(clausify,[status(thm)],[f_1733_2]) ).
cnf(f_1733_4,plain,
( U_6247 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6246),U_6247) != 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_6246)) ),
inference(clausify,[status(thm)],[f_1733_2]) ).
cnf(f_1733_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6246),U_6247) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_6247 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_6246 != 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_6246)) ),
inference(clausify,[status(thm)],[f_1733_2]) ).
fof(f_1734_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_1734_2,plain,
! [U_6249,U_6248] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_6248)),U_6249) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6248),U_6249))),U_6249),
inference(variable_rename,[status(thm)],[f_1734_1]) ).
cnf(f_1734_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_6248)),U_6249) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6248),U_6249))),U_6249),
inference(clausify,[status(thm)],[f_1734_2]) ).
fof(f_1735_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_1735_2,plain,
! [U_6255,U_6254,U_6253,U_6252,U_6251,U_6250] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6250),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6250),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6250),U_6254),U_6251)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6250),U_6255),U_6253))),U_6252))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6250),U_6254),U_6255) != c_Groups_Oone__class_Oone(U_6250)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6250),c_Groups_Ozero__class_Ozero(U_6250)),U_6255))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6250),c_Groups_Ozero__class_Ozero(U_6250)),U_6254))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6250),U_6253),U_6252))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6250),U_6251),U_6252))
| ~ class_Rings_Olinordered__semiring__1(U_6250) ),
inference(variable_rename,[status(thm)],[f_1735_1]) ).
cnf(f_1735_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6250),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6250),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6250),U_6254),U_6251)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6250),U_6255),U_6253))),U_6252))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6250),U_6254),U_6255) != c_Groups_Oone__class_Oone(U_6250)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6250),c_Groups_Ozero__class_Ozero(U_6250)),U_6255))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6250),c_Groups_Ozero__class_Ozero(U_6250)),U_6254))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6250),U_6253),U_6252))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6250),U_6251),U_6252))
| ~ class_Rings_Olinordered__semiring__1(U_6250) ),
inference(clausify,[status(thm)],[f_1735_2]) ).
fof(f_1736_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_1736_2,plain,
! [U_6258,U_6257,U_6256] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6256),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6256),U_6257),hAPP(hAPP(c_Power_Opower__class_Opower(U_6256),U_6257),U_6258))),hAPP(hAPP(c_Power_Opower__class_Opower(U_6256),U_6257),U_6258)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6256),U_6257),c_Groups_Oone__class_Oone(U_6256)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6256),c_Groups_Ozero__class_Ozero(U_6256)),U_6257))
| ~ class_Rings_Olinordered__semidom(U_6256) ),
inference(variable_rename,[status(thm)],[f_1736_1]) ).
cnf(f_1736_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6256),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6256),U_6257),hAPP(hAPP(c_Power_Opower__class_Opower(U_6256),U_6257),U_6258))),hAPP(hAPP(c_Power_Opower__class_Opower(U_6256),U_6257),U_6258)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6256),U_6257),c_Groups_Oone__class_Oone(U_6256)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6256),c_Groups_Ozero__class_Ozero(U_6256)),U_6257))
| ~ class_Rings_Olinordered__semidom(U_6256) ),
inference(clausify,[status(thm)],[f_1736_2]) ).
fof(f_1737_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_1737_2,plain,
! [U_6260,U_6259] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6259),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6259),c_Groups_Oone__class_Oone(U_6259)),c_Groups_Oone__class_Oone(U_6259))),hAPP(c_Int_Onumber__class_Onumber__of(U_6259),U_6260)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6259),c_Int_OBit0(U_6260))
| ~ class_Int_Onumber__ring(U_6259) ),
inference(variable_rename,[status(thm)],[f_1737_1]) ).
cnf(f_1737_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6259),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6259),c_Groups_Oone__class_Oone(U_6259)),c_Groups_Oone__class_Oone(U_6259))),hAPP(c_Int_Onumber__class_Onumber__of(U_6259),U_6260)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6259),c_Int_OBit0(U_6260))
| ~ class_Int_Onumber__ring(U_6259) ),
inference(clausify,[status(thm)],[f_1737_2]) ).
fof(f_1738_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_1738_2,plain,
! [U_6263,U_6262,U_6261] :
( 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_6263)),U_6261)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6263)),U_6262)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6263))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6261),U_6262)) ),
inference(variable_rename,[status(thm)],[f_1738_1]) ).
cnf(f_1738_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_6263)),U_6261)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6263)),U_6262)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6263))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6261),U_6262)) ),
inference(clausify,[status(thm)],[f_1738_2]) ).
fof(f_1739_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_1739_2,plain,
! [U_6265,U_6264] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6264),U_6265),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_6264),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6264),U_6265),U_6265)),U_6265)
| ~ class_Groups_Omonoid__mult(U_6264) ),
inference(variable_rename,[status(thm)],[f_1739_1]) ).
cnf(f_1739_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6264),U_6265),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_6264),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6264),U_6265),U_6265)),U_6265)
| ~ class_Groups_Omonoid__mult(U_6264) ),
inference(clausify,[status(thm)],[f_1739_2]) ).
fof(f_1740_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_1740_2,plain,
! [U_6267,U_6266] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6266),U_6267) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6267),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6266),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_6267))
| U_6266 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6266),U_6267) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6266 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1740_1]) ).
fof(f_1740_3,plain,
( ! [U_6271,U_6269] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6269),U_6271) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6271),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6269),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_6271))
| U_6269 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6270,U_6268] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6268),U_6270) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6268 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1740_2]) ).
cnf(f_1740_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6268),U_6270) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6268 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1740_3]) ).
cnf(f_1740_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6269),U_6271) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6271),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6269),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_6271))
| U_6269 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1740_3]) ).
fof(f_1741_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_1741_2,plain,
! [U_6273,U_6272] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6273),U_6272) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6273),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6273),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6272),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_6272 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6273),U_6272) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_6272 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1741_1]) ).
fof(f_1741_3,plain,
( ! [U_6277,U_6275] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6277),U_6275) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6277),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6277),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6275),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_6275 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6276,U_6274] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6276),U_6274) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_6274 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1741_2]) ).
cnf(f_1741_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6276),U_6274) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_6274 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1741_3]) ).
cnf(f_1741_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6277),U_6275) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6277),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6277),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6275),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_6275 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1741_3]) ).
fof(f_1742_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_1742_2,plain,
! [U_6283,U_6282,U_6281,U_6280,U_6279,U_6278] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6278),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6278),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6278),U_6282),U_6279)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6278),U_6283),U_6281))),U_6280))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6278),U_6282),U_6283) != c_Groups_Oone__class_Oone(U_6278)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6278),c_Groups_Ozero__class_Ozero(U_6278)),U_6283))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6278),c_Groups_Ozero__class_Ozero(U_6278)),U_6282))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6278),U_6281),U_6280))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6278),U_6279),U_6280))
| ~ class_Rings_Olinordered__semiring__1__strict(U_6278) ),
inference(variable_rename,[status(thm)],[f_1742_1]) ).
cnf(f_1742_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6278),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6278),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6278),U_6282),U_6279)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6278),U_6283),U_6281))),U_6280))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6278),U_6282),U_6283) != c_Groups_Oone__class_Oone(U_6278)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6278),c_Groups_Ozero__class_Ozero(U_6278)),U_6283))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6278),c_Groups_Ozero__class_Ozero(U_6278)),U_6282))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6278),U_6281),U_6280))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6278),U_6279),U_6280))
| ~ class_Rings_Olinordered__semiring__1__strict(U_6278) ),
inference(clausify,[status(thm)],[f_1742_2]) ).
fof(f_1743_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_1743_2,plain,
! [U_6285,U_6284] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6284),U_6285),hAPP(c_Int_Onumber__class_Onumber__of(U_6284),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6284),U_6285),U_6285)
| ~ class_Int_Onumber__ring(U_6284) ),
inference(variable_rename,[status(thm)],[f_1743_1]) ).
cnf(f_1743_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6284),U_6285),hAPP(c_Int_Onumber__class_Onumber__of(U_6284),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6284),U_6285),U_6285)
| ~ class_Int_Onumber__ring(U_6284) ),
inference(clausify,[status(thm)],[f_1743_2]) ).
fof(f_1744_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_1744_2,plain,
! [U_6287,U_6286] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6286),hAPP(c_Int_Onumber__class_Onumber__of(U_6286),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_6287) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6286),U_6287),U_6287)
| ~ class_Int_Onumber__ring(U_6286) ),
inference(variable_rename,[status(thm)],[f_1744_1]) ).
cnf(f_1744_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6286),hAPP(c_Int_Onumber__class_Onumber__of(U_6286),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_6287) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6286),U_6287),U_6287)
| ~ class_Int_Onumber__ring(U_6286) ),
inference(clausify,[status(thm)],[f_1744_2]) ).
fof(f_1745_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_1745_2,plain,
! [U_6289,U_6288] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6288),U_6289),U_6289) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6288),U_6289),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_6288) ),
inference(variable_rename,[status(thm)],[f_1745_1]) ).
cnf(f_1745_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6288),U_6289),U_6289) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6288),U_6289),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_6288) ),
inference(clausify,[status(thm)],[f_1745_2]) ).
fof(f_1746_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_1746_2,plain,
! [U_6291,U_6290] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6290),U_6291),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_6290),U_6291),U_6291)
| ~ class_Groups_Omonoid__mult(U_6290) ),
inference(variable_rename,[status(thm)],[f_1746_1]) ).
cnf(f_1746_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6290),U_6291),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_6290),U_6291),U_6291)
| ~ class_Groups_Omonoid__mult(U_6290) ),
inference(clausify,[status(thm)],[f_1746_2]) ).
fof(f_1747_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_1747_2,plain,
! [U_6292] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6292),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_6292),U_6292),
inference(variable_rename,[status(thm)],[f_1747_1]) ).
cnf(f_1747_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6292),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_6292),U_6292),
inference(clausify,[status(thm)],[f_1747_2]) ).
fof(f_1748_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_1748_2,plain,
! [U_6293] : 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_6293) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6293),U_6293),
inference(variable_rename,[status(thm)],[f_1748_1]) ).
cnf(f_1748_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_6293) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6293),U_6293),
inference(clausify,[status(thm)],[f_1748_2]) ).
fof(f_1749_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_1749_2,plain,
! [U_6296,U_6295,U_6294] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6294),U_6295),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_6296)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6294),hAPP(hAPP(c_Power_Opower__class_Opower(U_6294),U_6295),U_6296)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Groups_Omonoid__mult(U_6294) ),
inference(variable_rename,[status(thm)],[f_1749_1]) ).
cnf(f_1749_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6294),U_6295),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_6296)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6294),hAPP(hAPP(c_Power_Opower__class_Opower(U_6294),U_6295),U_6296)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Groups_Omonoid__mult(U_6294) ),
inference(clausify,[status(thm)],[f_1749_2]) ).
fof(f_1750_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_1750_2,plain,
! [U_6298,U_6297] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6297),hAPP(c_Int_Onumber__class_Onumber__of(U_6297),U_6298)),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_6297),hAPP(c_Int_Onumber__class_Onumber__of(U_6297),U_6298)),hAPP(c_Int_Onumber__class_Onumber__of(U_6297),U_6298))
| ~ class_Int_Onumber(U_6297)
| ~ class_Groups_Omonoid__mult(U_6297) ),
inference(variable_rename,[status(thm)],[f_1750_1]) ).
cnf(f_1750_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6297),hAPP(c_Int_Onumber__class_Onumber__of(U_6297),U_6298)),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_6297),hAPP(c_Int_Onumber__class_Onumber__of(U_6297),U_6298)),hAPP(c_Int_Onumber__class_Onumber__of(U_6297),U_6298))
| ~ class_Int_Onumber(U_6297)
| ~ class_Groups_Omonoid__mult(U_6297) ),
inference(clausify,[status(thm)],[f_1750_2]) ).
fof(f_1751_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_1751_2,plain,
! [U_6301,U_6300,U_6299] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6299),hAPP(c_Groups_Ouminus__class_Ouminus(U_6299),U_6300)),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_6301)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6299),U_6300),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_6301))
| ~ class_Rings_Oring__1(U_6299) ),
inference(variable_rename,[status(thm)],[f_1751_1]) ).
cnf(f_1751_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6299),hAPP(c_Groups_Ouminus__class_Ouminus(U_6299),U_6300)),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_6301)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6299),U_6300),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_6301))
| ~ class_Rings_Oring__1(U_6299) ),
inference(clausify,[status(thm)],[f_1751_2]) ).
fof(f_1752_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_1752_2,plain,
! [U_6304,U_6303,U_6302] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6302),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6302),U_6303),U_6304)),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_6302),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6302),hAPP(hAPP(c_Power_Opower__class_Opower(U_6302),U_6303),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_6302),U_6304),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_6302),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6302),hAPP(c_Int_Onumber__class_Onumber__of(U_6302),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_6303)),U_6304))
| ~ class_Int_Onumber__ring(U_6302) ),
inference(variable_rename,[status(thm)],[f_1752_1]) ).
cnf(f_1752_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6302),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6302),U_6303),U_6304)),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_6302),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6302),hAPP(hAPP(c_Power_Opower__class_Opower(U_6302),U_6303),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_6302),U_6304),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_6302),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6302),hAPP(c_Int_Onumber__class_Onumber__of(U_6302),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_6303)),U_6304))
| ~ class_Int_Onumber__ring(U_6302) ),
inference(clausify,[status(thm)],[f_1752_2]) ).
fof(f_1753_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_1753_2,plain,
! [U_6309,U_6308,U_6307,U_6306,U_6305] :
( ( ( 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_6306),U_6307)),U_6308)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6305),U_6307)),U_6309)))
| ~ 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_6306),U_6305)),U_6307)),U_6308)),U_6309)) )
& ( 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_6306),U_6305)),U_6307)),U_6308)),U_6309))
| ~ 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_6306),U_6307)),U_6308)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6305),U_6307)),U_6309))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6305),U_6306)) ),
inference(variable_rename,[status(thm)],[f_1753_1]) ).
cnf(f_1753_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_6306),U_6305)),U_6307)),U_6308)),U_6309))
| ~ 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_6306),U_6307)),U_6308)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6305),U_6307)),U_6309)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6305),U_6306)) ),
inference(clausify,[status(thm)],[f_1753_2]) ).
cnf(f_1753_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_6306),U_6307)),U_6308)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6305),U_6307)),U_6309)))
| ~ 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_6306),U_6305)),U_6307)),U_6308)),U_6309))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6305),U_6306)) ),
inference(clausify,[status(thm)],[f_1753_2]) ).
fof(f_1754_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_1754_2,plain,
! [U_6314,U_6313,U_6312,U_6311,U_6310] :
( ( ( 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_6310),U_6312)),U_6313)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6311),U_6312)),U_6314)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6313),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_6311),U_6310)),U_6312)),U_6314))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6313),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_6311),U_6310)),U_6312)),U_6314)))
| ~ 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_6310),U_6312)),U_6313)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6311),U_6312)),U_6314))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6310),U_6311)) ),
inference(variable_rename,[status(thm)],[f_1754_1]) ).
cnf(f_1754_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6313),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_6311),U_6310)),U_6312)),U_6314)))
| ~ 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_6310),U_6312)),U_6313)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6311),U_6312)),U_6314)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6310),U_6311)) ),
inference(clausify,[status(thm)],[f_1754_2]) ).
cnf(f_1754_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_6310),U_6312)),U_6313)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6311),U_6312)),U_6314)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6313),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_6311),U_6310)),U_6312)),U_6314)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6310),U_6311)) ),
inference(clausify,[status(thm)],[f_1754_2]) ).
fof(f_1755_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_1755_2,plain,
! [U_6317,U_6316,U_6315] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6317))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6316),U_6315))
| U_6315 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6316),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6315),U_6317))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6315)) ),
inference(variable_rename,[status(thm)],[f_1755_1]) ).
cnf(f_1755_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6317))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6316),U_6315))
| U_6315 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6316),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6315),U_6317))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6315)) ),
inference(clausify,[status(thm)],[f_1755_2]) ).
fof(f_1756_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_1756_2,plain,
! [U_6320,U_6319,U_6318] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6320),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_6319))
| U_6318 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6318),U_6320))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6318)) ),
inference(variable_rename,[status(thm)],[f_1756_1]) ).
cnf(f_1756_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6320),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_6319))
| U_6318 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6318),U_6320))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6318)) ),
inference(clausify,[status(thm)],[f_1756_2]) ).
fof(f_1757_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_1757_2,plain,
! [U_6325,U_6324,U_6323,U_6322,U_6321] :
( ( ( 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_6322),U_6323)),U_6324)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6321),U_6323)),U_6325)))
| ~ 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_6322),U_6321)),U_6323)),U_6324)),U_6325)) )
& ( 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_6322),U_6321)),U_6323)),U_6324)),U_6325))
| ~ 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_6322),U_6323)),U_6324)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6321),U_6323)),U_6325))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6321),U_6322)) ),
inference(variable_rename,[status(thm)],[f_1757_1]) ).
cnf(f_1757_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_6322),U_6321)),U_6323)),U_6324)),U_6325))
| ~ 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_6322),U_6323)),U_6324)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6321),U_6323)),U_6325)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6321),U_6322)) ),
inference(clausify,[status(thm)],[f_1757_2]) ).
cnf(f_1757_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_6322),U_6323)),U_6324)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6321),U_6323)),U_6325)))
| ~ 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_6322),U_6321)),U_6323)),U_6324)),U_6325))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6321),U_6322)) ),
inference(clausify,[status(thm)],[f_1757_2]) ).
fof(f_1758_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_1758_2,plain,
! [U_6330,U_6329,U_6328,U_6327,U_6326] :
( 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_6327),U_6328)),U_6329)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6326),U_6328)),U_6330)) = 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_6327),U_6326)),U_6328)),U_6329)),U_6330)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6326),U_6327)) ),
inference(variable_rename,[status(thm)],[f_1758_1]) ).
cnf(f_1758_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_6327),U_6328)),U_6329)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6326),U_6328)),U_6330)) = 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_6327),U_6326)),U_6328)),U_6329)),U_6330)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6326),U_6327)) ),
inference(clausify,[status(thm)],[f_1758_2]) ).
fof(f_1759_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_1759_2,plain,
! [U_6333,U_6332,U_6331] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6331),U_6332)),U_6333) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6331),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6332),U_6333)),
inference(variable_rename,[status(thm)],[f_1759_1]) ).
cnf(f_1759_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6331),U_6332)),U_6333) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6331),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6332),U_6333)),
inference(clausify,[status(thm)],[f_1759_2]) ).
fof(f_1760_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_1760_2,plain,
! [U_6335,U_6334] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6334),U_6335) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6335),U_6334),
inference(variable_rename,[status(thm)],[f_1760_1]) ).
cnf(f_1760_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6334),U_6335) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6335),U_6334),
inference(clausify,[status(thm)],[f_1760_2]) ).
fof(f_1761_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_1761_2,plain,
! [U_6338,U_6337,U_6336] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6336),U_6337) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6336),U_6338)
| ( U_6337 != U_6338
& U_6336 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_6337 = U_6338
| U_6336 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6336),U_6337) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6336),U_6338) ) ),
inference(variable_rename,[status(thm)],[f_1761_1]) ).
fof(f_1761_3,plain,
( ! [U_6344,U_6342,U_6340] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6340),U_6342) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6340),U_6344)
| ( U_6342 != U_6344
& U_6340 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_6343,U_6341,U_6339] :
( U_6341 = U_6343
| U_6339 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6339),U_6341) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6339),U_6343) ) ),
inference(miniscope,[status(thm)],[f_1761_2]) ).
cnf(f_1761_4,plain,
( U_6341 = U_6343
| U_6339 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6339),U_6341) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6339),U_6343) ),
inference(clausify,[status(thm)],[f_1761_3]) ).
cnf(f_1761_5,plain,
( U_6340 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6340),U_6342) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6340),U_6344) ),
inference(clausify,[status(thm)],[f_1761_3]) ).
cnf(f_1761_6,plain,
( U_6342 != U_6344
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6340),U_6342) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6340),U_6344) ),
inference(clausify,[status(thm)],[f_1761_3]) ).
fof(f_1762_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_1762_2,plain,
! [U_6348,U_6347,U_6346,U_6345] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6345),U_6346)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6347),U_6346)),U_6348)) = 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_6345),U_6347)),U_6346)),U_6348),
inference(variable_rename,[status(thm)],[f_1762_1]) ).
cnf(f_1762_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6345),U_6346)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6347),U_6346)),U_6348)) = 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_6345),U_6347)),U_6346)),U_6348),
inference(clausify,[status(thm)],[f_1762_2]) ).
fof(f_1763_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_1763_2,plain,
! [U_6351,U_6350,U_6349] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6349),U_6350)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6349),U_6351)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6350),U_6351)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6350),U_6351))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6349),U_6350)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6349),U_6351))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6349)) ),
inference(variable_rename,[status(thm)],[f_1763_1]) ).
cnf(f_1763_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6350),U_6351))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6349),U_6350)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6349),U_6351)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6349)) ),
inference(clausify,[status(thm)],[f_1763_2]) ).
cnf(f_1763_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6349),U_6350)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6349),U_6351)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6350),U_6351))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6349)) ),
inference(clausify,[status(thm)],[f_1763_2]) ).
fof(f_1764_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_1764_2,plain,
! [U_6354,U_6353,U_6352] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6352),U_6353) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6352),U_6354)
| U_6353 != U_6354 )
& ( U_6353 = U_6354
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6352),U_6353) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6352),U_6354) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6352)) ),
inference(variable_rename,[status(thm)],[f_1764_1]) ).
cnf(f_1764_3,plain,
( U_6353 = U_6354
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6352),U_6353) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6352),U_6354)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6352)) ),
inference(clausify,[status(thm)],[f_1764_2]) ).
cnf(f_1764_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6352),U_6353) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6352),U_6354)
| U_6353 != U_6354
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6352)) ),
inference(clausify,[status(thm)],[f_1764_2]) ).
fof(f_1765_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_1765_2,plain,
! [U_6357,U_6356,U_6355] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6355),U_6356)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6355),U_6357)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6356),U_6357)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6356),U_6357))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6355),U_6356)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6355),U_6357))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6355)) ),
inference(variable_rename,[status(thm)],[f_1765_1]) ).
cnf(f_1765_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6356),U_6357))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6355),U_6356)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6355),U_6357)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6355)) ),
inference(clausify,[status(thm)],[f_1765_2]) ).
cnf(f_1765_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_6355),U_6356)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6355),U_6357)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6356),U_6357))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6355)) ),
inference(clausify,[status(thm)],[f_1765_2]) ).
fof(f_1766_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_1766_2,plain,
! [U_6363,U_6362,U_6361,U_6360,U_6359,U_6358] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6362),U_6359))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6361),U_6358))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6361))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6363))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6360),U_6358))
| ~ 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_6361),U_6362)),U_6363)),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_6358),U_6359)),U_6360) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6361),U_6362)),U_6363) ),
inference(variable_rename,[status(thm)],[f_1766_1]) ).
cnf(f_1766_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6362),U_6359))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6361),U_6358))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6361))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6363))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6360),U_6358))
| ~ 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_6361),U_6362)),U_6363)),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_6358),U_6359)),U_6360) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6361),U_6362)),U_6363) ),
inference(clausify,[status(thm)],[f_1766_2]) ).
fof(f_1767_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_1767_2,plain,
! [U_6368,U_6367,U_6366,U_6365,U_6364] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6367),U_6365))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6364),U_6366))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6364),U_6368))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6368),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_6364),U_6365)),U_6366)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6364),U_6367)),U_6368))) ),
inference(variable_rename,[status(thm)],[f_1767_1]) ).
cnf(f_1767_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6367),U_6365))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6364),U_6366))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6364),U_6368))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6368),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_6364),U_6365)),U_6366)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6364),U_6367)),U_6368))) ),
inference(clausify,[status(thm)],[f_1767_2]) ).
fof(f_1768_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_1768_2,plain,
! [U_6374,U_6373,U_6372,U_6371,U_6370,U_6369] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6370),U_6373))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6372),U_6369))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6372))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6371))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6374),U_6372))
| ~ 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_6372),U_6373)),U_6374)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6369),U_6370)),U_6371) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6372),U_6373)),U_6374) ),
inference(variable_rename,[status(thm)],[f_1768_1]) ).
cnf(f_1768_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6370),U_6373))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6372),U_6369))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6372))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6371))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6374),U_6372))
| ~ 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_6372),U_6373)),U_6374)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6369),U_6370)),U_6371) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6372),U_6373)),U_6374) ),
inference(clausify,[status(thm)],[f_1768_2]) ).
fof(f_1769_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_1769_2,plain,
! [U_6379,U_6378,U_6377,U_6376,U_6375] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6376),U_6378))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6379),U_6375))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6377),U_6375))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6377))
| ~ 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_6375),U_6376)),U_6377)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6375),U_6378)),U_6379))) ),
inference(variable_rename,[status(thm)],[f_1769_1]) ).
cnf(f_1769_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6376),U_6378))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6379),U_6375))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6377),U_6375))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6377))
| ~ 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_6375),U_6376)),U_6377)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6375),U_6378)),U_6379))) ),
inference(clausify,[status(thm)],[f_1769_2]) ).
fof(f_1770_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_1770_2,plain,
! [U_6382,U_6381,U_6380] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6381),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_6380))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6382))
| ~ 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_6380),U_6381)),U_6382)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1770_1]) ).
cnf(f_1770_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6381),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_6380))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6382))
| ~ 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_6380),U_6381)),U_6382)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1770_2]) ).
fof(f_1771_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_1771_2,plain,
! [U_6385,U_6384,U_6383] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6384))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6383))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6385),U_6383))
| ~ 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_6383),U_6384)),U_6385))) ),
inference(variable_rename,[status(thm)],[f_1771_1]) ).
cnf(f_1771_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6384))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6383))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6385),U_6383))
| ~ 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_6383),U_6384)),U_6385))) ),
inference(clausify,[status(thm)],[f_1771_2]) ).
fof(f_1772_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_1772_2,plain,
! [U_6390,U_6389,U_6388,U_6387,U_6386] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6386),U_6388)),U_6389) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6387),U_6388)),U_6390)
| U_6389 != 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_6387),U_6386)),U_6388)),U_6390) )
& ( U_6389 = 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_6387),U_6386)),U_6388)),U_6390)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6386),U_6388)),U_6389) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6387),U_6388)),U_6390) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6386),U_6387)) ),
inference(variable_rename,[status(thm)],[f_1772_1]) ).
cnf(f_1772_3,plain,
( U_6389 = 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_6387),U_6386)),U_6388)),U_6390)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6386),U_6388)),U_6389) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6387),U_6388)),U_6390)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6386),U_6387)) ),
inference(clausify,[status(thm)],[f_1772_2]) ).
cnf(f_1772_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6386),U_6388)),U_6389) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6387),U_6388)),U_6390)
| U_6389 != 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_6387),U_6386)),U_6388)),U_6390)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6386),U_6387)) ),
inference(clausify,[status(thm)],[f_1772_2]) ).
fof(f_1773_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_1773_2,plain,
! [U_6395,U_6394,U_6393,U_6392,U_6391] :
( 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_6391),U_6393)),U_6394)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6392),U_6393)),U_6395)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6394),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_6392),U_6391)),U_6393)),U_6395))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6391),U_6392)) ),
inference(variable_rename,[status(thm)],[f_1773_1]) ).
cnf(f_1773_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_6391),U_6393)),U_6394)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6392),U_6393)),U_6395)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6394),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_6392),U_6391)),U_6393)),U_6395))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6391),U_6392)) ),
inference(clausify,[status(thm)],[f_1773_2]) ).
fof(f_1774_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_1774_2,plain,
! [U_6400,U_6399,U_6398,U_6397,U_6396] :
( ( ( 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_6396),U_6398)),U_6399)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6397),U_6398)),U_6400)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6399),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_6397),U_6396)),U_6398)),U_6400))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6399),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_6397),U_6396)),U_6398)),U_6400)))
| ~ 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_6396),U_6398)),U_6399)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6397),U_6398)),U_6400))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6396),U_6397)) ),
inference(variable_rename,[status(thm)],[f_1774_1]) ).
cnf(f_1774_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6399),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_6397),U_6396)),U_6398)),U_6400)))
| ~ 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_6396),U_6398)),U_6399)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6397),U_6398)),U_6400)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6396),U_6397)) ),
inference(clausify,[status(thm)],[f_1774_2]) ).
cnf(f_1774_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_6396),U_6398)),U_6399)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6397),U_6398)),U_6400)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6399),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_6397),U_6396)),U_6398)),U_6400)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6396),U_6397)) ),
inference(clausify,[status(thm)],[f_1774_2]) ).
fof(f_1775_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_1775_2,plain,
! [U_6405,U_6404,U_6403,U_6402,U_6401] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6402),U_6403)),U_6404) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6401),U_6403)),U_6405)
| 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_6402),U_6401)),U_6403)),U_6404) != U_6405 )
& ( 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_6402),U_6401)),U_6403)),U_6404) = U_6405
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6402),U_6403)),U_6404) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6401),U_6403)),U_6405) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6401),U_6402)) ),
inference(variable_rename,[status(thm)],[f_1775_1]) ).
cnf(f_1775_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_6402),U_6401)),U_6403)),U_6404) = U_6405
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6402),U_6403)),U_6404) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6401),U_6403)),U_6405)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6401),U_6402)) ),
inference(clausify,[status(thm)],[f_1775_2]) ).
cnf(f_1775_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6402),U_6403)),U_6404) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6401),U_6403)),U_6405)
| 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_6402),U_6401)),U_6403)),U_6404) != U_6405
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6401),U_6402)) ),
inference(clausify,[status(thm)],[f_1775_2]) ).
fof(f_1776_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_1776_2,plain,
! [U_6407,U_6406] :
( ( c_Code__Numeral_Onat__of__aux(U_6406,U_6407) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6406),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_6407))
| U_6406 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ( c_Code__Numeral_Onat__of__aux(U_6406,U_6407) = U_6407
| U_6406 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(variable_rename,[status(thm)],[f_1776_1]) ).
fof(f_1776_3,plain,
( ! [U_6411,U_6409] :
( c_Code__Numeral_Onat__of__aux(U_6409,U_6411) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6409),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_6411))
| U_6409 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ! [U_6410,U_6408] :
( c_Code__Numeral_Onat__of__aux(U_6408,U_6410) = U_6410
| U_6408 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(miniscope,[status(thm)],[f_1776_2]) ).
cnf(f_1776_4,plain,
( c_Code__Numeral_Onat__of__aux(U_6408,U_6410) = U_6410
| U_6408 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_1776_3]) ).
cnf(f_1776_5,plain,
( c_Code__Numeral_Onat__of__aux(U_6409,U_6411) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6409),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_6411))
| U_6409 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_1776_3]) ).
fof(f_1777_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_1777_2,plain,
! [U_6413,U_6412] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_6413)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6412))) = 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_6413)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6412)))),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_6412))) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_6413)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6412))) = 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_6413),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6412)))),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_6412))) ) ),
inference(variable_rename,[status(thm)],[f_1777_1]) ).
fof(f_1777_3,plain,
( ! [U_6417,U_6415] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_6417)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6415))) = 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_6417)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6415)))),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_6415))) )
& ! [U_6416,U_6414] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_6416)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6414))) = 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_6416),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6414)))),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_6414))) ) ),
inference(miniscope,[status(thm)],[f_1777_2]) ).
cnf(f_1777_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_6416)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6414))) = 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_6416),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6414)))),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_6414))) ),
inference(clausify,[status(thm)],[f_1777_3]) ).
cnf(f_1777_5,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_6417)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6415))) = 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_6417)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6415)))),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_6415))) ),
inference(clausify,[status(thm)],[f_1777_3]) ).
fof(f_1778_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_1778_2,plain,
! [U_6419,U_6418] :
( 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_6419)),hAPP(hAPP(c_Groups_Otimes__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_6418)) = 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_6419),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6418))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6418),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1778_1]) ).
cnf(f_1778_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_6419)),hAPP(hAPP(c_Groups_Otimes__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_6418)) = 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_6419),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6418))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6418),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1778_2]) ).
fof(f_1779_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_1779_2,plain,
! [U_6421,U_6420] :
( 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_6421)),hAPP(hAPP(c_Groups_Otimes__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_6420)) = 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_6421,U_6420)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6420)) ),
inference(variable_rename,[status(thm)],[f_1779_1]) ).
cnf(f_1779_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_6421)),hAPP(hAPP(c_Groups_Otimes__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_6420)) = 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_6421,U_6420)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6420)) ),
inference(clausify,[status(thm)],[f_1779_2]) ).
fof(f_1780_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_1780_2,plain,
! [U_6423,U_6422] :
( 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_6423))),hAPP(hAPP(c_Groups_Otimes__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_6422)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6423),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6422)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6422),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1780_1]) ).
cnf(f_1780_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_6423))),hAPP(hAPP(c_Groups_Otimes__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_6422)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6423),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6422)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6422),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1780_2]) ).
fof(f_1781_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_1781_2,plain,
! [U_6426,U_6425,U_6424] : 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_6424),U_6425)),U_6425)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6424,U_6425))),U_6426) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6424),U_6426),
inference(variable_rename,[status(thm)],[f_1781_1]) ).
cnf(f_1781_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6424),U_6425)),U_6425)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6424,U_6425))),U_6426) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6424),U_6426),
inference(clausify,[status(thm)],[f_1781_2]) ).
fof(f_1782_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_1782_2,plain,
! [U_6430,U_6429,U_6428,U_6427] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6427),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6427),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6427),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6427),U_6428),U_6429)),U_6429)),c_Divides_Odiv__class_Omod(U_6427,U_6428,U_6429))),U_6430) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6427),U_6428),U_6430)
| ~ class_Divides_Osemiring__div(U_6427) ),
inference(variable_rename,[status(thm)],[f_1782_1]) ).
cnf(f_1782_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6427),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6427),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6427),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6427),U_6428),U_6429)),U_6429)),c_Divides_Odiv__class_Omod(U_6427,U_6428,U_6429))),U_6430) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6427),U_6428),U_6430)
| ~ class_Divides_Osemiring__div(U_6427) ),
inference(clausify,[status(thm)],[f_1782_2]) ).
fof(f_1783_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_1783_2,plain,
! [U_6433,U_6432,U_6431] : 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_6431),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6432),U_6431))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6432,U_6431))),U_6433) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6432),U_6433),
inference(variable_rename,[status(thm)],[f_1783_1]) ).
cnf(f_1783_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_6431),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6432),U_6431))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6432,U_6431))),U_6433) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6432),U_6433),
inference(clausify,[status(thm)],[f_1783_2]) ).
fof(f_1784_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_1784_2,plain,
! [U_6437,U_6436,U_6435,U_6434] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6434),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6434),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6434),U_6435),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6434),U_6436),U_6435))),c_Divides_Odiv__class_Omod(U_6434,U_6436,U_6435))),U_6437) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6434),U_6436),U_6437)
| ~ class_Divides_Osemiring__div(U_6434) ),
inference(variable_rename,[status(thm)],[f_1784_1]) ).
cnf(f_1784_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6434),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6434),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6434),U_6435),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6434),U_6436),U_6435))),c_Divides_Odiv__class_Omod(U_6434,U_6436,U_6435))),U_6437) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6434),U_6436),U_6437)
| ~ class_Divides_Osemiring__div(U_6434) ),
inference(clausify,[status(thm)],[f_1784_2]) ).
fof(f_1785_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_1785_2,plain,
! [U_6440,U_6439,U_6438] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6438),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6438),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6438),U_6439),U_6440)),U_6440)),c_Divides_Odiv__class_Omod(U_6438,U_6439,U_6440)) = U_6439
| ~ class_Divides_Osemiring__div(U_6438) ),
inference(variable_rename,[status(thm)],[f_1785_1]) ).
cnf(f_1785_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6438),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6438),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6438),U_6439),U_6440)),U_6440)),c_Divides_Odiv__class_Omod(U_6438,U_6439,U_6440)) = U_6439
| ~ class_Divides_Osemiring__div(U_6438) ),
inference(clausify,[status(thm)],[f_1785_2]) ).
fof(f_1786_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_1786_2,plain,
! [U_6443,U_6442,U_6441] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6441),U_6442),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6441),U_6443),U_6442))),c_Divides_Odiv__class_Omod(U_6441,U_6443,U_6442)) = U_6443
| ~ class_Divides_Osemiring__div(U_6441) ),
inference(variable_rename,[status(thm)],[f_1786_1]) ).
cnf(f_1786_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6441),U_6442),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6441),U_6443),U_6442))),c_Divides_Odiv__class_Omod(U_6441,U_6443,U_6442)) = U_6443
| ~ class_Divides_Osemiring__div(U_6441) ),
inference(clausify,[status(thm)],[f_1786_2]) ).
fof(f_1787_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_1787_2,plain,
! [U_6446,U_6445,U_6444] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6444),c_Divides_Odiv__class_Omod(U_6444,U_6445,U_6446)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6444),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6444),U_6445),U_6446)),U_6446)) = U_6445
| ~ class_Divides_Osemiring__div(U_6444) ),
inference(variable_rename,[status(thm)],[f_1787_1]) ).
cnf(f_1787_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6444),c_Divides_Odiv__class_Omod(U_6444,U_6445,U_6446)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6444),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6444),U_6445),U_6446)),U_6446)) = U_6445
| ~ class_Divides_Osemiring__div(U_6444) ),
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_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_1788_2,plain,
! [U_6449,U_6448,U_6447] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6447),U_6448)),U_6449) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6447),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6448),U_6449))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6447),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6448,U_6449))),U_6449)),
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_Otimes__class_Otimes(tc_Int_Oint),U_6447),U_6448)),U_6449) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6447),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6448),U_6449))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6447),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6448,U_6449))),U_6449)),
inference(clausify,[status(thm)],[f_1788_2]) ).
fof(f_1789_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_1789_2,plain,
! [U_6451,U_6450] : U_6450 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6451),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6450),U_6451))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6450,U_6451)),
inference(variable_rename,[status(thm)],[f_1789_1]) ).
cnf(f_1789_3,plain,
U_6450 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6451),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6450),U_6451))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6450,U_6451)),
inference(clausify,[status(thm)],[f_1789_2]) ).
fof(f_1790_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_1790_2,plain,
! [U_6457,U_6456,U_6455,U_6454,U_6453,U_6452] :
( c_Divides_Odiv__class_Omod(U_6452,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6452),U_6453),U_6456),U_6454) = c_Divides_Odiv__class_Omod(U_6452,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6452),U_6455),U_6457),U_6454)
| c_Divides_Odiv__class_Omod(U_6452,U_6456,U_6454) != c_Divides_Odiv__class_Omod(U_6452,U_6457,U_6454)
| c_Divides_Odiv__class_Omod(U_6452,U_6453,U_6454) != c_Divides_Odiv__class_Omod(U_6452,U_6455,U_6454)
| ~ class_Divides_Oring__div(U_6452) ),
inference(variable_rename,[status(thm)],[f_1790_1]) ).
cnf(f_1790_3,plain,
( c_Divides_Odiv__class_Omod(U_6452,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6452),U_6453),U_6456),U_6454) = c_Divides_Odiv__class_Omod(U_6452,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6452),U_6455),U_6457),U_6454)
| c_Divides_Odiv__class_Omod(U_6452,U_6456,U_6454) != c_Divides_Odiv__class_Omod(U_6452,U_6457,U_6454)
| c_Divides_Odiv__class_Omod(U_6452,U_6453,U_6454) != c_Divides_Odiv__class_Omod(U_6452,U_6455,U_6454)
| ~ class_Divides_Oring__div(U_6452) ),
inference(clausify,[status(thm)],[f_1790_2]) ).
fof(f_1791_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_1791_2,plain,
! [U_6461,U_6460,U_6459,U_6458] :
( c_Divides_Odiv__class_Omod(U_6458,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6458),U_6459),U_6460),U_6461) = c_Divides_Odiv__class_Omod(U_6458,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6458),c_Divides_Odiv__class_Omod(U_6458,U_6459,U_6461)),c_Divides_Odiv__class_Omod(U_6458,U_6460,U_6461)),U_6461)
| ~ class_Divides_Oring__div(U_6458) ),
inference(variable_rename,[status(thm)],[f_1791_1]) ).
cnf(f_1791_3,plain,
( c_Divides_Odiv__class_Omod(U_6458,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6458),U_6459),U_6460),U_6461) = c_Divides_Odiv__class_Omod(U_6458,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6458),c_Divides_Odiv__class_Omod(U_6458,U_6459,U_6461)),c_Divides_Odiv__class_Omod(U_6458,U_6460,U_6461)),U_6461)
| ~ class_Divides_Oring__div(U_6458) ),
inference(clausify,[status(thm)],[f_1791_2]) ).
fof(f_1792_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_1792_2,plain,
! [U_6465,U_6464,U_6463,U_6462] :
( c_Divides_Odiv__class_Omod(U_6462,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6462),U_6463),U_6464),U_6465) = c_Divides_Odiv__class_Omod(U_6462,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6462),c_Divides_Odiv__class_Omod(U_6462,U_6463,U_6465)),U_6464),U_6465)
| ~ class_Divides_Oring__div(U_6462) ),
inference(variable_rename,[status(thm)],[f_1792_1]) ).
cnf(f_1792_3,plain,
( c_Divides_Odiv__class_Omod(U_6462,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6462),U_6463),U_6464),U_6465) = c_Divides_Odiv__class_Omod(U_6462,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6462),c_Divides_Odiv__class_Omod(U_6462,U_6463,U_6465)),U_6464),U_6465)
| ~ class_Divides_Oring__div(U_6462) ),
inference(clausify,[status(thm)],[f_1792_2]) ).
fof(f_1793_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_1793_2,plain,
! [U_6469,U_6468,U_6467,U_6466] :
( c_Divides_Odiv__class_Omod(U_6466,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6466),U_6467),U_6468),U_6469) = c_Divides_Odiv__class_Omod(U_6466,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6466),U_6467),c_Divides_Odiv__class_Omod(U_6466,U_6468,U_6469)),U_6469)
| ~ class_Divides_Oring__div(U_6466) ),
inference(variable_rename,[status(thm)],[f_1793_1]) ).
cnf(f_1793_3,plain,
( c_Divides_Odiv__class_Omod(U_6466,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6466),U_6467),U_6468),U_6469) = c_Divides_Odiv__class_Omod(U_6466,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6466),U_6467),c_Divides_Odiv__class_Omod(U_6466,U_6468,U_6469)),U_6469)
| ~ class_Divides_Oring__div(U_6466) ),
inference(clausify,[status(thm)],[f_1793_2]) ).
fof(f_1794_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_1794_2,plain,
! [U_6471,U_6470] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6470,U_6471) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6470),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6470),U_6471)),U_6471)),
inference(variable_rename,[status(thm)],[f_1794_1]) ).
cnf(f_1794_3,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6470,U_6471) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6470),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6470),U_6471)),U_6471)),
inference(clausify,[status(thm)],[f_1794_2]) ).
fof(f_1795_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_1795_2,plain,
! [U_6473,U_6472] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6472),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6473),U_6472)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6473),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6473,U_6472)),
inference(variable_rename,[status(thm)],[f_1795_1]) ).
cnf(f_1795_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6472),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6473),U_6472)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6473),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6473,U_6472)),
inference(clausify,[status(thm)],[f_1795_2]) ).
fof(f_1796_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_1796_2,plain,
! [U_6477,U_6476,U_6475,U_6474] :
( c_Divides_Odiv__class_Omod(U_6474,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6474),U_6475),U_6476),U_6477) = c_Divides_Odiv__class_Omod(U_6474,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6474),U_6475),c_Divides_Odiv__class_Omod(U_6474,U_6476,U_6477)),U_6477)
| ~ class_Divides_Osemiring__div(U_6474) ),
inference(variable_rename,[status(thm)],[f_1796_1]) ).
cnf(f_1796_3,plain,
( c_Divides_Odiv__class_Omod(U_6474,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6474),U_6475),U_6476),U_6477) = c_Divides_Odiv__class_Omod(U_6474,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6474),U_6475),c_Divides_Odiv__class_Omod(U_6474,U_6476,U_6477)),U_6477)
| ~ class_Divides_Osemiring__div(U_6474) ),
inference(clausify,[status(thm)],[f_1796_2]) ).
fof(f_1797_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_1797_2,plain,
! [U_6481,U_6480,U_6479,U_6478] :
( c_Divides_Odiv__class_Omod(U_6478,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6478),U_6479),U_6480),U_6481) = c_Divides_Odiv__class_Omod(U_6478,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6478),c_Divides_Odiv__class_Omod(U_6478,U_6479,U_6481)),U_6480),U_6481)
| ~ class_Divides_Osemiring__div(U_6478) ),
inference(variable_rename,[status(thm)],[f_1797_1]) ).
cnf(f_1797_3,plain,
( c_Divides_Odiv__class_Omod(U_6478,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6478),U_6479),U_6480),U_6481) = c_Divides_Odiv__class_Omod(U_6478,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6478),c_Divides_Odiv__class_Omod(U_6478,U_6479,U_6481)),U_6480),U_6481)
| ~ class_Divides_Osemiring__div(U_6478) ),
inference(clausify,[status(thm)],[f_1797_2]) ).
fof(f_1798_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_1798_2,plain,
! [U_6485,U_6484,U_6483,U_6482] :
( c_Divides_Odiv__class_Omod(U_6482,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6482),U_6483),U_6484),U_6485) = c_Divides_Odiv__class_Omod(U_6482,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6482),c_Divides_Odiv__class_Omod(U_6482,U_6483,U_6485)),c_Divides_Odiv__class_Omod(U_6482,U_6484,U_6485)),U_6485)
| ~ class_Divides_Osemiring__div(U_6482) ),
inference(variable_rename,[status(thm)],[f_1798_1]) ).
cnf(f_1798_3,plain,
( c_Divides_Odiv__class_Omod(U_6482,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6482),U_6483),U_6484),U_6485) = c_Divides_Odiv__class_Omod(U_6482,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6482),c_Divides_Odiv__class_Omod(U_6482,U_6483,U_6485)),c_Divides_Odiv__class_Omod(U_6482,U_6484,U_6485)),U_6485)
| ~ class_Divides_Osemiring__div(U_6482) ),
inference(clausify,[status(thm)],[f_1798_2]) ).
fof(f_1799_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_1799_2,plain,
! [U_6489,U_6488,U_6487,U_6486] :
( c_Divides_Odiv__class_Omod(U_6486,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6486),U_6487),U_6488),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6486),U_6487),U_6489)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6486),U_6487),c_Divides_Odiv__class_Omod(U_6486,U_6488,U_6489))
| ~ class_Divides_Osemiring__div(U_6486) ),
inference(variable_rename,[status(thm)],[f_1799_1]) ).
cnf(f_1799_3,plain,
( c_Divides_Odiv__class_Omod(U_6486,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6486),U_6487),U_6488),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6486),U_6487),U_6489)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6486),U_6487),c_Divides_Odiv__class_Omod(U_6486,U_6488,U_6489))
| ~ class_Divides_Osemiring__div(U_6486) ),
inference(clausify,[status(thm)],[f_1799_2]) ).
fof(f_1800_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_1800_2,plain,
! [U_6493,U_6492,U_6491,U_6490] :
( c_Divides_Odiv__class_Omod(U_6490,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6490),U_6491),U_6492),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6490),U_6493),U_6492)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6490),c_Divides_Odiv__class_Omod(U_6490,U_6491,U_6493)),U_6492)
| ~ class_Divides_Osemiring__div(U_6490) ),
inference(variable_rename,[status(thm)],[f_1800_1]) ).
cnf(f_1800_3,plain,
( c_Divides_Odiv__class_Omod(U_6490,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6490),U_6491),U_6492),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6490),U_6493),U_6492)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6490),c_Divides_Odiv__class_Omod(U_6490,U_6491,U_6493)),U_6492)
| ~ class_Divides_Osemiring__div(U_6490) ),
inference(clausify,[status(thm)],[f_1800_2]) ).
fof(f_1801_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_1801_2,plain,
! [U_6497,U_6496,U_6495,U_6494] :
( c_Divides_Odiv__class_Omod(U_6494,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6494),c_Divides_Odiv__class_Omod(U_6494,U_6495,U_6496)),U_6497),U_6496) = c_Divides_Odiv__class_Omod(U_6494,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6494),U_6495),U_6497),U_6496)
| ~ class_Divides_Osemiring__div(U_6494) ),
inference(variable_rename,[status(thm)],[f_1801_1]) ).
cnf(f_1801_3,plain,
( c_Divides_Odiv__class_Omod(U_6494,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6494),c_Divides_Odiv__class_Omod(U_6494,U_6495,U_6496)),U_6497),U_6496) = c_Divides_Odiv__class_Omod(U_6494,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6494),U_6495),U_6497),U_6496)
| ~ class_Divides_Osemiring__div(U_6494) ),
inference(clausify,[status(thm)],[f_1801_2]) ).
fof(f_1802_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_1802_2,plain,
! [U_6503,U_6502,U_6501,U_6500,U_6499,U_6498] :
( c_Divides_Odiv__class_Omod(U_6498,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6498),U_6499),U_6502),U_6500) = c_Divides_Odiv__class_Omod(U_6498,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6498),U_6501),U_6503),U_6500)
| c_Divides_Odiv__class_Omod(U_6498,U_6502,U_6500) != c_Divides_Odiv__class_Omod(U_6498,U_6503,U_6500)
| c_Divides_Odiv__class_Omod(U_6498,U_6499,U_6500) != c_Divides_Odiv__class_Omod(U_6498,U_6501,U_6500)
| ~ class_Divides_Osemiring__div(U_6498) ),
inference(variable_rename,[status(thm)],[f_1802_1]) ).
cnf(f_1802_3,plain,
( c_Divides_Odiv__class_Omod(U_6498,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6498),U_6499),U_6502),U_6500) = c_Divides_Odiv__class_Omod(U_6498,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6498),U_6501),U_6503),U_6500)
| c_Divides_Odiv__class_Omod(U_6498,U_6502,U_6500) != c_Divides_Odiv__class_Omod(U_6498,U_6503,U_6500)
| c_Divides_Odiv__class_Omod(U_6498,U_6499,U_6500) != c_Divides_Odiv__class_Omod(U_6498,U_6501,U_6500)
| ~ class_Divides_Osemiring__div(U_6498) ),
inference(clausify,[status(thm)],[f_1802_2]) ).
fof(f_1803_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_1803_2,plain,
! [U_6505,U_6504] :
( c_Divides_Odiv__class_Omod(U_6504,c_Groups_Ozero__class_Ozero(U_6504),U_6505) = c_Groups_Ozero__class_Ozero(U_6504)
| ~ class_Divides_Osemiring__div(U_6504) ),
inference(variable_rename,[status(thm)],[f_1803_1]) ).
cnf(f_1803_3,plain,
( c_Divides_Odiv__class_Omod(U_6504,c_Groups_Ozero__class_Ozero(U_6504),U_6505) = c_Groups_Ozero__class_Ozero(U_6504)
| ~ class_Divides_Osemiring__div(U_6504) ),
inference(clausify,[status(thm)],[f_1803_2]) ).
fof(f_1804_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_1804_2,plain,
! [U_6507,U_6506] :
( c_Divides_Odiv__class_Omod(U_6506,U_6507,c_Groups_Ozero__class_Ozero(U_6506)) = U_6507
| ~ class_Divides_Osemiring__div(U_6506) ),
inference(variable_rename,[status(thm)],[f_1804_1]) ).
cnf(f_1804_3,plain,
( c_Divides_Odiv__class_Omod(U_6506,U_6507,c_Groups_Ozero__class_Ozero(U_6506)) = U_6507
| ~ class_Divides_Osemiring__div(U_6506) ),
inference(clausify,[status(thm)],[f_1804_2]) ).
fof(f_1805_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_1805_2,plain,
! [U_6509,U_6508] :
( c_Divides_Odiv__class_Omod(U_6508,U_6509,U_6509) = c_Groups_Ozero__class_Ozero(U_6508)
| ~ class_Divides_Osemiring__div(U_6508) ),
inference(variable_rename,[status(thm)],[f_1805_1]) ).
cnf(f_1805_3,plain,
( c_Divides_Odiv__class_Omod(U_6508,U_6509,U_6509) = c_Groups_Ozero__class_Ozero(U_6508)
| ~ class_Divides_Osemiring__div(U_6508) ),
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),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_1806_2,plain,
! [U_6511,U_6510] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6510,U_6511)),U_6511) = 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),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6510,U_6511)),U_6511) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1806_2]) ).
fof(f_1807_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_1807_2,plain,
! [U_6514,U_6513,U_6512] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6512),c_Divides_Odiv__class_Omod(U_6512,U_6513,U_6514)),U_6514) = c_Groups_Ozero__class_Ozero(U_6512)
| ~ class_Divides_Osemiring__div(U_6512) ),
inference(variable_rename,[status(thm)],[f_1807_1]) ).
cnf(f_1807_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6512),c_Divides_Odiv__class_Omod(U_6512,U_6513,U_6514)),U_6514) = c_Groups_Ozero__class_Ozero(U_6512)
| ~ class_Divides_Osemiring__div(U_6512) ),
inference(clausify,[status(thm)],[f_1807_2]) ).
fof(f_1808_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_1808_2,plain,
! [U_6515] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6515,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_6515
& hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6515),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_1808_1]) ).
fof(f_1808_3,plain,
( ! [U_6517] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6517,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_6517
& ! [U_6516] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6516),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(miniscope,[status(thm)],[f_1808_2]) ).
cnf(f_1808_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6516),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1808_3]) ).
cnf(f_1808_5,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6517,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_6517,
inference(clausify,[status(thm)],[f_1808_3]) ).
fof(f_1809_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_1809_2,plain,
! [U_6518] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6518) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_1809_1]) ).
cnf(f_1809_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6518) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1809_2]) ).
fof(f_1810_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_1810_2,plain,
! [U_6521,U_6520,U_6519] :
( c_Divides_Odiv__class_Omod(U_6519,c_Divides_Odiv__class_Omod(U_6519,U_6520,U_6521),U_6521) = c_Divides_Odiv__class_Omod(U_6519,U_6520,U_6521)
| ~ class_Divides_Osemiring__div(U_6519) ),
inference(variable_rename,[status(thm)],[f_1810_1]) ).
cnf(f_1810_3,plain,
( c_Divides_Odiv__class_Omod(U_6519,c_Divides_Odiv__class_Omod(U_6519,U_6520,U_6521),U_6521) = c_Divides_Odiv__class_Omod(U_6519,U_6520,U_6521)
| ~ class_Divides_Osemiring__div(U_6519) ),
inference(clausify,[status(thm)],[f_1810_2]) ).
fof(f_1811_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_1811_2,plain,
! [U_6525,U_6524,U_6523,U_6522] :
( c_Divides_Odiv__class_Omod(U_6522,hAPP(c_Groups_Ouminus__class_Ouminus(U_6522),U_6523),U_6524) = c_Divides_Odiv__class_Omod(U_6522,hAPP(c_Groups_Ouminus__class_Ouminus(U_6522),U_6525),U_6524)
| c_Divides_Odiv__class_Omod(U_6522,U_6523,U_6524) != c_Divides_Odiv__class_Omod(U_6522,U_6525,U_6524)
| ~ class_Divides_Oring__div(U_6522) ),
inference(variable_rename,[status(thm)],[f_1811_1]) ).
cnf(f_1811_3,plain,
( c_Divides_Odiv__class_Omod(U_6522,hAPP(c_Groups_Ouminus__class_Ouminus(U_6522),U_6523),U_6524) = c_Divides_Odiv__class_Omod(U_6522,hAPP(c_Groups_Ouminus__class_Ouminus(U_6522),U_6525),U_6524)
| c_Divides_Odiv__class_Omod(U_6522,U_6523,U_6524) != c_Divides_Odiv__class_Omod(U_6522,U_6525,U_6524)
| ~ class_Divides_Oring__div(U_6522) ),
inference(clausify,[status(thm)],[f_1811_2]) ).
fof(f_1812_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_1812_2,plain,
! [U_6528,U_6527,U_6526] :
( c_Divides_Odiv__class_Omod(U_6526,hAPP(c_Groups_Ouminus__class_Ouminus(U_6526),U_6527),U_6528) = c_Divides_Odiv__class_Omod(U_6526,hAPP(c_Groups_Ouminus__class_Ouminus(U_6526),c_Divides_Odiv__class_Omod(U_6526,U_6527,U_6528)),U_6528)
| ~ class_Divides_Oring__div(U_6526) ),
inference(variable_rename,[status(thm)],[f_1812_1]) ).
cnf(f_1812_3,plain,
( c_Divides_Odiv__class_Omod(U_6526,hAPP(c_Groups_Ouminus__class_Ouminus(U_6526),U_6527),U_6528) = c_Divides_Odiv__class_Omod(U_6526,hAPP(c_Groups_Ouminus__class_Ouminus(U_6526),c_Divides_Odiv__class_Omod(U_6526,U_6527,U_6528)),U_6528)
| ~ class_Divides_Oring__div(U_6526) ),
inference(clausify,[status(thm)],[f_1812_2]) ).
fof(f_1813_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_1813_2,plain,
! [U_6531,U_6530,U_6529] :
( c_Divides_Odiv__class_Omod(U_6529,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6529),U_6530),U_6531),U_6531) = c_Divides_Odiv__class_Omod(U_6529,U_6530,U_6531)
| ~ class_Divides_Osemiring__div(U_6529) ),
inference(variable_rename,[status(thm)],[f_1813_1]) ).
cnf(f_1813_3,plain,
( c_Divides_Odiv__class_Omod(U_6529,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6529),U_6530),U_6531),U_6531) = c_Divides_Odiv__class_Omod(U_6529,U_6530,U_6531)
| ~ class_Divides_Osemiring__div(U_6529) ),
inference(clausify,[status(thm)],[f_1813_2]) ).
fof(f_1814_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_1814_2,plain,
! [U_6534,U_6533,U_6532] :
( c_Divides_Odiv__class_Omod(U_6532,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6532),U_6533),U_6534),U_6533) = c_Divides_Odiv__class_Omod(U_6532,U_6534,U_6533)
| ~ class_Divides_Osemiring__div(U_6532) ),
inference(variable_rename,[status(thm)],[f_1814_1]) ).
cnf(f_1814_3,plain,
( c_Divides_Odiv__class_Omod(U_6532,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6532),U_6533),U_6534),U_6533) = c_Divides_Odiv__class_Omod(U_6532,U_6534,U_6533)
| ~ class_Divides_Osemiring__div(U_6532) ),
inference(clausify,[status(thm)],[f_1814_2]) ).
fof(f_1815_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_1815_2,plain,
! [U_6538,U_6537,U_6536,U_6535] :
( c_Divides_Odiv__class_Omod(U_6535,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6535),U_6536),U_6537),U_6538) = c_Divides_Odiv__class_Omod(U_6535,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6535),U_6536),c_Divides_Odiv__class_Omod(U_6535,U_6537,U_6538)),U_6538)
| ~ class_Divides_Osemiring__div(U_6535) ),
inference(variable_rename,[status(thm)],[f_1815_1]) ).
cnf(f_1815_3,plain,
( c_Divides_Odiv__class_Omod(U_6535,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6535),U_6536),U_6537),U_6538) = c_Divides_Odiv__class_Omod(U_6535,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6535),U_6536),c_Divides_Odiv__class_Omod(U_6535,U_6537,U_6538)),U_6538)
| ~ class_Divides_Osemiring__div(U_6535) ),
inference(clausify,[status(thm)],[f_1815_2]) ).
fof(f_1816_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_1816_2,plain,
! [U_6542,U_6541,U_6540,U_6539] :
( c_Divides_Odiv__class_Omod(U_6539,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6539),U_6540),U_6541),U_6542) = c_Divides_Odiv__class_Omod(U_6539,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6539),c_Divides_Odiv__class_Omod(U_6539,U_6540,U_6542)),U_6541),U_6542)
| ~ class_Divides_Osemiring__div(U_6539) ),
inference(variable_rename,[status(thm)],[f_1816_1]) ).
cnf(f_1816_3,plain,
( c_Divides_Odiv__class_Omod(U_6539,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6539),U_6540),U_6541),U_6542) = c_Divides_Odiv__class_Omod(U_6539,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6539),c_Divides_Odiv__class_Omod(U_6539,U_6540,U_6542)),U_6541),U_6542)
| ~ class_Divides_Osemiring__div(U_6539) ),
inference(clausify,[status(thm)],[f_1816_2]) ).
fof(f_1817_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_1817_2,plain,
! [U_6546,U_6545,U_6544,U_6543] :
( c_Divides_Odiv__class_Omod(U_6543,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6543),U_6544),U_6545),U_6546) = c_Divides_Odiv__class_Omod(U_6543,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6543),c_Divides_Odiv__class_Omod(U_6543,U_6544,U_6546)),c_Divides_Odiv__class_Omod(U_6543,U_6545,U_6546)),U_6546)
| ~ class_Divides_Osemiring__div(U_6543) ),
inference(variable_rename,[status(thm)],[f_1817_1]) ).
cnf(f_1817_3,plain,
( c_Divides_Odiv__class_Omod(U_6543,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6543),U_6544),U_6545),U_6546) = c_Divides_Odiv__class_Omod(U_6543,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6543),c_Divides_Odiv__class_Omod(U_6543,U_6544,U_6546)),c_Divides_Odiv__class_Omod(U_6543,U_6545,U_6546)),U_6546)
| ~ class_Divides_Osemiring__div(U_6543) ),
inference(clausify,[status(thm)],[f_1817_2]) ).
fof(f_1818_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_1818_2,plain,
! [U_6549,U_6548,U_6547] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6547),U_6548)),U_6549) = 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_6547),U_6549)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6548),U_6549))),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_6547,U_6549)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6548,U_6549))),U_6549)),
inference(variable_rename,[status(thm)],[f_1818_1]) ).
cnf(f_1818_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6547),U_6548)),U_6549) = 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_6547),U_6549)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6548),U_6549))),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_6547,U_6549)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6548,U_6549))),U_6549)),
inference(clausify,[status(thm)],[f_1818_2]) ).
fof(f_1819_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_1819_2,plain,
! [U_6553,U_6552,U_6551,U_6550] :
( c_Divides_Odiv__class_Omod(U_6550,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6550),U_6551),c_Divides_Odiv__class_Omod(U_6550,U_6552,U_6553)),U_6553) = c_Divides_Odiv__class_Omod(U_6550,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6550),U_6551),U_6552),U_6553)
| ~ class_Divides_Osemiring__div(U_6550) ),
inference(variable_rename,[status(thm)],[f_1819_1]) ).
cnf(f_1819_3,plain,
( c_Divides_Odiv__class_Omod(U_6550,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6550),U_6551),c_Divides_Odiv__class_Omod(U_6550,U_6552,U_6553)),U_6553) = c_Divides_Odiv__class_Omod(U_6550,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6550),U_6551),U_6552),U_6553)
| ~ class_Divides_Osemiring__div(U_6550) ),
inference(clausify,[status(thm)],[f_1819_2]) ).
fof(f_1820_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_1820_2,plain,
! [U_6557,U_6556,U_6555,U_6554] :
( c_Divides_Odiv__class_Omod(U_6554,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6554),c_Divides_Odiv__class_Omod(U_6554,U_6555,U_6556)),U_6557),U_6556) = c_Divides_Odiv__class_Omod(U_6554,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6554),U_6555),U_6557),U_6556)
| ~ class_Divides_Osemiring__div(U_6554) ),
inference(variable_rename,[status(thm)],[f_1820_1]) ).
cnf(f_1820_3,plain,
( c_Divides_Odiv__class_Omod(U_6554,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6554),c_Divides_Odiv__class_Omod(U_6554,U_6555,U_6556)),U_6557),U_6556) = c_Divides_Odiv__class_Omod(U_6554,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6554),U_6555),U_6557),U_6556)
| ~ class_Divides_Osemiring__div(U_6554) ),
inference(clausify,[status(thm)],[f_1820_2]) ).
fof(f_1821_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_1821_2,plain,
! [U_6563,U_6562,U_6561,U_6560,U_6559,U_6558] :
( c_Divides_Odiv__class_Omod(U_6558,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6558),U_6559),U_6562),U_6560) = c_Divides_Odiv__class_Omod(U_6558,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6558),U_6561),U_6563),U_6560)
| c_Divides_Odiv__class_Omod(U_6558,U_6562,U_6560) != c_Divides_Odiv__class_Omod(U_6558,U_6563,U_6560)
| c_Divides_Odiv__class_Omod(U_6558,U_6559,U_6560) != c_Divides_Odiv__class_Omod(U_6558,U_6561,U_6560)
| ~ class_Divides_Osemiring__div(U_6558) ),
inference(variable_rename,[status(thm)],[f_1821_1]) ).
cnf(f_1821_3,plain,
( c_Divides_Odiv__class_Omod(U_6558,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6558),U_6559),U_6562),U_6560) = c_Divides_Odiv__class_Omod(U_6558,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6558),U_6561),U_6563),U_6560)
| c_Divides_Odiv__class_Omod(U_6558,U_6562,U_6560) != c_Divides_Odiv__class_Omod(U_6558,U_6563,U_6560)
| c_Divides_Odiv__class_Omod(U_6558,U_6559,U_6560) != c_Divides_Odiv__class_Omod(U_6558,U_6561,U_6560)
| ~ class_Divides_Osemiring__div(U_6558) ),
inference(clausify,[status(thm)],[f_1821_2]) ).
fof(f_1822_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_1822_2,plain,
! [U_6564] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_6564) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_1822_1]) ).
cnf(f_1822_3,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_6564) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1822_2]) ).
fof(f_1823_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_1823_2,plain,
! [U_6565] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6565,U_6565) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_1823_1]) ).
cnf(f_1823_3,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6565,U_6565) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1823_2]) ).
fof(f_1824_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_1824_2,plain,
! [U_6567,U_6566] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6566)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6567)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6566),U_6567),
inference(variable_rename,[status(thm)],[f_1824_1]) ).
cnf(f_1824_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6566)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6567)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6566),U_6567),
inference(clausify,[status(thm)],[f_1824_2]) ).
fof(f_1825_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_1825_2,plain,
! [U_6569,U_6568] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6568),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6569)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6568)),U_6569),
inference(variable_rename,[status(thm)],[f_1825_1]) ).
cnf(f_1825_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6568),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6569)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6568)),U_6569),
inference(clausify,[status(thm)],[f_1825_2]) ).
fof(f_1826_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_1826_2,plain,
! [U_6572,U_6571,U_6570] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6570),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6571,U_6572)),U_6572) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6570),U_6571),U_6572),
inference(variable_rename,[status(thm)],[f_1826_1]) ).
cnf(f_1826_3,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6570),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6571,U_6572)),U_6572) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6570),U_6571),U_6572),
inference(clausify,[status(thm)],[f_1826_2]) ).
fof(f_1827_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_1827_2,plain,
! [U_6575,U_6574,U_6573] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6573),U_6574),U_6575) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6573),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6574,U_6575)),U_6575),
inference(variable_rename,[status(thm)],[f_1827_1]) ).
cnf(f_1827_3,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6573),U_6574),U_6575) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6573),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6574,U_6575)),U_6575),
inference(clausify,[status(thm)],[f_1827_2]) ).
fof(f_1828_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_1828_2,plain,
! [U_6578,U_6577,U_6576] : 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_6576,U_6577)),U_6578),U_6577) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6576),U_6578),U_6577),
inference(variable_rename,[status(thm)],[f_1828_1]) ).
cnf(f_1828_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_6576,U_6577)),U_6578),U_6577) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6576),U_6578),U_6577),
inference(clausify,[status(thm)],[f_1828_2]) ).
fof(f_1829_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_1829_2,plain,
! [U_6581,U_6580,U_6579] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6579),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6580,U_6581)),U_6581) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6579),U_6580),U_6581),
inference(variable_rename,[status(thm)],[f_1829_1]) ).
cnf(f_1829_3,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6579),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6580,U_6581)),U_6581) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6579),U_6580),U_6581),
inference(clausify,[status(thm)],[f_1829_2]) ).
fof(f_1830_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_1830_2,plain,
! [U_6583,U_6582] : 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_6582,U_6583)),U_6583) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6582),U_6583),
inference(variable_rename,[status(thm)],[f_1830_1]) ).
cnf(f_1830_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_6582,U_6583)),U_6583) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6582),U_6583),
inference(clausify,[status(thm)],[f_1830_2]) ).
fof(f_1831_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_1831_2,plain,
! [U_6585,U_6584] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6584),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6585)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6584,U_6585)),
inference(variable_rename,[status(thm)],[f_1831_1]) ).
cnf(f_1831_3,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6584),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6585)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6584,U_6585)),
inference(clausify,[status(thm)],[f_1831_2]) ).
fof(f_1832_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_1832_2,plain,
! [U_6587,U_6586] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6586,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6587)) = 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_6586),U_6587)),
inference(variable_rename,[status(thm)],[f_1832_1]) ).
cnf(f_1832_3,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6586,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6587)) = 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_6586),U_6587)),
inference(clausify,[status(thm)],[f_1832_2]) ).
fof(f_1833_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_1833_2,plain,
! [U_6589,U_6588] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6588),U_6589),c_Groups_Ozero__class_Ozero(U_6588)) = c_Groups_Ozero__class_Ozero(U_6588)
| ~ class_Divides_Osemiring__div(U_6588) ),
inference(variable_rename,[status(thm)],[f_1833_1]) ).
cnf(f_1833_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6588),U_6589),c_Groups_Ozero__class_Ozero(U_6588)) = c_Groups_Ozero__class_Ozero(U_6588)
| ~ class_Divides_Osemiring__div(U_6588) ),
inference(clausify,[status(thm)],[f_1833_2]) ).
fof(f_1834_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_1834_2,plain,
! [U_6591,U_6590] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6590),c_Groups_Ozero__class_Ozero(U_6590)),U_6591) = c_Groups_Ozero__class_Ozero(U_6590)
| ~ class_Divides_Osemiring__div(U_6590) ),
inference(variable_rename,[status(thm)],[f_1834_1]) ).
cnf(f_1834_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6590),c_Groups_Ozero__class_Ozero(U_6590)),U_6591) = c_Groups_Ozero__class_Ozero(U_6590)
| ~ class_Divides_Osemiring__div(U_6590) ),
inference(clausify,[status(thm)],[f_1834_2]) ).
fof(f_1835_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_1835_2,plain,
! [U_6593,U_6592] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6592),U_6593),c_Groups_Oone__class_Oone(U_6592)) = U_6593
| ~ class_Divides_Osemiring__div(U_6592) ),
inference(variable_rename,[status(thm)],[f_1835_1]) ).
cnf(f_1835_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6592),U_6593),c_Groups_Oone__class_Oone(U_6592)) = U_6593
| ~ class_Divides_Osemiring__div(U_6592) ),
inference(clausify,[status(thm)],[f_1835_2]) ).
fof(f_1836_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_1836_2,plain,
! [U_6596,U_6595,U_6594] : 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_6594,U_6595)),U_6596),U_6595) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6594),U_6596),U_6595),
inference(variable_rename,[status(thm)],[f_1836_1]) ).
cnf(f_1836_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_6594,U_6595)),U_6596),U_6595) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6594),U_6596),U_6595),
inference(clausify,[status(thm)],[f_1836_2]) ).
fof(f_1837_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_1837_2,plain,
! [U_6599,U_6598,U_6597] :
( c_Divides_Odiv__class_Omod(U_6597,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6597),U_6598),U_6599),U_6598) = c_Groups_Ozero__class_Ozero(U_6597)
| ~ class_Divides_Osemiring__div(U_6597) ),
inference(variable_rename,[status(thm)],[f_1837_1]) ).
cnf(f_1837_3,plain,
( c_Divides_Odiv__class_Omod(U_6597,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6597),U_6598),U_6599),U_6598) = c_Groups_Ozero__class_Ozero(U_6597)
| ~ class_Divides_Osemiring__div(U_6597) ),
inference(clausify,[status(thm)],[f_1837_2]) ).
fof(f_1838_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_1838_2,plain,
! [U_6602,U_6601,U_6600] :
( c_Divides_Odiv__class_Omod(U_6600,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6600),U_6601),U_6602),U_6602) = c_Groups_Ozero__class_Ozero(U_6600)
| ~ class_Divides_Osemiring__div(U_6600) ),
inference(variable_rename,[status(thm)],[f_1838_1]) ).
cnf(f_1838_3,plain,
( c_Divides_Odiv__class_Omod(U_6600,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6600),U_6601),U_6602),U_6602) = c_Groups_Ozero__class_Ozero(U_6600)
| ~ class_Divides_Osemiring__div(U_6600) ),
inference(clausify,[status(thm)],[f_1838_2]) ).
fof(f_1839_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_1839_2,plain,
! [U_6605,U_6604,U_6603] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6604,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6605),U_6603)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6605),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6604),U_6605),U_6603))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6604,U_6605))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6603)) ),
inference(variable_rename,[status(thm)],[f_1839_1]) ).
cnf(f_1839_3,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6604,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6605),U_6603)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6605),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6604),U_6605),U_6603))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6604,U_6605))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6603)) ),
inference(clausify,[status(thm)],[f_1839_2]) ).
fof(f_1840_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_1840_2,plain,
! [U_6609,U_6608,U_6607,U_6606] :
( c_Divides_Odiv__class_Omod(U_6606,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6606),U_6607),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6606),U_6608),U_6609)),U_6609) = c_Divides_Odiv__class_Omod(U_6606,U_6607,U_6609)
| ~ class_Divides_Osemiring__div(U_6606) ),
inference(variable_rename,[status(thm)],[f_1840_1]) ).
cnf(f_1840_3,plain,
( c_Divides_Odiv__class_Omod(U_6606,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6606),U_6607),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6606),U_6608),U_6609)),U_6609) = c_Divides_Odiv__class_Omod(U_6606,U_6607,U_6609)
| ~ class_Divides_Osemiring__div(U_6606) ),
inference(clausify,[status(thm)],[f_1840_2]) ).
fof(f_1841_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_1841_2,plain,
! [U_6613,U_6612,U_6611,U_6610] :
( c_Divides_Odiv__class_Omod(U_6610,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6610),U_6611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6610),U_6612),U_6613)),U_6612) = c_Divides_Odiv__class_Omod(U_6610,U_6611,U_6612)
| ~ class_Divides_Osemiring__div(U_6610) ),
inference(variable_rename,[status(thm)],[f_1841_1]) ).
cnf(f_1841_3,plain,
( c_Divides_Odiv__class_Omod(U_6610,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6610),U_6611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6610),U_6612),U_6613)),U_6612) = c_Divides_Odiv__class_Omod(U_6610,U_6611,U_6612)
| ~ class_Divides_Osemiring__div(U_6610) ),
inference(clausify,[status(thm)],[f_1841_2]) ).
fof(f_1842_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_1842_2,plain,
! [U_6615,U_6614] :
( c_Divides_Odiv__class_Omod(U_6614,U_6615,c_Groups_Oone__class_Oone(U_6614)) = c_Groups_Ozero__class_Ozero(U_6614)
| ~ class_Divides_Osemiring__div(U_6614) ),
inference(variable_rename,[status(thm)],[f_1842_1]) ).
cnf(f_1842_3,plain,
( c_Divides_Odiv__class_Omod(U_6614,U_6615,c_Groups_Oone__class_Oone(U_6614)) = c_Groups_Ozero__class_Ozero(U_6614)
| ~ class_Divides_Osemiring__div(U_6614) ),
inference(clausify,[status(thm)],[f_1842_2]) ).
fof(f_1843_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_1843_2,plain,
! [U_6617,U_6616] :
( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6617)),U_6616) = 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_6617),U_6616))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6617,U_6616) = 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_6617)),U_6616) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6617),U_6616))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6617,U_6616) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| U_6616 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_1843_1]) ).
cnf(f_1843_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6617)),U_6616) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6617),U_6616))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6617,U_6616) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6616 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1843_2]) ).
cnf(f_1843_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6617)),U_6616) = 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_6617),U_6616))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6617,U_6616) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6616 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1843_2]) ).
fof(f_1844_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_1844_2,plain,
! [U_6619,U_6618] :
( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6619),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6618)) = 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_6619),U_6618))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6619,U_6618) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6619),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6618)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6619),U_6618))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6619,U_6618) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| U_6618 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_1844_1]) ).
cnf(f_1844_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6619),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6618)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6619),U_6618))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6619,U_6618) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6618 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1844_2]) ).
cnf(f_1844_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6619),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6618)) = 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_6619),U_6618))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6619,U_6618) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6618 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1844_2]) ).
fof(f_1845_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_1845_2,plain,
! [U_6621,U_6620] :
( 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_6620),U_6621)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6621))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6620)) ),
inference(variable_rename,[status(thm)],[f_1845_1]) ).
cnf(f_1845_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_6620),U_6621)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6621))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6620)) ),
inference(clausify,[status(thm)],[f_1845_2]) ).
fof(f_1846_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_1846_2,plain,
! [U_6623,U_6622] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6622),U_6623)),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_6623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6622),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1846_1]) ).
cnf(f_1846_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6622),U_6623)),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_6623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6622),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1846_2]) ).
fof(f_1847_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_1847_2,plain,
! [U_6625,U_6624] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6625),U_6624)),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_6625)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6625))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6625),U_6624)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6624),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1847_1]) ).
cnf(f_1847_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6625))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6625),U_6624)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6624),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1847_2]) ).
cnf(f_1847_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6625),U_6624)),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_6625))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6624),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1847_2]) ).
fof(f_1848_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_1848_2,plain,
! [U_6627,U_6626] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6627),U_6626)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6627),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6627),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_6627),U_6626)),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_6626)) ),
inference(variable_rename,[status(thm)],[f_1848_1]) ).
cnf(f_1848_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6627),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_6627),U_6626)),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_6626)) ),
inference(clausify,[status(thm)],[f_1848_2]) ).
cnf(f_1848_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6627),U_6626)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6627),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_6626)) ),
inference(clausify,[status(thm)],[f_1848_2]) ).
fof(f_1849_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_1849_2,plain,
! [U_6628] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6628),U_6628) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_6628 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_1849_1]) ).
cnf(f_1849_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6628),U_6628) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_6628 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1849_2]) ).
fof(f_1850_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_1850_2,plain,
! [U_6630,U_6629] :
( 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_6629,U_6630)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6630))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6629)) ),
inference(variable_rename,[status(thm)],[f_1850_1]) ).
cnf(f_1850_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_6629,U_6630)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6630))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6629)) ),
inference(clausify,[status(thm)],[f_1850_2]) ).
fof(f_1851_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_1851_2,plain,
! [U_6632,U_6631] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6631,U_6632)),U_6631))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6631)) ),
inference(variable_rename,[status(thm)],[f_1851_1]) ).
cnf(f_1851_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6631,U_6632)),U_6631))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6631)) ),
inference(clausify,[status(thm)],[f_1851_2]) ).
fof(f_1852_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_1852_2,plain,
! [U_6634,U_6633] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6633),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6634,U_6633)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6633),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1852_1]) ).
cnf(f_1852_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6633),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6634,U_6633)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6633),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1852_2]) ).
fof(f_1853_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_1853_2,plain,
! [U_6636,U_6635] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6636,U_6635)),U_6635))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6635)) ),
inference(variable_rename,[status(thm)],[f_1853_1]) ).
cnf(f_1853_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6636,U_6635)),U_6635))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6635)) ),
inference(clausify,[status(thm)],[f_1853_2]) ).
fof(f_1854_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_1854_2,plain,
! [U_6638,U_6637] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6637))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6638))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6637)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6638)),
inference(variable_rename,[status(thm)],[f_1854_1]) ).
cnf(f_1854_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_6637))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6638))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6637)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6638)),
inference(clausify,[status(thm)],[f_1854_2]) ).
fof(f_1855_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_1855_2,plain,
! [U_6642,U_6641] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6641,U_6642) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ! [U_6640] : U_6641 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6642),U_6640) )
& ( ? [U_6639] : U_6641 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6642),U_6639)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6641,U_6642) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_1855_1]) ).
fof(f_1855_3,plain,
( ! [U_6646,U_6644] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6644,U_6646) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ! [U_6640] : U_6644 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6646),U_6640) )
& ! [U_6645,U_6643] :
( ? [U_6639] : U_6643 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6645),U_6639)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6643,U_6645) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_1855_2]) ).
fof(f_1855_4,plain,
( ! [U_6646,U_6644] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6644,U_6646) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ! [U_6640] : U_6644 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6646),U_6640) )
& ! [U_6645,U_6643] :
( U_6643 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6645),sK132(U_6645,U_6643))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6643,U_6645) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(U_6639,sK132(U_6645,U_6643))],[f_1855_3]) ).
cnf(f_1855_5,plain,
( U_6643 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6645),sK132(U_6645,U_6643))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6643,U_6645) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1855_4]) ).
cnf(f_1855_6,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6644,U_6646) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6644 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6646),U_6640) ),
inference(clausify,[status(thm)],[f_1855_4]) ).
fof(f_1856_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_1856_2,plain,
! [U_6648,U_6647] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6647,U_6648) != 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_6647),U_6648) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_1856_1]) ).
cnf(f_1856_3,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6647,U_6648) != 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_6647),U_6648) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1856_2]) ).
fof(f_1857_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_1857_2,plain,
! [U_6650,U_6649] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6649,U_6650) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6649,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6650)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_1857_1]) ).
cnf(f_1857_3,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6649,U_6650) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6649,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6650)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1857_2]) ).
fof(f_1858_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_1858_2,plain,
! [U_6654,U_6653,U_6652,U_6651] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6651),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6651),U_6652),U_6653)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6651),U_6652),U_6654)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6651),U_6653),U_6654)
| U_6652 = c_Groups_Ozero__class_Ozero(U_6651)
| ~ class_Divides_Osemiring__div(U_6651) ),
inference(variable_rename,[status(thm)],[f_1858_1]) ).
cnf(f_1858_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6651),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6651),U_6652),U_6653)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6651),U_6652),U_6654)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6651),U_6653),U_6654)
| U_6652 = c_Groups_Ozero__class_Ozero(U_6651)
| ~ class_Divides_Osemiring__div(U_6651) ),
inference(clausify,[status(thm)],[f_1858_2]) ).
fof(f_1859_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_1859_2,plain,
! [U_6658,U_6657,U_6656,U_6655] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6655),U_6657),U_6656)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6655),U_6658),U_6656)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6655),U_6657),U_6658)
| U_6656 = c_Groups_Ozero__class_Ozero(U_6655)
| ~ class_Divides_Osemiring__div(U_6655) ),
inference(variable_rename,[status(thm)],[f_1859_1]) ).
cnf(f_1859_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6655),U_6657),U_6656)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6655),U_6658),U_6656)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6655),U_6657),U_6658)
| U_6656 = c_Groups_Ozero__class_Ozero(U_6655)
| ~ class_Divides_Osemiring__div(U_6655) ),
inference(clausify,[status(thm)],[f_1859_2]) ).
fof(f_1860_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_1860_2,plain,
! [U_6661,U_6660,U_6659] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6659),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6659),U_6660),U_6661)),U_6660) = U_6661
| U_6660 = c_Groups_Ozero__class_Ozero(U_6659)
| ~ class_Divides_Osemiring__div(U_6659) ),
inference(variable_rename,[status(thm)],[f_1860_1]) ).
cnf(f_1860_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6659),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6659),U_6660),U_6661)),U_6660) = U_6661
| U_6660 = c_Groups_Ozero__class_Ozero(U_6659)
| ~ class_Divides_Osemiring__div(U_6659) ),
inference(clausify,[status(thm)],[f_1860_2]) ).
fof(f_1861_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_1861_2,plain,
! [U_6664,U_6663,U_6662] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6662),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6662),U_6664),U_6663)),U_6663) = U_6664
| U_6663 = c_Groups_Ozero__class_Ozero(U_6662)
| ~ class_Divides_Osemiring__div(U_6662) ),
inference(variable_rename,[status(thm)],[f_1861_1]) ).
cnf(f_1861_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6662),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6662),U_6664),U_6663)),U_6663) = U_6664
| U_6663 = c_Groups_Ozero__class_Ozero(U_6662)
| ~ class_Divides_Osemiring__div(U_6662) ),
inference(clausify,[status(thm)],[f_1861_2]) ).
fof(f_1862_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_1862_2,plain,
! [U_6668,U_6667,U_6666,U_6665] :
( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6665),U_6666),U_6667)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6665),U_6666),U_6668)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6665),U_6667),U_6668)
| U_6666 = c_Groups_Ozero__class_Ozero(U_6665) )
& ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6665),U_6666),U_6667)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6665),U_6666),U_6668)) = c_Groups_Ozero__class_Ozero(U_6665)
| U_6666 != c_Groups_Ozero__class_Ozero(U_6665) ) )
| ~ class_Divides_Osemiring__div(U_6665) ),
inference(variable_rename,[status(thm)],[f_1862_1]) ).
cnf(f_1862_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6665),U_6666),U_6667)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6665),U_6666),U_6668)) = c_Groups_Ozero__class_Ozero(U_6665)
| U_6666 != c_Groups_Ozero__class_Ozero(U_6665)
| ~ class_Divides_Osemiring__div(U_6665) ),
inference(clausify,[status(thm)],[f_1862_2]) ).
cnf(f_1862_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6665),U_6666),U_6667)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6665),U_6666),U_6668)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6665),U_6667),U_6668)
| U_6666 = c_Groups_Ozero__class_Ozero(U_6665)
| ~ class_Divides_Osemiring__div(U_6665) ),
inference(clausify,[status(thm)],[f_1862_2]) ).
fof(f_1863_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_1863_2,plain,
! [U_6670,U_6669] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6669),U_6670),U_6670) = c_Groups_Oone__class_Oone(U_6669)
| U_6670 = c_Groups_Ozero__class_Ozero(U_6669)
| ~ class_Divides_Osemiring__div(U_6669) ),
inference(variable_rename,[status(thm)],[f_1863_1]) ).
cnf(f_1863_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6669),U_6670),U_6670) = c_Groups_Oone__class_Oone(U_6669)
| U_6670 = c_Groups_Ozero__class_Ozero(U_6669)
| ~ class_Divides_Osemiring__div(U_6669) ),
inference(clausify,[status(thm)],[f_1863_2]) ).
fof(f_1864_1,plain,
! [V_n_2,V_P_2,V_k_2] :
( ( ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
| ? [B_i,B_j] :
( ~ hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
& V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) ) )
& ( ! [B_i,B_j] :
( hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
| V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
| ~ hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_split__neg__lemma]) ).
fof(f_1864_2,plain,
! [U_6677,U_6676,U_6675] :
( ( ( hBOOL(hAPP(hAPP(U_6676,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6677),U_6675)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6677,U_6675)))
| ? [U_6674,U_6673] :
( ~ hBOOL(hAPP(hAPP(U_6676,U_6674),U_6673))
& U_6677 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6675),U_6674)),U_6673)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6673),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6675),U_6673)) ) )
& ( ! [U_6672,U_6671] :
( hBOOL(hAPP(hAPP(U_6676,U_6672),U_6671))
| U_6677 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6675),U_6672)),U_6671)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6671),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6675),U_6671)) )
| ~ hBOOL(hAPP(hAPP(U_6676,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6677),U_6675)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6677,U_6675))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6675),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1864_1]) ).
fof(f_1864_3,plain,
! [U_6677,U_6676,U_6675] :
( ( ( hBOOL(hAPP(hAPP(U_6676,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6677),U_6675)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6677,U_6675)))
| ? [U_6673] :
( ~ hBOOL(hAPP(hAPP(U_6676,sK133(U_6677,U_6676,U_6675)),U_6673))
& U_6677 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6675),sK133(U_6677,U_6676,U_6675))),U_6673)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6673),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6675),U_6673)) ) )
& ( ! [U_6672,U_6671] :
( hBOOL(hAPP(hAPP(U_6676,U_6672),U_6671))
| U_6677 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6675),U_6672)),U_6671)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6671),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6675),U_6671)) )
| ~ hBOOL(hAPP(hAPP(U_6676,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6677),U_6675)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6677,U_6675))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6675),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK133]),skolemize(U_6674,sK133(U_6677,U_6676,U_6675))],[f_1864_2]) ).
fof(f_1864_4,plain,
! [U_6677,U_6676,U_6675] :
( ( ( hBOOL(hAPP(hAPP(U_6676,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6677),U_6675)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6677,U_6675)))
| ( ~ hBOOL(hAPP(hAPP(U_6676,sK133(U_6677,U_6676,U_6675)),sK134(U_6677,U_6676,U_6675)))
& U_6677 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6675),sK133(U_6677,U_6676,U_6675))),sK134(U_6677,U_6676,U_6675))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK134(U_6677,U_6676,U_6675)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6675),sK134(U_6677,U_6676,U_6675))) ) )
& ( ! [U_6672,U_6671] :
( hBOOL(hAPP(hAPP(U_6676,U_6672),U_6671))
| U_6677 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6675),U_6672)),U_6671)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6671),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6675),U_6671)) )
| ~ hBOOL(hAPP(hAPP(U_6676,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6677),U_6675)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6677,U_6675))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6675),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(U_6673,sK134(U_6677,U_6676,U_6675))],[f_1864_3]) ).
cnf(f_1864_5,plain,
( hBOOL(hAPP(hAPP(U_6676,U_6672),U_6671))
| U_6677 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6675),U_6672)),U_6671)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6671),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6675),U_6671))
| ~ hBOOL(hAPP(hAPP(U_6676,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6677),U_6675)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6677,U_6675)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6675),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1864_4]) ).
cnf(f_1864_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6675),sK134(U_6677,U_6676,U_6675)))
| hBOOL(hAPP(hAPP(U_6676,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6677),U_6675)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6677,U_6675)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6675),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1864_4]) ).
cnf(f_1864_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK134(U_6677,U_6676,U_6675)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(U_6676,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6677),U_6675)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6677,U_6675)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6675),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1864_4]) ).
cnf(f_1864_8,plain,
( U_6677 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6675),sK133(U_6677,U_6676,U_6675))),sK134(U_6677,U_6676,U_6675))
| hBOOL(hAPP(hAPP(U_6676,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6677),U_6675)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6677,U_6675)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6675),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1864_4]) ).
cnf(f_1864_9,plain,
( ~ hBOOL(hAPP(hAPP(U_6676,sK133(U_6677,U_6676,U_6675)),sK134(U_6677,U_6676,U_6675)))
| hBOOL(hAPP(hAPP(U_6676,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6677),U_6675)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6677,U_6675)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6675),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1864_4]) ).
fof(f_1865_1,plain,
! [V_n_2,V_P_2,V_k_2] :
( ( ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
| ? [B_i,B_j] :
( ~ hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
& V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) ) )
& ( ! [B_i,B_j] :
( hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
| V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
| ~ hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) ),
inference(fof_nnf,[status(thm)],[fact_split__pos__lemma]) ).
fof(f_1865_2,plain,
! [U_6684,U_6683,U_6682] :
( ( ( hBOOL(hAPP(hAPP(U_6683,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6684),U_6682)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6684,U_6682)))
| ? [U_6681,U_6680] :
( ~ hBOOL(hAPP(hAPP(U_6683,U_6681),U_6680))
& U_6684 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6682),U_6681)),U_6680)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6680),U_6682))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6680)) ) )
& ( ! [U_6679,U_6678] :
( hBOOL(hAPP(hAPP(U_6683,U_6679),U_6678))
| U_6684 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6682),U_6679)),U_6678)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6678),U_6682))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6678)) )
| ~ hBOOL(hAPP(hAPP(U_6683,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6684),U_6682)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6684,U_6682))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6682)) ),
inference(variable_rename,[status(thm)],[f_1865_1]) ).
fof(f_1865_3,plain,
! [U_6684,U_6683,U_6682] :
( ( ( hBOOL(hAPP(hAPP(U_6683,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6684),U_6682)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6684,U_6682)))
| ? [U_6680] :
( ~ hBOOL(hAPP(hAPP(U_6683,sK135(U_6684,U_6683,U_6682)),U_6680))
& U_6684 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6682),sK135(U_6684,U_6683,U_6682))),U_6680)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6680),U_6682))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6680)) ) )
& ( ! [U_6679,U_6678] :
( hBOOL(hAPP(hAPP(U_6683,U_6679),U_6678))
| U_6684 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6682),U_6679)),U_6678)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6678),U_6682))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6678)) )
| ~ hBOOL(hAPP(hAPP(U_6683,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6684),U_6682)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6684,U_6682))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6682)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK135]),skolemize(U_6681,sK135(U_6684,U_6683,U_6682))],[f_1865_2]) ).
fof(f_1865_4,plain,
! [U_6684,U_6683,U_6682] :
( ( ( hBOOL(hAPP(hAPP(U_6683,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6684),U_6682)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6684,U_6682)))
| ( ~ hBOOL(hAPP(hAPP(U_6683,sK135(U_6684,U_6683,U_6682)),sK136(U_6684,U_6683,U_6682)))
& U_6684 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6682),sK135(U_6684,U_6683,U_6682))),sK136(U_6684,U_6683,U_6682))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK136(U_6684,U_6683,U_6682)),U_6682))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK136(U_6684,U_6683,U_6682))) ) )
& ( ! [U_6679,U_6678] :
( hBOOL(hAPP(hAPP(U_6683,U_6679),U_6678))
| U_6684 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6682),U_6679)),U_6678)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6678),U_6682))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6678)) )
| ~ hBOOL(hAPP(hAPP(U_6683,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6684),U_6682)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6684,U_6682))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6682)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK136]),skolemize(U_6680,sK136(U_6684,U_6683,U_6682))],[f_1865_3]) ).
cnf(f_1865_5,plain,
( hBOOL(hAPP(hAPP(U_6683,U_6679),U_6678))
| U_6684 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6682),U_6679)),U_6678)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6678),U_6682))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6678))
| ~ hBOOL(hAPP(hAPP(U_6683,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6684),U_6682)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6684,U_6682)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6682)) ),
inference(clausify,[status(thm)],[f_1865_4]) ).
cnf(f_1865_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK136(U_6684,U_6683,U_6682)))
| hBOOL(hAPP(hAPP(U_6683,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6684),U_6682)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6684,U_6682)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6682)) ),
inference(clausify,[status(thm)],[f_1865_4]) ).
cnf(f_1865_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK136(U_6684,U_6683,U_6682)),U_6682))
| hBOOL(hAPP(hAPP(U_6683,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6684),U_6682)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6684,U_6682)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6682)) ),
inference(clausify,[status(thm)],[f_1865_4]) ).
cnf(f_1865_8,plain,
( U_6684 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6682),sK135(U_6684,U_6683,U_6682))),sK136(U_6684,U_6683,U_6682))
| hBOOL(hAPP(hAPP(U_6683,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6684),U_6682)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6684,U_6682)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6682)) ),
inference(clausify,[status(thm)],[f_1865_4]) ).
cnf(f_1865_9,plain,
( ~ hBOOL(hAPP(hAPP(U_6683,sK135(U_6684,U_6683,U_6682)),sK136(U_6684,U_6683,U_6682)))
| hBOOL(hAPP(hAPP(U_6683,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6684),U_6682)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6684,U_6682)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6682)) ),
inference(clausify,[status(thm)],[f_1865_4]) ).
fof(f_1866_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_1866_2,plain,
! [U_6686,U_6685] :
( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6685),U_6686) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6686),U_6685))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6685),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6685),U_6686))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6685)) )
& U_6686 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6686),U_6685))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6685),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6685),U_6686))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6685)) )
| U_6686 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6685),U_6686) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_1866_1]) ).
fof(f_1866_3,plain,
( ! [U_6690,U_6688] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6688),U_6690) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6690),U_6688))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6688),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6688),U_6690))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6688)) )
& U_6690 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_6689,U_6687] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6689),U_6687))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6687),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6687),U_6689))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6687)) )
| U_6689 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6687),U_6689) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_1866_2]) ).
cnf(f_1866_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6687),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_6687))
| U_6689 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6687),U_6689) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1866_3]) ).
cnf(f_1866_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6689),U_6687))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6687))
| U_6689 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6687),U_6689) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1866_3]) ).
cnf(f_1866_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6687),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6687),U_6689))
| U_6689 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6687),U_6689) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1866_3]) ).
cnf(f_1866_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6689),U_6687))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6687),U_6689))
| U_6689 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6687),U_6689) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1866_3]) ).
cnf(f_1866_8,plain,
( U_6690 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6688),U_6690) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1866_3]) ).
cnf(f_1866_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6688),U_6690))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6688))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6688),U_6690) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1866_3]) ).
cnf(f_1866_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6690),U_6688))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6688),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6688),U_6690) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1866_3]) ).
fof(f_1867_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_1867_2,plain,
! [U_6692,U_6691] :
( ( ( 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_6692),U_6691)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6692)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6692))
| ~ 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_6692),U_6691))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6691)) ),
inference(variable_rename,[status(thm)],[f_1867_1]) ).
cnf(f_1867_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6692))
| ~ 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_6692),U_6691)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6691)) ),
inference(clausify,[status(thm)],[f_1867_2]) ).
cnf(f_1867_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_6692),U_6691)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6692))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6691)) ),
inference(clausify,[status(thm)],[f_1867_2]) ).
fof(f_1868_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_1868_2,plain,
! [U_6694,U_6693] :
( ( ( 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_6694),U_6693)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6693),U_6694)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6693),U_6694))
| ~ 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_6694),U_6693))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6693)) ),
inference(variable_rename,[status(thm)],[f_1868_1]) ).
cnf(f_1868_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6693),U_6694))
| ~ 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_6694),U_6693)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6693)) ),
inference(clausify,[status(thm)],[f_1868_2]) ).
cnf(f_1868_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_6694),U_6693)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6693),U_6694))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6693)) ),
inference(clausify,[status(thm)],[f_1868_2]) ).
fof(f_1869_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_1869_2,plain,
! [U_6696,U_6695] :
( ( ( 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_6695),U_6696)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6696))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6696),U_6695)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6696))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6696),U_6695)) )
| ~ 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_6695),U_6696))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6695)) ),
inference(variable_rename,[status(thm)],[f_1869_1]) ).
cnf(f_1869_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6696),U_6695))
| ~ 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_6695),U_6696)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6695)) ),
inference(clausify,[status(thm)],[f_1869_2]) ).
cnf(f_1869_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6696))
| ~ 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_6695),U_6696)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6695)) ),
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)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6695),U_6696)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6696))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6696),U_6695))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6695)) ),
inference(clausify,[status(thm)],[f_1869_2]) ).
fof(f_1870_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_1870_2,plain,
! [U_6699,U_6698,U_6697] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6697),U_6699)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6697),U_6698)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6698),U_6699))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6698))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6697)) ),
inference(variable_rename,[status(thm)],[f_1870_1]) ).
cnf(f_1870_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_6697),U_6699)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6697),U_6698)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6698),U_6699))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6698))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6697)) ),
inference(clausify,[status(thm)],[f_1870_2]) ).
fof(f_1871_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_1871_2,plain,
! [U_6701,U_6700] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6700),U_6701)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6701),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_6700)) ),
inference(variable_rename,[status(thm)],[f_1871_1]) ).
cnf(f_1871_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6700),U_6701)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6701),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_6700)) ),
inference(clausify,[status(thm)],[f_1871_2]) ).
fof(f_1872_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_1872_2,plain,
! [U_6703,U_6702] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6702),U_6703) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6702),U_6703))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6702)) ),
inference(variable_rename,[status(thm)],[f_1872_1]) ).
cnf(f_1872_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6702),U_6703) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6702),U_6703))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6702)) ),
inference(clausify,[status(thm)],[f_1872_2]) ).
fof(f_1873_1,plain,
! [V_a_2,V_b_2] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__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_1873_2,plain,
! [U_6705,U_6704] :
( ( ( 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_6705),U_6704)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6705),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6705),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_6705),U_6704))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6704),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1873_1]) ).
cnf(f_1873_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6705),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_6705),U_6704)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6704),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1873_2]) ).
cnf(f_1873_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6705),U_6704)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6705),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6704),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1873_2]) ).
fof(f_1874_1,plain,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__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_1874_2,plain,
! [U_6707,U_6706] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6706),U_6707)),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_6707))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6706),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1874_1]) ).
cnf(f_1874_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6706),U_6707)),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_6707))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6706),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1874_2]) ).
fof(f_1875_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_1875_2,plain,
! [U_6710,U_6709,U_6708] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6708),U_6709)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6708),U_6710)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6709),U_6710))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6709))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6708),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1875_1]) ).
cnf(f_1875_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_6708),U_6709)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6708),U_6710)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6709),U_6710))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6709))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6708),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1875_2]) ).
fof(f_1876_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_1876_2,plain,
! [U_6712,U_6711] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6711),U_6712) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6712),U_6711))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6711),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_6711),U_6712) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6712),U_6711))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6711),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1876_2]) ).
fof(f_1877_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_1877_2,plain,
! [U_6715,U_6714,U_6713] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6713),U_6715)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6714),U_6715)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6715))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6713),U_6714)) ),
inference(variable_rename,[status(thm)],[f_1877_1]) ).
cnf(f_1877_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_6713),U_6715)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6714),U_6715)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6715))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6713),U_6714)) ),
inference(clausify,[status(thm)],[f_1877_2]) ).
fof(f_1878_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_1878_2,plain,
! [U_6718,U_6717,U_6716] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6717),U_6718)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6716),U_6718)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6718),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6716),U_6717)) ),
inference(variable_rename,[status(thm)],[f_1878_1]) ).
cnf(f_1878_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_6717),U_6718)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6716),U_6718)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6718),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6716),U_6717)) ),
inference(clausify,[status(thm)],[f_1878_2]) ).
fof(f_1879_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_1879_2,plain,
! [U_6720,U_6719] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6719),U_6720)),U_6719))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6720))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6719)) ),
inference(variable_rename,[status(thm)],[f_1879_1]) ).
cnf(f_1879_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6719),U_6720)),U_6719))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6720))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6719)) ),
inference(clausify,[status(thm)],[f_1879_2]) ).
fof(f_1880_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_1880_2,plain,
! [U_6723,U_6722,U_6721] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6723),U_6721)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6722),U_6723)),U_6721)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6721)) ),
inference(variable_rename,[status(thm)],[f_1880_1]) ).
cnf(f_1880_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6723),U_6721)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6722),U_6723)),U_6721)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6721)) ),
inference(clausify,[status(thm)],[f_1880_2]) ).
fof(f_1881_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_1881_2,plain,
! [U_6725,U_6724] :
( 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_6725,U_6724)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6724)) ),
inference(variable_rename,[status(thm)],[f_1881_1]) ).
cnf(f_1881_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_6725,U_6724)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6724)) ),
inference(clausify,[status(thm)],[f_1881_2]) ).
fof(f_1882_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_1882_2,plain,
! [U_6727,U_6726] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6727,U_6726)),U_6726))
& 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_6727,U_6726))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6726)) ),
inference(variable_rename,[status(thm)],[f_1882_1]) ).
cnf(f_1882_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_6727,U_6726)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6726)) ),
inference(clausify,[status(thm)],[f_1882_2]) ).
cnf(f_1882_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6727,U_6726)),U_6726))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6726)) ),
inference(clausify,[status(thm)],[f_1882_2]) ).
fof(f_1883_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_1883_2,plain,
! [U_6729,U_6728] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6728,U_6729) = U_6728
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6728),U_6729))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6728)) ),
inference(variable_rename,[status(thm)],[f_1883_1]) ).
cnf(f_1883_3,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6728,U_6729) = U_6728
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6728),U_6729))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6728)) ),
inference(clausify,[status(thm)],[f_1883_2]) ).
fof(f_1884_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_1884_2,plain,
! [U_6731,U_6730] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6731,U_6730)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6730),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1884_1]) ).
cnf(f_1884_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6731,U_6730)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6730),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1884_2]) ).
fof(f_1885_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_1885_2,plain,
! [U_6733,U_6732] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6732),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6733,U_6732)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6733,U_6732)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6732),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1885_1]) ).
cnf(f_1885_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6733,U_6732)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6732),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1885_2]) ).
cnf(f_1885_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6732),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6733,U_6732)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6732),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1885_2]) ).
fof(f_1886_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_1886_2,plain,
! [U_6735,U_6734] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6734,U_6735) = U_6734
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6735),U_6734))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6734),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1886_1]) ).
cnf(f_1886_3,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6734,U_6735) = U_6734
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6735),U_6734))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6734),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1886_2]) ).
fof(f_1887_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_1887_2,plain,
! [U_6737,U_6736] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6736,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6737)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6736,U_6737)),U_6737)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6736,U_6737) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6736,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6737)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6736,U_6737) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_1887_1]) ).
fof(f_1887_3,plain,
( ! [U_6741,U_6739] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6739,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6741)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6739,U_6741)),U_6741)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6739,U_6741) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_6740,U_6738] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6738,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6740)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6738,U_6740) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_1887_2]) ).
cnf(f_1887_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6738,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6740)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6738,U_6740) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1887_3]) ).
cnf(f_1887_5,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6739,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6741)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6739,U_6741)),U_6741)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6739,U_6741) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1887_3]) ).
fof(f_1888_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_1888_2,plain,
! [U_6743,U_6742] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6742),U_6743) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6743),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6742,U_6743))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6742,U_6743) = 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_6742),U_6743) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6742,U_6743) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_1888_1]) ).
fof(f_1888_3,plain,
( ! [U_6747,U_6745] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6745),U_6747) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6747),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6745,U_6747))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6745,U_6747) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_6746,U_6744] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6744),U_6746) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6744,U_6746) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_1888_2]) ).
cnf(f_1888_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6744),U_6746) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6744,U_6746) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1888_3]) ).
cnf(f_1888_5,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6745),U_6747) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6747),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6745,U_6747))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6745,U_6747) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1888_3]) ).
fof(f_1889_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_1889_2,plain,
! [U_6751,U_6750,U_6749,U_6748] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6748),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6748),U_6750),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6748),U_6751),U_6749))),U_6749) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6748),U_6751),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6748),U_6750),U_6749))
| U_6749 = c_Groups_Ozero__class_Ozero(U_6748)
| ~ class_Divides_Osemiring__div(U_6748) ),
inference(variable_rename,[status(thm)],[f_1889_1]) ).
cnf(f_1889_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6748),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6748),U_6750),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6748),U_6751),U_6749))),U_6749) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6748),U_6751),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6748),U_6750),U_6749))
| U_6749 = c_Groups_Ozero__class_Ozero(U_6748)
| ~ class_Divides_Osemiring__div(U_6748) ),
inference(clausify,[status(thm)],[f_1889_2]) ).
fof(f_1890_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_1890_2,plain,
! [U_6755,U_6754,U_6753,U_6752] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6752),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6752),U_6754),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6752),U_6753),U_6755))),U_6753) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6752),U_6755),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6752),U_6754),U_6753))
| U_6753 = c_Groups_Ozero__class_Ozero(U_6752)
| ~ class_Divides_Osemiring__div(U_6752) ),
inference(variable_rename,[status(thm)],[f_1890_1]) ).
cnf(f_1890_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6752),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6752),U_6754),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6752),U_6753),U_6755))),U_6753) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6752),U_6755),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6752),U_6754),U_6753))
| U_6753 = c_Groups_Ozero__class_Ozero(U_6752)
| ~ class_Divides_Osemiring__div(U_6752) ),
inference(clausify,[status(thm)],[f_1890_2]) ).
fof(f_1891_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_1891_2,plain,
! [U_6758,U_6757,U_6756] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6756),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6756),U_6757),U_6758)),U_6757) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6756),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6756),U_6758),U_6757)),c_Groups_Oone__class_Oone(U_6756))
| U_6757 = c_Groups_Ozero__class_Ozero(U_6756)
| ~ class_Divides_Osemiring__div(U_6756) ),
inference(variable_rename,[status(thm)],[f_1891_1]) ).
cnf(f_1891_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6756),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6756),U_6757),U_6758)),U_6757) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6756),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6756),U_6758),U_6757)),c_Groups_Oone__class_Oone(U_6756))
| U_6757 = c_Groups_Ozero__class_Ozero(U_6756)
| ~ class_Divides_Osemiring__div(U_6756) ),
inference(clausify,[status(thm)],[f_1891_2]) ).
fof(f_1892_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_1892_2,plain,
! [U_6761,U_6760,U_6759] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6759),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6759),U_6761),U_6760)),U_6760) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6759),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6759),U_6761),U_6760)),c_Groups_Oone__class_Oone(U_6759))
| U_6760 = c_Groups_Ozero__class_Ozero(U_6759)
| ~ class_Divides_Osemiring__div(U_6759) ),
inference(variable_rename,[status(thm)],[f_1892_1]) ).
cnf(f_1892_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6759),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6759),U_6761),U_6760)),U_6760) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6759),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6759),U_6761),U_6760)),c_Groups_Oone__class_Oone(U_6759))
| U_6760 = c_Groups_Ozero__class_Ozero(U_6759)
| ~ class_Divides_Osemiring__div(U_6759) ),
inference(clausify,[status(thm)],[f_1892_2]) ).
fof(f_1893_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_1893_2,plain,
! [U_6763,U_6762] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6762,U_6763) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6762),U_6763)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6762),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)),U_6762)) ),
inference(variable_rename,[status(thm)],[f_1893_1]) ).
cnf(f_1893_3,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6762,U_6763) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6762),U_6763)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6762),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)),U_6762)) ),
inference(clausify,[status(thm)],[f_1893_2]) ).
fof(f_1894_1,plain,
! [V_k_2,V_n_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
| ( ? [B_i] :
( ~ hBOOL(hAPP(V_P_2,B_i))
& ? [B_j] :
( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [B_i] :
( ~ hBOOL(hAPP(V_P_2,B_i))
& ? [B_j] :
( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) )
| ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( ( ! [B_i] :
( hBOOL(hAPP(V_P_2,B_i))
| ! [B_j] :
( V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [B_i] :
( hBOOL(hAPP(V_P_2,B_i))
| ! [B_j] :
( V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) )
& ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__zdiv]) ).
fof(f_1894_2,plain,
! [U_6774,U_6773,U_6772] :
( ( hBOOL(hAPP(U_6772,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6773),U_6774)))
| ( ? [U_6771] :
( ~ hBOOL(hAPP(U_6772,U_6771))
& ? [U_6770] :
( U_6773 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6774),U_6771)),U_6770)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6770),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6774),U_6770)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6774),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [U_6769] :
( ~ hBOOL(hAPP(U_6772,U_6769))
& ? [U_6768] :
( U_6773 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6774),U_6769)),U_6768)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6768),U_6774))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6768)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6774)) )
| ( ~ hBOOL(hAPP(U_6772,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_6774 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( ( ! [U_6767] :
( hBOOL(hAPP(U_6772,U_6767))
| ! [U_6766] :
( U_6773 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6774),U_6767)),U_6766)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6766),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6774),U_6766)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6774),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_6765] :
( hBOOL(hAPP(U_6772,U_6765))
| ! [U_6764] :
( U_6773 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6774),U_6765)),U_6764)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6764),U_6774))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6764)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6774)) )
& ( hBOOL(hAPP(U_6772,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6774 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_6772,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6773),U_6774))) ) ),
inference(variable_rename,[status(thm)],[f_1894_1]) ).
fof(f_1894_3,plain,
( ! [U_6780,U_6778,U_6776] :
( hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780)))
| ( ? [U_6771] :
( ~ hBOOL(hAPP(U_6776,U_6771))
& ? [U_6770] :
( U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),U_6771)),U_6770)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6770),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),U_6770)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [U_6769] :
( ~ hBOOL(hAPP(U_6776,U_6769))
& ? [U_6768] :
( U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),U_6769)),U_6768)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6768),U_6780))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6768)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6780)) )
| ( ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_6779,U_6777,U_6775] :
( ( ( ! [U_6767] :
( hBOOL(hAPP(U_6775,U_6767))
| ! [U_6766] :
( U_6777 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6779),U_6767)),U_6766)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6766),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6779),U_6766)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6779),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_6765] :
( hBOOL(hAPP(U_6775,U_6765))
| ! [U_6764] :
( U_6777 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6779),U_6765)),U_6764)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6764),U_6779))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6764)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6779)) )
& ( hBOOL(hAPP(U_6775,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6779 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_6775,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6777),U_6779))) ) ),
inference(miniscope,[status(thm)],[f_1894_2]) ).
fof(f_1894_4,plain,
( ! [U_6780,U_6778,U_6776] :
( hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780)))
| ( ? [U_6771] :
( ~ hBOOL(hAPP(U_6776,U_6771))
& ? [U_6770] :
( U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),U_6771)),U_6770)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6770),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),U_6770)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_6776,sK137(U_6780,U_6778,U_6776)))
& ? [U_6768] :
( U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK137(U_6780,U_6778,U_6776))),U_6768)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6768),U_6780))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6768)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6780)) )
| ( ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_6779,U_6777,U_6775] :
( ( ( ! [U_6767] :
( hBOOL(hAPP(U_6775,U_6767))
| ! [U_6766] :
( U_6777 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6779),U_6767)),U_6766)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6766),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6779),U_6766)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6779),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_6765] :
( hBOOL(hAPP(U_6775,U_6765))
| ! [U_6764] :
( U_6777 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6779),U_6765)),U_6764)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6764),U_6779))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6764)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6779)) )
& ( hBOOL(hAPP(U_6775,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6779 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_6775,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6777),U_6779))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK137]),skolemize(U_6769,sK137(U_6780,U_6778,U_6776))],[f_1894_3]) ).
fof(f_1894_5,plain,
( ! [U_6780,U_6778,U_6776] :
( hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780)))
| ( ? [U_6771] :
( ~ hBOOL(hAPP(U_6776,U_6771))
& ? [U_6770] :
( U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),U_6771)),U_6770)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6770),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),U_6770)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_6776,sK137(U_6780,U_6778,U_6776)))
& U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK137(U_6780,U_6778,U_6776))),sK138(U_6780,U_6778,U_6776))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK138(U_6780,U_6778,U_6776)),U_6780))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK138(U_6780,U_6778,U_6776)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6780)) )
| ( ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_6779,U_6777,U_6775] :
( ( ( ! [U_6767] :
( hBOOL(hAPP(U_6775,U_6767))
| ! [U_6766] :
( U_6777 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6779),U_6767)),U_6766)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6766),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6779),U_6766)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6779),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_6765] :
( hBOOL(hAPP(U_6775,U_6765))
| ! [U_6764] :
( U_6777 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6779),U_6765)),U_6764)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6764),U_6779))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6764)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6779)) )
& ( hBOOL(hAPP(U_6775,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6779 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_6775,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6777),U_6779))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK138]),skolemize(U_6768,sK138(U_6780,U_6778,U_6776))],[f_1894_4]) ).
fof(f_1894_6,plain,
( ! [U_6780,U_6778,U_6776] :
( hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780)))
| ( ~ hBOOL(hAPP(U_6776,sK139(U_6780,U_6778,U_6776)))
& ? [U_6770] :
( U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK139(U_6780,U_6778,U_6776))),U_6770)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6770),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),U_6770)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_6776,sK137(U_6780,U_6778,U_6776)))
& U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK137(U_6780,U_6778,U_6776))),sK138(U_6780,U_6778,U_6776))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK138(U_6780,U_6778,U_6776)),U_6780))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK138(U_6780,U_6778,U_6776)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6780)) )
| ( ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_6779,U_6777,U_6775] :
( ( ( ! [U_6767] :
( hBOOL(hAPP(U_6775,U_6767))
| ! [U_6766] :
( U_6777 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6779),U_6767)),U_6766)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6766),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6779),U_6766)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6779),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_6765] :
( hBOOL(hAPP(U_6775,U_6765))
| ! [U_6764] :
( U_6777 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6779),U_6765)),U_6764)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6764),U_6779))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6764)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6779)) )
& ( hBOOL(hAPP(U_6775,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6779 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_6775,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6777),U_6779))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK139]),skolemize(U_6771,sK139(U_6780,U_6778,U_6776))],[f_1894_5]) ).
fof(f_1894_7,plain,
( ! [U_6780,U_6778,U_6776] :
( hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780)))
| ( ~ hBOOL(hAPP(U_6776,sK139(U_6780,U_6778,U_6776)))
& U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK139(U_6780,U_6778,U_6776))),sK140(U_6780,U_6778,U_6776))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK140(U_6780,U_6778,U_6776)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),sK140(U_6780,U_6778,U_6776)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_6776,sK137(U_6780,U_6778,U_6776)))
& U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK137(U_6780,U_6778,U_6776))),sK138(U_6780,U_6778,U_6776))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK138(U_6780,U_6778,U_6776)),U_6780))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK138(U_6780,U_6778,U_6776)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6780)) )
| ( ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_6779,U_6777,U_6775] :
( ( ( ! [U_6767] :
( hBOOL(hAPP(U_6775,U_6767))
| ! [U_6766] :
( U_6777 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6779),U_6767)),U_6766)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6766),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6779),U_6766)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6779),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_6765] :
( hBOOL(hAPP(U_6775,U_6765))
| ! [U_6764] :
( U_6777 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6779),U_6765)),U_6764)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6764),U_6779))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6764)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6779)) )
& ( hBOOL(hAPP(U_6775,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6779 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_6775,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6777),U_6779))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK140]),skolemize(U_6770,sK140(U_6780,U_6778,U_6776))],[f_1894_6]) ).
cnf(f_1894_8,plain,
( hBOOL(hAPP(U_6775,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6779 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_6775,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6777),U_6779))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_9,plain,
( hBOOL(hAPP(U_6775,U_6765))
| U_6777 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6779),U_6765)),U_6764)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6764),U_6779))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6764))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6779))
| ~ hBOOL(hAPP(U_6775,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6777),U_6779))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_10,plain,
( hBOOL(hAPP(U_6775,U_6767))
| U_6777 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6779),U_6767)),U_6766)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6766),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6779),U_6766))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6779),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_6775,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6777),U_6779))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6780))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_12,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK138(U_6780,U_6778,U_6776)))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_13,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK138(U_6780,U_6778,U_6776)),U_6780))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_14,plain,
( U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK137(U_6780,U_6778,U_6776))),sK138(U_6780,U_6778,U_6776))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_15,plain,
( ~ hBOOL(hAPP(U_6776,sK137(U_6780,U_6778,U_6776)))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_16,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6780))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_17,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK138(U_6780,U_6778,U_6776)))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_18,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK138(U_6780,U_6778,U_6776)),U_6780))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_19,plain,
( U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK137(U_6780,U_6778,U_6776))),sK138(U_6780,U_6778,U_6776))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_20,plain,
( ~ hBOOL(hAPP(U_6776,sK137(U_6780,U_6778,U_6776)))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_21,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6780))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),sK140(U_6780,U_6778,U_6776)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_22,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK138(U_6780,U_6778,U_6776)))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),sK140(U_6780,U_6778,U_6776)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_23,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK138(U_6780,U_6778,U_6776)),U_6780))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),sK140(U_6780,U_6778,U_6776)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_24,plain,
( U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK137(U_6780,U_6778,U_6776))),sK138(U_6780,U_6778,U_6776))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),sK140(U_6780,U_6778,U_6776)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_25,plain,
( ~ hBOOL(hAPP(U_6776,sK137(U_6780,U_6778,U_6776)))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),sK140(U_6780,U_6778,U_6776)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_26,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6780))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK140(U_6780,U_6778,U_6776)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_27,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK138(U_6780,U_6778,U_6776)))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK140(U_6780,U_6778,U_6776)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_28,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK138(U_6780,U_6778,U_6776)),U_6780))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK140(U_6780,U_6778,U_6776)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_29,plain,
( U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK137(U_6780,U_6778,U_6776))),sK138(U_6780,U_6778,U_6776))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK140(U_6780,U_6778,U_6776)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_30,plain,
( ~ hBOOL(hAPP(U_6776,sK137(U_6780,U_6778,U_6776)))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK140(U_6780,U_6778,U_6776)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_31,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6780))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK139(U_6780,U_6778,U_6776))),sK140(U_6780,U_6778,U_6776))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_32,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK138(U_6780,U_6778,U_6776)))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK139(U_6780,U_6778,U_6776))),sK140(U_6780,U_6778,U_6776))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_33,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK138(U_6780,U_6778,U_6776)),U_6780))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK139(U_6780,U_6778,U_6776))),sK140(U_6780,U_6778,U_6776))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_34,plain,
( U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK137(U_6780,U_6778,U_6776))),sK138(U_6780,U_6778,U_6776))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK139(U_6780,U_6778,U_6776))),sK140(U_6780,U_6778,U_6776))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_35,plain,
( ~ hBOOL(hAPP(U_6776,sK137(U_6780,U_6778,U_6776)))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK139(U_6780,U_6778,U_6776))),sK140(U_6780,U_6778,U_6776))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_36,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6780))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_6776,sK139(U_6780,U_6778,U_6776)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_37,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK138(U_6780,U_6778,U_6776)))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_6776,sK139(U_6780,U_6778,U_6776)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_38,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK138(U_6780,U_6778,U_6776)),U_6780))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_6776,sK139(U_6780,U_6778,U_6776)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_39,plain,
( U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK137(U_6780,U_6778,U_6776))),sK138(U_6780,U_6778,U_6776))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_6776,sK139(U_6780,U_6778,U_6776)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_40,plain,
( ~ hBOOL(hAPP(U_6776,sK137(U_6780,U_6778,U_6776)))
| U_6780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_6776,sK139(U_6780,U_6778,U_6776)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_41,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6780))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),sK140(U_6780,U_6778,U_6776)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_42,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK138(U_6780,U_6778,U_6776)))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),sK140(U_6780,U_6778,U_6776)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_43,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK138(U_6780,U_6778,U_6776)),U_6780))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),sK140(U_6780,U_6778,U_6776)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_44,plain,
( U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK137(U_6780,U_6778,U_6776))),sK138(U_6780,U_6778,U_6776))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),sK140(U_6780,U_6778,U_6776)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_45,plain,
( ~ hBOOL(hAPP(U_6776,sK137(U_6780,U_6778,U_6776)))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6780),sK140(U_6780,U_6778,U_6776)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_46,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6780))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK140(U_6780,U_6778,U_6776)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_47,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK138(U_6780,U_6778,U_6776)))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK140(U_6780,U_6778,U_6776)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_48,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK138(U_6780,U_6778,U_6776)),U_6780))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK140(U_6780,U_6778,U_6776)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_49,plain,
( U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK137(U_6780,U_6778,U_6776))),sK138(U_6780,U_6778,U_6776))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK140(U_6780,U_6778,U_6776)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_50,plain,
( ~ hBOOL(hAPP(U_6776,sK137(U_6780,U_6778,U_6776)))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK140(U_6780,U_6778,U_6776)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_51,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6780))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK139(U_6780,U_6778,U_6776))),sK140(U_6780,U_6778,U_6776))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_52,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK138(U_6780,U_6778,U_6776)))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK139(U_6780,U_6778,U_6776))),sK140(U_6780,U_6778,U_6776))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_53,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK138(U_6780,U_6778,U_6776)),U_6780))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK139(U_6780,U_6778,U_6776))),sK140(U_6780,U_6778,U_6776))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_54,plain,
( U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK137(U_6780,U_6778,U_6776))),sK138(U_6780,U_6778,U_6776))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK139(U_6780,U_6778,U_6776))),sK140(U_6780,U_6778,U_6776))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_55,plain,
( ~ hBOOL(hAPP(U_6776,sK137(U_6780,U_6778,U_6776)))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK139(U_6780,U_6778,U_6776))),sK140(U_6780,U_6778,U_6776))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_56,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6780))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_6776,sK139(U_6780,U_6778,U_6776)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_57,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK138(U_6780,U_6778,U_6776)))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_6776,sK139(U_6780,U_6778,U_6776)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_58,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK138(U_6780,U_6778,U_6776)),U_6780))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_6776,sK139(U_6780,U_6778,U_6776)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_59,plain,
( U_6778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6780),sK137(U_6780,U_6778,U_6776))),sK138(U_6780,U_6778,U_6776))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_6776,sK139(U_6780,U_6778,U_6776)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
cnf(f_1894_60,plain,
( ~ hBOOL(hAPP(U_6776,sK137(U_6780,U_6778,U_6776)))
| ~ hBOOL(hAPP(U_6776,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_6776,sK139(U_6780,U_6778,U_6776)))
| hBOOL(hAPP(U_6776,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6778),U_6780))) ),
inference(clausify,[status(thm)],[f_1894_7]) ).
fof(f_1895_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_1895_2,plain,
! [U_6784,U_6783,U_6782,U_6781] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6781),U_6782) = U_6783
| U_6782 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6784),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6782),U_6784)) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6782)) )
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6784),U_6782))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6784)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6782)) )
| U_6781 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6782),U_6783)),U_6784) ),
inference(variable_rename,[status(thm)],[f_1895_1]) ).
cnf(f_1895_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6782))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6782))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6781),U_6782) = U_6783
| U_6782 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6781 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6782),U_6783)),U_6784) ),
inference(clausify,[status(thm)],[f_1895_2]) ).
cnf(f_1895_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6784),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6782),U_6784))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6782))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6781),U_6782) = U_6783
| U_6782 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6781 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6782),U_6783)),U_6784) ),
inference(clausify,[status(thm)],[f_1895_2]) ).
cnf(f_1895_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6782))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6784),U_6782))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6784))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6781),U_6782) = U_6783
| U_6782 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6781 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6782),U_6783)),U_6784) ),
inference(clausify,[status(thm)],[f_1895_2]) ).
cnf(f_1895_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6784),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6782),U_6784))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6784),U_6782))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6784))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6781),U_6782) = U_6783
| U_6782 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6781 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6782),U_6783)),U_6784) ),
inference(clausify,[status(thm)],[f_1895_2]) ).
fof(f_1896_1,plain,
! [V_k_2,V_n_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
| ( ? [B_i,B_j] :
( ~ hBOOL(hAPP(V_P_2,B_j))
& V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [B_i,B_j] :
( ~ hBOOL(hAPP(V_P_2,B_j))
& V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) )
| ( ~ hBOOL(hAPP(V_P_2,V_n_2))
& V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( ( ! [B_i,B_j] :
( hBOOL(hAPP(V_P_2,B_j))
| V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [B_i,B_j] :
( hBOOL(hAPP(V_P_2,B_j))
| V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) )
& ( hBOOL(hAPP(V_P_2,V_n_2))
| V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__zmod]) ).
fof(f_1896_2,plain,
! [U_6795,U_6794,U_6793] :
( ( hBOOL(hAPP(U_6793,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6794,U_6795)))
| ( ? [U_6792,U_6791] :
( ~ hBOOL(hAPP(U_6793,U_6791))
& U_6794 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6795),U_6792)),U_6791)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6791),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6795),U_6791)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6795),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [U_6790,U_6789] :
( ~ hBOOL(hAPP(U_6793,U_6789))
& U_6794 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6795),U_6790)),U_6789)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6789),U_6795))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6789)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6795)) )
| ( ~ hBOOL(hAPP(U_6793,U_6794))
& U_6795 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( ( ! [U_6788,U_6787] :
( hBOOL(hAPP(U_6793,U_6787))
| U_6794 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6795),U_6788)),U_6787)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6787),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6795),U_6787)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6795),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_6786,U_6785] :
( hBOOL(hAPP(U_6793,U_6785))
| U_6794 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6795),U_6786)),U_6785)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6785),U_6795))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6785)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6795)) )
& ( hBOOL(hAPP(U_6793,U_6794))
| U_6795 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_6793,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6794,U_6795))) ) ),
inference(variable_rename,[status(thm)],[f_1896_1]) ).
fof(f_1896_3,plain,
( ! [U_6801,U_6799,U_6797] :
( hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801)))
| ( ? [U_6792,U_6791] :
( ~ hBOOL(hAPP(U_6797,U_6791))
& U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),U_6792)),U_6791)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6791),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),U_6791)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [U_6790,U_6789] :
( ~ hBOOL(hAPP(U_6797,U_6789))
& U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),U_6790)),U_6789)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6789),U_6801))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6789)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6801)) )
| ( ~ hBOOL(hAPP(U_6797,U_6799))
& U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_6800,U_6798,U_6796] :
( ( ( ! [U_6788,U_6787] :
( hBOOL(hAPP(U_6796,U_6787))
| U_6798 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6800),U_6788)),U_6787)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6787),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6800),U_6787)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6800),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_6786,U_6785] :
( hBOOL(hAPP(U_6796,U_6785))
| U_6798 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6800),U_6786)),U_6785)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6785),U_6800))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6785)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6800)) )
& ( hBOOL(hAPP(U_6796,U_6798))
| U_6800 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_6796,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6798,U_6800))) ) ),
inference(miniscope,[status(thm)],[f_1896_2]) ).
fof(f_1896_4,plain,
( ! [U_6801,U_6799,U_6797] :
( hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801)))
| ( ? [U_6792,U_6791] :
( ~ hBOOL(hAPP(U_6797,U_6791))
& U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),U_6792)),U_6791)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6791),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),U_6791)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [U_6789] :
( ~ hBOOL(hAPP(U_6797,U_6789))
& U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK141(U_6801,U_6799,U_6797))),U_6789)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6789),U_6801))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6789)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6801)) )
| ( ~ hBOOL(hAPP(U_6797,U_6799))
& U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_6800,U_6798,U_6796] :
( ( ( ! [U_6788,U_6787] :
( hBOOL(hAPP(U_6796,U_6787))
| U_6798 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6800),U_6788)),U_6787)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6787),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6800),U_6787)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6800),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_6786,U_6785] :
( hBOOL(hAPP(U_6796,U_6785))
| U_6798 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6800),U_6786)),U_6785)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6785),U_6800))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6785)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6800)) )
& ( hBOOL(hAPP(U_6796,U_6798))
| U_6800 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_6796,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6798,U_6800))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK141]),skolemize(U_6790,sK141(U_6801,U_6799,U_6797))],[f_1896_3]) ).
fof(f_1896_5,plain,
( ! [U_6801,U_6799,U_6797] :
( hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801)))
| ( ? [U_6792,U_6791] :
( ~ hBOOL(hAPP(U_6797,U_6791))
& U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),U_6792)),U_6791)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6791),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),U_6791)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_6797,sK142(U_6801,U_6799,U_6797)))
& U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK141(U_6801,U_6799,U_6797))),sK142(U_6801,U_6799,U_6797))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK142(U_6801,U_6799,U_6797)),U_6801))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK142(U_6801,U_6799,U_6797)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6801)) )
| ( ~ hBOOL(hAPP(U_6797,U_6799))
& U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_6800,U_6798,U_6796] :
( ( ( ! [U_6788,U_6787] :
( hBOOL(hAPP(U_6796,U_6787))
| U_6798 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6800),U_6788)),U_6787)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6787),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6800),U_6787)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6800),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_6786,U_6785] :
( hBOOL(hAPP(U_6796,U_6785))
| U_6798 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6800),U_6786)),U_6785)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6785),U_6800))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6785)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6800)) )
& ( hBOOL(hAPP(U_6796,U_6798))
| U_6800 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_6796,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6798,U_6800))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(U_6789,sK142(U_6801,U_6799,U_6797))],[f_1896_4]) ).
fof(f_1896_6,plain,
( ! [U_6801,U_6799,U_6797] :
( hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801)))
| ( ? [U_6791] :
( ~ hBOOL(hAPP(U_6797,U_6791))
& U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK143(U_6801,U_6799,U_6797))),U_6791)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6791),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),U_6791)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_6797,sK142(U_6801,U_6799,U_6797)))
& U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK141(U_6801,U_6799,U_6797))),sK142(U_6801,U_6799,U_6797))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK142(U_6801,U_6799,U_6797)),U_6801))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK142(U_6801,U_6799,U_6797)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6801)) )
| ( ~ hBOOL(hAPP(U_6797,U_6799))
& U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_6800,U_6798,U_6796] :
( ( ( ! [U_6788,U_6787] :
( hBOOL(hAPP(U_6796,U_6787))
| U_6798 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6800),U_6788)),U_6787)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6787),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6800),U_6787)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6800),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_6786,U_6785] :
( hBOOL(hAPP(U_6796,U_6785))
| U_6798 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6800),U_6786)),U_6785)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6785),U_6800))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6785)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6800)) )
& ( hBOOL(hAPP(U_6796,U_6798))
| U_6800 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_6796,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6798,U_6800))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK143]),skolemize(U_6792,sK143(U_6801,U_6799,U_6797))],[f_1896_5]) ).
fof(f_1896_7,plain,
( ! [U_6801,U_6799,U_6797] :
( hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801)))
| ( ~ hBOOL(hAPP(U_6797,sK144(U_6801,U_6799,U_6797)))
& U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK143(U_6801,U_6799,U_6797))),sK144(U_6801,U_6799,U_6797))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK144(U_6801,U_6799,U_6797)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),sK144(U_6801,U_6799,U_6797)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_6797,sK142(U_6801,U_6799,U_6797)))
& U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK141(U_6801,U_6799,U_6797))),sK142(U_6801,U_6799,U_6797))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK142(U_6801,U_6799,U_6797)),U_6801))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK142(U_6801,U_6799,U_6797)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6801)) )
| ( ~ hBOOL(hAPP(U_6797,U_6799))
& U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_6800,U_6798,U_6796] :
( ( ( ! [U_6788,U_6787] :
( hBOOL(hAPP(U_6796,U_6787))
| U_6798 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6800),U_6788)),U_6787)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6787),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6800),U_6787)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6800),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_6786,U_6785] :
( hBOOL(hAPP(U_6796,U_6785))
| U_6798 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6800),U_6786)),U_6785)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6785),U_6800))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6785)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6800)) )
& ( hBOOL(hAPP(U_6796,U_6798))
| U_6800 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_6796,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6798,U_6800))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK144]),skolemize(U_6791,sK144(U_6801,U_6799,U_6797))],[f_1896_6]) ).
cnf(f_1896_8,plain,
( hBOOL(hAPP(U_6796,U_6798))
| U_6800 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_6796,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6798,U_6800))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_9,plain,
( hBOOL(hAPP(U_6796,U_6785))
| U_6798 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6800),U_6786)),U_6785)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6785),U_6800))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6785))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6800))
| ~ hBOOL(hAPP(U_6796,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6798,U_6800))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_10,plain,
( hBOOL(hAPP(U_6796,U_6787))
| U_6798 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6800),U_6788)),U_6787)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6787),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6800),U_6787))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6800),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_6796,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6798,U_6800))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6801))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_12,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK142(U_6801,U_6799,U_6797)))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_13,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK142(U_6801,U_6799,U_6797)),U_6801))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_14,plain,
( U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK141(U_6801,U_6799,U_6797))),sK142(U_6801,U_6799,U_6797))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_15,plain,
( ~ hBOOL(hAPP(U_6797,sK142(U_6801,U_6799,U_6797)))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_16,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6801))
| ~ hBOOL(hAPP(U_6797,U_6799))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_17,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK142(U_6801,U_6799,U_6797)))
| ~ hBOOL(hAPP(U_6797,U_6799))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_18,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK142(U_6801,U_6799,U_6797)),U_6801))
| ~ hBOOL(hAPP(U_6797,U_6799))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_19,plain,
( U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK141(U_6801,U_6799,U_6797))),sK142(U_6801,U_6799,U_6797))
| ~ hBOOL(hAPP(U_6797,U_6799))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_20,plain,
( ~ hBOOL(hAPP(U_6797,sK142(U_6801,U_6799,U_6797)))
| ~ hBOOL(hAPP(U_6797,U_6799))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_21,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6801))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),sK144(U_6801,U_6799,U_6797)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_22,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK142(U_6801,U_6799,U_6797)))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),sK144(U_6801,U_6799,U_6797)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_23,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK142(U_6801,U_6799,U_6797)),U_6801))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),sK144(U_6801,U_6799,U_6797)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_24,plain,
( U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK141(U_6801,U_6799,U_6797))),sK142(U_6801,U_6799,U_6797))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),sK144(U_6801,U_6799,U_6797)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_25,plain,
( ~ hBOOL(hAPP(U_6797,sK142(U_6801,U_6799,U_6797)))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),sK144(U_6801,U_6799,U_6797)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_26,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6801))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK144(U_6801,U_6799,U_6797)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_27,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK142(U_6801,U_6799,U_6797)))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK144(U_6801,U_6799,U_6797)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_28,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK142(U_6801,U_6799,U_6797)),U_6801))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK144(U_6801,U_6799,U_6797)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_29,plain,
( U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK141(U_6801,U_6799,U_6797))),sK142(U_6801,U_6799,U_6797))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK144(U_6801,U_6799,U_6797)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_30,plain,
( ~ hBOOL(hAPP(U_6797,sK142(U_6801,U_6799,U_6797)))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK144(U_6801,U_6799,U_6797)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_31,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6801))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK143(U_6801,U_6799,U_6797))),sK144(U_6801,U_6799,U_6797))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_32,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK142(U_6801,U_6799,U_6797)))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK143(U_6801,U_6799,U_6797))),sK144(U_6801,U_6799,U_6797))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_33,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK142(U_6801,U_6799,U_6797)),U_6801))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK143(U_6801,U_6799,U_6797))),sK144(U_6801,U_6799,U_6797))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_34,plain,
( U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK141(U_6801,U_6799,U_6797))),sK142(U_6801,U_6799,U_6797))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK143(U_6801,U_6799,U_6797))),sK144(U_6801,U_6799,U_6797))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_35,plain,
( ~ hBOOL(hAPP(U_6797,sK142(U_6801,U_6799,U_6797)))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK143(U_6801,U_6799,U_6797))),sK144(U_6801,U_6799,U_6797))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_36,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6801))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_6797,sK144(U_6801,U_6799,U_6797)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_37,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK142(U_6801,U_6799,U_6797)))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_6797,sK144(U_6801,U_6799,U_6797)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_38,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK142(U_6801,U_6799,U_6797)),U_6801))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_6797,sK144(U_6801,U_6799,U_6797)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_39,plain,
( U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK141(U_6801,U_6799,U_6797))),sK142(U_6801,U_6799,U_6797))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_6797,sK144(U_6801,U_6799,U_6797)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_40,plain,
( ~ hBOOL(hAPP(U_6797,sK142(U_6801,U_6799,U_6797)))
| U_6801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_6797,sK144(U_6801,U_6799,U_6797)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_41,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6801))
| ~ hBOOL(hAPP(U_6797,U_6799))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),sK144(U_6801,U_6799,U_6797)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_42,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK142(U_6801,U_6799,U_6797)))
| ~ hBOOL(hAPP(U_6797,U_6799))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),sK144(U_6801,U_6799,U_6797)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_43,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK142(U_6801,U_6799,U_6797)),U_6801))
| ~ hBOOL(hAPP(U_6797,U_6799))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),sK144(U_6801,U_6799,U_6797)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_44,plain,
( U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK141(U_6801,U_6799,U_6797))),sK142(U_6801,U_6799,U_6797))
| ~ hBOOL(hAPP(U_6797,U_6799))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),sK144(U_6801,U_6799,U_6797)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_45,plain,
( ~ hBOOL(hAPP(U_6797,sK142(U_6801,U_6799,U_6797)))
| ~ hBOOL(hAPP(U_6797,U_6799))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6801),sK144(U_6801,U_6799,U_6797)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_46,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6801))
| ~ hBOOL(hAPP(U_6797,U_6799))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK144(U_6801,U_6799,U_6797)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_47,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK142(U_6801,U_6799,U_6797)))
| ~ hBOOL(hAPP(U_6797,U_6799))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK144(U_6801,U_6799,U_6797)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_48,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK142(U_6801,U_6799,U_6797)),U_6801))
| ~ hBOOL(hAPP(U_6797,U_6799))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK144(U_6801,U_6799,U_6797)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_49,plain,
( U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK141(U_6801,U_6799,U_6797))),sK142(U_6801,U_6799,U_6797))
| ~ hBOOL(hAPP(U_6797,U_6799))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK144(U_6801,U_6799,U_6797)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_50,plain,
( ~ hBOOL(hAPP(U_6797,sK142(U_6801,U_6799,U_6797)))
| ~ hBOOL(hAPP(U_6797,U_6799))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK144(U_6801,U_6799,U_6797)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_51,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6801))
| ~ hBOOL(hAPP(U_6797,U_6799))
| U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK143(U_6801,U_6799,U_6797))),sK144(U_6801,U_6799,U_6797))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_52,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK142(U_6801,U_6799,U_6797)))
| ~ hBOOL(hAPP(U_6797,U_6799))
| U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK143(U_6801,U_6799,U_6797))),sK144(U_6801,U_6799,U_6797))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_53,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK142(U_6801,U_6799,U_6797)),U_6801))
| ~ hBOOL(hAPP(U_6797,U_6799))
| U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK143(U_6801,U_6799,U_6797))),sK144(U_6801,U_6799,U_6797))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_54,plain,
( U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK141(U_6801,U_6799,U_6797))),sK142(U_6801,U_6799,U_6797))
| ~ hBOOL(hAPP(U_6797,U_6799))
| U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK143(U_6801,U_6799,U_6797))),sK144(U_6801,U_6799,U_6797))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_55,plain,
( ~ hBOOL(hAPP(U_6797,sK142(U_6801,U_6799,U_6797)))
| ~ hBOOL(hAPP(U_6797,U_6799))
| U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK143(U_6801,U_6799,U_6797))),sK144(U_6801,U_6799,U_6797))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_56,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6801))
| ~ hBOOL(hAPP(U_6797,U_6799))
| ~ hBOOL(hAPP(U_6797,sK144(U_6801,U_6799,U_6797)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_57,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK142(U_6801,U_6799,U_6797)))
| ~ hBOOL(hAPP(U_6797,U_6799))
| ~ hBOOL(hAPP(U_6797,sK144(U_6801,U_6799,U_6797)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_58,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK142(U_6801,U_6799,U_6797)),U_6801))
| ~ hBOOL(hAPP(U_6797,U_6799))
| ~ hBOOL(hAPP(U_6797,sK144(U_6801,U_6799,U_6797)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_59,plain,
( U_6799 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6801),sK141(U_6801,U_6799,U_6797))),sK142(U_6801,U_6799,U_6797))
| ~ hBOOL(hAPP(U_6797,U_6799))
| ~ hBOOL(hAPP(U_6797,sK144(U_6801,U_6799,U_6797)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
cnf(f_1896_60,plain,
( ~ hBOOL(hAPP(U_6797,sK142(U_6801,U_6799,U_6797)))
| ~ hBOOL(hAPP(U_6797,U_6799))
| ~ hBOOL(hAPP(U_6797,sK144(U_6801,U_6799,U_6797)))
| hBOOL(hAPP(U_6797,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6799,U_6801))) ),
inference(clausify,[status(thm)],[f_1896_7]) ).
fof(f_1897_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_1897_2,plain,
! [U_6805,U_6804,U_6803,U_6802] :
( 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_6804),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6805,U_6802))),U_6803)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6803),U_6804))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6803))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6802)) ),
inference(variable_rename,[status(thm)],[f_1897_1]) ).
cnf(f_1897_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_6804),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6805,U_6802))),U_6803)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6803),U_6804))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6803))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6802)) ),
inference(clausify,[status(thm)],[f_1897_2]) ).
fof(f_1898_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_1898_2,plain,
! [U_6809,U_6808,U_6807,U_6806] :
( 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_6808),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6809,U_6806))),U_6807)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6808),U_6806)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6807),U_6808))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6807))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6806)) ),
inference(variable_rename,[status(thm)],[f_1898_1]) ).
cnf(f_1898_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_6808),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6809,U_6806))),U_6807)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6808),U_6806)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6807),U_6808))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6807))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6806)) ),
inference(clausify,[status(thm)],[f_1898_2]) ).
fof(f_1899_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_1899_2,plain,
! [U_6813,U_6812,U_6811,U_6810] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6811),U_6810)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6811),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6813,U_6810))),U_6812)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6812),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6811),U_6812))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6810)) ),
inference(variable_rename,[status(thm)],[f_1899_1]) ).
cnf(f_1899_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6811),U_6810)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6811),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6813,U_6810))),U_6812)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6812),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6811),U_6812))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6810)) ),
inference(clausify,[status(thm)],[f_1899_2]) ).
fof(f_1900_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_1900_2,plain,
! [U_6817,U_6816,U_6815,U_6814] :
( 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_6815),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6817,U_6814))),U_6816)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6816),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6815),U_6816))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6814)) ),
inference(variable_rename,[status(thm)],[f_1900_1]) ).
cnf(f_1900_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6815),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6817,U_6814))),U_6816)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6816),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6815),U_6816))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6814)) ),
inference(clausify,[status(thm)],[f_1900_2]) ).
fof(f_1901_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_1901_2,plain,
! [U_6821,U_6820,U_6819,U_6818] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6818,U_6819) = U_6821
| U_6819 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6821),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6819),U_6821)) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6819)) )
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6821),U_6819))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6821)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6819)) )
| U_6818 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6819),U_6820)),U_6821) ),
inference(variable_rename,[status(thm)],[f_1901_1]) ).
cnf(f_1901_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6819))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6819))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6818,U_6819) = U_6821
| U_6819 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6818 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6819),U_6820)),U_6821) ),
inference(clausify,[status(thm)],[f_1901_2]) ).
cnf(f_1901_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6821),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6819),U_6821))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6819))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6818,U_6819) = U_6821
| U_6819 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6818 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6819),U_6820)),U_6821) ),
inference(clausify,[status(thm)],[f_1901_2]) ).
cnf(f_1901_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6819))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6821),U_6819))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6821))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6818,U_6819) = U_6821
| U_6819 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6818 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6819),U_6820)),U_6821) ),
inference(clausify,[status(thm)],[f_1901_2]) ).
cnf(f_1901_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6821),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6819),U_6821))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6821),U_6819))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6821))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6818,U_6819) = U_6821
| U_6819 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6818 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6819),U_6820)),U_6821) ),
inference(clausify,[status(thm)],[f_1901_2]) ).
fof(f_1902_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_1902_2,plain,
! [U_6823,U_6822] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6822)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6823))) = hAPP(hAPP(c_Groups_Otimes__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_6822),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6823))),
inference(variable_rename,[status(thm)],[f_1902_1]) ).
cnf(f_1902_3,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6822)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6823))) = hAPP(hAPP(c_Groups_Otimes__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_6822),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6823))),
inference(clausify,[status(thm)],[f_1902_2]) ).
fof(f_1903_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_1903_2,plain,
! [U_6825,U_6824] :
( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_6825))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6824))) = 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_6825)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6824))
| 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_6824))) )
& ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_6825))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6824))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6825)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6824))
| ~ 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_6824))) ) ),
inference(variable_rename,[status(thm)],[f_1903_1]) ).
fof(f_1903_3,plain,
( ! [U_6829,U_6827] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_6829))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6827))) = 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_6829)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6827))
| 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_6827))) )
& ! [U_6828,U_6826] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_6828))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6826))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6828)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6826))
| ~ 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_6826))) ) ),
inference(miniscope,[status(thm)],[f_1903_2]) ).
cnf(f_1903_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_6828))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6826))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6828)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6826))
| ~ 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_6826))) ),
inference(clausify,[status(thm)],[f_1903_3]) ).
cnf(f_1903_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_6829))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_6827))) = 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_6829)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6827))
| 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_6827))) ),
inference(clausify,[status(thm)],[f_1903_3]) ).
fof(f_1904_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_1904_2,plain,
! [U_6831,U_6830] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6831),U_6830)),U_6831) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6831),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6830),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_6831))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6830)) ),
inference(variable_rename,[status(thm)],[f_1904_1]) ).
cnf(f_1904_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6831),U_6830)),U_6831) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6831),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6830),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_6831))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6830)) ),
inference(clausify,[status(thm)],[f_1904_2]) ).
fof(f_1905_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_1905_2,plain,
! [U_6833,U_6832] :
( 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_6833))),hAPP(hAPP(c_Groups_Otimes__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_6832)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6833),U_6832)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6832)) ),
inference(variable_rename,[status(thm)],[f_1905_1]) ).
cnf(f_1905_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_6833))),hAPP(hAPP(c_Groups_Otimes__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_6832)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6833),U_6832)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6832)) ),
inference(clausify,[status(thm)],[f_1905_2]) ).
fof(f_1906_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_1906_2,plain,
! [U_6835,U_6834] :
( ( c_SMT_Oz3div(U_6835,U_6834) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6835),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6834)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6834)) )
& ( c_SMT_Oz3div(U_6835,U_6834) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6835),U_6834)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6834)) ) ),
inference(variable_rename,[status(thm)],[f_1906_1]) ).
fof(f_1906_3,plain,
( ! [U_6839,U_6837] :
( c_SMT_Oz3div(U_6839,U_6837) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6839),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6837)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6837)) )
& ! [U_6838,U_6836] :
( c_SMT_Oz3div(U_6838,U_6836) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6838),U_6836)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6836)) ) ),
inference(miniscope,[status(thm)],[f_1906_2]) ).
cnf(f_1906_4,plain,
( c_SMT_Oz3div(U_6838,U_6836) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6838),U_6836)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6836)) ),
inference(clausify,[status(thm)],[f_1906_3]) ).
cnf(f_1906_5,plain,
( c_SMT_Oz3div(U_6839,U_6837) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6839),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6837)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6837)) ),
inference(clausify,[status(thm)],[f_1906_3]) ).
fof(f_1907_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_1907_2,plain,
! [U_6841,U_6840] :
( ( c_SMT_Oz3mod(U_6841,U_6840) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6841,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6840))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6840)) )
& ( c_SMT_Oz3mod(U_6841,U_6840) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6841,U_6840)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6840)) ) ),
inference(variable_rename,[status(thm)],[f_1907_1]) ).
fof(f_1907_3,plain,
( ! [U_6845,U_6843] :
( c_SMT_Oz3mod(U_6845,U_6843) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6845,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6843))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6843)) )
& ! [U_6844,U_6842] :
( c_SMT_Oz3mod(U_6844,U_6842) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6844,U_6842)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6842)) ) ),
inference(miniscope,[status(thm)],[f_1907_2]) ).
cnf(f_1907_4,plain,
( c_SMT_Oz3mod(U_6844,U_6842) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6844,U_6842)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6842)) ),
inference(clausify,[status(thm)],[f_1907_3]) ).
cnf(f_1907_5,plain,
( c_SMT_Oz3mod(U_6845,U_6843) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6845,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6843))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6843)) ),
inference(clausify,[status(thm)],[f_1907_3]) ).
fof(f_1908_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_1908_2,plain,
! [U_6847,U_6846] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6846),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_6847))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6846),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6846),hAPP(c_Int_Onat,U_6847))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6846),hAPP(c_Int_Onat,U_6847)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6847))
| ~ class_Rings_Osemiring__1(U_6846) ),
inference(variable_rename,[status(thm)],[f_1908_1]) ).
cnf(f_1908_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6846),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_6847))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6846),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6846),hAPP(c_Int_Onat,U_6847))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6846),hAPP(c_Int_Onat,U_6847)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6847))
| ~ class_Rings_Osemiring__1(U_6846) ),
inference(clausify,[status(thm)],[f_1908_2]) ).
fof(f_1909_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_1909_2,plain,
! [U_6848] :
( c_Power_Opower__class_Opower(U_6848) = c_Power_Opower_Opower(U_6848,c_Groups_Oone__class_Oone(U_6848),c_Groups_Otimes__class_Otimes(U_6848))
| ~ class_Power_Opower(U_6848) ),
inference(variable_rename,[status(thm)],[f_1909_1]) ).
cnf(f_1909_3,plain,
( c_Power_Opower__class_Opower(U_6848) = c_Power_Opower_Opower(U_6848,c_Groups_Oone__class_Oone(U_6848),c_Groups_Otimes__class_Otimes(U_6848))
| ~ class_Power_Opower(U_6848) ),
inference(clausify,[status(thm)],[f_1909_2]) ).
fof(f_1910_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_1910_2,plain,
! [U_6850,U_6849] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6849),hAPP(c_Int_Onumber__class_Onumber__of(U_6849),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_6850))) = hAPP(c_Int_Onumber__class_Onumber__of(U_6849),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_6849) ),
inference(variable_rename,[status(thm)],[f_1910_1]) ).
cnf(f_1910_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6849),hAPP(c_Int_Onumber__class_Onumber__of(U_6849),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_6850))) = hAPP(c_Int_Onumber__class_Onumber__of(U_6849),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_6849) ),
inference(clausify,[status(thm)],[f_1910_2]) ).
fof(f_1911_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_1911_2,plain,
! [U_6853,U_6852,U_6851] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6851),U_6852)),U_6853) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6851),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6852),U_6853))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6851),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6852,U_6853))),U_6853)),
inference(variable_rename,[status(thm)],[f_1911_1]) ).
cnf(f_1911_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6851),U_6852)),U_6853) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6851),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6852),U_6853))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6851),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6852,U_6853))),U_6853)),
inference(clausify,[status(thm)],[f_1911_2]) ).
fof(f_1912_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_1912_2,plain,
! [U_6856,U_6855,U_6854] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6854,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6855),U_6856)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6855),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6854),U_6855),U_6856))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6854,U_6855)),
inference(variable_rename,[status(thm)],[f_1912_1]) ).
cnf(f_1912_3,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6854,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6855),U_6856)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6855),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6854),U_6855),U_6856))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6854,U_6855)),
inference(clausify,[status(thm)],[f_1912_2]) ).
fof(f_1913_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_1913_2,plain,
! [U_6858,U_6857] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6857,U_6858) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6857),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6857),U_6858)),U_6858)),
inference(variable_rename,[status(thm)],[f_1913_1]) ).
cnf(f_1913_3,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6857,U_6858) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6857),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6857),U_6858)),U_6858)),
inference(clausify,[status(thm)],[f_1913_2]) ).
fof(f_1914_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_1914_2,plain,
! [U_6860,U_6859] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6859),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6860),U_6859)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6860),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6860,U_6859)),
inference(variable_rename,[status(thm)],[f_1914_1]) ).
cnf(f_1914_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6859),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6860),U_6859)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6860),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6860,U_6859)),
inference(clausify,[status(thm)],[f_1914_2]) ).
fof(f_1915_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_1915_2,plain,
! [U_6862,U_6861] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6861),U_6862)),U_6862) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6861),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6861,U_6862)),
inference(variable_rename,[status(thm)],[f_1915_1]) ).
cnf(f_1915_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6861),U_6862)),U_6862) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6861),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6861,U_6862)),
inference(clausify,[status(thm)],[f_1915_2]) ).
fof(f_1916_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_1916_2,plain,
! [U_6865,U_6864,U_6863] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6863),U_6864)),U_6865) = 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_6863),U_6865)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6864),U_6865))),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_6863,U_6865)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6864,U_6865))),U_6865)),
inference(variable_rename,[status(thm)],[f_1916_1]) ).
cnf(f_1916_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6863),U_6864)),U_6865) = 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_6863),U_6865)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6864),U_6865))),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_6863,U_6865)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6864,U_6865))),U_6865)),
inference(clausify,[status(thm)],[f_1916_2]) ).
fof(f_1917_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_1917_2,plain,
! [U_6868,U_6867,U_6866] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6866),U_6868)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6867),U_6868)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6866),U_6867)) ),
inference(variable_rename,[status(thm)],[f_1917_1]) ).
cnf(f_1917_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_6866),U_6868)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6867),U_6868)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6866),U_6867)) ),
inference(clausify,[status(thm)],[f_1917_2]) ).
fof(f_1918_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_1918_2,plain,
! [U_6870,U_6869] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6869),U_6870)),U_6869)),
inference(variable_rename,[status(thm)],[f_1918_1]) ).
cnf(f_1918_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_6869),U_6870)),U_6869)),
inference(clausify,[status(thm)],[f_1918_2]) ).
fof(f_1919_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_1919_2,plain,
! [U_6872,U_6871] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6871),U_6872) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6871,U_6872)),U_6872),
inference(variable_rename,[status(thm)],[f_1919_1]) ).
cnf(f_1919_3,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6871),U_6872) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6871,U_6872)),U_6872),
inference(clausify,[status(thm)],[f_1919_2]) ).
fof(f_1920_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_1920_2,plain,
! [U_6875,U_6874,U_6873] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6874),U_6875)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6873),U_6874)),U_6875),
inference(variable_rename,[status(thm)],[f_1920_1]) ).
cnf(f_1920_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6874),U_6875)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6873),U_6874)),U_6875),
inference(clausify,[status(thm)],[f_1920_2]) ).
fof(f_1921_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_1921_2,plain,
! [U_6877,U_6876] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6876,U_6877) = U_6876
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6876),U_6877)) ),
inference(variable_rename,[status(thm)],[f_1921_1]) ).
cnf(f_1921_3,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6876,U_6877) = U_6876
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6876),U_6877)) ),
inference(clausify,[status(thm)],[f_1921_2]) ).
fof(f_1922_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_1922_2,plain,
! [U_6879,U_6878] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6878,U_6879)),U_6878)),
inference(variable_rename,[status(thm)],[f_1922_1]) ).
cnf(f_1922_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6878,U_6879)),U_6878)),
inference(clausify,[status(thm)],[f_1922_2]) ).
fof(f_1923_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_1923_2,plain,
! [U_6882,U_6881,U_6880] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6880),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6881,U_6882)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6880),U_6881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6880),U_6882)),
inference(variable_rename,[status(thm)],[f_1923_1]) ).
cnf(f_1923_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6880),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6881,U_6882)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6880),U_6881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6880),U_6882)),
inference(clausify,[status(thm)],[f_1923_2]) ).
fof(f_1924_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_1924_2,plain,
! [U_6885,U_6884,U_6883] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6883,U_6884)),U_6885) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6883),U_6885),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6884),U_6885)),
inference(variable_rename,[status(thm)],[f_1924_1]) ).
cnf(f_1924_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6883,U_6884)),U_6885) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6883),U_6885),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6884),U_6885)),
inference(clausify,[status(thm)],[f_1924_2]) ).
fof(f_1925_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_1925_2,plain,
! [U_6886] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6886)) = U_6886,
inference(variable_rename,[status(thm)],[f_1925_1]) ).
cnf(f_1925_3,plain,
hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6886)) = U_6886,
inference(clausify,[status(thm)],[f_1925_2]) ).
fof(f_1926_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_1926_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_1926_1]) ).
fof(f_1927_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_1927_2,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
inference(clausify,[status(thm)],[f_1927_1]) ).
fof(f_1928_1,plain,
c_Int_OMin != c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_rel__simps_I40_J]) ).
cnf(f_1928_2,plain,
c_Int_OMin != c_Int_OPls,
inference(clausify,[status(thm)],[f_1928_1]) ).
fof(f_1929_1,plain,
c_Int_OPls != c_Int_OMin,
inference(fof_nnf,[status(thm)],[fact_rel__simps_I37_J]) ).
cnf(f_1929_2,plain,
c_Int_OPls != c_Int_OMin,
inference(clausify,[status(thm)],[f_1929_1]) ).
fof(f_1930_1,plain,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
inference(fof_nnf,[status(thm)],[fact_Bit1__Min]) ).
cnf(f_1930_2,plain,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
inference(clausify,[status(thm)],[f_1930_1]) ).
fof(f_1931_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_1931_2,plain,
! [U_6887] :
( ( c_Int_OMin = c_Int_OBit1(U_6887)
| c_Int_OMin != U_6887 )
& ( c_Int_OMin = U_6887
| c_Int_OMin != c_Int_OBit1(U_6887) ) ),
inference(variable_rename,[status(thm)],[f_1931_1]) ).
fof(f_1931_3,plain,
( ! [U_6889] :
( c_Int_OMin = c_Int_OBit1(U_6889)
| c_Int_OMin != U_6889 )
& ! [U_6888] :
( c_Int_OMin = U_6888
| c_Int_OMin != c_Int_OBit1(U_6888) ) ),
inference(miniscope,[status(thm)],[f_1931_2]) ).
cnf(f_1931_4,plain,
( c_Int_OMin = U_6888
| c_Int_OMin != c_Int_OBit1(U_6888) ),
inference(clausify,[status(thm)],[f_1931_3]) ).
cnf(f_1931_5,plain,
( c_Int_OMin = c_Int_OBit1(U_6889)
| c_Int_OMin != U_6889 ),
inference(clausify,[status(thm)],[f_1931_3]) ).
fof(f_1932_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_1932_2,plain,
! [U_6890] :
( ( c_Int_OBit1(U_6890) = c_Int_OMin
| U_6890 != c_Int_OMin )
& ( U_6890 = c_Int_OMin
| c_Int_OBit1(U_6890) != c_Int_OMin ) ),
inference(variable_rename,[status(thm)],[f_1932_1]) ).
fof(f_1932_3,plain,
( ! [U_6892] :
( c_Int_OBit1(U_6892) = c_Int_OMin
| U_6892 != c_Int_OMin )
& ! [U_6891] :
( U_6891 = c_Int_OMin
| c_Int_OBit1(U_6891) != c_Int_OMin ) ),
inference(miniscope,[status(thm)],[f_1932_2]) ).
cnf(f_1932_4,plain,
( U_6891 = c_Int_OMin
| c_Int_OBit1(U_6891) != c_Int_OMin ),
inference(clausify,[status(thm)],[f_1932_3]) ).
cnf(f_1932_5,plain,
( c_Int_OBit1(U_6892) = c_Int_OMin
| U_6892 != c_Int_OMin ),
inference(clausify,[status(thm)],[f_1932_3]) ).
fof(f_1933_1,plain,
! [V_l] : c_Int_OMin != c_Int_OBit0(V_l),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I42_J]) ).
fof(f_1933_2,plain,
! [U_6893] : c_Int_OMin != c_Int_OBit0(U_6893),
inference(variable_rename,[status(thm)],[f_1933_1]) ).
cnf(f_1933_3,plain,
c_Int_OMin != c_Int_OBit0(U_6893),
inference(clausify,[status(thm)],[f_1933_2]) ).
fof(f_1934_1,plain,
! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin,
inference(fof_nnf,[status(thm)],[fact_rel__simps_I45_J]) ).
fof(f_1934_2,plain,
! [U_6894] : c_Int_OBit0(U_6894) != c_Int_OMin,
inference(variable_rename,[status(thm)],[f_1934_1]) ).
cnf(f_1934_3,plain,
c_Int_OBit0(U_6894) != c_Int_OMin,
inference(clausify,[status(thm)],[f_1934_2]) ).
fof(f_1935_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_1935_2,plain,
! [U_6896,U_6895] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6895),U_6896)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_6895)),hAPP(c_Int_Onat,U_6896))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6895)) ),
inference(variable_rename,[status(thm)],[f_1935_1]) ).
cnf(f_1935_3,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6895),U_6896)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_6895)),hAPP(c_Int_Onat,U_6896))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6895)) ),
inference(clausify,[status(thm)],[f_1935_2]) ).
fof(f_1936_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_1936_2,plain,
! [U_6898,U_6897] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_6897)),hAPP(c_Int_Onat,U_6898)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6897),U_6898))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6898))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6897)) ),
inference(variable_rename,[status(thm)],[f_1936_1]) ).
cnf(f_1936_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_6897)),hAPP(c_Int_Onat,U_6898)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6897),U_6898))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6898))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6897)) ),
inference(clausify,[status(thm)],[f_1936_2]) ).
fof(f_1937_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_1937_2,plain,
! [U_6900,U_6899] :
( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6899,U_6900)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_6899),hAPP(c_Int_Onat,U_6900))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6900))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6899)) ),
inference(variable_rename,[status(thm)],[f_1937_1]) ).
cnf(f_1937_3,plain,
( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6899,U_6900)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_6899),hAPP(c_Int_Onat,U_6900))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6900))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6899)) ),
inference(clausify,[status(thm)],[f_1937_2]) ).
fof(f_1938_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_1938_2,plain,
! [U_6902,U_6901] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_6901),hAPP(c_Int_Onat,U_6902)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6901,U_6902))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6902))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6901)) ),
inference(variable_rename,[status(thm)],[f_1938_1]) ).
cnf(f_1938_3,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_6901),hAPP(c_Int_Onat,U_6902)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6901,U_6902))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6902))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6901)) ),
inference(clausify,[status(thm)],[f_1938_2]) ).
fof(f_1939_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_1939_2,plain,
! [U_6903] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6903),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_6903,
inference(variable_rename,[status(thm)],[f_1939_1]) ).
cnf(f_1939_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6903),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_6903,
inference(clausify,[status(thm)],[f_1939_2]) ).
fof(f_1940_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_1940_2,plain,
! [U_6905,U_6904] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6904),U_6905) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6904),U_6905)) ),
inference(variable_rename,[status(thm)],[f_1940_1]) ).
cnf(f_1940_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6904),U_6905) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6904),U_6905)) ),
inference(clausify,[status(thm)],[f_1940_2]) ).
fof(f_1941_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_1941_2,plain,
! [U_6908,U_6907,U_6906] :
( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6906),U_6907)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6906),U_6908)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6907),U_6908)
| U_6906 = 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_6906),U_6907)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6906),U_6908)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6906 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1941_1]) ).
fof(f_1941_3,plain,
( ! [U_6914,U_6912,U_6910] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6910),U_6912)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6910),U_6914)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6912),U_6914)
| U_6910 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6913,U_6911,U_6909] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6909),U_6911)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6909),U_6913)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6909 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1941_2]) ).
cnf(f_1941_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6909),U_6911)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6909),U_6913)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6909 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1941_3]) ).
cnf(f_1941_5,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6910),U_6912)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6910),U_6914)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6912),U_6914)
| U_6910 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1941_3]) ).
fof(f_1942_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_1942_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_1942_1]) ).
fof(f_1943_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_1943_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_1943_1]) ).
fof(f_1944_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_1944_2,plain,
! [U_6915] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6915,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_1944_1]) ).
cnf(f_1944_3,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6915,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_1944_2]) ).
fof(f_1945_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_1945_2,plain,
! [U_6917,U_6916] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6916),U_6917) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6916,U_6917))
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6916,U_6917)) = U_6917 )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6916),U_6917) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6916,U_6917)) != U_6917 ) ),
inference(variable_rename,[status(thm)],[f_1945_1]) ).
fof(f_1945_3,plain,
( ! [U_6921,U_6919] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6919),U_6921) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6919,U_6921))
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6919,U_6921)) = U_6921 )
& ! [U_6920,U_6918] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6918),U_6920) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6918,U_6920)) != U_6920 ) ),
inference(miniscope,[status(thm)],[f_1945_2]) ).
cnf(f_1945_4,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6918),U_6920) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6918,U_6920)) != U_6920 ),
inference(clausify,[status(thm)],[f_1945_3]) ).
cnf(f_1945_5,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6919),U_6921) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6919,U_6921))
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6919,U_6921)) = U_6921 ),
inference(clausify,[status(thm)],[f_1945_3]) ).
fof(f_1946_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_1946_2,plain,
! [U_6923,U_6922] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6923,U_6922)),U_6922))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6922)) ),
inference(variable_rename,[status(thm)],[f_1946_1]) ).
cnf(f_1946_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6923,U_6922)),U_6922))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6922)) ),
inference(clausify,[status(thm)],[f_1946_2]) ).
fof(f_1947_1,plain,
! [V_P_2] :
( ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
| ! [B_x] :
( ~ hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
| ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ) ),
inference(fof_nnf,[status(thm)],[fact_ex__nat]) ).
fof(f_1947_2,plain,
! [U_6928] :
( ( ? [U_6927] : hBOOL(hAPP(U_6928,U_6927))
| ! [U_6926] :
( ~ hBOOL(hAPP(U_6928,hAPP(c_Int_Onat,U_6926)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6926)) ) )
& ( ? [U_6925] :
( hBOOL(hAPP(U_6928,hAPP(c_Int_Onat,U_6925)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6925)) )
| ! [U_6924] : ~ hBOOL(hAPP(U_6928,U_6924)) ) ),
inference(variable_rename,[status(thm)],[f_1947_1]) ).
fof(f_1947_3,plain,
( ! [U_6930] :
( ? [U_6927] : hBOOL(hAPP(U_6930,U_6927))
| ! [U_6926] :
( ~ hBOOL(hAPP(U_6930,hAPP(c_Int_Onat,U_6926)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6926)) ) )
& ! [U_6929] :
( ? [U_6925] :
( hBOOL(hAPP(U_6929,hAPP(c_Int_Onat,U_6925)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6925)) )
| ! [U_6924] : ~ hBOOL(hAPP(U_6929,U_6924)) ) ),
inference(miniscope,[status(thm)],[f_1947_2]) ).
fof(f_1947_4,plain,
( ! [U_6930] :
( ? [U_6927] : hBOOL(hAPP(U_6930,U_6927))
| ! [U_6926] :
( ~ hBOOL(hAPP(U_6930,hAPP(c_Int_Onat,U_6926)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6926)) ) )
& ! [U_6929] :
( ( hBOOL(hAPP(U_6929,hAPP(c_Int_Onat,sK145(U_6929))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK145(U_6929))) )
| ! [U_6924] : ~ hBOOL(hAPP(U_6929,U_6924)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK145]),skolemize(U_6925,sK145(U_6929))],[f_1947_3]) ).
fof(f_1947_5,plain,
( ! [U_6930] :
( hBOOL(hAPP(U_6930,sK146(U_6930)))
| ! [U_6926] :
( ~ hBOOL(hAPP(U_6930,hAPP(c_Int_Onat,U_6926)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6926)) ) )
& ! [U_6929] :
( ( hBOOL(hAPP(U_6929,hAPP(c_Int_Onat,sK145(U_6929))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK145(U_6929))) )
| ! [U_6924] : ~ hBOOL(hAPP(U_6929,U_6924)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK146]),skolemize(U_6927,sK146(U_6930))],[f_1947_4]) ).
cnf(f_1947_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK145(U_6929)))
| ~ hBOOL(hAPP(U_6929,U_6924)) ),
inference(clausify,[status(thm)],[f_1947_5]) ).
cnf(f_1947_7,plain,
( hBOOL(hAPP(U_6929,hAPP(c_Int_Onat,sK145(U_6929))))
| ~ hBOOL(hAPP(U_6929,U_6924)) ),
inference(clausify,[status(thm)],[f_1947_5]) ).
cnf(f_1947_8,plain,
( hBOOL(hAPP(U_6930,sK146(U_6930)))
| ~ hBOOL(hAPP(U_6930,hAPP(c_Int_Onat,U_6926)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6926)) ),
inference(clausify,[status(thm)],[f_1947_5]) ).
fof(f_1948_1,plain,
! [V_P_2] :
( ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
| ? [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ) ),
inference(fof_nnf,[status(thm)],[fact_all__nat]) ).
fof(f_1948_2,plain,
! [U_6935] :
( ( ! [U_6934] : hBOOL(hAPP(U_6935,U_6934))
| ? [U_6933] :
( ~ hBOOL(hAPP(U_6935,hAPP(c_Int_Onat,U_6933)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6933)) ) )
& ( ! [U_6932] :
( hBOOL(hAPP(U_6935,hAPP(c_Int_Onat,U_6932)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6932)) )
| ? [U_6931] : ~ hBOOL(hAPP(U_6935,U_6931)) ) ),
inference(variable_rename,[status(thm)],[f_1948_1]) ).
fof(f_1948_3,plain,
( ! [U_6937] :
( ! [U_6934] : hBOOL(hAPP(U_6937,U_6934))
| ? [U_6933] :
( ~ hBOOL(hAPP(U_6937,hAPP(c_Int_Onat,U_6933)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6933)) ) )
& ! [U_6936] :
( ! [U_6932] :
( hBOOL(hAPP(U_6936,hAPP(c_Int_Onat,U_6932)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6932)) )
| ? [U_6931] : ~ hBOOL(hAPP(U_6936,U_6931)) ) ),
inference(miniscope,[status(thm)],[f_1948_2]) ).
fof(f_1948_4,plain,
( ! [U_6937] :
( ! [U_6934] : hBOOL(hAPP(U_6937,U_6934))
| ? [U_6933] :
( ~ hBOOL(hAPP(U_6937,hAPP(c_Int_Onat,U_6933)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6933)) ) )
& ! [U_6936] :
( ! [U_6932] :
( hBOOL(hAPP(U_6936,hAPP(c_Int_Onat,U_6932)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6932)) )
| ~ hBOOL(hAPP(U_6936,sK147(U_6936))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK147]),skolemize(U_6931,sK147(U_6936))],[f_1948_3]) ).
fof(f_1948_5,plain,
( ! [U_6937] :
( ! [U_6934] : hBOOL(hAPP(U_6937,U_6934))
| ( ~ hBOOL(hAPP(U_6937,hAPP(c_Int_Onat,sK148(U_6937))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK148(U_6937))) ) )
& ! [U_6936] :
( ! [U_6932] :
( hBOOL(hAPP(U_6936,hAPP(c_Int_Onat,U_6932)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6932)) )
| ~ hBOOL(hAPP(U_6936,sK147(U_6936))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(U_6933,sK148(U_6937))],[f_1948_4]) ).
cnf(f_1948_6,plain,
( hBOOL(hAPP(U_6936,hAPP(c_Int_Onat,U_6932)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6932))
| ~ hBOOL(hAPP(U_6936,sK147(U_6936))) ),
inference(clausify,[status(thm)],[f_1948_5]) ).
cnf(f_1948_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK148(U_6937)))
| hBOOL(hAPP(U_6937,U_6934)) ),
inference(clausify,[status(thm)],[f_1948_5]) ).
cnf(f_1948_8,plain,
( ~ hBOOL(hAPP(U_6937,hAPP(c_Int_Onat,sK148(U_6937))))
| hBOOL(hAPP(U_6937,U_6934)) ),
inference(clausify,[status(thm)],[f_1948_5]) ).
fof(f_1949_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_1949_2,plain,
! [U_6939,U_6938] :
( ( ( hAPP(c_Int_Onat,U_6938) = hAPP(c_Int_Onat,U_6939)
| U_6938 != U_6939 )
& ( U_6938 = U_6939
| hAPP(c_Int_Onat,U_6938) != hAPP(c_Int_Onat,U_6939) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6939))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6938)) ),
inference(variable_rename,[status(thm)],[f_1949_1]) ).
cnf(f_1949_3,plain,
( U_6938 = U_6939
| hAPP(c_Int_Onat,U_6938) != hAPP(c_Int_Onat,U_6939)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6939))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6938)) ),
inference(clausify,[status(thm)],[f_1949_2]) ).
cnf(f_1949_4,plain,
( hAPP(c_Int_Onat,U_6938) = hAPP(c_Int_Onat,U_6939)
| U_6938 != U_6939
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6939))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6938)) ),
inference(clausify,[status(thm)],[f_1949_2]) ).
fof(f_1950_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_1950_2,plain,
! [U_6941,U_6940] :
( ( ( hAPP(c_Int_Onat,U_6940) = hAPP(c_Int_Onat,U_6941)
| U_6940 != U_6941 )
& ( U_6940 = U_6941
| hAPP(c_Int_Onat,U_6940) != hAPP(c_Int_Onat,U_6941) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6941))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6940)) ),
inference(variable_rename,[status(thm)],[f_1950_1]) ).
cnf(f_1950_3,plain,
( U_6940 = U_6941
| hAPP(c_Int_Onat,U_6940) != hAPP(c_Int_Onat,U_6941)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6941))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6940)) ),
inference(clausify,[status(thm)],[f_1950_2]) ).
cnf(f_1950_4,plain,
( hAPP(c_Int_Onat,U_6940) = hAPP(c_Int_Onat,U_6941)
| U_6940 != U_6941
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6941))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6940)) ),
inference(clausify,[status(thm)],[f_1950_2]) ).
fof(f_1951_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_1951_2,plain,
! [U_6945,U_6944] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6944,U_6945) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ! [U_6943] : U_6944 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6945),U_6943) )
& ( ? [U_6942] : U_6944 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6945),U_6942)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6944,U_6945) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1951_1]) ).
fof(f_1951_3,plain,
( ! [U_6949,U_6947] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6947,U_6949) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ! [U_6943] : U_6947 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6949),U_6943) )
& ! [U_6948,U_6946] :
( ? [U_6942] : U_6946 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6948),U_6942)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6946,U_6948) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1951_2]) ).
fof(f_1951_4,plain,
( ! [U_6949,U_6947] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6947,U_6949) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ! [U_6943] : U_6947 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6949),U_6943) )
& ! [U_6948,U_6946] :
( U_6946 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6948),sK149(U_6948,U_6946))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6946,U_6948) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK149]),skolemize(U_6942,sK149(U_6948,U_6946))],[f_1951_3]) ).
cnf(f_1951_5,plain,
( U_6946 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6948),sK149(U_6948,U_6946))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6946,U_6948) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1951_4]) ).
cnf(f_1951_6,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6947,U_6949) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6947 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6949),U_6943) ),
inference(clausify,[status(thm)],[f_1951_4]) ).
fof(f_1952_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_1952_2,plain,
! [U_6951,U_6950] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6950,U_6951) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6950),U_6951),U_6951)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6950),U_6951)) ),
inference(variable_rename,[status(thm)],[f_1952_1]) ).
cnf(f_1952_3,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6950,U_6951) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6950),U_6951),U_6951)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6950),U_6951)) ),
inference(clausify,[status(thm)],[f_1952_2]) ).
fof(f_1953_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_1953_2,plain,
! [U_6953,U_6952] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6952,U_6953) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6952),U_6953),U_6953)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6952),U_6953)) )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6952,U_6953) = U_6952
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6952),U_6953)) ) ),
inference(variable_rename,[status(thm)],[f_1953_1]) ).
fof(f_1953_3,plain,
( ! [U_6957,U_6955] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6955,U_6957) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6955),U_6957),U_6957)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6955),U_6957)) )
& ! [U_6956,U_6954] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6954,U_6956) = U_6954
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6954),U_6956)) ) ),
inference(miniscope,[status(thm)],[f_1953_2]) ).
cnf(f_1953_4,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6954,U_6956) = U_6954
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6954),U_6956)) ),
inference(clausify,[status(thm)],[f_1953_3]) ).
cnf(f_1953_5,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6955,U_6957) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6955),U_6957),U_6957)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6955),U_6957)) ),
inference(clausify,[status(thm)],[f_1953_3]) ).
fof(f_1954_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_1954_2,plain,
! [U_6960,U_6959,U_6958] : 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_6958),U_6959)),U_6960),U_6959) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6960,U_6959),
inference(variable_rename,[status(thm)],[f_1954_1]) ).
cnf(f_1954_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_6958),U_6959)),U_6960),U_6959) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6960,U_6959),
inference(clausify,[status(thm)],[f_1954_2]) ).
fof(f_1955_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_1955_2,plain,
! [U_6962,U_6961] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6962,U_6961) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6962),U_6961),U_6961)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6961),U_6962)) ),
inference(variable_rename,[status(thm)],[f_1955_1]) ).
cnf(f_1955_3,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6962,U_6961) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6962),U_6961),U_6961)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6961),U_6962)) ),
inference(clausify,[status(thm)],[f_1955_2]) ).
fof(f_1956_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_1956_2,plain,
! [U_6964,U_6963] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6963),U_6964)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6963)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6964)),
inference(variable_rename,[status(thm)],[f_1956_1]) ).
cnf(f_1956_3,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6963),U_6964)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6963)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6964)),
inference(clausify,[status(thm)],[f_1956_2]) ).
fof(f_1957_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_1957_2,plain,
! [U_6966,U_6965] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6965)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6966)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6965),U_6966)),
inference(variable_rename,[status(thm)],[f_1957_1]) ).
cnf(f_1957_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6965)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6966)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6965),U_6966)),
inference(clausify,[status(thm)],[f_1957_2]) ).
fof(f_1958_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_1958_2,plain,
! [U_6967] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6967)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6967),
inference(variable_rename,[status(thm)],[f_1958_1]) ).
cnf(f_1958_3,plain,
hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6967)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6967),
inference(clausify,[status(thm)],[f_1958_2]) ).
fof(f_1959_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_1959_2,plain,
! [U_6968] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6968) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6968)),
inference(variable_rename,[status(thm)],[f_1959_1]) ).
cnf(f_1959_3,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6968) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6968)),
inference(clausify,[status(thm)],[f_1959_2]) ).
fof(f_1960_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_1960_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_1960_1]) ).
fof(f_1961_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_1961_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_1961_1]) ).
fof(f_1962_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_1962_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_1962_1]) ).
fof(f_1963_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_1963_2,plain,
! [U_6969] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_6969)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6969),c_Int_OMin)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6969),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_6969)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[f_1963_1]) ).
fof(f_1963_3,plain,
( ! [U_6971] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_6971)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6971),c_Int_OMin)) )
& ! [U_6970] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6970),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_6970)),c_Int_OMin)) ) ),
inference(miniscope,[status(thm)],[f_1963_2]) ).
cnf(f_1963_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6970),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_6970)),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_1963_3]) ).
cnf(f_1963_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_6971)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6971),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_1963_3]) ).
fof(f_1964_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_1964_2,plain,
! [U_6972] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_6972)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_6972)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_6972))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_6972))) ) ),
inference(variable_rename,[status(thm)],[f_1964_1]) ).
fof(f_1964_3,plain,
( ! [U_6974] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_6974)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_6974)) )
& ! [U_6973] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_6973))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_6973))) ) ),
inference(miniscope,[status(thm)],[f_1964_2]) ).
cnf(f_1964_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_6973))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_6973))) ),
inference(clausify,[status(thm)],[f_1964_3]) ).
cnf(f_1964_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_6974)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_6974)) ),
inference(clausify,[status(thm)],[f_1964_3]) ).
fof(f_1965_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_1965_2,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(clausify,[status(thm)],[f_1965_1]) ).
fof(f_1966_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_1966_2,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(clausify,[status(thm)],[f_1966_1]) ).
fof(f_1967_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_1967_2,plain,
! [U_6975] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_6975)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6975),c_Int_OMin)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6975),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_6975)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[f_1967_1]) ).
fof(f_1967_3,plain,
( ! [U_6977] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_6977)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6977),c_Int_OMin)) )
& ! [U_6976] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6976),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_6976)),c_Int_OMin)) ) ),
inference(miniscope,[status(thm)],[f_1967_2]) ).
cnf(f_1967_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6976),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_6976)),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_1967_3]) ).
cnf(f_1967_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_6977)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6977),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_1967_3]) ).
fof(f_1968_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_1968_2,plain,
! [U_6978] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_6978)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_6978)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_6978))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_6978))) ) ),
inference(variable_rename,[status(thm)],[f_1968_1]) ).
fof(f_1968_3,plain,
( ! [U_6980] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_6980)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_6980)) )
& ! [U_6979] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_6979))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_6979))) ) ),
inference(miniscope,[status(thm)],[f_1968_2]) ).
cnf(f_1968_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_6979))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_6979))) ),
inference(clausify,[status(thm)],[f_1968_3]) ).
cnf(f_1968_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_6980)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_6980)) ),
inference(clausify,[status(thm)],[f_1968_3]) ).
fof(f_1969_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_1969_2,plain,
! [U_6981] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_6981)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6981),c_Int_OMin)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6981),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_6981)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[f_1969_1]) ).
fof(f_1969_3,plain,
( ! [U_6983] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_6983)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6983),c_Int_OMin)) )
& ! [U_6982] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6982),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_6982)),c_Int_OMin)) ) ),
inference(miniscope,[status(thm)],[f_1969_2]) ).
cnf(f_1969_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6982),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_6982)),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_1969_3]) ).
cnf(f_1969_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_6983)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6983),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_1969_3]) ).
fof(f_1970_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_1970_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_1970_1]) ).
fof(f_1971_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_1971_2,plain,
! [U_6984] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_6984)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_6984)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_6984))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_6984))) ) ),
inference(variable_rename,[status(thm)],[f_1971_1]) ).
fof(f_1971_3,plain,
( ! [U_6986] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_6986)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_6986)) )
& ! [U_6985] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_6985))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_6985))) ) ),
inference(miniscope,[status(thm)],[f_1971_2]) ).
cnf(f_1971_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_6985))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_6985))) ),
inference(clausify,[status(thm)],[f_1971_3]) ).
cnf(f_1971_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_6986)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_6986)) ),
inference(clausify,[status(thm)],[f_1971_3]) ).
fof(f_1972_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_1972_2,plain,
! [U_6988,U_6987] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6987,U_6988)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6987),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6988)),
inference(variable_rename,[status(thm)],[f_1972_1]) ).
cnf(f_1972_3,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6987,U_6988)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6987),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6988)),
inference(clausify,[status(thm)],[f_1972_2]) ).
fof(f_1973_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_1973_2,plain,
! [U_6990,U_6989] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6989),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6990)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6989,U_6990)),
inference(variable_rename,[status(thm)],[f_1973_1]) ).
cnf(f_1973_3,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6989),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6990)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6989,U_6990)),
inference(clausify,[status(thm)],[f_1973_2]) ).
fof(f_1974_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_1974_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_1974_1]) ).
fof(f_1975_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_1975_2,plain,
! [U_6991] :
( hAPP(c_Int_Onat,U_6991) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6991)) ),
inference(variable_rename,[status(thm)],[f_1975_1]) ).
cnf(f_1975_3,plain,
( hAPP(c_Int_Onat,U_6991) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6991)) ),
inference(clausify,[status(thm)],[f_1975_2]) ).
fof(f_1976_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_1976_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_1976_1]) ).
fof(f_1977_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_1977_2,plain,
! [U_6992] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_6992) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6992),
inference(variable_rename,[status(thm)],[f_1977_1]) ).
cnf(f_1977_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_6992) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6992),
inference(clausify,[status(thm)],[f_1977_2]) ).
fof(f_1978_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_1978_2,plain,
! [U_6993] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_6993)) = U_6993
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6993)) ),
inference(variable_rename,[status(thm)],[f_1978_1]) ).
cnf(f_1978_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_6993)) = U_6993
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6993)) ),
inference(clausify,[status(thm)],[f_1978_2]) ).
fof(f_1979_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_1979_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_1979_1]) ).
fof(f_1980_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_1980_2,plain,
! [U_6995,U_6994] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6994),U_6995) = 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_6994)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6995))),
inference(variable_rename,[status(thm)],[f_1980_1]) ).
cnf(f_1980_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6994),U_6995) = 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_6994)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6995))),
inference(clausify,[status(thm)],[f_1980_2]) ).
fof(f_1981_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_1981_2,plain,
! [U_6996] : 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_6996)) = U_6996,
inference(variable_rename,[status(thm)],[f_1981_1]) ).
cnf(f_1981_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_6996)) = U_6996,
inference(clausify,[status(thm)],[f_1981_2]) ).
fof(f_1982_1,plain,
c_Int_Opred(c_Int_OPls) = c_Int_OMin,
inference(fof_nnf,[status(thm)],[fact_pred__Pls]) ).
cnf(f_1982_2,plain,
c_Int_Opred(c_Int_OPls) = c_Int_OMin,
inference(clausify,[status(thm)],[f_1982_1]) ).
fof(f_1983_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_1983_2,plain,
! [U_6997] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_6997) = c_Int_Opred(U_6997),
inference(variable_rename,[status(thm)],[f_1983_1]) ).
cnf(f_1983_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_6997) = c_Int_Opred(U_6997),
inference(clausify,[status(thm)],[f_1983_2]) ).
fof(f_1984_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_1984_2,plain,
! [U_6998] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6998),c_Int_OMin) = c_Int_Opred(U_6998),
inference(variable_rename,[status(thm)],[f_1984_1]) ).
cnf(f_1984_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6998),c_Int_OMin) = c_Int_Opred(U_6998),
inference(clausify,[status(thm)],[f_1984_2]) ).
fof(f_1985_1,plain,
c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
inference(fof_nnf,[status(thm)],[fact_pred__Min]) ).
cnf(f_1985_2,plain,
c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
inference(clausify,[status(thm)],[f_1985_1]) ).
fof(f_1986_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_1986_2,plain,
! [U_6999] :
( ~ c_Int_Oiszero(U_6999,hAPP(c_Int_Onumber__class_Onumber__of(U_6999),c_Int_OMin))
| ~ class_Int_Onumber__ring(U_6999) ),
inference(variable_rename,[status(thm)],[f_1986_1]) ).
cnf(f_1986_3,plain,
( ~ c_Int_Oiszero(U_6999,hAPP(c_Int_Onumber__class_Onumber__of(U_6999),c_Int_OMin))
| ~ class_Int_Onumber__ring(U_6999) ),
inference(clausify,[status(thm)],[f_1986_2]) ).
fof(f_1987_1,plain,
c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_succ__Min]) ).
cnf(f_1987_2,plain,
c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
inference(clausify,[status(thm)],[f_1987_1]) ).
fof(f_1988_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_1988_2,plain,
! [U_7001,U_7000] :
( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7000)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7001)) = 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_7000)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7001)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7000))) )
& ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7000)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7001)) = 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_7000))) ) ),
inference(variable_rename,[status(thm)],[f_1988_1]) ).
fof(f_1988_3,plain,
( ! [U_7005,U_7003] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7003)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7005)) = 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_7003)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7005)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7003))) )
& ! [U_7004,U_7002] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7002)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7004)) = 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_7002))) ) ),
inference(miniscope,[status(thm)],[f_1988_2]) ).
cnf(f_1988_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7002)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7004)) = 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_7002))) ),
inference(clausify,[status(thm)],[f_1988_3]) ).
cnf(f_1988_5,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7003)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7005)) = 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_7003)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7005)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7003))) ),
inference(clausify,[status(thm)],[f_1988_3]) ).
fof(f_1989_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_1989_2,plain,
! [U_7007,U_7006] :
( ( ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7006),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7007)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7006),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7007)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7007))) )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7006),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7007)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7006)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7007))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7006))) )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7006),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7007)) = 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_7006))) ) ),
inference(variable_rename,[status(thm)],[f_1989_1]) ).
fof(f_1989_3,plain,
( ! [U_7011,U_7009] :
( ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7009),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7011)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7009),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7011)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7011))) )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7009),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7011)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7009)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7011))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7009))) )
& ! [U_7010,U_7008] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7008),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7010)) = 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_7008))) ) ),
inference(miniscope,[status(thm)],[f_1989_2]) ).
cnf(f_1989_4,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7008),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7010)) = 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_7008))) ),
inference(clausify,[status(thm)],[f_1989_3]) ).
cnf(f_1989_5,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7009),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7011)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7009)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7011)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7009))) ),
inference(clausify,[status(thm)],[f_1989_3]) ).
cnf(f_1989_6,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7009),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7011)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7009),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7011)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7011)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7009))) ),
inference(clausify,[status(thm)],[f_1989_3]) ).
fof(f_1990_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_1990_2,plain,
! [U_7012] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7012),c_Int_OMin) = c_Int_Osucc(U_7012),
inference(variable_rename,[status(thm)],[f_1990_1]) ).
cnf(f_1990_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7012),c_Int_OMin) = c_Int_Osucc(U_7012),
inference(clausify,[status(thm)],[f_1990_2]) ).
fof(f_1991_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_1991_2,plain,
! [U_7013] : 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_7013)) = 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_7013))),
inference(variable_rename,[status(thm)],[f_1991_1]) ).
cnf(f_1991_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_7013)) = 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_7013))),
inference(clausify,[status(thm)],[f_1991_2]) ).
fof(f_1992_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_1992_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_1992_1]) ).
fof(f_1993_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_1993_2,plain,
! [U_7016,U_7015,U_7014] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7016),U_7015)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7016),U_7014)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7014),U_7015))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7014)) ),
inference(variable_rename,[status(thm)],[f_1993_1]) ).
cnf(f_1993_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_7016),U_7015)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7016),U_7014)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7014),U_7015))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7014)) ),
inference(clausify,[status(thm)],[f_1993_2]) ).
fof(f_1994_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_1994_2,plain,
! [U_7019,U_7018,U_7017] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7017),U_7018)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7017),U_7019)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7018),U_7019)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7017)) ),
inference(variable_rename,[status(thm)],[f_1994_1]) ).
cnf(f_1994_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7017),U_7018)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7017),U_7019)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7018),U_7019)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7017)) ),
inference(clausify,[status(thm)],[f_1994_2]) ).
fof(f_1995_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_1995_2,plain,
! [U_7021,U_7020] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7020),U_7021)),U_7020) = U_7021
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7020)) ),
inference(variable_rename,[status(thm)],[f_1995_1]) ).
cnf(f_1995_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7020),U_7021)),U_7020) = U_7021
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7020)) ),
inference(clausify,[status(thm)],[f_1995_2]) ).
fof(f_1996_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_1996_2,plain,
! [U_7023,U_7022] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7023),U_7022)),U_7022) = U_7023
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7022)) ),
inference(variable_rename,[status(thm)],[f_1996_1]) ).
cnf(f_1996_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7023),U_7022)),U_7022) = U_7023
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7022)) ),
inference(clausify,[status(thm)],[f_1996_2]) ).
fof(f_1997_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_1997_2,plain,
! [U_7025,U_7024] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7025),U_7024)),U_7025))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7025))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_7024)) ),
inference(variable_rename,[status(thm)],[f_1997_1]) ).
cnf(f_1997_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7025),U_7024)),U_7025))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7025))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_7024)) ),
inference(clausify,[status(thm)],[f_1997_2]) ).
fof(f_1998_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_1998_2,plain,
! [U_7026] :
( ( hAPP(c_Int_Onat,U_7026) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7026),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7026),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onat,U_7026) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1998_1]) ).
fof(f_1998_3,plain,
( ! [U_7028] :
( hAPP(c_Int_Onat,U_7028) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7028),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_7027] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7027),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onat,U_7027) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1998_2]) ).
cnf(f_1998_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7027),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onat,U_7027) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1998_3]) ).
cnf(f_1998_5,plain,
( hAPP(c_Int_Onat,U_7028) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7028),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1998_3]) ).
fof(f_1999_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_1999_2,plain,
! [U_7029] :
( hAPP(c_Int_Onat,U_7029) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7029),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1999_1]) ).
cnf(f_1999_3,plain,
( hAPP(c_Int_Onat,U_7029) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7029),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1999_2]) ).
fof(f_2000_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_2000_2,plain,
! [U_7031,U_7030] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7031)),hAPP(c_Int_Onat,U_7030)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7031),U_7030)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7031),U_7030))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7031)),hAPP(c_Int_Onat,U_7030))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7030)) ),
inference(variable_rename,[status(thm)],[f_2000_1]) ).
cnf(f_2000_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7031),U_7030))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7031)),hAPP(c_Int_Onat,U_7030)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7030)) ),
inference(clausify,[status(thm)],[f_2000_2]) ).
cnf(f_2000_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7031)),hAPP(c_Int_Onat,U_7030)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7031),U_7030))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7030)) ),
inference(clausify,[status(thm)],[f_2000_2]) ).
fof(f_2001_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_2001_2,plain,
! [U_7033,U_7032] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7032)),hAPP(c_Int_Onat,U_7033)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7032),U_7033))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7033)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7032),U_7033))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7033)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7032)),hAPP(c_Int_Onat,U_7033))) ) ),
inference(variable_rename,[status(thm)],[f_2001_1]) ).
fof(f_2001_3,plain,
( ! [U_7037,U_7035] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7035)),hAPP(c_Int_Onat,U_7037)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7035),U_7037))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7037)) )
& ! [U_7036,U_7034] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7034),U_7036))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7036)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7034)),hAPP(c_Int_Onat,U_7036))) ) ),
inference(miniscope,[status(thm)],[f_2001_2]) ).
cnf(f_2001_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7036))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7034)),hAPP(c_Int_Onat,U_7036))) ),
inference(clausify,[status(thm)],[f_2001_3]) ).
cnf(f_2001_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7034),U_7036))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7034)),hAPP(c_Int_Onat,U_7036))) ),
inference(clausify,[status(thm)],[f_2001_3]) ).
cnf(f_2001_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7035)),hAPP(c_Int_Onat,U_7037)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7035),U_7037))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7037)) ),
inference(clausify,[status(thm)],[f_2001_3]) ).
fof(f_2002_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_2002_2,plain,
! [U_7039,U_7038] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7039,U_7038)),U_7038))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7038)) ),
inference(variable_rename,[status(thm)],[f_2002_1]) ).
cnf(f_2002_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7039,U_7038)),U_7038))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7038)) ),
inference(clausify,[status(thm)],[f_2002_2]) ).
fof(f_2003_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_2003_2,plain,
! [U_7041,U_7040] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7040)),hAPP(c_Int_Onat,U_7041)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7040),U_7041)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7040),U_7041))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7040)),hAPP(c_Int_Onat,U_7041))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7041))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7040)) ),
inference(variable_rename,[status(thm)],[f_2003_1]) ).
cnf(f_2003_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7040),U_7041))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7040)),hAPP(c_Int_Onat,U_7041)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7041))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7040)) ),
inference(clausify,[status(thm)],[f_2003_2]) ).
cnf(f_2003_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7040)),hAPP(c_Int_Onat,U_7041)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7040),U_7041))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7041))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7040)) ),
inference(clausify,[status(thm)],[f_2003_2]) ).
fof(f_2004_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_2004_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_2004_1]) ).
fof(f_2005_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_2005_2,plain,
! [U_7044,U_7043,U_7042] : 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_7042),U_7043)),U_7044)),U_7043) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7044),U_7043),
inference(variable_rename,[status(thm)],[f_2005_1]) ).
cnf(f_2005_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_7042),U_7043)),U_7044)),U_7043) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7044),U_7043),
inference(clausify,[status(thm)],[f_2005_2]) ).
fof(f_2006_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_2006_2,plain,
! [U_7045] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7045)) = U_7045
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7045)) ),
inference(variable_rename,[status(thm)],[f_2006_1]) ).
cnf(f_2006_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7045)) = U_7045
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7045)) ),
inference(clausify,[status(thm)],[f_2006_2]) ).
fof(f_2007_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_2007_2,plain,
! [U_7047,U_7046] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7046) = U_7047
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7047))
| U_7046 != hAPP(c_Int_Onat,U_7047) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7047))
& U_7046 = hAPP(c_Int_Onat,U_7047) )
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7046) != U_7047 ) ),
inference(variable_rename,[status(thm)],[f_2007_1]) ).
fof(f_2007_3,plain,
( ! [U_7051,U_7049] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7049) = U_7051
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7051))
| U_7049 != hAPP(c_Int_Onat,U_7051) )
& ! [U_7050,U_7048] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7050))
& U_7048 = hAPP(c_Int_Onat,U_7050) )
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7048) != U_7050 ) ),
inference(miniscope,[status(thm)],[f_2007_2]) ).
cnf(f_2007_4,plain,
( U_7048 = hAPP(c_Int_Onat,U_7050)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7048) != U_7050 ),
inference(clausify,[status(thm)],[f_2007_3]) ).
cnf(f_2007_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7050))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7048) != U_7050 ),
inference(clausify,[status(thm)],[f_2007_3]) ).
cnf(f_2007_6,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7049) = U_7051
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7051))
| U_7049 != hAPP(c_Int_Onat,U_7051) ),
inference(clausify,[status(thm)],[f_2007_3]) ).
fof(f_2008_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_2008_2,plain,
! [U_7052] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7052)) = 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_7052)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7052)) = U_7052
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7052)) ) ),
inference(variable_rename,[status(thm)],[f_2008_1]) ).
fof(f_2008_3,plain,
( ! [U_7054] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7054)) = 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_7054)) )
& ! [U_7053] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7053)) = U_7053
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7053)) ) ),
inference(miniscope,[status(thm)],[f_2008_2]) ).
cnf(f_2008_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7053)) = U_7053
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7053)) ),
inference(clausify,[status(thm)],[f_2008_3]) ).
cnf(f_2008_5,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7054)) = 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_7054)) ),
inference(clausify,[status(thm)],[f_2008_3]) ).
fof(f_2009_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_2009_2,plain,
! [U_7056,U_7055] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7055),U_7056),hAPP(c_Int_Onumber__class_Onumber__of(U_7055),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7055),U_7056)
| ~ class_Int_Onumber__ring(U_7055) ),
inference(variable_rename,[status(thm)],[f_2009_1]) ).
cnf(f_2009_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7055),U_7056),hAPP(c_Int_Onumber__class_Onumber__of(U_7055),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7055),U_7056)
| ~ class_Int_Onumber__ring(U_7055) ),
inference(clausify,[status(thm)],[f_2009_2]) ).
fof(f_2010_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_2010_2,plain,
! [U_7058,U_7057] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7057),hAPP(c_Int_Onumber__class_Onumber__of(U_7057),c_Int_OMin)),U_7058) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7057),U_7058)
| ~ class_Int_Onumber__ring(U_7057) ),
inference(variable_rename,[status(thm)],[f_2010_1]) ).
cnf(f_2010_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7057),hAPP(c_Int_Onumber__class_Onumber__of(U_7057),c_Int_OMin)),U_7058) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7057),U_7058)
| ~ class_Int_Onumber__ring(U_7057) ),
inference(clausify,[status(thm)],[f_2010_2]) ).
fof(f_2011_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_2011_2,plain,
! [U_7060,U_7059] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7059),hAPP(c_Int_Onat,U_7060)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7059)),U_7060)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7059)),U_7060))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7059),hAPP(c_Int_Onat,U_7060))) ) ),
inference(variable_rename,[status(thm)],[f_2011_1]) ).
fof(f_2011_3,plain,
( ! [U_7064,U_7062] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7062),hAPP(c_Int_Onat,U_7064)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7062)),U_7064)) )
& ! [U_7063,U_7061] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7061)),U_7063))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7061),hAPP(c_Int_Onat,U_7063))) ) ),
inference(miniscope,[status(thm)],[f_2011_2]) ).
cnf(f_2011_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_7061)),U_7063))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7061),hAPP(c_Int_Onat,U_7063))) ),
inference(clausify,[status(thm)],[f_2011_3]) ).
cnf(f_2011_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7062),hAPP(c_Int_Onat,U_7064)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7062)),U_7064)) ),
inference(clausify,[status(thm)],[f_2011_3]) ).
fof(f_2012_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_2012_2,plain,
! [U_7065] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_7065),c_Groups_Oone__class_Oone(U_7065)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7065),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_7065) ),
inference(variable_rename,[status(thm)],[f_2012_1]) ).
cnf(f_2012_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_7065),c_Groups_Oone__class_Oone(U_7065)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7065),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_7065) ),
inference(clausify,[status(thm)],[f_2012_2]) ).
fof(f_2013_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_2013_2,plain,
! [U_7066] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_7066),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7066),c_Groups_Oone__class_Oone(U_7066))
| ~ class_Int_Onumber__ring(U_7066) ),
inference(variable_rename,[status(thm)],[f_2013_1]) ).
cnf(f_2013_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_7066),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7066),c_Groups_Oone__class_Oone(U_7066))
| ~ class_Int_Onumber__ring(U_7066) ),
inference(clausify,[status(thm)],[f_2013_2]) ).
fof(f_2014_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_2014_2,plain,
! [U_7067] : 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_7067))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_2014_1]) ).
cnf(f_2014_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_7067))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_2014_2]) ).
fof(f_2015_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_2015_2,plain,
! [U_7068] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7068)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7068)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7068))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7068))) ) ),
inference(variable_rename,[status(thm)],[f_2015_1]) ).
fof(f_2015_3,plain,
( ! [U_7070] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7070)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7070)) )
& ! [U_7069] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7069))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7069))) ) ),
inference(miniscope,[status(thm)],[f_2015_2]) ).
cnf(f_2015_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7069))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7069))) ),
inference(clausify,[status(thm)],[f_2015_3]) ).
cnf(f_2015_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7070)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_7070)) ),
inference(clausify,[status(thm)],[f_2015_3]) ).
fof(f_2016_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_2016_2,plain,
! [U_7071] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7071)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7071),c_Int_OMin)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7071),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7071)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[f_2016_1]) ).
fof(f_2016_3,plain,
( ! [U_7073] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7073)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7073),c_Int_OMin)) )
& ! [U_7072] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7072),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7072)),c_Int_OMin)) ) ),
inference(miniscope,[status(thm)],[f_2016_2]) ).
cnf(f_2016_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7072),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7072)),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_2016_3]) ).
cnf(f_2016_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7073)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7073),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_2016_3]) ).
fof(f_2017_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_2017_2,plain,
! [U_7074] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7074,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_2017_1]) ).
cnf(f_2017_3,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7074,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_2017_2]) ).
fof(f_2018_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_2018_2,plain,
! [U_7075] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7075)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_7075)),
inference(variable_rename,[status(thm)],[f_2018_1]) ).
cnf(f_2018_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7075)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_7075)),
inference(clausify,[status(thm)],[f_2018_2]) ).
fof(f_2019_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_2019_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_2019_1]) ).
fof(f_2020_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_2020_2,plain,
! [U_7077,U_7076] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7076),U_7077) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ( ( U_7077 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_7076 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
& ( U_7077 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_7076 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
& ( ( U_7077 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
& U_7076 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
| ( U_7077 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& U_7076 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7076),U_7077) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_2020_1]) ).
fof(f_2020_3,plain,
( ! [U_7081,U_7079] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7079),U_7081) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ( ( U_7081 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_7079 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
& ( U_7081 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_7079 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
& ! [U_7080,U_7078] :
( ( U_7080 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
& U_7078 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
| ( U_7080 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& U_7078 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7078),U_7080) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_2020_2]) ).
cnf(f_2020_4,plain,
( U_7078 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_7078 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7078),U_7080) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2020_3]) ).
cnf(f_2020_5,plain,
( U_7080 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_7078 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7078),U_7080) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2020_3]) ).
cnf(f_2020_6,plain,
( U_7078 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_7080 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7078),U_7080) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2020_3]) ).
cnf(f_2020_7,plain,
( U_7080 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_7080 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7078),U_7080) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2020_3]) ).
cnf(f_2020_8,plain,
( U_7081 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_7079 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7079),U_7081) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2020_3]) ).
cnf(f_2020_9,plain,
( U_7081 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_7079 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7079),U_7081) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2020_3]) ).
fof(f_2021_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_2021_2,plain,
! [U_7083,U_7082] :
( U_7082 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_7082 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7082),U_7083) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_2021_1]) ).
cnf(f_2021_3,plain,
( U_7082 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_7082 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7082),U_7083) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2021_2]) ).
fof(f_2022_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_2022_2,plain,
! [U_7084] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7084)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_7084)),
inference(variable_rename,[status(thm)],[f_2022_1]) ).
cnf(f_2022_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_7084)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_7084)),
inference(clausify,[status(thm)],[f_2022_2]) ).
fof(f_2023_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_2023_2,plain,
! [U_7085] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7085)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_7085)),
inference(variable_rename,[status(thm)],[f_2023_1]) ).
cnf(f_2023_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_7085)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_7085)),
inference(clausify,[status(thm)],[f_2023_2]) ).
fof(f_2024_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_2024_2,plain,
! [U_7089,U_7088,U_7087,U_7086] : hAPP(hAPP(c_Power_Opower_Opower(U_7086,U_7087,U_7088),U_7089),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_7087,
inference(variable_rename,[status(thm)],[f_2024_1]) ).
cnf(f_2024_3,plain,
hAPP(hAPP(c_Power_Opower_Opower(U_7086,U_7087,U_7088),U_7089),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_7087,
inference(clausify,[status(thm)],[f_2024_2]) ).
fof(f_2025_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_2025_2,plain,
! [U_7094,U_7093,U_7092,U_7091,U_7090] : hAPP(hAPP(c_Power_Opower_Opower(U_7090,U_7091,U_7092),U_7093),hAPP(c_Nat_OSuc,U_7094)) = hAPP(hAPP(U_7092,U_7093),hAPP(hAPP(c_Power_Opower_Opower(U_7090,U_7091,U_7092),U_7093),U_7094)),
inference(variable_rename,[status(thm)],[f_2025_1]) ).
cnf(f_2025_3,plain,
hAPP(hAPP(c_Power_Opower_Opower(U_7090,U_7091,U_7092),U_7093),hAPP(c_Nat_OSuc,U_7094)) = hAPP(hAPP(U_7092,U_7093),hAPP(hAPP(c_Power_Opower_Opower(U_7090,U_7091,U_7092),U_7093),U_7094)),
inference(clausify,[status(thm)],[f_2025_2]) ).
fof(f_2026_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_2026_2,plain,
! [U_7095] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7095),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7095),
inference(variable_rename,[status(thm)],[f_2026_1]) ).
cnf(f_2026_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7095),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7095),
inference(clausify,[status(thm)],[f_2026_2]) ).
fof(f_2027_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_2027_2,plain,
! [U_7097,U_7096] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7096,U_7097) = 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_7096),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7097))),
inference(variable_rename,[status(thm)],[f_2027_1]) ).
cnf(f_2027_3,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7096,U_7097) = 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_7096),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7097))),
inference(clausify,[status(thm)],[f_2027_2]) ).
fof(f_2028_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_2028_2,plain,
! [U_7098] :
( ( 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_7098)) = 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_7098)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7098))) )
& ( 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_7098)) = 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_7098))) ) ),
inference(variable_rename,[status(thm)],[f_2028_1]) ).
fof(f_2028_3,plain,
( ! [U_7100] :
( 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_7100)) = 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_7100)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7100))) )
& ! [U_7099] :
( 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_7099)) = 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_7099))) ) ),
inference(miniscope,[status(thm)],[f_2028_2]) ).
cnf(f_2028_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_7099)) = 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_7099))) ),
inference(clausify,[status(thm)],[f_2028_3]) ).
cnf(f_2028_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_7100)) = 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_7100)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7100))) ),
inference(clausify,[status(thm)],[f_2028_3]) ).
fof(f_2029_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_2029_2,plain,
! [U_7101] : 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_7101)) = hAPP(c_Int_Onat,U_7101),
inference(variable_rename,[status(thm)],[f_2029_1]) ).
cnf(f_2029_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_7101)) = hAPP(c_Int_Onat,U_7101),
inference(clausify,[status(thm)],[f_2029_2]) ).
fof(f_2030_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_2030_2,plain,
! [U_7103,U_7102] :
( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7103),U_7102) = 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_7103),U_7102)),U_7102))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7103),U_7102)) )
& ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7103),U_7102) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7103),U_7102)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7102)) ),
inference(variable_rename,[status(thm)],[f_2030_1]) ).
cnf(f_2030_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7103),U_7102) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7103),U_7102))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7102)) ),
inference(clausify,[status(thm)],[f_2030_2]) ).
cnf(f_2030_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7103),U_7102) = 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_7103),U_7102)),U_7102))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7103),U_7102))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7102)) ),
inference(clausify,[status(thm)],[f_2030_2]) ).
fof(f_2031_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_2031_2,plain,
! [U_7105,U_7104] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7105),U_7104) = 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_7105),U_7104)),U_7104))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7105),U_7104))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7104)) ),
inference(variable_rename,[status(thm)],[f_2031_1]) ).
cnf(f_2031_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7105),U_7104) = 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_7105),U_7104)),U_7104))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7105),U_7104))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7104)) ),
inference(clausify,[status(thm)],[f_2031_2]) ).
fof(f_2032_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_2032_2,plain,
! [U_7107,U_7106] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_7106),U_7107)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7107),U_7106)),
inference(variable_rename,[status(thm)],[f_2032_1]) ).
cnf(f_2032_3,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_7106),U_7107)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7107),U_7106)),
inference(clausify,[status(thm)],[f_2032_2]) ).
fof(f_2033_1,plain,
! [V_k_2,V_n_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
| ( ? [B_i,B_j] :
( ~ hBOOL(hAPP(V_P_2,B_i))
& V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) )
& V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( ( ! [B_i,B_j] :
( hBOOL(hAPP(V_P_2,B_i))
| V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) )
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__div]) ).
fof(f_2033_2,plain,
! [U_7114,U_7113,U_7112] :
( ( hBOOL(hAPP(U_7112,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7113),U_7114)))
| ( ? [U_7111,U_7110] :
( ~ hBOOL(hAPP(U_7112,U_7111))
& U_7113 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7114),U_7111)),U_7110)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7110),U_7114)) )
& U_7114 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_7112,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_7114 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( ( ! [U_7109,U_7108] :
( hBOOL(hAPP(U_7112,U_7109))
| U_7113 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7114),U_7109)),U_7108)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7108),U_7114)) )
| U_7114 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_7112,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_7114 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_7112,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7113),U_7114))) ) ),
inference(variable_rename,[status(thm)],[f_2033_1]) ).
fof(f_2033_3,plain,
( ! [U_7120,U_7118,U_7116] :
( hBOOL(hAPP(U_7116,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7118),U_7120)))
| ( ? [U_7111,U_7110] :
( ~ hBOOL(hAPP(U_7116,U_7111))
& U_7118 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7120),U_7111)),U_7110)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7110),U_7120)) )
& U_7120 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_7116,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_7120 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_7119,U_7117,U_7115] :
( ( ( ! [U_7109,U_7108] :
( hBOOL(hAPP(U_7115,U_7109))
| U_7117 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7119),U_7109)),U_7108)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7108),U_7119)) )
| U_7119 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_7115,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_7119 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_7115,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7117),U_7119))) ) ),
inference(miniscope,[status(thm)],[f_2033_2]) ).
fof(f_2033_4,plain,
( ! [U_7120,U_7118,U_7116] :
( hBOOL(hAPP(U_7116,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7118),U_7120)))
| ( ? [U_7110] :
( ~ hBOOL(hAPP(U_7116,sK150(U_7120,U_7118,U_7116)))
& U_7118 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7120),sK150(U_7120,U_7118,U_7116))),U_7110)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7110),U_7120)) )
& U_7120 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_7116,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_7120 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_7119,U_7117,U_7115] :
( ( ( ! [U_7109,U_7108] :
( hBOOL(hAPP(U_7115,U_7109))
| U_7117 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7119),U_7109)),U_7108)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7108),U_7119)) )
| U_7119 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_7115,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_7119 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_7115,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7117),U_7119))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK150]),skolemize(U_7111,sK150(U_7120,U_7118,U_7116))],[f_2033_3]) ).
fof(f_2033_5,plain,
( ! [U_7120,U_7118,U_7116] :
( hBOOL(hAPP(U_7116,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7118),U_7120)))
| ( ~ hBOOL(hAPP(U_7116,sK150(U_7120,U_7118,U_7116)))
& U_7118 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7120),sK150(U_7120,U_7118,U_7116))),sK151(U_7120,U_7118,U_7116))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK151(U_7120,U_7118,U_7116)),U_7120))
& U_7120 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_7116,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_7120 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_7119,U_7117,U_7115] :
( ( ( ! [U_7109,U_7108] :
( hBOOL(hAPP(U_7115,U_7109))
| U_7117 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7119),U_7109)),U_7108)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7108),U_7119)) )
| U_7119 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_7115,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_7119 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_7115,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7117),U_7119))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK151]),skolemize(U_7110,sK151(U_7120,U_7118,U_7116))],[f_2033_4]) ).
cnf(f_2033_6,plain,
( hBOOL(hAPP(U_7115,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_7119 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_7115,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7117),U_7119))) ),
inference(clausify,[status(thm)],[f_2033_5]) ).
cnf(f_2033_7,plain,
( hBOOL(hAPP(U_7115,U_7109))
| U_7117 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7119),U_7109)),U_7108)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7108),U_7119))
| U_7119 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_7115,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7117),U_7119))) ),
inference(clausify,[status(thm)],[f_2033_5]) ).
cnf(f_2033_8,plain,
( U_7120 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_7120 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_7116,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7118),U_7120))) ),
inference(clausify,[status(thm)],[f_2033_5]) ).
cnf(f_2033_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK151(U_7120,U_7118,U_7116)),U_7120))
| U_7120 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_7116,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7118),U_7120))) ),
inference(clausify,[status(thm)],[f_2033_5]) ).
cnf(f_2033_10,plain,
( U_7118 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7120),sK150(U_7120,U_7118,U_7116))),sK151(U_7120,U_7118,U_7116))
| U_7120 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_7116,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7118),U_7120))) ),
inference(clausify,[status(thm)],[f_2033_5]) ).
cnf(f_2033_11,plain,
( ~ hBOOL(hAPP(U_7116,sK150(U_7120,U_7118,U_7116)))
| U_7120 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_7116,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7118),U_7120))) ),
inference(clausify,[status(thm)],[f_2033_5]) ).
cnf(f_2033_12,plain,
( U_7120 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_7116,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_7116,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7118),U_7120))) ),
inference(clausify,[status(thm)],[f_2033_5]) ).
cnf(f_2033_13,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK151(U_7120,U_7118,U_7116)),U_7120))
| ~ hBOOL(hAPP(U_7116,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_7116,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7118),U_7120))) ),
inference(clausify,[status(thm)],[f_2033_5]) ).
cnf(f_2033_14,plain,
( U_7118 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7120),sK150(U_7120,U_7118,U_7116))),sK151(U_7120,U_7118,U_7116))
| ~ hBOOL(hAPP(U_7116,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_7116,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7118),U_7120))) ),
inference(clausify,[status(thm)],[f_2033_5]) ).
cnf(f_2033_15,plain,
( ~ hBOOL(hAPP(U_7116,sK150(U_7120,U_7118,U_7116)))
| ~ hBOOL(hAPP(U_7116,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_7116,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7118),U_7120))) ),
inference(clausify,[status(thm)],[f_2033_5]) ).
fof(f_2034_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_2034_2,plain,
! [U_7121] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7121)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7121)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7121))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7121))) ) ),
inference(variable_rename,[status(thm)],[f_2034_1]) ).
fof(f_2034_3,plain,
( ! [U_7123] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7123)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7123)) )
& ! [U_7122] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7122))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7122))) ) ),
inference(miniscope,[status(thm)],[f_2034_2]) ).
cnf(f_2034_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7122))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7122))) ),
inference(clausify,[status(thm)],[f_2034_3]) ).
cnf(f_2034_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_7123)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7123)) ),
inference(clausify,[status(thm)],[f_2034_3]) ).
fof(f_2035_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_2035_2,plain,
! [U_7125,U_7124] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7124)),hAPP(c_Int_Onat,U_7125)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7124),U_7125)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7124),U_7125))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7124)),hAPP(c_Int_Onat,U_7125))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7125))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7124)) ),
inference(variable_rename,[status(thm)],[f_2035_1]) ).
cnf(f_2035_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7124),U_7125))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7124)),hAPP(c_Int_Onat,U_7125)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7125))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7124)) ),
inference(clausify,[status(thm)],[f_2035_2]) ).
cnf(f_2035_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7124)),hAPP(c_Int_Onat,U_7125)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7124),U_7125))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7125))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7124)) ),
inference(clausify,[status(thm)],[f_2035_2]) ).
fof(f_2036_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_2036_2,plain,
! [U_7127,U_7126] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7126)),hAPP(c_Int_Onat,U_7127)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7126),U_7127)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7126),U_7127))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7126)),hAPP(c_Int_Onat,U_7127))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7126)) ),
inference(variable_rename,[status(thm)],[f_2036_1]) ).
cnf(f_2036_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7126),U_7127))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7126)),hAPP(c_Int_Onat,U_7127)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7126)) ),
inference(clausify,[status(thm)],[f_2036_2]) ).
cnf(f_2036_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7126)),hAPP(c_Int_Onat,U_7127)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7126),U_7127))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7126)) ),
inference(clausify,[status(thm)],[f_2036_2]) ).
fof(f_2037_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_2037_2,plain,
! [U_7129,U_7128] :
( ( U_7128 = hAPP(c_Int_Onat,U_7129)
| ( U_7128 != 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_7129)) )
| ( U_7129 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7128)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7129)) ) )
& ( ( ( U_7128 = 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_7129)) )
& ( U_7129 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7128)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7129)) ) )
| U_7128 != hAPP(c_Int_Onat,U_7129) ) ),
inference(variable_rename,[status(thm)],[f_2037_1]) ).
fof(f_2037_3,plain,
( ! [U_7133,U_7131] :
( U_7131 = hAPP(c_Int_Onat,U_7133)
| ( U_7131 != 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_7133)) )
| ( U_7133 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7131)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7133)) ) )
& ! [U_7132,U_7130] :
( ( ( U_7130 = 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_7132)) )
& ( U_7132 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7130)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7132)) ) )
| U_7130 != hAPP(c_Int_Onat,U_7132) ) ),
inference(miniscope,[status(thm)],[f_2037_2]) ).
cnf(f_2037_4,plain,
( U_7132 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7130)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7132))
| U_7130 != hAPP(c_Int_Onat,U_7132) ),
inference(clausify,[status(thm)],[f_2037_3]) ).
cnf(f_2037_5,plain,
( U_7130 = 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_7132))
| U_7130 != hAPP(c_Int_Onat,U_7132) ),
inference(clausify,[status(thm)],[f_2037_3]) ).
cnf(f_2037_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7133))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7133))
| U_7131 = hAPP(c_Int_Onat,U_7133) ),
inference(clausify,[status(thm)],[f_2037_3]) ).
cnf(f_2037_7,plain,
( U_7131 != 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_7133))
| U_7131 = hAPP(c_Int_Onat,U_7133) ),
inference(clausify,[status(thm)],[f_2037_3]) ).
cnf(f_2037_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7133))
| U_7133 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7131)
| U_7131 = hAPP(c_Int_Onat,U_7133) ),
inference(clausify,[status(thm)],[f_2037_3]) ).
cnf(f_2037_9,plain,
( U_7131 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_7133 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7131)
| U_7131 = hAPP(c_Int_Onat,U_7133) ),
inference(clausify,[status(thm)],[f_2037_3]) ).
fof(f_2038_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_2038_2,plain,
! [U_7135,U_7134] :
( ( hAPP(c_Int_Onat,U_7134) = U_7135
| ( U_7135 != 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_7134)) )
| ( U_7134 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7135)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7134)) ) )
& ( ( ( U_7135 = 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_7134)) )
& ( U_7134 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7135)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7134)) ) )
| hAPP(c_Int_Onat,U_7134) != U_7135 ) ),
inference(variable_rename,[status(thm)],[f_2038_1]) ).
fof(f_2038_3,plain,
( ! [U_7139,U_7137] :
( hAPP(c_Int_Onat,U_7137) = U_7139
| ( U_7139 != 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_7137)) )
| ( U_7137 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7139)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7137)) ) )
& ! [U_7138,U_7136] :
( ( ( U_7138 = 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_7136)) )
& ( U_7136 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7138)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7136)) ) )
| hAPP(c_Int_Onat,U_7136) != U_7138 ) ),
inference(miniscope,[status(thm)],[f_2038_2]) ).
cnf(f_2038_4,plain,
( U_7136 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7138)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7136))
| hAPP(c_Int_Onat,U_7136) != U_7138 ),
inference(clausify,[status(thm)],[f_2038_3]) ).
cnf(f_2038_5,plain,
( U_7138 = 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_7136))
| hAPP(c_Int_Onat,U_7136) != U_7138 ),
inference(clausify,[status(thm)],[f_2038_3]) ).
cnf(f_2038_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7137))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7137))
| hAPP(c_Int_Onat,U_7137) = U_7139 ),
inference(clausify,[status(thm)],[f_2038_3]) ).
cnf(f_2038_7,plain,
( U_7139 != 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_7137))
| hAPP(c_Int_Onat,U_7137) = U_7139 ),
inference(clausify,[status(thm)],[f_2038_3]) ).
cnf(f_2038_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7137))
| U_7137 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7139)
| hAPP(c_Int_Onat,U_7137) = U_7139 ),
inference(clausify,[status(thm)],[f_2038_3]) ).
cnf(f_2038_9,plain,
( U_7139 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_7137 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7139)
| hAPP(c_Int_Onat,U_7137) = U_7139 ),
inference(clausify,[status(thm)],[f_2038_3]) ).
fof(f_2039_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_2039_2,plain,
! [U_7141,U_7140] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7140)),hAPP(c_Int_Onat,U_7141)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7140),U_7141)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7140),U_7141))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7140)),hAPP(c_Int_Onat,U_7141))) ) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7141))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7140)) ) ),
inference(variable_rename,[status(thm)],[f_2039_1]) ).
cnf(f_2039_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7140),U_7141))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7140)),hAPP(c_Int_Onat,U_7141)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7140)) ),
inference(clausify,[status(thm)],[f_2039_2]) ).
cnf(f_2039_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7140)),hAPP(c_Int_Onat,U_7141)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7140),U_7141))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7140)) ),
inference(clausify,[status(thm)],[f_2039_2]) ).
cnf(f_2039_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7140),U_7141))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7140)),hAPP(c_Int_Onat,U_7141)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7141)) ),
inference(clausify,[status(thm)],[f_2039_2]) ).
cnf(f_2039_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7140)),hAPP(c_Int_Onat,U_7141)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7140),U_7141))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7141)) ),
inference(clausify,[status(thm)],[f_2039_2]) ).
fof(f_2040_1,plain,
! [V_i_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
| ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ? [B_n] :
( ~ hBOOL(hAPP(V_P_2,B_n))
& V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) )
& ( ( ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [B_n] :
( hBOOL(hAPP(V_P_2,B_n))
| V_i_2 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) )
| ~ hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__nat]) ).
fof(f_2040_2,plain,
! [U_7145,U_7144] :
( ( hBOOL(hAPP(U_7144,hAPP(c_Int_Onat,U_7145)))
| ( ~ hBOOL(hAPP(U_7144,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7145),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ? [U_7143] :
( ~ hBOOL(hAPP(U_7144,U_7143))
& U_7145 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7143) ) )
& ( ( ( hBOOL(hAPP(U_7144,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7145),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_7142] :
( hBOOL(hAPP(U_7144,U_7142))
| U_7145 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7142) ) )
| ~ hBOOL(hAPP(U_7144,hAPP(c_Int_Onat,U_7145))) ) ),
inference(variable_rename,[status(thm)],[f_2040_1]) ).
fof(f_2040_3,plain,
( ! [U_7149,U_7147] :
( hBOOL(hAPP(U_7147,hAPP(c_Int_Onat,U_7149)))
| ( ~ hBOOL(hAPP(U_7147,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7149),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ? [U_7143] :
( ~ hBOOL(hAPP(U_7147,U_7143))
& U_7149 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7143) ) )
& ! [U_7148,U_7146] :
( ( ( hBOOL(hAPP(U_7146,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7148),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_7142] :
( hBOOL(hAPP(U_7146,U_7142))
| U_7148 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7142) ) )
| ~ hBOOL(hAPP(U_7146,hAPP(c_Int_Onat,U_7148))) ) ),
inference(miniscope,[status(thm)],[f_2040_2]) ).
fof(f_2040_4,plain,
( ! [U_7149,U_7147] :
( hBOOL(hAPP(U_7147,hAPP(c_Int_Onat,U_7149)))
| ( ~ hBOOL(hAPP(U_7147,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7149),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_7147,sK152(U_7149,U_7147)))
& U_7149 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK152(U_7149,U_7147)) ) )
& ! [U_7148,U_7146] :
( ( ( hBOOL(hAPP(U_7146,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7148),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_7142] :
( hBOOL(hAPP(U_7146,U_7142))
| U_7148 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7142) ) )
| ~ hBOOL(hAPP(U_7146,hAPP(c_Int_Onat,U_7148))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK152]),skolemize(U_7143,sK152(U_7149,U_7147))],[f_2040_3]) ).
cnf(f_2040_5,plain,
( hBOOL(hAPP(U_7146,U_7142))
| U_7148 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7142)
| ~ hBOOL(hAPP(U_7146,hAPP(c_Int_Onat,U_7148))) ),
inference(clausify,[status(thm)],[f_2040_4]) ).
cnf(f_2040_6,plain,
( hBOOL(hAPP(U_7146,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7148),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_7146,hAPP(c_Int_Onat,U_7148))) ),
inference(clausify,[status(thm)],[f_2040_4]) ).
cnf(f_2040_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7149),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_7149 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK152(U_7149,U_7147))
| hBOOL(hAPP(U_7147,hAPP(c_Int_Onat,U_7149))) ),
inference(clausify,[status(thm)],[f_2040_4]) ).
cnf(f_2040_8,plain,
( ~ hBOOL(hAPP(U_7147,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_7149 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK152(U_7149,U_7147))
| hBOOL(hAPP(U_7147,hAPP(c_Int_Onat,U_7149))) ),
inference(clausify,[status(thm)],[f_2040_4]) ).
cnf(f_2040_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7149),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_7147,sK152(U_7149,U_7147)))
| hBOOL(hAPP(U_7147,hAPP(c_Int_Onat,U_7149))) ),
inference(clausify,[status(thm)],[f_2040_4]) ).
cnf(f_2040_10,plain,
( ~ hBOOL(hAPP(U_7147,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(U_7147,sK152(U_7149,U_7147)))
| hBOOL(hAPP(U_7147,hAPP(c_Int_Onat,U_7149))) ),
inference(clausify,[status(thm)],[f_2040_4]) ).
fof(f_2041_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_2041_2,plain,
! [U_7153,U_7152,U_7151,U_7150] :
( 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_7152),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7153,U_7150))),U_7151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7152),U_7150)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7151),U_7152))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7150)) ),
inference(variable_rename,[status(thm)],[f_2041_1]) ).
cnf(f_2041_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_7152),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7153,U_7150))),U_7151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7152),U_7150)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7151),U_7152))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7150)) ),
inference(clausify,[status(thm)],[f_2041_2]) ).
fof(f_2042_1,plain,
! [V_k_2,V_n_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
| ( ? [B_i,B_j] :
( ~ hBOOL(hAPP(V_P_2,B_j))
& V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) )
& V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(V_P_2,V_n_2))
& V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( ( ! [B_i,B_j] :
( hBOOL(hAPP(V_P_2,B_j))
| V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) )
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(V_P_2,V_n_2))
| V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__mod]) ).
fof(f_2042_2,plain,
! [U_7160,U_7159,U_7158] :
( ( hBOOL(hAPP(U_7158,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7159,U_7160)))
| ( ? [U_7157,U_7156] :
( ~ hBOOL(hAPP(U_7158,U_7156))
& U_7159 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7160),U_7157)),U_7156)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7156),U_7160)) )
& U_7160 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_7158,U_7159))
& U_7160 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( ( ! [U_7155,U_7154] :
( hBOOL(hAPP(U_7158,U_7154))
| U_7159 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7160),U_7155)),U_7154)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7154),U_7160)) )
| U_7160 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_7158,U_7159))
| U_7160 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_7158,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7159,U_7160))) ) ),
inference(variable_rename,[status(thm)],[f_2042_1]) ).
fof(f_2042_3,plain,
( ! [U_7166,U_7164,U_7162] :
( hBOOL(hAPP(U_7162,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7164,U_7166)))
| ( ? [U_7157,U_7156] :
( ~ hBOOL(hAPP(U_7162,U_7156))
& U_7164 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7166),U_7157)),U_7156)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7156),U_7166)) )
& U_7166 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_7162,U_7164))
& U_7166 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_7165,U_7163,U_7161] :
( ( ( ! [U_7155,U_7154] :
( hBOOL(hAPP(U_7161,U_7154))
| U_7163 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7165),U_7155)),U_7154)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7154),U_7165)) )
| U_7165 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_7161,U_7163))
| U_7165 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_7161,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7163,U_7165))) ) ),
inference(miniscope,[status(thm)],[f_2042_2]) ).
fof(f_2042_4,plain,
( ! [U_7166,U_7164,U_7162] :
( hBOOL(hAPP(U_7162,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7164,U_7166)))
| ( ? [U_7156] :
( ~ hBOOL(hAPP(U_7162,U_7156))
& U_7164 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7166),sK153(U_7166,U_7164,U_7162))),U_7156)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7156),U_7166)) )
& U_7166 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_7162,U_7164))
& U_7166 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_7165,U_7163,U_7161] :
( ( ( ! [U_7155,U_7154] :
( hBOOL(hAPP(U_7161,U_7154))
| U_7163 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7165),U_7155)),U_7154)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7154),U_7165)) )
| U_7165 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_7161,U_7163))
| U_7165 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_7161,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7163,U_7165))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK153]),skolemize(U_7157,sK153(U_7166,U_7164,U_7162))],[f_2042_3]) ).
fof(f_2042_5,plain,
( ! [U_7166,U_7164,U_7162] :
( hBOOL(hAPP(U_7162,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7164,U_7166)))
| ( ~ hBOOL(hAPP(U_7162,sK154(U_7166,U_7164,U_7162)))
& U_7164 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7166),sK153(U_7166,U_7164,U_7162))),sK154(U_7166,U_7164,U_7162))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK154(U_7166,U_7164,U_7162)),U_7166))
& U_7166 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_7162,U_7164))
& U_7166 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_7165,U_7163,U_7161] :
( ( ( ! [U_7155,U_7154] :
( hBOOL(hAPP(U_7161,U_7154))
| U_7163 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7165),U_7155)),U_7154)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7154),U_7165)) )
| U_7165 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_7161,U_7163))
| U_7165 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_7161,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7163,U_7165))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK154]),skolemize(U_7156,sK154(U_7166,U_7164,U_7162))],[f_2042_4]) ).
cnf(f_2042_6,plain,
( hBOOL(hAPP(U_7161,U_7163))
| U_7165 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_7161,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7163,U_7165))) ),
inference(clausify,[status(thm)],[f_2042_5]) ).
cnf(f_2042_7,plain,
( hBOOL(hAPP(U_7161,U_7154))
| U_7163 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7165),U_7155)),U_7154)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7154),U_7165))
| U_7165 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_7161,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7163,U_7165))) ),
inference(clausify,[status(thm)],[f_2042_5]) ).
cnf(f_2042_8,plain,
( U_7166 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_7166 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_7162,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7164,U_7166))) ),
inference(clausify,[status(thm)],[f_2042_5]) ).
cnf(f_2042_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK154(U_7166,U_7164,U_7162)),U_7166))
| U_7166 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_7162,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7164,U_7166))) ),
inference(clausify,[status(thm)],[f_2042_5]) ).
cnf(f_2042_10,plain,
( U_7164 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7166),sK153(U_7166,U_7164,U_7162))),sK154(U_7166,U_7164,U_7162))
| U_7166 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_7162,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7164,U_7166))) ),
inference(clausify,[status(thm)],[f_2042_5]) ).
cnf(f_2042_11,plain,
( ~ hBOOL(hAPP(U_7162,sK154(U_7166,U_7164,U_7162)))
| U_7166 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_7162,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7164,U_7166))) ),
inference(clausify,[status(thm)],[f_2042_5]) ).
cnf(f_2042_12,plain,
( U_7166 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_7162,U_7164))
| hBOOL(hAPP(U_7162,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7164,U_7166))) ),
inference(clausify,[status(thm)],[f_2042_5]) ).
cnf(f_2042_13,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK154(U_7166,U_7164,U_7162)),U_7166))
| ~ hBOOL(hAPP(U_7162,U_7164))
| hBOOL(hAPP(U_7162,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7164,U_7166))) ),
inference(clausify,[status(thm)],[f_2042_5]) ).
cnf(f_2042_14,plain,
( U_7164 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7166),sK153(U_7166,U_7164,U_7162))),sK154(U_7166,U_7164,U_7162))
| ~ hBOOL(hAPP(U_7162,U_7164))
| hBOOL(hAPP(U_7162,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7164,U_7166))) ),
inference(clausify,[status(thm)],[f_2042_5]) ).
cnf(f_2042_15,plain,
( ~ hBOOL(hAPP(U_7162,sK154(U_7166,U_7164,U_7162)))
| ~ hBOOL(hAPP(U_7162,U_7164))
| hBOOL(hAPP(U_7162,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7164,U_7166))) ),
inference(clausify,[status(thm)],[f_2042_5]) ).
fof(f_2043_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_2043_2,plain,
! [U_7168,U_7167] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7167)),hAPP(c_Int_Onat,U_7168)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7167),U_7168))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7168))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7167)) ),
inference(variable_rename,[status(thm)],[f_2043_1]) ).
cnf(f_2043_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7167)),hAPP(c_Int_Onat,U_7168)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7167),U_7168))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7168))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7167)) ),
inference(clausify,[status(thm)],[f_2043_2]) ).
fof(f_2044_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_2044_2,plain,
! [U_7170,U_7169] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7169),U_7170)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7169)),hAPP(c_Int_Onat,U_7170))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7170))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7169)) ),
inference(variable_rename,[status(thm)],[f_2044_1]) ).
cnf(f_2044_3,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7169),U_7170)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7169)),hAPP(c_Int_Onat,U_7170))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7170))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7169)) ),
inference(clausify,[status(thm)],[f_2044_2]) ).
fof(f_2045_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_2045_2,plain,
! [U_7172,U_7171] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7171) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7172)
| ~ 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_7172)))
| U_7171 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7172)) )
& ( ( 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_7172)))
& U_7171 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7172)) )
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7171) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7172) ) ),
inference(variable_rename,[status(thm)],[f_2045_1]) ).
fof(f_2045_3,plain,
( ! [U_7176,U_7174] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7174) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7176)
| ~ 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_7176)))
| U_7174 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7176)) )
& ! [U_7175,U_7173] :
( ( 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_7175)))
& U_7173 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7175)) )
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7173) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7175) ) ),
inference(miniscope,[status(thm)],[f_2045_2]) ).
cnf(f_2045_4,plain,
( U_7173 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7175))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7173) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7175) ),
inference(clausify,[status(thm)],[f_2045_3]) ).
cnf(f_2045_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7175)))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7173) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7175) ),
inference(clausify,[status(thm)],[f_2045_3]) ).
cnf(f_2045_6,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7174) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7176)
| ~ 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_7176)))
| U_7174 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7176)) ),
inference(clausify,[status(thm)],[f_2045_3]) ).
fof(f_2046_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_2046_2,plain,
! [U_7178,U_7177] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_7177)),hAPP(c_Int_Onat,U_7178)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7177),U_7178))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7178))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7177)) ),
inference(variable_rename,[status(thm)],[f_2046_1]) ).
cnf(f_2046_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_7177)),hAPP(c_Int_Onat,U_7178)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7177),U_7178))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7178))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7177)) ),
inference(clausify,[status(thm)],[f_2046_2]) ).
fof(f_2047_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_2047_2,plain,
! [U_7180,U_7179] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7179),U_7180)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_7179)),hAPP(c_Int_Onat,U_7180))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7179)) ),
inference(variable_rename,[status(thm)],[f_2047_1]) ).
cnf(f_2047_3,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7179),U_7180)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_7179)),hAPP(c_Int_Onat,U_7180))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7179)) ),
inference(clausify,[status(thm)],[f_2047_2]) ).
fof(f_2048_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_2048_2,plain,
! [U_7182,U_7181] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7181),U_7182) = 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_7181)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7182))),
inference(variable_rename,[status(thm)],[f_2048_1]) ).
cnf(f_2048_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7181),U_7182) = 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_7181)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7182))),
inference(clausify,[status(thm)],[f_2048_2]) ).
fof(f_2049_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_2049_2,plain,
! [U_7184,U_7183] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7184),U_7183)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7184)),hAPP(c_Int_Onat,U_7183))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7183),U_7184))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7183)) ),
inference(variable_rename,[status(thm)],[f_2049_1]) ).
cnf(f_2049_3,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7184),U_7183)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7184)),hAPP(c_Int_Onat,U_7183))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7183),U_7184))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7183)) ),
inference(clausify,[status(thm)],[f_2049_2]) ).
fof(f_2050_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_2050_2,plain,
! [U_7186,U_7185] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7185),U_7186)),U_7185) = 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_7185)) ),
inference(variable_rename,[status(thm)],[f_2050_1]) ).
cnf(f_2050_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_7185),U_7186)),U_7185) = 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_7185)) ),
inference(clausify,[status(thm)],[f_2050_2]) ).
fof(f_2051_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_2051_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_2051_1]) ).
fof(f_2052_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_2052_2,plain,
! [U_7188,U_7187] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_7187,U_7188)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7188),U_7187)),
inference(variable_rename,[status(thm)],[f_2052_1]) ).
cnf(f_2052_3,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_7187,U_7188)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7188),U_7187)),
inference(clausify,[status(thm)],[f_2052_2]) ).
fof(f_2053_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_2053_2,plain,
! [U_7189] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),U_7189) = 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_7189)) ),
inference(variable_rename,[status(thm)],[f_2053_1]) ).
cnf(f_2053_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_7189) = 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_7189)) ),
inference(clausify,[status(thm)],[f_2053_2]) ).
fof(f_2054_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_2054_2,plain,
! [U_7191,U_7190] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_7190)),U_7191) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7190),U_7191))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7190)) ),
inference(variable_rename,[status(thm)],[f_2054_1]) ).
cnf(f_2054_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_7190)),U_7191) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7190),U_7191))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7190)) ),
inference(clausify,[status(thm)],[f_2054_2]) ).
fof(f_2055_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_2055_2,plain,
! [U_7193,U_7192] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7192),U_7193)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_7192)),U_7193)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7192)) ),
inference(variable_rename,[status(thm)],[f_2055_1]) ).
cnf(f_2055_3,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7192),U_7193)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_7192)),U_7193)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7192)) ),
inference(clausify,[status(thm)],[f_2055_2]) ).
fof(f_2056_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_2056_2,plain,
! [U_7194] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7194) = 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_7194))),
inference(variable_rename,[status(thm)],[f_2056_1]) ).
cnf(f_2056_3,plain,
hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7194) = 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_7194))),
inference(clausify,[status(thm)],[f_2056_2]) ).
fof(f_2057_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_2057_2,plain,
! [U_7196,U_7195] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7195)),hAPP(c_Int_Onat,U_7196)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_7195,U_7196))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7196))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7195)) ),
inference(variable_rename,[status(thm)],[f_2057_1]) ).
cnf(f_2057_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7195)),hAPP(c_Int_Onat,U_7196)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_7195,U_7196))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7196))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7195)) ),
inference(clausify,[status(thm)],[f_2057_2]) ).
fof(f_2058_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_2058_2,plain,
! [U_7198,U_7197] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7198),U_7197) = 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_7198),U_7197)),U_7197))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7197),U_7198))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7197)) ),
inference(variable_rename,[status(thm)],[f_2058_1]) ).
cnf(f_2058_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7198),U_7197) = 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_7198),U_7197)),U_7197))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7197),U_7198))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7197)) ),
inference(clausify,[status(thm)],[f_2058_2]) ).
fof(f_2059_1,plain,
! [V_n_2,V_m_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
| ( ! [B_q] :
( ~ hBOOL(hAPP(V_P_2,B_q))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,B_q))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2)) )
& ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
& ( ? [B_q] :
( hBOOL(hAPP(V_P_2,B_q))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,B_q))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2)) )
| ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__div_H]) ).
fof(f_2059_2,plain,
! [U_7203,U_7202,U_7201] :
( ( hBOOL(hAPP(U_7201,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7202),U_7203)))
| ( ! [U_7200] :
( ~ hBOOL(hAPP(U_7201,U_7200))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7202),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7203),hAPP(c_Nat_OSuc,U_7200))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7203),U_7200)),U_7202)) )
& ( ~ hBOOL(hAPP(U_7201,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_7203 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
& ( ? [U_7199] :
( hBOOL(hAPP(U_7201,U_7199))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7202),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7203),hAPP(c_Nat_OSuc,U_7199))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7203),U_7199)),U_7202)) )
| ( hBOOL(hAPP(U_7201,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_7203 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(U_7201,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7202),U_7203))) ) ),
inference(variable_rename,[status(thm)],[f_2059_1]) ).
fof(f_2059_3,plain,
( ! [U_7209,U_7207,U_7205] :
( hBOOL(hAPP(U_7205,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7207),U_7209)))
| ( ! [U_7200] :
( ~ hBOOL(hAPP(U_7205,U_7200))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7207),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7209),hAPP(c_Nat_OSuc,U_7200))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7209),U_7200)),U_7207)) )
& ( ~ hBOOL(hAPP(U_7205,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_7209 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
& ! [U_7208,U_7206,U_7204] :
( ? [U_7199] :
( hBOOL(hAPP(U_7204,U_7199))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7206),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7208),hAPP(c_Nat_OSuc,U_7199))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7208),U_7199)),U_7206)) )
| ( hBOOL(hAPP(U_7204,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_7208 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(U_7204,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7206),U_7208))) ) ),
inference(miniscope,[status(thm)],[f_2059_2]) ).
fof(f_2059_4,plain,
( ! [U_7209,U_7207,U_7205] :
( hBOOL(hAPP(U_7205,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7207),U_7209)))
| ( ! [U_7200] :
( ~ hBOOL(hAPP(U_7205,U_7200))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7207),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7209),hAPP(c_Nat_OSuc,U_7200))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7209),U_7200)),U_7207)) )
& ( ~ hBOOL(hAPP(U_7205,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_7209 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
& ! [U_7208,U_7206,U_7204] :
( ( hBOOL(hAPP(U_7204,sK155(U_7208,U_7206,U_7204)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7206),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7208),hAPP(c_Nat_OSuc,sK155(U_7208,U_7206,U_7204)))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7208),sK155(U_7208,U_7206,U_7204))),U_7206)) )
| ( hBOOL(hAPP(U_7204,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_7208 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(U_7204,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7206),U_7208))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK155]),skolemize(U_7199,sK155(U_7208,U_7206,U_7204))],[f_2059_3]) ).
cnf(f_2059_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_7208),sK155(U_7208,U_7206,U_7204))),U_7206))
| U_7208 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_7204,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7206),U_7208))) ),
inference(clausify,[status(thm)],[f_2059_4]) ).
cnf(f_2059_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7206),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7208),hAPP(c_Nat_OSuc,sK155(U_7208,U_7206,U_7204)))))
| U_7208 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_7204,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7206),U_7208))) ),
inference(clausify,[status(thm)],[f_2059_4]) ).
cnf(f_2059_7,plain,
( hBOOL(hAPP(U_7204,sK155(U_7208,U_7206,U_7204)))
| U_7208 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_7204,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7206),U_7208))) ),
inference(clausify,[status(thm)],[f_2059_4]) ).
cnf(f_2059_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_7208),sK155(U_7208,U_7206,U_7204))),U_7206))
| hBOOL(hAPP(U_7204,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(U_7204,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7206),U_7208))) ),
inference(clausify,[status(thm)],[f_2059_4]) ).
cnf(f_2059_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7206),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7208),hAPP(c_Nat_OSuc,sK155(U_7208,U_7206,U_7204)))))
| hBOOL(hAPP(U_7204,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(U_7204,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7206),U_7208))) ),
inference(clausify,[status(thm)],[f_2059_4]) ).
cnf(f_2059_10,plain,
( hBOOL(hAPP(U_7204,sK155(U_7208,U_7206,U_7204)))
| hBOOL(hAPP(U_7204,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(U_7204,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7206),U_7208))) ),
inference(clausify,[status(thm)],[f_2059_4]) ).
cnf(f_2059_11,plain,
( ~ hBOOL(hAPP(U_7205,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_7209 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_7205,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7207),U_7209))) ),
inference(clausify,[status(thm)],[f_2059_4]) ).
cnf(f_2059_12,plain,
( ~ hBOOL(hAPP(U_7205,U_7200))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7207),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7209),hAPP(c_Nat_OSuc,U_7200))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7209),U_7200)),U_7207))
| hBOOL(hAPP(U_7205,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7207),U_7209))) ),
inference(clausify,[status(thm)],[f_2059_4]) ).
fof(f_2060_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_2060_2,plain,
! [U_7212,U_7211,U_7210] :
( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7212),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7210),hAPP(c_Nat_OSuc,U_7211))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7210),U_7211)),U_7212)) )
| U_7211 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7212),U_7210) )
& ( U_7211 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7212),U_7210)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7212),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7210),hAPP(c_Nat_OSuc,U_7211))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7210),U_7211)),U_7212)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7210)) ),
inference(variable_rename,[status(thm)],[f_2060_1]) ).
cnf(f_2060_3,plain,
( U_7211 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7212),U_7210)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7212),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7210),hAPP(c_Nat_OSuc,U_7211))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7210),U_7211)),U_7212))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7210)) ),
inference(clausify,[status(thm)],[f_2060_2]) ).
cnf(f_2060_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_7210),U_7211)),U_7212))
| U_7211 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7212),U_7210)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7210)) ),
inference(clausify,[status(thm)],[f_2060_2]) ).
cnf(f_2060_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7212),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7210),hAPP(c_Nat_OSuc,U_7211))))
| U_7211 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7212),U_7210)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7210)) ),
inference(clausify,[status(thm)],[f_2060_2]) ).
fof(f_2061_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_2061_2,plain,
! [U_7214,U_7213] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7213)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7214)) = 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_7213)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7214)),
inference(variable_rename,[status(thm)],[f_2061_1]) ).
cnf(f_2061_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_7213)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7214)) = 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_7213)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7214)),
inference(clausify,[status(thm)],[f_2061_2]) ).
fof(f_2062_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_2062_2,plain,
! [U_7216,U_7215] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7215)))),U_7216) = 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_7215)),U_7216),
inference(variable_rename,[status(thm)],[f_2062_1]) ).
cnf(f_2062_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_7215)))),U_7216) = 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_7215)),U_7216),
inference(clausify,[status(thm)],[f_2062_2]) ).
fof(f_2063_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_2063_2,plain,
! [U_7218,U_7217] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7217),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7218)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7217),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_7218)),
inference(variable_rename,[status(thm)],[f_2063_1]) ).
cnf(f_2063_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7217),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7218)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7217),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_7218)),
inference(clausify,[status(thm)],[f_2063_2]) ).
fof(f_2064_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_2064_2,plain,
! [U_7219] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7219))),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_7219),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_2064_1]) ).
cnf(f_2064_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7219))),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_7219),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(clausify,[status(thm)],[f_2064_2]) ).
fof(f_2065_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_2065_2,plain,
! [U_7220] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7220),U_7220)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_7220,
inference(variable_rename,[status(thm)],[f_2065_1]) ).
cnf(f_2065_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7220),U_7220)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_7220,
inference(clausify,[status(thm)],[f_2065_2]) ).
fof(f_2066_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_2066_2,plain,
! [U_7221] :
( ( 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_7221)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7221)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7221))
| ~ 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_7221))) ) ),
inference(variable_rename,[status(thm)],[f_2066_1]) ).
fof(f_2066_3,plain,
( ! [U_7223] :
( 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_7223)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7223)) )
& ! [U_7222] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7222))
| ~ 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_7222))) ) ),
inference(miniscope,[status(thm)],[f_2066_2]) ).
cnf(f_2066_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7222))
| ~ 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_7222))) ),
inference(clausify,[status(thm)],[f_2066_3]) ).
cnf(f_2066_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_7223)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7223)) ),
inference(clausify,[status(thm)],[f_2066_3]) ).
fof(f_2067_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_2067_2,plain,
! [U_7225,U_7224] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7224)),U_7225))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7224),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7225))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7224),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7225)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7224)),U_7225)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7224)) ),
inference(variable_rename,[status(thm)],[f_2067_1]) ).
cnf(f_2067_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7224),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7225)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7224)),U_7225))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7224)) ),
inference(clausify,[status(thm)],[f_2067_2]) ).
cnf(f_2067_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7224)),U_7225))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7224),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7225)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7224)) ),
inference(clausify,[status(thm)],[f_2067_2]) ).
fof(f_2068_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_2068_2,plain,
! [U_7226] :
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_7226)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7226))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7226)) ),
inference(variable_rename,[status(thm)],[f_2068_1]) ).
cnf(f_2068_3,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_7226)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7226))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7226)) ),
inference(clausify,[status(thm)],[f_2068_2]) ).
fof(f_2069_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_2069_2,plain,
! [U_7228,U_7227] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7227))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7228)) = 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_7227),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7228)),
inference(variable_rename,[status(thm)],[f_2069_1]) ).
cnf(f_2069_3,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7227))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7228)) = 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_7227),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7228)),
inference(clausify,[status(thm)],[f_2069_2]) ).
fof(f_2070_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_2070_2,plain,
! [U_7230,U_7229] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7229))),U_7230) = 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_7229),U_7230),
inference(variable_rename,[status(thm)],[f_2070_1]) ).
cnf(f_2070_3,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7229))),U_7230) = 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_7229),U_7230),
inference(clausify,[status(thm)],[f_2070_2]) ).
fof(f_2071_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_2071_2,plain,
! [U_7232,U_7231] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7231,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7232)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7231,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_7232)),
inference(variable_rename,[status(thm)],[f_2071_1]) ).
cnf(f_2071_3,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7231,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7232)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7231,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_7232)),
inference(clausify,[status(thm)],[f_2071_2]) ).
fof(f_2072_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_2072_2,plain,
! [U_7233] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7233)),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_7233,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_2072_1]) ).
cnf(f_2072_3,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7233)),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_7233,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(clausify,[status(thm)],[f_2072_2]) ).
fof(f_2073_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_2073_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_2073_1]) ).
fof(f_2074_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_2074_2,plain,
! [U_7235,U_7234] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7234),U_7235)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7234))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7235)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7234),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_2074_1]) ).
cnf(f_2074_3,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7234),U_7235)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7234))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7235)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7234),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2074_2]) ).
fof(f_2075_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_2075_2,plain,
! [U_7237,U_7236] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7236,U_7237)) = 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_7237),U_7236)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[f_2075_1]) ).
cnf(f_2075_3,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7236,U_7237)) = 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_7237),U_7236)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_2075_2]) ).
fof(f_2076_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_2076_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_2076_1]) ).
fof(f_2077_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_2077_2,plain,
! [U_7239,U_7238] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_7238,U_7239)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7239),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7238),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[f_2077_1]) ).
cnf(f_2077_3,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_7238,U_7239)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7239),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7238),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(clausify,[status(thm)],[f_2077_2]) ).
fof(f_2078_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_2078_2,plain,
! [U_7241,U_7240] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7240),U_7241) = 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_7240),U_7241)),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_7240)) ),
inference(variable_rename,[status(thm)],[f_2078_1]) ).
cnf(f_2078_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7240),U_7241) = 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_7240),U_7241)),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_7240)) ),
inference(clausify,[status(thm)],[f_2078_2]) ).
fof(f_2079_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_2079_2,plain,
! [U_7242] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_7242) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7242),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_7242)) ),
inference(variable_rename,[status(thm)],[f_2079_1]) ).
cnf(f_2079_3,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_7242) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7242),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_7242)) ),
inference(clausify,[status(thm)],[f_2079_2]) ).
fof(f_2080_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_2080_2,plain,
! [U_7244,U_7243] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7243)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7244)) = 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_7243)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7244)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7243))) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7243)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7244)) = 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_7244))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7243))) ) ),
inference(variable_rename,[status(thm)],[f_2080_1]) ).
fof(f_2080_3,plain,
( ! [U_7248,U_7246] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7246)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7248)) = 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_7246)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7248)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7246))) )
& ! [U_7247,U_7245] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7245)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7247)) = 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_7247))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7245))) ) ),
inference(miniscope,[status(thm)],[f_2080_2]) ).
cnf(f_2080_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7245)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7247)) = 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_7247))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7245))) ),
inference(clausify,[status(thm)],[f_2080_3]) ).
cnf(f_2080_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7246)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7248)) = 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_7246)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7248)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7246))) ),
inference(clausify,[status(thm)],[f_2080_3]) ).
fof(f_2081_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_2081_2,plain,
! [U_7250,U_7249] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7249)),U_7250) = 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_7249)),U_7250))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7249))) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7249)),U_7250) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7250)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7249))) ) ),
inference(variable_rename,[status(thm)],[f_2081_1]) ).
fof(f_2081_3,plain,
( ! [U_7254,U_7252] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7252)),U_7254) = 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_7252)),U_7254))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7252))) )
& ! [U_7253,U_7251] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7251)),U_7253) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7253)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7251))) ) ),
inference(miniscope,[status(thm)],[f_2081_2]) ).
cnf(f_2081_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7251)),U_7253) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7253)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7251))) ),
inference(clausify,[status(thm)],[f_2081_3]) ).
cnf(f_2081_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7252)),U_7254) = 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_7252)),U_7254))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7252))) ),
inference(clausify,[status(thm)],[f_2081_3]) ).
fof(f_2082_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_2082_2,plain,
! [U_7255] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7255) = 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_7255)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7255)) ),
inference(variable_rename,[status(thm)],[f_2082_1]) ).
cnf(f_2082_3,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7255) = 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_7255)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7255)) ),
inference(clausify,[status(thm)],[f_2082_2]) ).
fof(f_2083_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_2083_2,plain,
! [U_7256] :
( 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_7256),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_7256)) ),
inference(variable_rename,[status(thm)],[f_2083_1]) ).
cnf(f_2083_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_7256),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_7256)) ),
inference(clausify,[status(thm)],[f_2083_2]) ).
fof(f_2084_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_2084_2,plain,
! [U_7257] :
( ( 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_7257,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_7257,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_7257,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_7257,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_2084_1]) ).
fof(f_2084_3,plain,
( ! [U_7259] :
( 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_7259,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_7259,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_7258] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7258,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_7258,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
inference(miniscope,[status(thm)],[f_2084_2]) ).
cnf(f_2084_4,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_7258,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_7258,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
inference(clausify,[status(thm)],[f_2084_3]) ).
cnf(f_2084_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_7259,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_7259,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_2084_3]) ).
fof(f_2085_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_2085_2,plain,
! [U_7260] :
( 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_7260),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_7260)) ),
inference(variable_rename,[status(thm)],[f_2085_1]) ).
cnf(f_2085_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_7260),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_7260)) ),
inference(clausify,[status(thm)],[f_2085_2]) ).
fof(f_2086_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_2086_2,plain,
! [U_7262,U_7261] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7261),hAPP(c_Int_Onumber__class_Onumber__of(U_7261),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_7262)) = c_Groups_Oone__class_Oone(U_7261)
| ~ class_Int_Onumber__ring(U_7261) ),
inference(variable_rename,[status(thm)],[f_2086_1]) ).
cnf(f_2086_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7261),hAPP(c_Int_Onumber__class_Onumber__of(U_7261),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_7262)) = c_Groups_Oone__class_Oone(U_7261)
| ~ class_Int_Onumber__ring(U_7261) ),
inference(clausify,[status(thm)],[f_2086_2]) ).
fof(f_2087_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_2087_2,plain,
! [U_7263] :
( ( ( ( hAPP(c_Code__Numeral_Oint__of,U_7263) = 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_7263),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_7263,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_7263) = hAPP(hAPP(c_Groups_Otimes__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_7263),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_7263,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_7263 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ( hAPP(c_Code__Numeral_Oint__of,U_7263) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_7263 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(variable_rename,[status(thm)],[f_2087_1]) ).
fof(f_2087_3,plain,
( ! [U_7265] :
( ( ( hAPP(c_Code__Numeral_Oint__of,U_7265) = 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_7265),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_7265,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_7265) = hAPP(hAPP(c_Groups_Otimes__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_7265),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_7265,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_7265 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ! [U_7264] :
( hAPP(c_Code__Numeral_Oint__of,U_7264) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_7264 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(miniscope,[status(thm)],[f_2087_2]) ).
cnf(f_2087_4,plain,
( hAPP(c_Code__Numeral_Oint__of,U_7264) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_7264 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_2087_3]) ).
cnf(f_2087_5,plain,
( hAPP(c_Code__Numeral_Oint__of,U_7265) = hAPP(hAPP(c_Groups_Otimes__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_7265),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_7265,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_7265 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_2087_3]) ).
cnf(f_2087_6,plain,
( hAPP(c_Code__Numeral_Oint__of,U_7265) = 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_7265),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_7265,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_7265 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_2087_3]) ).
fof(f_2088_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_2088_2,plain,
! [U_7267,U_7266] : c_Int_Onat__aux(U_7266,U_7267) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7266)),U_7267),
inference(variable_rename,[status(thm)],[f_2088_1]) ).
cnf(f_2088_3,plain,
c_Int_Onat__aux(U_7266,U_7267) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7266)),U_7267),
inference(clausify,[status(thm)],[f_2088_2]) ).
fof(f_2089_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_2089_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_2089_1]) ).
fof(f_2090_1,plain,
! [V_P_2,V_d_2] :
( ( ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
| ! [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_d_2))) ) )
& ( ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_d_2))) )
| ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ) )
| ? [B_x,B_k] :
( ( ~ hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2)))) )
| ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2))))
& hBOOL(hAPP(V_P_2,B_x)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) ),
inference(fof_nnf,[status(thm)],[fact_periodic__finite__ex]) ).
fof(f_2090_2,plain,
! [U_7275,U_7274] :
( ( ( ? [U_7273] : hBOOL(hAPP(U_7275,U_7273))
| ! [U_7272] :
( ~ hBOOL(hAPP(U_7275,U_7272))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7272),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7274))) ) )
& ( ? [U_7271] :
( hBOOL(hAPP(U_7275,U_7271))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7271),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7274))) )
| ! [U_7270] : ~ hBOOL(hAPP(U_7275,U_7270)) ) )
| ? [U_7269,U_7268] :
( ( ~ hBOOL(hAPP(U_7275,U_7269))
& hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7268),U_7274)))) )
| ( ~ hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7268),U_7274))))
& hBOOL(hAPP(U_7275,U_7269)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7274)) ),
inference(variable_rename,[status(thm)],[f_2090_1]) ).
fof(f_2090_3,plain,
! [U_7275,U_7274] :
( ( ( ? [U_7273] : hBOOL(hAPP(U_7275,U_7273))
| ! [U_7272] :
( ~ hBOOL(hAPP(U_7275,U_7272))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7272),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7274))) ) )
& ( ? [U_7271] :
( hBOOL(hAPP(U_7275,U_7271))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7271),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7274))) )
| ! [U_7270] : ~ hBOOL(hAPP(U_7275,U_7270)) ) )
| ? [U_7279] :
( ? [U_7277] : hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7279),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7277),U_7274))))
& ~ hBOOL(hAPP(U_7275,U_7279)) )
| ? [U_7278] :
( ? [U_7276] : ~ hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7278),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7276),U_7274))))
& hBOOL(hAPP(U_7275,U_7278)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7274)) ),
inference(miniscope,[status(thm)],[f_2090_2]) ).
fof(f_2090_4,plain,
! [U_7275,U_7274] :
( ( ( ? [U_7273] : hBOOL(hAPP(U_7275,U_7273))
| ! [U_7272] :
( ~ hBOOL(hAPP(U_7275,U_7272))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7272),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7274))) ) )
& ( ? [U_7271] :
( hBOOL(hAPP(U_7275,U_7271))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7271),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7274))) )
| ! [U_7270] : ~ hBOOL(hAPP(U_7275,U_7270)) ) )
| ? [U_7279] :
( ? [U_7277] : hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7279),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7277),U_7274))))
& ~ hBOOL(hAPP(U_7275,U_7279)) )
| ( ? [U_7276] : ~ hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK156(U_7275,U_7274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7276),U_7274))))
& hBOOL(hAPP(U_7275,sK156(U_7275,U_7274))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7274)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK156]),skolemize(U_7278,sK156(U_7275,U_7274))],[f_2090_3]) ).
fof(f_2090_5,plain,
! [U_7275,U_7274] :
( ( ( ? [U_7273] : hBOOL(hAPP(U_7275,U_7273))
| ! [U_7272] :
( ~ hBOOL(hAPP(U_7275,U_7272))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7272),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7274))) ) )
& ( ? [U_7271] :
( hBOOL(hAPP(U_7275,U_7271))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7271),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7274))) )
| ! [U_7270] : ~ hBOOL(hAPP(U_7275,U_7270)) ) )
| ? [U_7279] :
( ? [U_7277] : hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7279),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7277),U_7274))))
& ~ hBOOL(hAPP(U_7275,U_7279)) )
| ( ~ hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK156(U_7275,U_7274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK157(U_7275,U_7274)),U_7274))))
& hBOOL(hAPP(U_7275,sK156(U_7275,U_7274))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7274)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK157]),skolemize(U_7276,sK157(U_7275,U_7274))],[f_2090_4]) ).
fof(f_2090_6,plain,
! [U_7275,U_7274] :
( ( ( ? [U_7273] : hBOOL(hAPP(U_7275,U_7273))
| ! [U_7272] :
( ~ hBOOL(hAPP(U_7275,U_7272))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7272),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7274))) ) )
& ( ? [U_7271] :
( hBOOL(hAPP(U_7275,U_7271))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7271),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7274))) )
| ! [U_7270] : ~ hBOOL(hAPP(U_7275,U_7270)) ) )
| ( ? [U_7277] : hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK158(U_7275,U_7274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7277),U_7274))))
& ~ hBOOL(hAPP(U_7275,sK158(U_7275,U_7274))) )
| ( ~ hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK156(U_7275,U_7274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK157(U_7275,U_7274)),U_7274))))
& hBOOL(hAPP(U_7275,sK156(U_7275,U_7274))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7274)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK158]),skolemize(U_7279,sK158(U_7275,U_7274))],[f_2090_5]) ).
fof(f_2090_7,plain,
! [U_7275,U_7274] :
( ( ( ? [U_7273] : hBOOL(hAPP(U_7275,U_7273))
| ! [U_7272] :
( ~ hBOOL(hAPP(U_7275,U_7272))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7272),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7274))) ) )
& ( ? [U_7271] :
( hBOOL(hAPP(U_7275,U_7271))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7271),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7274))) )
| ! [U_7270] : ~ hBOOL(hAPP(U_7275,U_7270)) ) )
| ( hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK158(U_7275,U_7274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK159(U_7275,U_7274)),U_7274))))
& ~ hBOOL(hAPP(U_7275,sK158(U_7275,U_7274))) )
| ( ~ hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK156(U_7275,U_7274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK157(U_7275,U_7274)),U_7274))))
& hBOOL(hAPP(U_7275,sK156(U_7275,U_7274))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7274)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK159]),skolemize(U_7277,sK159(U_7275,U_7274))],[f_2090_6]) ).
fof(f_2090_8,plain,
! [U_7275,U_7274] :
( ( ( ? [U_7273] : hBOOL(hAPP(U_7275,U_7273))
| ! [U_7272] :
( ~ hBOOL(hAPP(U_7275,U_7272))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7272),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7274))) ) )
& ( ( hBOOL(hAPP(U_7275,sK160(U_7275,U_7274)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK160(U_7275,U_7274)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7274))) )
| ! [U_7270] : ~ hBOOL(hAPP(U_7275,U_7270)) ) )
| ( hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK158(U_7275,U_7274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK159(U_7275,U_7274)),U_7274))))
& ~ hBOOL(hAPP(U_7275,sK158(U_7275,U_7274))) )
| ( ~ hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK156(U_7275,U_7274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK157(U_7275,U_7274)),U_7274))))
& hBOOL(hAPP(U_7275,sK156(U_7275,U_7274))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7274)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK160]),skolemize(U_7271,sK160(U_7275,U_7274))],[f_2090_7]) ).
fof(f_2090_9,plain,
! [U_7275,U_7274] :
( ( ( hBOOL(hAPP(U_7275,sK161(U_7275,U_7274)))
| ! [U_7272] :
( ~ hBOOL(hAPP(U_7275,U_7272))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7272),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7274))) ) )
& ( ( hBOOL(hAPP(U_7275,sK160(U_7275,U_7274)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK160(U_7275,U_7274)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7274))) )
| ! [U_7270] : ~ hBOOL(hAPP(U_7275,U_7270)) ) )
| ( hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK158(U_7275,U_7274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK159(U_7275,U_7274)),U_7274))))
& ~ hBOOL(hAPP(U_7275,sK158(U_7275,U_7274))) )
| ( ~ hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK156(U_7275,U_7274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK157(U_7275,U_7274)),U_7274))))
& hBOOL(hAPP(U_7275,sK156(U_7275,U_7274))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7274)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK161]),skolemize(U_7273,sK161(U_7275,U_7274))],[f_2090_8]) ).
cnf(f_2090_10,plain,
( ~ hBOOL(hAPP(U_7275,sK158(U_7275,U_7274)))
| hBOOL(hAPP(U_7275,sK156(U_7275,U_7274)))
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK160(U_7275,U_7274)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7274)))
| ~ hBOOL(hAPP(U_7275,U_7270))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7274)) ),
inference(clausify,[status(thm)],[f_2090_9]) ).
cnf(f_2090_11,plain,
( hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK158(U_7275,U_7274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK159(U_7275,U_7274)),U_7274))))
| hBOOL(hAPP(U_7275,sK156(U_7275,U_7274)))
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK160(U_7275,U_7274)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7274)))
| ~ hBOOL(hAPP(U_7275,U_7270))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7274)) ),
inference(clausify,[status(thm)],[f_2090_9]) ).
cnf(f_2090_12,plain,
( ~ hBOOL(hAPP(U_7275,sK158(U_7275,U_7274)))
| hBOOL(hAPP(U_7275,sK156(U_7275,U_7274)))
| hBOOL(hAPP(U_7275,sK160(U_7275,U_7274)))
| ~ hBOOL(hAPP(U_7275,U_7270))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7274)) ),
inference(clausify,[status(thm)],[f_2090_9]) ).
cnf(f_2090_13,plain,
( hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK158(U_7275,U_7274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK159(U_7275,U_7274)),U_7274))))
| hBOOL(hAPP(U_7275,sK156(U_7275,U_7274)))
| hBOOL(hAPP(U_7275,sK160(U_7275,U_7274)))
| ~ hBOOL(hAPP(U_7275,U_7270))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7274)) ),
inference(clausify,[status(thm)],[f_2090_9]) ).
cnf(f_2090_14,plain,
( ~ hBOOL(hAPP(U_7275,sK158(U_7275,U_7274)))
| ~ hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK156(U_7275,U_7274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK157(U_7275,U_7274)),U_7274))))
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK160(U_7275,U_7274)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7274)))
| ~ hBOOL(hAPP(U_7275,U_7270))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7274)) ),
inference(clausify,[status(thm)],[f_2090_9]) ).
cnf(f_2090_15,plain,
( hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK158(U_7275,U_7274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK159(U_7275,U_7274)),U_7274))))
| ~ hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK156(U_7275,U_7274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK157(U_7275,U_7274)),U_7274))))
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK160(U_7275,U_7274)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7274)))
| ~ hBOOL(hAPP(U_7275,U_7270))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7274)) ),
inference(clausify,[status(thm)],[f_2090_9]) ).
cnf(f_2090_16,plain,
( ~ hBOOL(hAPP(U_7275,sK158(U_7275,U_7274)))
| ~ hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK156(U_7275,U_7274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK157(U_7275,U_7274)),U_7274))))
| hBOOL(hAPP(U_7275,sK160(U_7275,U_7274)))
| ~ hBOOL(hAPP(U_7275,U_7270))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7274)) ),
inference(clausify,[status(thm)],[f_2090_9]) ).
cnf(f_2090_17,plain,
( hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK158(U_7275,U_7274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK159(U_7275,U_7274)),U_7274))))
| ~ hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK156(U_7275,U_7274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK157(U_7275,U_7274)),U_7274))))
| hBOOL(hAPP(U_7275,sK160(U_7275,U_7274)))
| ~ hBOOL(hAPP(U_7275,U_7270))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7274)) ),
inference(clausify,[status(thm)],[f_2090_9]) ).
cnf(f_2090_18,plain,
( ~ hBOOL(hAPP(U_7275,sK158(U_7275,U_7274)))
| hBOOL(hAPP(U_7275,sK156(U_7275,U_7274)))
| hBOOL(hAPP(U_7275,sK161(U_7275,U_7274)))
| ~ hBOOL(hAPP(U_7275,U_7272))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7272),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7274)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7274)) ),
inference(clausify,[status(thm)],[f_2090_9]) ).
cnf(f_2090_19,plain,
( hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK158(U_7275,U_7274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK159(U_7275,U_7274)),U_7274))))
| hBOOL(hAPP(U_7275,sK156(U_7275,U_7274)))
| hBOOL(hAPP(U_7275,sK161(U_7275,U_7274)))
| ~ hBOOL(hAPP(U_7275,U_7272))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7272),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7274)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7274)) ),
inference(clausify,[status(thm)],[f_2090_9]) ).
cnf(f_2090_20,plain,
( ~ hBOOL(hAPP(U_7275,sK158(U_7275,U_7274)))
| ~ hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK156(U_7275,U_7274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK157(U_7275,U_7274)),U_7274))))
| hBOOL(hAPP(U_7275,sK161(U_7275,U_7274)))
| ~ hBOOL(hAPP(U_7275,U_7272))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7272),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7274)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7274)) ),
inference(clausify,[status(thm)],[f_2090_9]) ).
cnf(f_2090_21,plain,
( hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK158(U_7275,U_7274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK159(U_7275,U_7274)),U_7274))))
| ~ hBOOL(hAPP(U_7275,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK156(U_7275,U_7274)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK157(U_7275,U_7274)),U_7274))))
| hBOOL(hAPP(U_7275,sK161(U_7275,U_7274)))
| ~ hBOOL(hAPP(U_7275,U_7272))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7272),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_7274)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7274)) ),
inference(clausify,[status(thm)],[f_2090_9]) ).
fof(f_2091_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_2091_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_2091_1]) ).
fof(f_2092_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_2092_2,plain,
! [U_7281,U_7280] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7280),U_7281) = 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_7280)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7281)))
| ~ c_Nat__Transfer_Onat__set(U_7281)
| ~ c_Nat__Transfer_Onat__set(U_7280) ),
inference(variable_rename,[status(thm)],[f_2092_1]) ).
cnf(f_2092_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7280),U_7281) = 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_7280)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7281)))
| ~ c_Nat__Transfer_Onat__set(U_7281)
| ~ c_Nat__Transfer_Onat__set(U_7280) ),
inference(clausify,[status(thm)],[f_2092_2]) ).
fof(f_2093_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_2093_2,plain,
! [U_7283,U_7282] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7282),U_7283) = 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_7282)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7283)))
| ~ c_Nat__Transfer_Onat__set(U_7283)
| ~ c_Nat__Transfer_Onat__set(U_7282) ),
inference(variable_rename,[status(thm)],[f_2093_1]) ).
cnf(f_2093_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7282),U_7283) = 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_7282)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7283)))
| ~ c_Nat__Transfer_Onat__set(U_7283)
| ~ c_Nat__Transfer_Onat__set(U_7282) ),
inference(clausify,[status(thm)],[f_2093_2]) ).
fof(f_2094_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_2094_2,plain,
! [U_7284] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(U_7284)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(U_7284)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_2094_1]) ).
cnf(f_2094_3,plain,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(U_7284)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(U_7284)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_2094_2]) ).
fof(f_2095_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_2095_2,plain,
! [U_7286,U_7285] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7285),U_7286))
| ~ 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_7285)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7286))) )
& ( 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_7285)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7286)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7285),U_7286)) ) )
| ~ c_Nat__Transfer_Onat__set(U_7286)
| ~ c_Nat__Transfer_Onat__set(U_7285) ),
inference(variable_rename,[status(thm)],[f_2095_1]) ).
cnf(f_2095_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_7285)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7286)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7285),U_7286))
| ~ c_Nat__Transfer_Onat__set(U_7286)
| ~ c_Nat__Transfer_Onat__set(U_7285) ),
inference(clausify,[status(thm)],[f_2095_2]) ).
cnf(f_2095_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7285),U_7286))
| ~ 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_7285)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7286)))
| ~ c_Nat__Transfer_Onat__set(U_7286)
| ~ c_Nat__Transfer_Onat__set(U_7285) ),
inference(clausify,[status(thm)],[f_2095_2]) ).
fof(f_2096_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_2096_2,plain,
! [U_7288,U_7287] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7287),U_7288))
| ~ 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_7287)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7288))) )
& ( 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_7287)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7288)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7287),U_7288)) ) )
| ~ c_Nat__Transfer_Onat__set(U_7288)
| ~ c_Nat__Transfer_Onat__set(U_7287) ),
inference(variable_rename,[status(thm)],[f_2096_1]) ).
cnf(f_2096_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_7287)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7288)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7287),U_7288))
| ~ c_Nat__Transfer_Onat__set(U_7288)
| ~ c_Nat__Transfer_Onat__set(U_7287) ),
inference(clausify,[status(thm)],[f_2096_2]) ).
cnf(f_2096_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7287),U_7288))
| ~ 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_7287)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7288)))
| ~ c_Nat__Transfer_Onat__set(U_7288)
| ~ c_Nat__Transfer_Onat__set(U_7287) ),
inference(clausify,[status(thm)],[f_2096_2]) ).
fof(f_2097_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_2097_2,plain,
! [U_7290,U_7289] :
( ( c_Code__Numeral_OSuc__code__numeral(U_7289) = c_Code__Numeral_OSuc__code__numeral(U_7290)
| U_7289 != U_7290 )
& ( U_7289 = U_7290
| c_Code__Numeral_OSuc__code__numeral(U_7289) != c_Code__Numeral_OSuc__code__numeral(U_7290) ) ),
inference(variable_rename,[status(thm)],[f_2097_1]) ).
fof(f_2097_3,plain,
( ! [U_7294,U_7292] :
( c_Code__Numeral_OSuc__code__numeral(U_7292) = c_Code__Numeral_OSuc__code__numeral(U_7294)
| U_7292 != U_7294 )
& ! [U_7293,U_7291] :
( U_7291 = U_7293
| c_Code__Numeral_OSuc__code__numeral(U_7291) != c_Code__Numeral_OSuc__code__numeral(U_7293) ) ),
inference(miniscope,[status(thm)],[f_2097_2]) ).
cnf(f_2097_4,plain,
( U_7291 = U_7293
| c_Code__Numeral_OSuc__code__numeral(U_7291) != c_Code__Numeral_OSuc__code__numeral(U_7293) ),
inference(clausify,[status(thm)],[f_2097_3]) ).
cnf(f_2097_5,plain,
( c_Code__Numeral_OSuc__code__numeral(U_7292) = c_Code__Numeral_OSuc__code__numeral(U_7294)
| U_7292 != U_7294 ),
inference(clausify,[status(thm)],[f_2097_3]) ).
fof(f_2098_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_2098_2,plain,
! [U_7295] : c_Code__Numeral_OSuc__code__numeral(U_7295) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(variable_rename,[status(thm)],[f_2098_1]) ).
cnf(f_2098_3,plain,
c_Code__Numeral_OSuc__code__numeral(U_7295) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_2098_2]) ).
fof(f_2099_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_2099_2,plain,
! [U_7296] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(U_7296),
inference(variable_rename,[status(thm)],[f_2099_1]) ).
cnf(f_2099_3,plain,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(U_7296),
inference(clausify,[status(thm)],[f_2099_2]) ).
fof(f_2100_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_2100_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_2100_1]) ).
fof(f_2101_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_2101_2,plain,
! [U_7298,U_7297] :
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7297),U_7298))
| ~ c_Nat__Transfer_Onat__set(U_7298)
| ~ c_Nat__Transfer_Onat__set(U_7297) ),
inference(variable_rename,[status(thm)],[f_2101_1]) ).
cnf(f_2101_3,plain,
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7297),U_7298))
| ~ c_Nat__Transfer_Onat__set(U_7298)
| ~ c_Nat__Transfer_Onat__set(U_7297) ),
inference(clausify,[status(thm)],[f_2101_2]) ).
fof(f_2102_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_2102_2,plain,
! [U_7300,U_7299] :
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7299),U_7300))
| ~ c_Nat__Transfer_Onat__set(U_7300)
| ~ c_Nat__Transfer_Onat__set(U_7299) ),
inference(variable_rename,[status(thm)],[f_2102_1]) ).
cnf(f_2102_3,plain,
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7299),U_7300))
| ~ c_Nat__Transfer_Onat__set(U_7300)
| ~ c_Nat__Transfer_Onat__set(U_7299) ),
inference(clausify,[status(thm)],[f_2102_2]) ).
fof(f_2103_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_2103_2,plain,
! [U_7303] :
( ( c_Nat__Transfer_Onat__set(U_7303)
| ? [U_7302] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7302))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7302),U_7303)) ) )
& ( ! [U_7301] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7301))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7301),U_7303)) )
| ~ c_Nat__Transfer_Onat__set(U_7303) ) ),
inference(variable_rename,[status(thm)],[f_2103_1]) ).
fof(f_2103_3,plain,
( ! [U_7305] :
( c_Nat__Transfer_Onat__set(U_7305)
| ? [U_7302] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7302))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7302),U_7305)) ) )
& ! [U_7304] :
( ! [U_7301] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7301))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7301),U_7304)) )
| ~ c_Nat__Transfer_Onat__set(U_7304) ) ),
inference(miniscope,[status(thm)],[f_2103_2]) ).
fof(f_2103_4,plain,
( ! [U_7305] :
( c_Nat__Transfer_Onat__set(U_7305)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK162(U_7305)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK162(U_7305)),U_7305)) ) )
& ! [U_7304] :
( ! [U_7301] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7301))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7301),U_7304)) )
| ~ c_Nat__Transfer_Onat__set(U_7304) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK162]),skolemize(U_7302,sK162(U_7305))],[f_2103_3]) ).
cnf(f_2103_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7301))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7301),U_7304))
| ~ c_Nat__Transfer_Onat__set(U_7304) ),
inference(clausify,[status(thm)],[f_2103_4]) ).
cnf(f_2103_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK162(U_7305)),U_7305))
| c_Nat__Transfer_Onat__set(U_7305) ),
inference(clausify,[status(thm)],[f_2103_4]) ).
cnf(f_2103_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK162(U_7305)))
| c_Nat__Transfer_Onat__set(U_7305) ),
inference(clausify,[status(thm)],[f_2103_4]) ).
fof(f_2104_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_2104_2,plain,
! [U_7306] : 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_7306)),
inference(variable_rename,[status(thm)],[f_2104_1]) ).
cnf(f_2104_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_7306)),
inference(clausify,[status(thm)],[f_2104_2]) ).
fof(f_2105_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_2105_2,plain,
! [U_7308,U_7307] :
( ( ( U_7307 = U_7308
| hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7307) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7308) )
& ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7307) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7308)
| U_7307 != U_7308 ) )
| ~ c_Nat__Transfer_Onat__set(U_7308)
| ~ c_Nat__Transfer_Onat__set(U_7307) ),
inference(variable_rename,[status(thm)],[f_2105_1]) ).
cnf(f_2105_3,plain,
( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7307) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7308)
| U_7307 != U_7308
| ~ c_Nat__Transfer_Onat__set(U_7308)
| ~ c_Nat__Transfer_Onat__set(U_7307) ),
inference(clausify,[status(thm)],[f_2105_2]) ).
cnf(f_2105_4,plain,
( U_7307 = U_7308
| hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7307) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7308)
| ~ c_Nat__Transfer_Onat__set(U_7308)
| ~ c_Nat__Transfer_Onat__set(U_7307) ),
inference(clausify,[status(thm)],[f_2105_2]) ).
fof(f_2106_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_2106_2,plain,
! [U_7310,U_7309] :
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7309,U_7310))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7309)) ),
inference(variable_rename,[status(thm)],[f_2106_1]) ).
cnf(f_2106_3,plain,
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7309,U_7310))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7309)) ),
inference(clausify,[status(thm)],[f_2106_2]) ).
fof(f_2107_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_2107_2,plain,
! [U_7312,U_7311] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7312))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7312),U_7311))
| ~ c_Nat__Transfer_Onat__set(U_7311) ),
inference(variable_rename,[status(thm)],[f_2107_1]) ).
cnf(f_2107_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7312))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7312),U_7311))
| ~ c_Nat__Transfer_Onat__set(U_7311) ),
inference(clausify,[status(thm)],[f_2107_2]) ).
fof(f_2108_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_2108_2,plain,
! [U_7313] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_7313)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = U_7313,
inference(variable_rename,[status(thm)],[f_2108_1]) ).
cnf(f_2108_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_7313)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = U_7313,
inference(clausify,[status(thm)],[f_2108_2]) ).
fof(f_2109_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_2109_2,plain,
! [U_7314] :
( 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_7314)) = U_7314
| ~ c_Nat__Transfer_Onat__set(U_7314) ),
inference(variable_rename,[status(thm)],[f_2109_1]) ).
cnf(f_2109_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_7314)) = U_7314
| ~ c_Nat__Transfer_Onat__set(U_7314) ),
inference(clausify,[status(thm)],[f_2109_2]) ).
fof(f_2110_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_2110_2,plain,
! [U_7315] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_7315))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7315))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7315)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_7315)) ) )
| ~ c_Nat__Transfer_Onat__set(U_7315) ),
inference(variable_rename,[status(thm)],[f_2110_1]) ).
cnf(f_2110_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_7315)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_7315))
| ~ c_Nat__Transfer_Onat__set(U_7315) ),
inference(clausify,[status(thm)],[f_2110_2]) ).
cnf(f_2110_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_7315))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7315)))
| ~ c_Nat__Transfer_Onat__set(U_7315) ),
inference(clausify,[status(thm)],[f_2110_2]) ).
fof(f_2111_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_2111_2,plain,
! [U_7316] :
( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_7316) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7316))
| ~ c_Nat__Transfer_Onat__set(U_7316) ),
inference(variable_rename,[status(thm)],[f_2111_1]) ).
cnf(f_2111_3,plain,
( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_7316) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7316))
| ~ c_Nat__Transfer_Onat__set(U_7316) ),
inference(clausify,[status(thm)],[f_2111_2]) ).
fof(f_2112_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_2112_2,plain,
! [U_7317] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_7317)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),U_7317)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_2112_1]) ).
cnf(f_2112_3,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_7317)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),U_7317)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_2112_2]) ).
fof(f_2113_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_2113_2,plain,
! [U_7319,U_7318] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7318),U_7319))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_7318)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7319))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_7318)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7319)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7318),U_7319)) ) )
| ~ c_Nat__Transfer_Onat__set(U_7319)
| ~ c_Nat__Transfer_Ois__nat(U_7318) ),
inference(variable_rename,[status(thm)],[f_2113_1]) ).
cnf(f_2113_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_7318)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7319)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7318),U_7319))
| ~ c_Nat__Transfer_Onat__set(U_7319)
| ~ c_Nat__Transfer_Ois__nat(U_7318) ),
inference(clausify,[status(thm)],[f_2113_2]) ).
cnf(f_2113_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7318),U_7319))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_7318)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7319)))
| ~ c_Nat__Transfer_Onat__set(U_7319)
| ~ c_Nat__Transfer_Ois__nat(U_7318) ),
inference(clausify,[status(thm)],[f_2113_2]) ).
fof(f_2114_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_2114_2,plain,
! [U_7325,U_7324,U_7323,U_7322,U_7321] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7321),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7322,U_7321),U_7324),U_7323)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7321),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7321),hAPP(c_Finite__Set_Ocard(U_7322),U_7323))),U_7325)))
| ? [U_7320] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7321),hAPP(U_7324,U_7320)),U_7325))
& hBOOL(hAPP(hAPP(c_member(U_7322),U_7320),U_7323)) )
| ~ class_Rings_Osemiring__1(U_7321)
| ~ class_Groups_Oordered__ab__semigroup__add(U_7321) ),
inference(variable_rename,[status(thm)],[f_2114_1]) ).
fof(f_2114_3,plain,
! [U_7325,U_7324,U_7323,U_7322,U_7321] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7321),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7322,U_7321),U_7324),U_7323)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7321),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7321),hAPP(c_Finite__Set_Ocard(U_7322),U_7323))),U_7325)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7321),hAPP(U_7324,sK163(U_7325,U_7324,U_7323,U_7322,U_7321))),U_7325))
& hBOOL(hAPP(hAPP(c_member(U_7322),sK163(U_7325,U_7324,U_7323,U_7322,U_7321)),U_7323)) )
| ~ class_Rings_Osemiring__1(U_7321)
| ~ class_Groups_Oordered__ab__semigroup__add(U_7321) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK163]),skolemize(U_7320,sK163(U_7325,U_7324,U_7323,U_7322,U_7321))],[f_2114_2]) ).
cnf(f_2114_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_7322),sK163(U_7325,U_7324,U_7323,U_7322,U_7321)),U_7323))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7321),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7322,U_7321),U_7324),U_7323)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7321),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7321),hAPP(c_Finite__Set_Ocard(U_7322),U_7323))),U_7325)))
| ~ class_Rings_Osemiring__1(U_7321)
| ~ class_Groups_Oordered__ab__semigroup__add(U_7321) ),
inference(clausify,[status(thm)],[f_2114_3]) ).
cnf(f_2114_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7321),hAPP(U_7324,sK163(U_7325,U_7324,U_7323,U_7322,U_7321))),U_7325))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7321),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7322,U_7321),U_7324),U_7323)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7321),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7321),hAPP(c_Finite__Set_Ocard(U_7322),U_7323))),U_7325)))
| ~ class_Rings_Osemiring__1(U_7321)
| ~ class_Groups_Oordered__ab__semigroup__add(U_7321) ),
inference(clausify,[status(thm)],[f_2114_3]) ).
fof(f_2115_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_2115_2,plain,
! [U_7327,U_7326] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7326,U_7327) = 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_7326),hAPP(c_Int_Onat,U_7327)))
| ~ c_Nat__Transfer_Ois__nat(U_7327)
| ~ c_Nat__Transfer_Ois__nat(U_7326) ),
inference(variable_rename,[status(thm)],[f_2115_1]) ).
cnf(f_2115_3,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7326,U_7327) = 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_7326),hAPP(c_Int_Onat,U_7327)))
| ~ c_Nat__Transfer_Ois__nat(U_7327)
| ~ c_Nat__Transfer_Ois__nat(U_7326) ),
inference(clausify,[status(thm)],[f_2115_2]) ).
fof(f_2116_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_2116_2,plain,
! [U_7329,U_7328] :
( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_7328),U_7329) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7328),hAPP(c_Int_Onat,U_7329))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7329),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hAPP(c_Int_Oring__1__class_Oof__int(U_7328),U_7329) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7328),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7328),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7329))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7329),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
| ~ class_Rings_Oring__1(U_7328) ),
inference(variable_rename,[status(thm)],[f_2116_1]) ).
cnf(f_2116_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7328),U_7329) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7328),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7328),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7329))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7329),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Rings_Oring__1(U_7328) ),
inference(clausify,[status(thm)],[f_2116_2]) ).
cnf(f_2116_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7328),U_7329) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7328),hAPP(c_Int_Onat,U_7329))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7329),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Rings_Oring__1(U_7328) ),
inference(clausify,[status(thm)],[f_2116_2]) ).
fof(f_2117_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_2117_2,plain,
! [U_7332,U_7331,U_7330] :
( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_7330),U_7331) = hAPP(c_Int_Oring__1__class_Oof__int(U_7330),U_7332)
| U_7331 != U_7332 )
& ( U_7331 = U_7332
| hAPP(c_Int_Oring__1__class_Oof__int(U_7330),U_7331) != hAPP(c_Int_Oring__1__class_Oof__int(U_7330),U_7332) ) )
| ~ class_Int_Oring__char__0(U_7330) ),
inference(variable_rename,[status(thm)],[f_2117_1]) ).
cnf(f_2117_3,plain,
( U_7331 = U_7332
| hAPP(c_Int_Oring__1__class_Oof__int(U_7330),U_7331) != hAPP(c_Int_Oring__1__class_Oof__int(U_7330),U_7332)
| ~ class_Int_Oring__char__0(U_7330) ),
inference(clausify,[status(thm)],[f_2117_2]) ).
cnf(f_2117_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7330),U_7331) = hAPP(c_Int_Oring__1__class_Oof__int(U_7330),U_7332)
| U_7331 != U_7332
| ~ class_Int_Oring__char__0(U_7330) ),
inference(clausify,[status(thm)],[f_2117_2]) ).
fof(f_2118_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_2118_2,plain,
! [U_7334,U_7333] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_7333),U_7334) = hAPP(c_Int_Oring__1__class_Oof__int(U_7333),U_7334)
| ~ class_Int_Onumber__ring(U_7333) ),
inference(variable_rename,[status(thm)],[f_2118_1]) ).
cnf(f_2118_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_7333),U_7334) = hAPP(c_Int_Oring__1__class_Oof__int(U_7333),U_7334)
| ~ class_Int_Onumber__ring(U_7333) ),
inference(clausify,[status(thm)],[f_2118_2]) ).
fof(f_2119_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_2119_2,plain,
! [U_7335] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7335) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_7335),
inference(variable_rename,[status(thm)],[f_2119_1]) ).
cnf(f_2119_3,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7335) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_7335),
inference(clausify,[status(thm)],[f_2119_2]) ).
fof(f_2120_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_2120_2,plain,
! [U_7336] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7336)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7336),
inference(variable_rename,[status(thm)],[f_2120_1]) ).
cnf(f_2120_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_7336)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7336),
inference(clausify,[status(thm)],[f_2120_2]) ).
fof(f_2121_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_2121_2,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_2121_1]) ).
fof(f_2122_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_2122_2,plain,
! [U_7338,U_7337] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7337),U_7338))
| ~ c_Nat__Transfer_Ois__nat(U_7338)
| ~ c_Nat__Transfer_Ois__nat(U_7337) ),
inference(variable_rename,[status(thm)],[f_2122_1]) ).
cnf(f_2122_3,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7337),U_7338))
| ~ c_Nat__Transfer_Ois__nat(U_7338)
| ~ c_Nat__Transfer_Ois__nat(U_7337) ),
inference(clausify,[status(thm)],[f_2122_2]) ).
fof(f_2123_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_2123_2,plain,
! [U_7339] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7339)),
inference(variable_rename,[status(thm)],[f_2123_1]) ).
cnf(f_2123_3,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7339)),
inference(clausify,[status(thm)],[f_2123_2]) ).
fof(f_2124_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_2124_2,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_2124_1]) ).
fof(f_2125_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_2125_2,plain,
! [U_7341,U_7340] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7340),U_7341))
| ~ c_Nat__Transfer_Ois__nat(U_7341)
| ~ c_Nat__Transfer_Ois__nat(U_7340) ),
inference(variable_rename,[status(thm)],[f_2125_1]) ).
cnf(f_2125_3,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7340),U_7341))
| ~ c_Nat__Transfer_Ois__nat(U_7341)
| ~ c_Nat__Transfer_Ois__nat(U_7340) ),
inference(clausify,[status(thm)],[f_2125_2]) ).
fof(f_2126_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_2126_2,plain,
! [U_7343,U_7342] :
( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7342,U_7343))
| ~ c_Nat__Transfer_Ois__nat(U_7343)
| ~ c_Nat__Transfer_Ois__nat(U_7342) ),
inference(variable_rename,[status(thm)],[f_2126_1]) ).
cnf(f_2126_3,plain,
( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7342,U_7343))
| ~ c_Nat__Transfer_Ois__nat(U_7343)
| ~ c_Nat__Transfer_Ois__nat(U_7342) ),
inference(clausify,[status(thm)],[f_2126_2]) ).
fof(f_2127_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_2127_2,plain,
! [U_7345,U_7344] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7344),U_7345))
| ~ c_Nat__Transfer_Ois__nat(U_7345)
| ~ c_Nat__Transfer_Ois__nat(U_7344) ),
inference(variable_rename,[status(thm)],[f_2127_1]) ).
cnf(f_2127_3,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7344),U_7345))
| ~ c_Nat__Transfer_Ois__nat(U_7345)
| ~ c_Nat__Transfer_Ois__nat(U_7344) ),
inference(clausify,[status(thm)],[f_2127_2]) ).
fof(f_2128_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_2128_2,plain,
! [U_7347,U_7346] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7346),U_7347))
| ~ c_Nat__Transfer_Ois__nat(U_7346) ),
inference(variable_rename,[status(thm)],[f_2128_1]) ).
cnf(f_2128_3,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7346),U_7347))
| ~ c_Nat__Transfer_Ois__nat(U_7346) ),
inference(clausify,[status(thm)],[f_2128_2]) ).
fof(f_2129_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_2129_2,plain,
! [U_7349,U_7348] :
( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_7348,U_7349))
| ~ c_Nat__Transfer_Ois__nat(U_7349)
| ~ c_Nat__Transfer_Ois__nat(U_7348) ),
inference(variable_rename,[status(thm)],[f_2129_1]) ).
cnf(f_2129_3,plain,
( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_7348,U_7349))
| ~ c_Nat__Transfer_Ois__nat(U_7349)
| ~ c_Nat__Transfer_Ois__nat(U_7348) ),
inference(clausify,[status(thm)],[f_2129_2]) ).
fof(f_2130_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_2130_2,plain,
! [U_7351,U_7350] :
( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_7350),U_7351) = c_Groups_Ozero__class_Ozero(U_7350)
| U_7351 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( U_7351 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(c_Int_Oring__1__class_Oof__int(U_7350),U_7351) != c_Groups_Ozero__class_Ozero(U_7350) ) )
| ~ class_Int_Oring__char__0(U_7350) ),
inference(variable_rename,[status(thm)],[f_2130_1]) ).
cnf(f_2130_3,plain,
( U_7351 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(c_Int_Oring__1__class_Oof__int(U_7350),U_7351) != c_Groups_Ozero__class_Ozero(U_7350)
| ~ class_Int_Oring__char__0(U_7350) ),
inference(clausify,[status(thm)],[f_2130_2]) ).
cnf(f_2130_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7350),U_7351) = c_Groups_Ozero__class_Ozero(U_7350)
| U_7351 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ class_Int_Oring__char__0(U_7350) ),
inference(clausify,[status(thm)],[f_2130_2]) ).
fof(f_2131_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_2131_2,plain,
! [U_7353,U_7352] :
( ( ( c_Groups_Ozero__class_Ozero(U_7352) = hAPP(c_Int_Oring__1__class_Oof__int(U_7352),U_7353)
| U_7353 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( U_7353 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Groups_Ozero__class_Ozero(U_7352) != hAPP(c_Int_Oring__1__class_Oof__int(U_7352),U_7353) ) )
| ~ class_Int_Oring__char__0(U_7352) ),
inference(variable_rename,[status(thm)],[f_2131_1]) ).
cnf(f_2131_3,plain,
( U_7353 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Groups_Ozero__class_Ozero(U_7352) != hAPP(c_Int_Oring__1__class_Oof__int(U_7352),U_7353)
| ~ class_Int_Oring__char__0(U_7352) ),
inference(clausify,[status(thm)],[f_2131_2]) ).
cnf(f_2131_4,plain,
( c_Groups_Ozero__class_Ozero(U_7352) = hAPP(c_Int_Oring__1__class_Oof__int(U_7352),U_7353)
| U_7353 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ class_Int_Oring__char__0(U_7352) ),
inference(clausify,[status(thm)],[f_2131_2]) ).
fof(f_2132_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_2132_2,plain,
! [U_7354] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7354),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_7354)
| ~ class_Rings_Oring__1(U_7354) ),
inference(variable_rename,[status(thm)],[f_2132_1]) ).
cnf(f_2132_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7354),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_7354)
| ~ class_Rings_Oring__1(U_7354) ),
inference(clausify,[status(thm)],[f_2132_2]) ).
fof(f_2133_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_2133_2,plain,
! [U_7357,U_7356,U_7355] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7355),hAPP(c_Int_Oring__1__class_Oof__int(U_7355),U_7356)),hAPP(c_Int_Oring__1__class_Oof__int(U_7355),U_7357)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7356),U_7357)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7356),U_7357))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7355),hAPP(c_Int_Oring__1__class_Oof__int(U_7355),U_7356)),hAPP(c_Int_Oring__1__class_Oof__int(U_7355),U_7357))) ) )
| ~ class_Rings_Olinordered__idom(U_7355) ),
inference(variable_rename,[status(thm)],[f_2133_1]) ).
cnf(f_2133_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7356),U_7357))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7355),hAPP(c_Int_Oring__1__class_Oof__int(U_7355),U_7356)),hAPP(c_Int_Oring__1__class_Oof__int(U_7355),U_7357)))
| ~ class_Rings_Olinordered__idom(U_7355) ),
inference(clausify,[status(thm)],[f_2133_2]) ).
cnf(f_2133_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7355),hAPP(c_Int_Oring__1__class_Oof__int(U_7355),U_7356)),hAPP(c_Int_Oring__1__class_Oof__int(U_7355),U_7357)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7356),U_7357))
| ~ class_Rings_Olinordered__idom(U_7355) ),
inference(clausify,[status(thm)],[f_2133_2]) ).
fof(f_2134_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_2134_2,plain,
! [U_7360,U_7359,U_7358] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7358),hAPP(c_Int_Oring__1__class_Oof__int(U_7358),U_7359)),hAPP(c_Int_Oring__1__class_Oof__int(U_7358),U_7360)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7359),U_7360)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7359),U_7360))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7358),hAPP(c_Int_Oring__1__class_Oof__int(U_7358),U_7359)),hAPP(c_Int_Oring__1__class_Oof__int(U_7358),U_7360))) ) )
| ~ class_Rings_Olinordered__idom(U_7358) ),
inference(variable_rename,[status(thm)],[f_2134_1]) ).
cnf(f_2134_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7359),U_7360))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7358),hAPP(c_Int_Oring__1__class_Oof__int(U_7358),U_7359)),hAPP(c_Int_Oring__1__class_Oof__int(U_7358),U_7360)))
| ~ class_Rings_Olinordered__idom(U_7358) ),
inference(clausify,[status(thm)],[f_2134_2]) ).
cnf(f_2134_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7358),hAPP(c_Int_Oring__1__class_Oof__int(U_7358),U_7359)),hAPP(c_Int_Oring__1__class_Oof__int(U_7358),U_7360)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7359),U_7360))
| ~ class_Rings_Olinordered__idom(U_7358) ),
inference(clausify,[status(thm)],[f_2134_2]) ).
fof(f_2135_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_2135_2,plain,
! [U_7363,U_7362,U_7361] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7361),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7362),U_7363)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7361),hAPP(c_Int_Oring__1__class_Oof__int(U_7361),U_7362)),hAPP(c_Int_Oring__1__class_Oof__int(U_7361),U_7363))
| ~ class_Rings_Oring__1(U_7361) ),
inference(variable_rename,[status(thm)],[f_2135_1]) ).
cnf(f_2135_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7361),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7362),U_7363)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7361),hAPP(c_Int_Oring__1__class_Oof__int(U_7361),U_7362)),hAPP(c_Int_Oring__1__class_Oof__int(U_7361),U_7363))
| ~ class_Rings_Oring__1(U_7361) ),
inference(clausify,[status(thm)],[f_2135_2]) ).
fof(f_2136_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_2136_2,plain,
! [U_7365,U_7364] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7364),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7365)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7364),U_7365)
| ~ class_Int_Onumber__ring(U_7364) ),
inference(variable_rename,[status(thm)],[f_2136_1]) ).
cnf(f_2136_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7364),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7365)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7364),U_7365)
| ~ class_Int_Onumber__ring(U_7364) ),
inference(clausify,[status(thm)],[f_2136_2]) ).
fof(f_2137_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_2137_2,plain,
! [U_7368,U_7367,U_7366] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7366),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7367),U_7368)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7366),hAPP(c_Int_Oring__1__class_Oof__int(U_7366),U_7367)),hAPP(c_Int_Oring__1__class_Oof__int(U_7366),U_7368))
| ~ class_Rings_Oring__1(U_7366) ),
inference(variable_rename,[status(thm)],[f_2137_1]) ).
cnf(f_2137_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7366),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7367),U_7368)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7366),hAPP(c_Int_Oring__1__class_Oof__int(U_7366),U_7367)),hAPP(c_Int_Oring__1__class_Oof__int(U_7366),U_7368))
| ~ class_Rings_Oring__1(U_7366) ),
inference(clausify,[status(thm)],[f_2137_2]) ).
fof(f_2138_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_2138_2,plain,
! [U_7369] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7369),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_7369)
| ~ class_Rings_Oring__1(U_7369) ),
inference(variable_rename,[status(thm)],[f_2138_1]) ).
cnf(f_2138_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7369),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_7369)
| ~ class_Rings_Oring__1(U_7369) ),
inference(clausify,[status(thm)],[f_2138_2]) ).
fof(f_2139_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_2139_2,plain,
! [U_7372,U_7371,U_7370] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7370),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7371),U_7372)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7370),hAPP(c_Int_Oring__1__class_Oof__int(U_7370),U_7371)),hAPP(c_Int_Oring__1__class_Oof__int(U_7370),U_7372))
| ~ class_Rings_Oring__1(U_7370) ),
inference(variable_rename,[status(thm)],[f_2139_1]) ).
cnf(f_2139_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7370),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7371),U_7372)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7370),hAPP(c_Int_Oring__1__class_Oof__int(U_7370),U_7371)),hAPP(c_Int_Oring__1__class_Oof__int(U_7370),U_7372))
| ~ class_Rings_Oring__1(U_7370) ),
inference(clausify,[status(thm)],[f_2139_2]) ).
fof(f_2140_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_2140_2,plain,
! [U_7374,U_7373] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7373),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7374)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7373),U_7374)
| ~ class_Rings_Oring__1(U_7373) ),
inference(variable_rename,[status(thm)],[f_2140_1]) ).
cnf(f_2140_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7373),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7374)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7373),U_7374)
| ~ class_Rings_Oring__1(U_7373) ),
inference(clausify,[status(thm)],[f_2140_2]) ).
fof(f_2141_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_2141_2,plain,
! [U_7376,U_7375] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7375),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7376)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7375),hAPP(c_Int_Oring__1__class_Oof__int(U_7375),U_7376))
| ~ class_Rings_Oring__1(U_7375) ),
inference(variable_rename,[status(thm)],[f_2141_1]) ).
cnf(f_2141_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7375),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7376)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7375),hAPP(c_Int_Oring__1__class_Oof__int(U_7375),U_7376))
| ~ class_Rings_Oring__1(U_7375) ),
inference(clausify,[status(thm)],[f_2141_2]) ).
fof(f_2142_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_2142_2,plain,
! [U_7378,U_7377] :
( hBOOL(hAPP(hAPP(c_member(U_7377),hAPP(c_Int_Oring__1__class_Oof__int(U_7377),U_7378)),c_Int_Oring__1__class_OInts(U_7377)))
| ~ class_Rings_Oring__1(U_7377) ),
inference(variable_rename,[status(thm)],[f_2142_1]) ).
cnf(f_2142_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_7377),hAPP(c_Int_Oring__1__class_Oof__int(U_7377),U_7378)),c_Int_Oring__1__class_OInts(U_7377)))
| ~ class_Rings_Oring__1(U_7377) ),
inference(clausify,[status(thm)],[f_2142_2]) ).
fof(f_2143_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_2143_2,plain,
! [U_7381,U_7380,U_7379] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7379),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7380),U_7381)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7379),hAPP(c_Int_Oring__1__class_Oof__int(U_7379),U_7380)),U_7381)
| ~ class_Rings_Oring__1(U_7379) ),
inference(variable_rename,[status(thm)],[f_2143_1]) ).
cnf(f_2143_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7379),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7380),U_7381)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7379),hAPP(c_Int_Oring__1__class_Oof__int(U_7379),U_7380)),U_7381)
| ~ class_Rings_Oring__1(U_7379) ),
inference(clausify,[status(thm)],[f_2143_2]) ).
fof(f_2144_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_2144_2,plain,
! [U_7382] :
( ( c_Nat__Transfer_Ois__nat(U_7382)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7382)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7382))
| ~ c_Nat__Transfer_Ois__nat(U_7382) ) ),
inference(variable_rename,[status(thm)],[f_2144_1]) ).
fof(f_2144_3,plain,
( ! [U_7384] :
( c_Nat__Transfer_Ois__nat(U_7384)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7384)) )
& ! [U_7383] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7383))
| ~ c_Nat__Transfer_Ois__nat(U_7383) ) ),
inference(miniscope,[status(thm)],[f_2144_2]) ).
cnf(f_2144_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7383))
| ~ c_Nat__Transfer_Ois__nat(U_7383) ),
inference(clausify,[status(thm)],[f_2144_3]) ).
cnf(f_2144_5,plain,
( c_Nat__Transfer_Ois__nat(U_7384)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7384)) ),
inference(clausify,[status(thm)],[f_2144_3]) ).
fof(f_2145_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_2145_2,plain,
! [U_7386,U_7385] :
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7385,U_7386))
| ~ c_Nat__Transfer_Ois__nat(U_7385) ),
inference(variable_rename,[status(thm)],[f_2145_1]) ).
cnf(f_2145_3,plain,
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7385,U_7386))
| ~ c_Nat__Transfer_Ois__nat(U_7385) ),
inference(clausify,[status(thm)],[f_2145_2]) ).
fof(f_2146_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_2146_2,plain,
! [U_7388,U_7387] :
( c_Nat__Transfer_Ois__nat(U_7388)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7388),U_7387))
| ~ c_Nat__Transfer_Onat__set(U_7387) ),
inference(variable_rename,[status(thm)],[f_2146_1]) ).
cnf(f_2146_3,plain,
( c_Nat__Transfer_Ois__nat(U_7388)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_7388),U_7387))
| ~ c_Nat__Transfer_Onat__set(U_7387) ),
inference(clausify,[status(thm)],[f_2146_2]) ).
fof(f_2147_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_2147_2,plain,
! [U_7389] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_7389),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7389),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_7389) ),
inference(variable_rename,[status(thm)],[f_2147_1]) ).
cnf(f_2147_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_7389),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7389),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_7389) ),
inference(clausify,[status(thm)],[f_2147_2]) ).
fof(f_2148_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_2148_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_2148_1]) ).
fof(f_2149_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_2149_2,plain,
! [U_7391,U_7390] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7390),hAPP(c_Int_Oring__1__class_Oof__int(U_7390),U_7391)),c_Groups_Ozero__class_Ozero(U_7390)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7391),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7391),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7390),hAPP(c_Int_Oring__1__class_Oof__int(U_7390),U_7391)),c_Groups_Ozero__class_Ozero(U_7390))) ) )
| ~ class_Rings_Olinordered__idom(U_7390) ),
inference(variable_rename,[status(thm)],[f_2149_1]) ).
cnf(f_2149_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7391),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7390),hAPP(c_Int_Oring__1__class_Oof__int(U_7390),U_7391)),c_Groups_Ozero__class_Ozero(U_7390)))
| ~ class_Rings_Olinordered__idom(U_7390) ),
inference(clausify,[status(thm)],[f_2149_2]) ).
cnf(f_2149_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7390),hAPP(c_Int_Oring__1__class_Oof__int(U_7390),U_7391)),c_Groups_Ozero__class_Ozero(U_7390)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7391),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Rings_Olinordered__idom(U_7390) ),
inference(clausify,[status(thm)],[f_2149_2]) ).
fof(f_2150_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_2150_2,plain,
! [U_7393,U_7392] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7392),c_Groups_Ozero__class_Ozero(U_7392)),hAPP(c_Int_Oring__1__class_Oof__int(U_7392),U_7393)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7393)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7393))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7392),c_Groups_Ozero__class_Ozero(U_7392)),hAPP(c_Int_Oring__1__class_Oof__int(U_7392),U_7393))) ) )
| ~ class_Rings_Olinordered__idom(U_7392) ),
inference(variable_rename,[status(thm)],[f_2150_1]) ).
cnf(f_2150_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7393))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7392),c_Groups_Ozero__class_Ozero(U_7392)),hAPP(c_Int_Oring__1__class_Oof__int(U_7392),U_7393)))
| ~ class_Rings_Olinordered__idom(U_7392) ),
inference(clausify,[status(thm)],[f_2150_2]) ).
cnf(f_2150_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7392),c_Groups_Ozero__class_Ozero(U_7392)),hAPP(c_Int_Oring__1__class_Oof__int(U_7392),U_7393)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7393))
| ~ class_Rings_Olinordered__idom(U_7392) ),
inference(clausify,[status(thm)],[f_2150_2]) ).
fof(f_2151_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_2151_2,plain,
! [U_7395,U_7394] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7394),c_Groups_Ozero__class_Ozero(U_7394)),hAPP(c_Int_Oring__1__class_Oof__int(U_7394),U_7395)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7395)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7395))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7394),c_Groups_Ozero__class_Ozero(U_7394)),hAPP(c_Int_Oring__1__class_Oof__int(U_7394),U_7395))) ) )
| ~ class_Rings_Olinordered__idom(U_7394) ),
inference(variable_rename,[status(thm)],[f_2151_1]) ).
cnf(f_2151_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7395))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7394),c_Groups_Ozero__class_Ozero(U_7394)),hAPP(c_Int_Oring__1__class_Oof__int(U_7394),U_7395)))
| ~ class_Rings_Olinordered__idom(U_7394) ),
inference(clausify,[status(thm)],[f_2151_2]) ).
cnf(f_2151_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7394),c_Groups_Ozero__class_Ozero(U_7394)),hAPP(c_Int_Oring__1__class_Oof__int(U_7394),U_7395)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7395))
| ~ class_Rings_Olinordered__idom(U_7394) ),
inference(clausify,[status(thm)],[f_2151_2]) ).
fof(f_2152_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_2152_2,plain,
! [U_7397,U_7396] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7396),hAPP(c_Int_Oring__1__class_Oof__int(U_7396),U_7397)),c_Groups_Ozero__class_Ozero(U_7396)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7397),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7397),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7396),hAPP(c_Int_Oring__1__class_Oof__int(U_7396),U_7397)),c_Groups_Ozero__class_Ozero(U_7396))) ) )
| ~ class_Rings_Olinordered__idom(U_7396) ),
inference(variable_rename,[status(thm)],[f_2152_1]) ).
cnf(f_2152_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7397),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7396),hAPP(c_Int_Oring__1__class_Oof__int(U_7396),U_7397)),c_Groups_Ozero__class_Ozero(U_7396)))
| ~ class_Rings_Olinordered__idom(U_7396) ),
inference(clausify,[status(thm)],[f_2152_2]) ).
cnf(f_2152_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7396),hAPP(c_Int_Oring__1__class_Oof__int(U_7396),U_7397)),c_Groups_Ozero__class_Ozero(U_7396)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7397),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Rings_Olinordered__idom(U_7396) ),
inference(clausify,[status(thm)],[f_2152_2]) ).
fof(f_2153_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_2153_2,plain,
! [U_7399,U_7398] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7398),hAPP(c_Int_Onat,U_7399)) = hAPP(c_Int_Oring__1__class_Oof__int(U_7398),U_7399)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7399))
| ~ class_Rings_Oring__1(U_7398) ),
inference(variable_rename,[status(thm)],[f_2153_1]) ).
cnf(f_2153_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7398),hAPP(c_Int_Onat,U_7399)) = hAPP(c_Int_Oring__1__class_Oof__int(U_7398),U_7399)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7399))
| ~ class_Rings_Oring__1(U_7398) ),
inference(clausify,[status(thm)],[f_2153_2]) ).
fof(f_2154_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_2154_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_2154_1]) ).
fof(f_2155_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_2155_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_2155_1]) ).
fof(f_2156_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_2156_2,plain,
! [U_7404,U_7403,U_7402,U_7401,U_7400] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7400,U_7401,c_Groups_Otimes__class_Otimes(U_7400)),U_7404),c_Groups_Oone__class_Oone(U_7400)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7401,tc_HOL_Obool)),U_7402),U_7403)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7400),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7400,U_7401,c_Groups_Otimes__class_Otimes(U_7400)),U_7404),c_Groups_Oone__class_Oone(U_7400)),U_7402)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7400,U_7401,c_Groups_Otimes__class_Otimes(U_7400)),U_7404),c_Groups_Oone__class_Oone(U_7400)),U_7403))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7401,tc_HOL_Obool)),U_7402),U_7403) != c_Orderings_Obot__class_Obot(tc_fun(U_7401,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7401),U_7403))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7401),U_7402))
| ~ class_Groups_Ocomm__monoid__mult(U_7400) ),
inference(variable_rename,[status(thm)],[f_2156_1]) ).
cnf(f_2156_3,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7400,U_7401,c_Groups_Otimes__class_Otimes(U_7400)),U_7404),c_Groups_Oone__class_Oone(U_7400)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7401,tc_HOL_Obool)),U_7402),U_7403)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7400),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7400,U_7401,c_Groups_Otimes__class_Otimes(U_7400)),U_7404),c_Groups_Oone__class_Oone(U_7400)),U_7402)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7400,U_7401,c_Groups_Otimes__class_Otimes(U_7400)),U_7404),c_Groups_Oone__class_Oone(U_7400)),U_7403))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7401,tc_HOL_Obool)),U_7402),U_7403) != c_Orderings_Obot__class_Obot(tc_fun(U_7401,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7401),U_7403))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7401),U_7402))
| ~ class_Groups_Ocomm__monoid__mult(U_7400) ),
inference(clausify,[status(thm)],[f_2156_2]) ).
fof(f_2157_1,plain,
! [V_k_2,V_P_2,V_d_2] :
( ! [B_x] :
( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2))))
| ~ hBOOL(hAPP(V_P_2,B_x)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2)))
& hBOOL(hAPP(V_P_2,B_x)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) ),
inference(fof_nnf,[status(thm)],[fact_decr__mult__lemma]) ).
fof(f_2157_2,plain,
! [U_7409,U_7408,U_7407] :
( ! [U_7406] :
( hBOOL(hAPP(U_7408,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7409),U_7407))))
| ~ hBOOL(hAPP(U_7408,U_7406)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7409))
| ? [U_7405] :
( ~ hBOOL(hAPP(U_7408,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7405),U_7407)))
& hBOOL(hAPP(U_7408,U_7405)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7407)) ),
inference(variable_rename,[status(thm)],[f_2157_1]) ).
fof(f_2157_3,plain,
! [U_7409,U_7408,U_7407] :
( ! [U_7406] :
( hBOOL(hAPP(U_7408,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7409),U_7407))))
| ~ hBOOL(hAPP(U_7408,U_7406)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7409))
| ( ~ hBOOL(hAPP(U_7408,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK164(U_7409,U_7408,U_7407)),U_7407)))
& hBOOL(hAPP(U_7408,sK164(U_7409,U_7408,U_7407))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7407)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK164]),skolemize(U_7405,sK164(U_7409,U_7408,U_7407))],[f_2157_2]) ).
cnf(f_2157_4,plain,
( hBOOL(hAPP(U_7408,sK164(U_7409,U_7408,U_7407)))
| hBOOL(hAPP(U_7408,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7409),U_7407))))
| ~ hBOOL(hAPP(U_7408,U_7406))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7409))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7407)) ),
inference(clausify,[status(thm)],[f_2157_3]) ).
cnf(f_2157_5,plain,
( ~ hBOOL(hAPP(U_7408,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK164(U_7409,U_7408,U_7407)),U_7407)))
| hBOOL(hAPP(U_7408,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7409),U_7407))))
| ~ hBOOL(hAPP(U_7408,U_7406))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7409))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7407)) ),
inference(clausify,[status(thm)],[f_2157_3]) ).
fof(f_2158_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_2158_2,plain,
! [U_7411] :
( ? [U_7410] : U_7411 = 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_7410)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7411),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_2158_1]) ).
fof(f_2158_3,plain,
! [U_7411] :
( U_7411 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK165(U_7411))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7411),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK165]),skolemize(U_7410,sK165(U_7411))],[f_2158_2]) ).
cnf(f_2158_4,plain,
( U_7411 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK165(U_7411))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7411),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2158_3]) ).
fof(f_2159_1,plain,
! [V_k_2,V_P_2,V_d_2] :
( ! [B_x] :
( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2))))
| ~ hBOOL(hAPP(V_P_2,B_x)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2)))
& hBOOL(hAPP(V_P_2,B_x)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) ),
inference(fof_nnf,[status(thm)],[fact_incr__mult__lemma]) ).
fof(f_2159_2,plain,
! [U_7416,U_7415,U_7414] :
( ! [U_7413] :
( hBOOL(hAPP(U_7415,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7413),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7416),U_7414))))
| ~ hBOOL(hAPP(U_7415,U_7413)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7416))
| ? [U_7412] :
( ~ hBOOL(hAPP(U_7415,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7412),U_7414)))
& hBOOL(hAPP(U_7415,U_7412)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7414)) ),
inference(variable_rename,[status(thm)],[f_2159_1]) ).
fof(f_2159_3,plain,
! [U_7416,U_7415,U_7414] :
( ! [U_7413] :
( hBOOL(hAPP(U_7415,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7413),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7416),U_7414))))
| ~ hBOOL(hAPP(U_7415,U_7413)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7416))
| ( ~ hBOOL(hAPP(U_7415,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK166(U_7416,U_7415,U_7414)),U_7414)))
& hBOOL(hAPP(U_7415,sK166(U_7416,U_7415,U_7414))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7414)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK166]),skolemize(U_7412,sK166(U_7416,U_7415,U_7414))],[f_2159_2]) ).
cnf(f_2159_4,plain,
( hBOOL(hAPP(U_7415,sK166(U_7416,U_7415,U_7414)))
| hBOOL(hAPP(U_7415,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7413),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7416),U_7414))))
| ~ hBOOL(hAPP(U_7415,U_7413))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7416))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7414)) ),
inference(clausify,[status(thm)],[f_2159_3]) ).
cnf(f_2159_5,plain,
( ~ hBOOL(hAPP(U_7415,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK166(U_7416,U_7415,U_7414)),U_7414)))
| hBOOL(hAPP(U_7415,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7413),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7416),U_7414))))
| ~ hBOOL(hAPP(U_7415,U_7413))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7416))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7414)) ),
inference(clausify,[status(thm)],[f_2159_3]) ).
fof(f_2160_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_2160_2,plain,
! [U_7422,U_7421,U_7420] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7422),hAPP(c_Finite__Set_Ocard(tc_fun(U_7420,tc_HOL_Obool)),U_7421)) = hAPP(c_Finite__Set_Ocard(U_7420),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7420,tc_HOL_Obool),U_7421))
| ? [U_7419] :
( ? [U_7418] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7420,tc_HOL_Obool)),U_7419),U_7418) != c_Orderings_Obot__class_Obot(tc_fun(U_7420,tc_HOL_Obool))
& U_7419 != U_7418
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_7420,tc_HOL_Obool)),U_7418),U_7421)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_7420,tc_HOL_Obool)),U_7419),U_7421)) )
| ? [U_7417] :
( hAPP(c_Finite__Set_Ocard(U_7420),U_7417) != U_7422
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_7420,tc_HOL_Obool)),U_7417),U_7421)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7420),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7420,tc_HOL_Obool),U_7421)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_7420,tc_HOL_Obool)),U_7421)) ),
inference(variable_rename,[status(thm)],[f_2160_1]) ).
fof(f_2160_3,plain,
! [U_7422,U_7421,U_7420] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7422),hAPP(c_Finite__Set_Ocard(tc_fun(U_7420,tc_HOL_Obool)),U_7421)) = hAPP(c_Finite__Set_Ocard(U_7420),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7420,tc_HOL_Obool),U_7421))
| ? [U_7419] :
( ? [U_7418] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7420,tc_HOL_Obool)),U_7419),U_7418) != c_Orderings_Obot__class_Obot(tc_fun(U_7420,tc_HOL_Obool))
& U_7419 != U_7418
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_7420,tc_HOL_Obool)),U_7418),U_7421)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_7420,tc_HOL_Obool)),U_7419),U_7421)) )
| ( hAPP(c_Finite__Set_Ocard(U_7420),sK167(U_7422,U_7421,U_7420)) != U_7422
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_7420,tc_HOL_Obool)),sK167(U_7422,U_7421,U_7420)),U_7421)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7420),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7420,tc_HOL_Obool),U_7421)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_7420,tc_HOL_Obool)),U_7421)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK167]),skolemize(U_7417,sK167(U_7422,U_7421,U_7420))],[f_2160_2]) ).
fof(f_2160_4,plain,
! [U_7422,U_7421,U_7420] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7422),hAPP(c_Finite__Set_Ocard(tc_fun(U_7420,tc_HOL_Obool)),U_7421)) = hAPP(c_Finite__Set_Ocard(U_7420),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7420,tc_HOL_Obool),U_7421))
| ( ? [U_7418] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7420,tc_HOL_Obool)),sK168(U_7422,U_7421,U_7420)),U_7418) != c_Orderings_Obot__class_Obot(tc_fun(U_7420,tc_HOL_Obool))
& sK168(U_7422,U_7421,U_7420) != U_7418
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_7420,tc_HOL_Obool)),U_7418),U_7421)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_7420,tc_HOL_Obool)),sK168(U_7422,U_7421,U_7420)),U_7421)) )
| ( hAPP(c_Finite__Set_Ocard(U_7420),sK167(U_7422,U_7421,U_7420)) != U_7422
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_7420,tc_HOL_Obool)),sK167(U_7422,U_7421,U_7420)),U_7421)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7420),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7420,tc_HOL_Obool),U_7421)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_7420,tc_HOL_Obool)),U_7421)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK168]),skolemize(U_7419,sK168(U_7422,U_7421,U_7420))],[f_2160_3]) ).
fof(f_2160_5,plain,
! [U_7422,U_7421,U_7420] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7422),hAPP(c_Finite__Set_Ocard(tc_fun(U_7420,tc_HOL_Obool)),U_7421)) = hAPP(c_Finite__Set_Ocard(U_7420),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7420,tc_HOL_Obool),U_7421))
| ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7420,tc_HOL_Obool)),sK168(U_7422,U_7421,U_7420)),sK169(U_7422,U_7421,U_7420)) != c_Orderings_Obot__class_Obot(tc_fun(U_7420,tc_HOL_Obool))
& sK168(U_7422,U_7421,U_7420) != sK169(U_7422,U_7421,U_7420)
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_7420,tc_HOL_Obool)),sK169(U_7422,U_7421,U_7420)),U_7421))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_7420,tc_HOL_Obool)),sK168(U_7422,U_7421,U_7420)),U_7421)) )
| ( hAPP(c_Finite__Set_Ocard(U_7420),sK167(U_7422,U_7421,U_7420)) != U_7422
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_7420,tc_HOL_Obool)),sK167(U_7422,U_7421,U_7420)),U_7421)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7420),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7420,tc_HOL_Obool),U_7421)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_7420,tc_HOL_Obool)),U_7421)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK169]),skolemize(U_7418,sK169(U_7422,U_7421,U_7420))],[f_2160_4]) ).
cnf(f_2160_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_7420,tc_HOL_Obool)),sK168(U_7422,U_7421,U_7420)),U_7421))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7422),hAPP(c_Finite__Set_Ocard(tc_fun(U_7420,tc_HOL_Obool)),U_7421)) = hAPP(c_Finite__Set_Ocard(U_7420),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7420,tc_HOL_Obool),U_7421))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_7420,tc_HOL_Obool)),sK167(U_7422,U_7421,U_7420)),U_7421))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7420),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7420,tc_HOL_Obool),U_7421)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_7420,tc_HOL_Obool)),U_7421)) ),
inference(clausify,[status(thm)],[f_2160_5]) ).
cnf(f_2160_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_7420,tc_HOL_Obool)),sK169(U_7422,U_7421,U_7420)),U_7421))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7422),hAPP(c_Finite__Set_Ocard(tc_fun(U_7420,tc_HOL_Obool)),U_7421)) = hAPP(c_Finite__Set_Ocard(U_7420),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7420,tc_HOL_Obool),U_7421))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_7420,tc_HOL_Obool)),sK167(U_7422,U_7421,U_7420)),U_7421))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7420),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7420,tc_HOL_Obool),U_7421)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_7420,tc_HOL_Obool)),U_7421)) ),
inference(clausify,[status(thm)],[f_2160_5]) ).
cnf(f_2160_8,plain,
( sK168(U_7422,U_7421,U_7420) != sK169(U_7422,U_7421,U_7420)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7422),hAPP(c_Finite__Set_Ocard(tc_fun(U_7420,tc_HOL_Obool)),U_7421)) = hAPP(c_Finite__Set_Ocard(U_7420),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7420,tc_HOL_Obool),U_7421))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_7420,tc_HOL_Obool)),sK167(U_7422,U_7421,U_7420)),U_7421))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7420),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7420,tc_HOL_Obool),U_7421)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_7420,tc_HOL_Obool)),U_7421)) ),
inference(clausify,[status(thm)],[f_2160_5]) ).
cnf(f_2160_9,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7420,tc_HOL_Obool)),sK168(U_7422,U_7421,U_7420)),sK169(U_7422,U_7421,U_7420)) != c_Orderings_Obot__class_Obot(tc_fun(U_7420,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7422),hAPP(c_Finite__Set_Ocard(tc_fun(U_7420,tc_HOL_Obool)),U_7421)) = hAPP(c_Finite__Set_Ocard(U_7420),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7420,tc_HOL_Obool),U_7421))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_7420,tc_HOL_Obool)),sK167(U_7422,U_7421,U_7420)),U_7421))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7420),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7420,tc_HOL_Obool),U_7421)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_7420,tc_HOL_Obool)),U_7421)) ),
inference(clausify,[status(thm)],[f_2160_5]) ).
cnf(f_2160_10,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_7420,tc_HOL_Obool)),sK168(U_7422,U_7421,U_7420)),U_7421))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7422),hAPP(c_Finite__Set_Ocard(tc_fun(U_7420,tc_HOL_Obool)),U_7421)) = hAPP(c_Finite__Set_Ocard(U_7420),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7420,tc_HOL_Obool),U_7421))
| hAPP(c_Finite__Set_Ocard(U_7420),sK167(U_7422,U_7421,U_7420)) != U_7422
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7420),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7420,tc_HOL_Obool),U_7421)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_7420,tc_HOL_Obool)),U_7421)) ),
inference(clausify,[status(thm)],[f_2160_5]) ).
cnf(f_2160_11,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_7420,tc_HOL_Obool)),sK169(U_7422,U_7421,U_7420)),U_7421))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7422),hAPP(c_Finite__Set_Ocard(tc_fun(U_7420,tc_HOL_Obool)),U_7421)) = hAPP(c_Finite__Set_Ocard(U_7420),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7420,tc_HOL_Obool),U_7421))
| hAPP(c_Finite__Set_Ocard(U_7420),sK167(U_7422,U_7421,U_7420)) != U_7422
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7420),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7420,tc_HOL_Obool),U_7421)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_7420,tc_HOL_Obool)),U_7421)) ),
inference(clausify,[status(thm)],[f_2160_5]) ).
cnf(f_2160_12,plain,
( sK168(U_7422,U_7421,U_7420) != sK169(U_7422,U_7421,U_7420)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7422),hAPP(c_Finite__Set_Ocard(tc_fun(U_7420,tc_HOL_Obool)),U_7421)) = hAPP(c_Finite__Set_Ocard(U_7420),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7420,tc_HOL_Obool),U_7421))
| hAPP(c_Finite__Set_Ocard(U_7420),sK167(U_7422,U_7421,U_7420)) != U_7422
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7420),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7420,tc_HOL_Obool),U_7421)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_7420,tc_HOL_Obool)),U_7421)) ),
inference(clausify,[status(thm)],[f_2160_5]) ).
cnf(f_2160_13,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7420,tc_HOL_Obool)),sK168(U_7422,U_7421,U_7420)),sK169(U_7422,U_7421,U_7420)) != c_Orderings_Obot__class_Obot(tc_fun(U_7420,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7422),hAPP(c_Finite__Set_Ocard(tc_fun(U_7420,tc_HOL_Obool)),U_7421)) = hAPP(c_Finite__Set_Ocard(U_7420),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7420,tc_HOL_Obool),U_7421))
| hAPP(c_Finite__Set_Ocard(U_7420),sK167(U_7422,U_7421,U_7420)) != U_7422
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7420),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_7420,tc_HOL_Obool),U_7421)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_7420,tc_HOL_Obool)),U_7421)) ),
inference(clausify,[status(thm)],[f_2160_5]) ).
fof(f_2161_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_2161_2,plain,
! [U_7427,U_7426,U_7425,U_7424,U_7423] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7423,U_7424,U_7425),U_7426),U_7427),c_Orderings_Obot__class_Obot(tc_fun(U_7424,tc_HOL_Obool))) = U_7427,
inference(variable_rename,[status(thm)],[f_2161_1]) ).
cnf(f_2161_3,plain,
hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7423,U_7424,U_7425),U_7426),U_7427),c_Orderings_Obot__class_Obot(tc_fun(U_7424,tc_HOL_Obool))) = U_7427,
inference(clausify,[status(thm)],[f_2161_2]) ).
fof(f_2162_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_2162_2,plain,
! [U_7434,U_7433,U_7432,U_7431,U_7430,U_7429,U_7428] :
( hAPP(U_7433,U_7434) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7428,U_7429,U_7430),U_7432),U_7431),U_7434)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7429),U_7434))
| ~ c_Finite__Set_Ofolding__image__simple(U_7428,U_7429,U_7430,U_7431,U_7432,U_7433) ),
inference(variable_rename,[status(thm)],[f_2162_1]) ).
cnf(f_2162_3,plain,
( hAPP(U_7433,U_7434) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7428,U_7429,U_7430),U_7432),U_7431),U_7434)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7429),U_7434))
| ~ c_Finite__Set_Ofolding__image__simple(U_7428,U_7429,U_7430,U_7431,U_7432,U_7433) ),
inference(clausify,[status(thm)],[f_2162_2]) ).
fof(f_2163_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_2163_2,plain,
! [U_7440,U_7439,U_7438,U_7437,U_7436,U_7435] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7435,U_7436,c_Groups_Otimes__class_Otimes(U_7435)),U_7439),U_7440),hAPP(hAPP(c_Set_Oinsert(U_7436),U_7438),U_7437)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7435),hAPP(U_7439,U_7438)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7435,U_7436,c_Groups_Otimes__class_Otimes(U_7435)),U_7439),U_7440),U_7437))
| hBOOL(hAPP(hAPP(c_member(U_7436),U_7438),U_7437))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7436),U_7437))
| ~ class_Groups_Oab__semigroup__mult(U_7435) ),
inference(variable_rename,[status(thm)],[f_2163_1]) ).
cnf(f_2163_3,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7435,U_7436,c_Groups_Otimes__class_Otimes(U_7435)),U_7439),U_7440),hAPP(hAPP(c_Set_Oinsert(U_7436),U_7438),U_7437)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7435),hAPP(U_7439,U_7438)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7435,U_7436,c_Groups_Otimes__class_Otimes(U_7435)),U_7439),U_7440),U_7437))
| hBOOL(hAPP(hAPP(c_member(U_7436),U_7438),U_7437))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7436),U_7437))
| ~ class_Groups_Oab__semigroup__mult(U_7435) ),
inference(clausify,[status(thm)],[f_2163_2]) ).
fof(f_2164_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_2164_2,plain,
! [U_7444,U_7443,U_7442,U_7441] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7442,U_7441),U_7444),U_7443) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7441,U_7442,c_Groups_Oplus__class_Oplus(U_7441)),U_7444),c_Groups_Ozero__class_Ozero(U_7441)),U_7443)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7442),U_7443))
| ~ class_Groups_Ocomm__monoid__add(U_7441) ),
inference(variable_rename,[status(thm)],[f_2164_1]) ).
cnf(f_2164_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7442,U_7441),U_7444),U_7443) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7441,U_7442,c_Groups_Oplus__class_Oplus(U_7441)),U_7444),c_Groups_Ozero__class_Ozero(U_7441)),U_7443)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7442),U_7443))
| ~ class_Groups_Ocomm__monoid__add(U_7441) ),
inference(clausify,[status(thm)],[f_2164_2]) ).
fof(f_2165_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_2165_2,plain,
! [U_7448,U_7447,U_7446,U_7445] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7446,U_7445),U_7448),U_7447) = c_Groups_Ozero__class_Ozero(U_7445)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_7446),U_7447)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7446,U_7445),U_7448),U_7447) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7445,U_7446,c_Groups_Oplus__class_Oplus(U_7445)),U_7448),c_Groups_Ozero__class_Ozero(U_7445)),U_7447)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7446),U_7447)) ) )
| ~ class_Groups_Ocomm__monoid__add(U_7445) ),
inference(variable_rename,[status(thm)],[f_2165_1]) ).
cnf(f_2165_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7446,U_7445),U_7448),U_7447) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7445,U_7446,c_Groups_Oplus__class_Oplus(U_7445)),U_7448),c_Groups_Ozero__class_Ozero(U_7445)),U_7447)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7446),U_7447))
| ~ class_Groups_Ocomm__monoid__add(U_7445) ),
inference(clausify,[status(thm)],[f_2165_2]) ).
cnf(f_2165_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7446,U_7445),U_7448),U_7447) = c_Groups_Ozero__class_Ozero(U_7445)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_7446),U_7447))
| ~ class_Groups_Ocomm__monoid__add(U_7445) ),
inference(clausify,[status(thm)],[f_2165_2]) ).
fof(f_2166_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_2166_2,plain,
! [U_7453,U_7452,U_7451,U_7450,U_7449] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7449),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7449,U_7450,c_Groups_Otimes__class_Otimes(U_7449)),U_7453),c_Groups_Oone__class_Oone(U_7449)),U_7451)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7449,U_7450,c_Groups_Otimes__class_Otimes(U_7449)),U_7453),c_Groups_Oone__class_Oone(U_7449)),U_7452)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7449),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7449,U_7450,c_Groups_Otimes__class_Otimes(U_7449)),U_7453),c_Groups_Oone__class_Oone(U_7449)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7450,tc_HOL_Obool)),U_7451),U_7452))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7449,U_7450,c_Groups_Otimes__class_Otimes(U_7449)),U_7453),c_Groups_Oone__class_Oone(U_7449)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7450,tc_HOL_Obool)),U_7451),U_7452)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7450),U_7452))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7450),U_7451))
| ~ class_Groups_Ocomm__monoid__mult(U_7449) ),
inference(variable_rename,[status(thm)],[f_2166_1]) ).
cnf(f_2166_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7449),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7449,U_7450,c_Groups_Otimes__class_Otimes(U_7449)),U_7453),c_Groups_Oone__class_Oone(U_7449)),U_7451)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7449,U_7450,c_Groups_Otimes__class_Otimes(U_7449)),U_7453),c_Groups_Oone__class_Oone(U_7449)),U_7452)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7449),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7449,U_7450,c_Groups_Otimes__class_Otimes(U_7449)),U_7453),c_Groups_Oone__class_Oone(U_7449)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7450,tc_HOL_Obool)),U_7451),U_7452))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7449,U_7450,c_Groups_Otimes__class_Otimes(U_7449)),U_7453),c_Groups_Oone__class_Oone(U_7449)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7450,tc_HOL_Obool)),U_7451),U_7452)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7450),U_7452))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7450),U_7451))
| ~ class_Groups_Ocomm__monoid__mult(U_7449) ),
inference(clausify,[status(thm)],[f_2166_2]) ).
fof(f_2167_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_2167_2,plain,
! [U_7460,U_7459,U_7458,U_7457,U_7456,U_7455,U_7454] :
( ( ( hAPP(hAPP(U_7458,U_7460),U_7459) = U_7457
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_7455),U_7459)) )
& ( hAPP(hAPP(U_7458,U_7460),U_7459) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7454,U_7455,U_7456),U_7460),U_7457),U_7459)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7455),U_7459)) ) )
| ~ c_Big__Operators_Ocomm__monoid__big(U_7454,U_7455,U_7456,U_7457,U_7458) ),
inference(variable_rename,[status(thm)],[f_2167_1]) ).
cnf(f_2167_3,plain,
( hAPP(hAPP(U_7458,U_7460),U_7459) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7454,U_7455,U_7456),U_7460),U_7457),U_7459)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7455),U_7459))
| ~ c_Big__Operators_Ocomm__monoid__big(U_7454,U_7455,U_7456,U_7457,U_7458) ),
inference(clausify,[status(thm)],[f_2167_2]) ).
cnf(f_2167_4,plain,
( hAPP(hAPP(U_7458,U_7460),U_7459) = U_7457
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_7455),U_7459))
| ~ c_Big__Operators_Ocomm__monoid__big(U_7454,U_7455,U_7456,U_7457,U_7458) ),
inference(clausify,[status(thm)],[f_2167_2]) ).
fof(f_2168_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_2168_2,plain,
! [U_7466,U_7465,U_7464,U_7463,U_7462] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7462,U_7463,c_Groups_Otimes__class_Otimes(U_7462)),U_7466),c_Groups_Oone__class_Oone(U_7462)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7463,tc_HOL_Obool)),U_7464),U_7465)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7462),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7462,U_7463,c_Groups_Otimes__class_Otimes(U_7462)),U_7466),c_Groups_Oone__class_Oone(U_7462)),U_7464)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7462,U_7463,c_Groups_Otimes__class_Otimes(U_7462)),U_7466),c_Groups_Oone__class_Oone(U_7462)),U_7465))
| ? [U_7461] :
( hAPP(U_7466,U_7461) != c_Groups_Oone__class_Oone(U_7462)
& hBOOL(hAPP(hAPP(c_member(U_7463),U_7461),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7463,tc_HOL_Obool)),U_7464),U_7465))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7463),U_7465))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7463),U_7464))
| ~ class_Groups_Ocomm__monoid__mult(U_7462) ),
inference(variable_rename,[status(thm)],[f_2168_1]) ).
fof(f_2168_3,plain,
! [U_7466,U_7465,U_7464,U_7463,U_7462] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7462,U_7463,c_Groups_Otimes__class_Otimes(U_7462)),U_7466),c_Groups_Oone__class_Oone(U_7462)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7463,tc_HOL_Obool)),U_7464),U_7465)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7462),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7462,U_7463,c_Groups_Otimes__class_Otimes(U_7462)),U_7466),c_Groups_Oone__class_Oone(U_7462)),U_7464)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7462,U_7463,c_Groups_Otimes__class_Otimes(U_7462)),U_7466),c_Groups_Oone__class_Oone(U_7462)),U_7465))
| ( hAPP(U_7466,sK170(U_7466,U_7465,U_7464,U_7463,U_7462)) != c_Groups_Oone__class_Oone(U_7462)
& hBOOL(hAPP(hAPP(c_member(U_7463),sK170(U_7466,U_7465,U_7464,U_7463,U_7462)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7463,tc_HOL_Obool)),U_7464),U_7465))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7463),U_7465))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7463),U_7464))
| ~ class_Groups_Ocomm__monoid__mult(U_7462) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK170]),skolemize(U_7461,sK170(U_7466,U_7465,U_7464,U_7463,U_7462))],[f_2168_2]) ).
cnf(f_2168_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_7463),sK170(U_7466,U_7465,U_7464,U_7463,U_7462)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7463,tc_HOL_Obool)),U_7464),U_7465)))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7462,U_7463,c_Groups_Otimes__class_Otimes(U_7462)),U_7466),c_Groups_Oone__class_Oone(U_7462)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7463,tc_HOL_Obool)),U_7464),U_7465)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7462),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7462,U_7463,c_Groups_Otimes__class_Otimes(U_7462)),U_7466),c_Groups_Oone__class_Oone(U_7462)),U_7464)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7462,U_7463,c_Groups_Otimes__class_Otimes(U_7462)),U_7466),c_Groups_Oone__class_Oone(U_7462)),U_7465))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7463),U_7465))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7463),U_7464))
| ~ class_Groups_Ocomm__monoid__mult(U_7462) ),
inference(clausify,[status(thm)],[f_2168_3]) ).
cnf(f_2168_5,plain,
( hAPP(U_7466,sK170(U_7466,U_7465,U_7464,U_7463,U_7462)) != c_Groups_Oone__class_Oone(U_7462)
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7462,U_7463,c_Groups_Otimes__class_Otimes(U_7462)),U_7466),c_Groups_Oone__class_Oone(U_7462)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7463,tc_HOL_Obool)),U_7464),U_7465)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7462),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7462,U_7463,c_Groups_Otimes__class_Otimes(U_7462)),U_7466),c_Groups_Oone__class_Oone(U_7462)),U_7464)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_7462,U_7463,c_Groups_Otimes__class_Otimes(U_7462)),U_7466),c_Groups_Oone__class_Oone(U_7462)),U_7465))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7463),U_7465))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7463),U_7464))
| ~ class_Groups_Ocomm__monoid__mult(U_7462) ),
inference(clausify,[status(thm)],[f_2168_3]) ).
fof(f_2169_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_2169_2,plain,
! [U_7468] :
( ? [U_7467] :
( U_7468 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7467)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7467)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7468)) ),
inference(variable_rename,[status(thm)],[f_2169_1]) ).
fof(f_2169_3,plain,
! [U_7468] :
( ( U_7468 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK171(U_7468))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK171(U_7468))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7468)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK171]),skolemize(U_7467,sK171(U_7468))],[f_2169_2]) ).
cnf(f_2169_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK171(U_7468)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7468)) ),
inference(clausify,[status(thm)],[f_2169_3]) ).
cnf(f_2169_5,plain,
( U_7468 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK171(U_7468))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7468)) ),
inference(clausify,[status(thm)],[f_2169_3]) ).
fof(f_2170_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_2170_2,plain,
! [U_7472,U_7471,U_7470,U_7469] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_7469,U_7470,U_7471,c_Code__Numeral_OSuc__code__numeral(U_7472)) = hAPP(U_7471,U_7472),
inference(variable_rename,[status(thm)],[f_2170_1]) ).
cnf(f_2170_3,plain,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_7469,U_7470,U_7471,c_Code__Numeral_OSuc__code__numeral(U_7472)) = hAPP(U_7471,U_7472),
inference(clausify,[status(thm)],[f_2170_2]) ).
fof(f_2171_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_2171_2,plain,
! [U_7479,U_7478,U_7477,U_7476,U_7475,U_7474,U_7473] :
( hAPP(hAPP(U_7477,U_7479),U_7478) = U_7476
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_7474),U_7478))
| ~ c_Big__Operators_Ocomm__monoid__big(U_7473,U_7474,U_7475,U_7476,U_7477) ),
inference(variable_rename,[status(thm)],[f_2171_1]) ).
fof(f_2171_3,plain,
! [U_7479,U_7478,U_7477,U_7476,U_7475,U_7474] :
( ! [U_7473] : ~ c_Big__Operators_Ocomm__monoid__big(U_7473,U_7474,U_7475,U_7476,U_7477)
| hAPP(hAPP(U_7477,U_7479),U_7478) = U_7476
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_7474),U_7478)) ),
inference(miniscope,[status(thm)],[f_2171_2]) ).
cnf(f_2171_4,plain,
( ~ c_Big__Operators_Ocomm__monoid__big(U_7473,U_7474,U_7475,U_7476,U_7477)
| hAPP(hAPP(U_7477,U_7479),U_7478) = U_7476
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_7474),U_7478)) ),
inference(clausify,[status(thm)],[f_2171_3]) ).
fof(f_2172_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_2172_2,plain,
! [U_7482,U_7481,U_7480] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_7480,U_7481,U_7482,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_7481,
inference(variable_rename,[status(thm)],[f_2172_1]) ).
cnf(f_2172_3,plain,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_7480,U_7481,U_7482,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_7481,
inference(clausify,[status(thm)],[f_2172_2]) ).
fof(f_2173_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_2173_2,plain,
! [U_7487,U_7486,U_7485,U_7484,U_7483] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7483,U_7483,c_Groups_Otimes__class_Otimes(U_7483),U_7487,hAPP(hAPP(c_Set_Oinsert(U_7483),U_7484),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7483,tc_HOL_Obool)),U_7485),hAPP(hAPP(c_Set_Oinsert(U_7483),U_7487),c_Orderings_Obot__class_Obot(tc_fun(U_7483,tc_HOL_Obool)))))),U_7486))
| hBOOL(hAPP(hAPP(c_member(U_7483),U_7484),U_7485))
| ~ hBOOL(hAPP(hAPP(c_member(U_7483),U_7487),U_7485))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7483,U_7483,c_Groups_Otimes__class_Otimes(U_7483),U_7484,U_7485),U_7486))
| ~ class_Groups_Oab__semigroup__mult(U_7483) ),
inference(variable_rename,[status(thm)],[f_2173_1]) ).
cnf(f_2173_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7483,U_7483,c_Groups_Otimes__class_Otimes(U_7483),U_7487,hAPP(hAPP(c_Set_Oinsert(U_7483),U_7484),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7483,tc_HOL_Obool)),U_7485),hAPP(hAPP(c_Set_Oinsert(U_7483),U_7487),c_Orderings_Obot__class_Obot(tc_fun(U_7483,tc_HOL_Obool)))))),U_7486))
| hBOOL(hAPP(hAPP(c_member(U_7483),U_7484),U_7485))
| ~ hBOOL(hAPP(hAPP(c_member(U_7483),U_7487),U_7485))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7483,U_7483,c_Groups_Otimes__class_Otimes(U_7483),U_7484,U_7485),U_7486))
| ~ class_Groups_Oab__semigroup__mult(U_7483) ),
inference(clausify,[status(thm)],[f_2173_2]) ).
fof(f_2174_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_2174_2,plain,
! [U_7490,U_7489,U_7488] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7489),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7490),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_7490),U_7489))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7488))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7488)) ),
inference(variable_rename,[status(thm)],[f_2174_1]) ).
cnf(f_2174_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7489),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7490),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_7490),U_7489))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7488))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7488)) ),
inference(clausify,[status(thm)],[f_2174_2]) ).
fof(f_2175_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_2175_2,plain,
! [U_7493,U_7492,U_7491] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7492),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_7492),U_7493))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7491))),U_7493))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7491)) ),
inference(variable_rename,[status(thm)],[f_2175_1]) ).
cnf(f_2175_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7492),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_7492),U_7493))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7491))),U_7493))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7491)) ),
inference(clausify,[status(thm)],[f_2175_2]) ).
fof(f_2176_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_2176_2,plain,
! [U_7496,U_7495,U_7494] :
( hAPP(c_Finite__Set_Ofold1(U_7494,c_Groups_Otimes__class_Otimes(U_7494)),hAPP(hAPP(c_Set_Oinsert(U_7494),U_7496),U_7495)) = hAPP(hAPP(c_Finite__Set_Ofold(U_7494,U_7494,c_Groups_Otimes__class_Otimes(U_7494)),U_7496),U_7495)
| hBOOL(hAPP(hAPP(c_member(U_7494),U_7496),U_7495))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7494),U_7495))
| ~ class_Groups_Oab__semigroup__mult(U_7494) ),
inference(variable_rename,[status(thm)],[f_2176_1]) ).
cnf(f_2176_3,plain,
( hAPP(c_Finite__Set_Ofold1(U_7494,c_Groups_Otimes__class_Otimes(U_7494)),hAPP(hAPP(c_Set_Oinsert(U_7494),U_7496),U_7495)) = hAPP(hAPP(c_Finite__Set_Ofold(U_7494,U_7494,c_Groups_Otimes__class_Otimes(U_7494)),U_7496),U_7495)
| hBOOL(hAPP(hAPP(c_member(U_7494),U_7496),U_7495))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7494),U_7495))
| ~ class_Groups_Oab__semigroup__mult(U_7494) ),
inference(clausify,[status(thm)],[f_2176_2]) ).
fof(f_2177_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_2177_2,plain,
! [U_7498,U_7497] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7497),hAPP(c_Groups_Oabs__class_Oabs(U_7497),U_7498)) = hAPP(c_Groups_Oabs__class_Oabs(U_7497),U_7498)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7497) ),
inference(variable_rename,[status(thm)],[f_2177_1]) ).
cnf(f_2177_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7497),hAPP(c_Groups_Oabs__class_Oabs(U_7497),U_7498)) = hAPP(c_Groups_Oabs__class_Oabs(U_7497),U_7498)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7497) ),
inference(clausify,[status(thm)],[f_2177_2]) ).
fof(f_2178_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_2178_2,plain,
! [U_7500,U_7499] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7499),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7499),U_7500)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7499),U_7500)
| ~ class_Rings_Olinordered__idom(U_7499) ),
inference(variable_rename,[status(thm)],[f_2178_1]) ).
cnf(f_2178_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7499),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7499),U_7500)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7499),U_7500)
| ~ class_Rings_Olinordered__idom(U_7499) ),
inference(clausify,[status(thm)],[f_2178_2]) ).
fof(f_2179_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_2179_2,plain,
! [U_7503,U_7502,U_7501] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7501),hAPP(hAPP(c_Power_Opower__class_Opower(U_7501),U_7502),U_7503)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7501),hAPP(c_Groups_Oabs__class_Oabs(U_7501),U_7502)),U_7503)
| ~ class_Rings_Olinordered__idom(U_7501) ),
inference(variable_rename,[status(thm)],[f_2179_1]) ).
cnf(f_2179_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7501),hAPP(hAPP(c_Power_Opower__class_Opower(U_7501),U_7502),U_7503)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7501),hAPP(c_Groups_Oabs__class_Oabs(U_7501),U_7502)),U_7503)
| ~ class_Rings_Olinordered__idom(U_7501) ),
inference(clausify,[status(thm)],[f_2179_2]) ).
fof(f_2180_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_2180_2,plain,
! [U_7505,U_7504] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7504),hAPP(c_Groups_Ouminus__class_Ouminus(U_7504),U_7505)) = hAPP(c_Groups_Oabs__class_Oabs(U_7504),U_7505)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7504) ),
inference(variable_rename,[status(thm)],[f_2180_1]) ).
cnf(f_2180_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7504),hAPP(c_Groups_Ouminus__class_Ouminus(U_7504),U_7505)) = hAPP(c_Groups_Oabs__class_Oabs(U_7504),U_7505)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7504) ),
inference(clausify,[status(thm)],[f_2180_2]) ).
fof(f_2181_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_2181_2,plain,
! [U_7506] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7506),c_Groups_Oone__class_Oone(U_7506)) = c_Groups_Oone__class_Oone(U_7506)
| ~ class_Rings_Olinordered__idom(U_7506) ),
inference(variable_rename,[status(thm)],[f_2181_1]) ).
cnf(f_2181_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7506),c_Groups_Oone__class_Oone(U_7506)) = c_Groups_Oone__class_Oone(U_7506)
| ~ class_Rings_Olinordered__idom(U_7506) ),
inference(clausify,[status(thm)],[f_2181_2]) ).
fof(f_2182_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_2182_2,plain,
! [U_7509,U_7508,U_7507] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7507),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7507),U_7508),U_7509)) = hAPP(c_Groups_Oabs__class_Oabs(U_7507),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7507),U_7509),U_7508))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7507) ),
inference(variable_rename,[status(thm)],[f_2182_1]) ).
cnf(f_2182_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7507),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7507),U_7508),U_7509)) = hAPP(c_Groups_Oabs__class_Oabs(U_7507),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7507),U_7509),U_7508))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7507) ),
inference(clausify,[status(thm)],[f_2182_2]) ).
fof(f_2183_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_2183_2,plain,
! [U_7511,U_7510] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7510),hAPP(c_Groups_Oabs__class_Oabs(U_7510),U_7511)),hAPP(c_Groups_Oabs__class_Oabs(U_7510),U_7511)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7510),U_7511),U_7511)
| ~ class_Rings_Olinordered__idom(U_7510) ),
inference(variable_rename,[status(thm)],[f_2183_1]) ).
cnf(f_2183_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7510),hAPP(c_Groups_Oabs__class_Oabs(U_7510),U_7511)),hAPP(c_Groups_Oabs__class_Oabs(U_7510),U_7511)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7510),U_7511),U_7511)
| ~ class_Rings_Olinordered__idom(U_7510) ),
inference(clausify,[status(thm)],[f_2183_2]) ).
fof(f_2184_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_2184_2,plain,
! [U_7514,U_7513,U_7512] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7512),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7512),U_7513),U_7514)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7512),hAPP(c_Groups_Oabs__class_Oabs(U_7512),U_7513)),hAPP(c_Groups_Oabs__class_Oabs(U_7512),U_7514))
| ~ class_Rings_Olinordered__idom(U_7512) ),
inference(variable_rename,[status(thm)],[f_2184_1]) ).
cnf(f_2184_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7512),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7512),U_7513),U_7514)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7512),hAPP(c_Groups_Oabs__class_Oabs(U_7512),U_7513)),hAPP(c_Groups_Oabs__class_Oabs(U_7512),U_7514))
| ~ class_Rings_Olinordered__idom(U_7512) ),
inference(clausify,[status(thm)],[f_2184_2]) ).
fof(f_2185_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_2185_2,plain,
! [U_7517,U_7516,U_7515] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7515),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7515),hAPP(c_Groups_Oabs__class_Oabs(U_7515),U_7516)),hAPP(c_Groups_Oabs__class_Oabs(U_7515),U_7517))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7515),hAPP(c_Groups_Oabs__class_Oabs(U_7515),U_7516)),hAPP(c_Groups_Oabs__class_Oabs(U_7515),U_7517))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7515) ),
inference(variable_rename,[status(thm)],[f_2185_1]) ).
cnf(f_2185_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7515),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7515),hAPP(c_Groups_Oabs__class_Oabs(U_7515),U_7516)),hAPP(c_Groups_Oabs__class_Oabs(U_7515),U_7517))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7515),hAPP(c_Groups_Oabs__class_Oabs(U_7515),U_7516)),hAPP(c_Groups_Oabs__class_Oabs(U_7515),U_7517))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7515) ),
inference(clausify,[status(thm)],[f_2185_2]) ).
fof(f_2186_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_2186_2,plain,
! [U_7519,U_7518] :
( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_7518),U_7519) = c_Groups_Ozero__class_Ozero(U_7518)
| U_7519 != c_Groups_Ozero__class_Ozero(U_7518) )
& ( U_7519 = c_Groups_Ozero__class_Ozero(U_7518)
| hAPP(c_Groups_Oabs__class_Oabs(U_7518),U_7519) != c_Groups_Ozero__class_Ozero(U_7518) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_7518) ),
inference(variable_rename,[status(thm)],[f_2186_1]) ).
cnf(f_2186_3,plain,
( U_7519 = c_Groups_Ozero__class_Ozero(U_7518)
| hAPP(c_Groups_Oabs__class_Oabs(U_7518),U_7519) != c_Groups_Ozero__class_Ozero(U_7518)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7518) ),
inference(clausify,[status(thm)],[f_2186_2]) ).
cnf(f_2186_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7518),U_7519) = c_Groups_Ozero__class_Ozero(U_7518)
| U_7519 != c_Groups_Ozero__class_Ozero(U_7518)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7518) ),
inference(clausify,[status(thm)],[f_2186_2]) ).
fof(f_2187_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_2187_2,plain,
! [U_7520] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7520),c_Groups_Ozero__class_Ozero(U_7520)) = c_Groups_Ozero__class_Ozero(U_7520)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7520) ),
inference(variable_rename,[status(thm)],[f_2187_1]) ).
cnf(f_2187_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7520),c_Groups_Ozero__class_Ozero(U_7520)) = c_Groups_Ozero__class_Ozero(U_7520)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7520) ),
inference(clausify,[status(thm)],[f_2187_2]) ).
fof(f_2188_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_2188_2,plain,
! [U_7523,U_7522,U_7521] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7521),U_7522),U_7523))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7521),hAPP(c_Groups_Oabs__class_Oabs(U_7521),U_7522)),U_7523))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7521) ),
inference(variable_rename,[status(thm)],[f_2188_1]) ).
cnf(f_2188_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7521),U_7522),U_7523))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7521),hAPP(c_Groups_Oabs__class_Oabs(U_7521),U_7522)),U_7523))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7521) ),
inference(clausify,[status(thm)],[f_2188_2]) ).
fof(f_2189_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_2189_2,plain,
! [U_7525,U_7524] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7524),U_7525),hAPP(c_Groups_Oabs__class_Oabs(U_7524),U_7525)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7524) ),
inference(variable_rename,[status(thm)],[f_2189_1]) ).
cnf(f_2189_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7524),U_7525),hAPP(c_Groups_Oabs__class_Oabs(U_7524),U_7525)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7524) ),
inference(clausify,[status(thm)],[f_2189_2]) ).
fof(f_2190_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_2190_2,plain,
! [U_7526] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7526)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7526),
inference(variable_rename,[status(thm)],[f_2190_1]) ).
cnf(f_2190_3,plain,
hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7526)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7526),
inference(clausify,[status(thm)],[f_2190_2]) ).
fof(f_2191_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_2191_2,plain,
! [U_7531,U_7530,U_7529,U_7528,U_7527] :
( U_7531 = U_7530
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7527,U_7528,U_7529,U_7530,c_Orderings_Obot__class_Obot(tc_fun(U_7527,tc_HOL_Obool))),U_7531)) ),
inference(variable_rename,[status(thm)],[f_2191_1]) ).
fof(f_2191_3,plain,
! [U_7531,U_7530] :
( ! [U_7529,U_7528,U_7527] : ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7527,U_7528,U_7529,U_7530,c_Orderings_Obot__class_Obot(tc_fun(U_7527,tc_HOL_Obool))),U_7531))
| U_7531 = U_7530 ),
inference(miniscope,[status(thm)],[f_2191_2]) ).
cnf(f_2191_4,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7527,U_7528,U_7529,U_7530,c_Orderings_Obot__class_Obot(tc_fun(U_7527,tc_HOL_Obool))),U_7531))
| U_7531 = U_7530 ),
inference(clausify,[status(thm)],[f_2191_3]) ).
fof(f_2192_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_2192_2,plain,
! [U_7535,U_7534,U_7533,U_7532] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7532,U_7533,U_7534,U_7535,c_Orderings_Obot__class_Obot(tc_fun(U_7532,tc_HOL_Obool))),U_7535)),
inference(variable_rename,[status(thm)],[f_2192_1]) ).
cnf(f_2192_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7532,U_7533,U_7534,U_7535,c_Orderings_Obot__class_Obot(tc_fun(U_7532,tc_HOL_Obool))),U_7535)),
inference(clausify,[status(thm)],[f_2192_2]) ).
fof(f_2193_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_2193_2,plain,
! [U_7539,U_7538,U_7537,U_7536] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7536,U_7537,U_7538,U_7539,c_Orderings_Obot__class_Obot(tc_fun(U_7536,tc_HOL_Obool))),U_7539)),
inference(variable_rename,[status(thm)],[f_2193_1]) ).
cnf(f_2193_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7536,U_7537,U_7538,U_7539,c_Orderings_Obot__class_Obot(tc_fun(U_7536,tc_HOL_Obool))),U_7539)),
inference(clausify,[status(thm)],[f_2193_2]) ).
fof(f_2194_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_2194_2,plain,
! [U_7545,U_7544,U_7543,U_7542,U_7541,U_7540] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7540),U_7544))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7540,U_7541,U_7542,U_7543,U_7544),U_7545)) ),
inference(variable_rename,[status(thm)],[f_2194_1]) ).
cnf(f_2194_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7540),U_7544))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7540,U_7541,U_7542,U_7543,U_7544),U_7545)) ),
inference(clausify,[status(thm)],[f_2194_2]) ).
fof(f_2195_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_2195_2,plain,
! [U_7552,U_7551,U_7550,U_7549,U_7548,U_7547,U_7546] :
( U_7552 = U_7551
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7546,U_7547,U_7548,U_7549,U_7550),U_7552))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7546,U_7547,U_7548,U_7549,U_7550),U_7551))
| ~ c_Finite__Set_Ofun__left__comm(U_7546,U_7547,U_7548) ),
inference(variable_rename,[status(thm)],[f_2195_1]) ).
cnf(f_2195_3,plain,
( U_7552 = U_7551
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7546,U_7547,U_7548,U_7549,U_7550),U_7552))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7546,U_7547,U_7548,U_7549,U_7550),U_7551))
| ~ c_Finite__Set_Ofun__left__comm(U_7546,U_7547,U_7548) ),
inference(clausify,[status(thm)],[f_2195_2]) ).
fof(f_2196_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_2196_2,plain,
! [U_7554,U_7553] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7553),c_Groups_Ozero__class_Ozero(U_7553)),hAPP(c_Groups_Oabs__class_Oabs(U_7553),U_7554)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7553) ),
inference(variable_rename,[status(thm)],[f_2196_1]) ).
cnf(f_2196_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7553),c_Groups_Ozero__class_Ozero(U_7553)),hAPP(c_Groups_Oabs__class_Oabs(U_7553),U_7554)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7553) ),
inference(clausify,[status(thm)],[f_2196_2]) ).
fof(f_2197_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_2197_2,plain,
! [U_7556,U_7555] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7555),hAPP(c_Groups_Oabs__class_Oabs(U_7555),U_7556)),c_Groups_Ozero__class_Ozero(U_7555)))
| U_7556 != c_Groups_Ozero__class_Ozero(U_7555) )
& ( U_7556 = c_Groups_Ozero__class_Ozero(U_7555)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7555),hAPP(c_Groups_Oabs__class_Oabs(U_7555),U_7556)),c_Groups_Ozero__class_Ozero(U_7555))) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_7555) ),
inference(variable_rename,[status(thm)],[f_2197_1]) ).
cnf(f_2197_3,plain,
( U_7556 = c_Groups_Ozero__class_Ozero(U_7555)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7555),hAPP(c_Groups_Oabs__class_Oabs(U_7555),U_7556)),c_Groups_Ozero__class_Ozero(U_7555)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7555) ),
inference(clausify,[status(thm)],[f_2197_2]) ).
cnf(f_2197_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7555),hAPP(c_Groups_Oabs__class_Oabs(U_7555),U_7556)),c_Groups_Ozero__class_Ozero(U_7555)))
| U_7556 != c_Groups_Ozero__class_Ozero(U_7555)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7555) ),
inference(clausify,[status(thm)],[f_2197_2]) ).
fof(f_2198_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_2198_2,plain,
! [U_7558,U_7557] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7557),U_7558) = U_7558
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7557),c_Groups_Ozero__class_Ozero(U_7557)),U_7558))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7557) ),
inference(variable_rename,[status(thm)],[f_2198_1]) ).
cnf(f_2198_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7557),U_7558) = U_7558
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7557),c_Groups_Ozero__class_Ozero(U_7557)),U_7558))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7557) ),
inference(clausify,[status(thm)],[f_2198_2]) ).
fof(f_2199_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_2199_2,plain,
! [U_7560,U_7559] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7559),hAPP(c_Groups_Oabs__class_Oabs(U_7559),U_7560)),c_Groups_Ozero__class_Ozero(U_7559)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7559) ),
inference(variable_rename,[status(thm)],[f_2199_1]) ).
cnf(f_2199_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7559),hAPP(c_Groups_Oabs__class_Oabs(U_7559),U_7560)),c_Groups_Ozero__class_Ozero(U_7559)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7559) ),
inference(clausify,[status(thm)],[f_2199_2]) ).
fof(f_2200_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_2200_2,plain,
! [U_7562,U_7561] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7561),c_Groups_Ozero__class_Ozero(U_7561)),hAPP(c_Groups_Oabs__class_Oabs(U_7561),U_7562)))
| U_7562 = c_Groups_Ozero__class_Ozero(U_7561) )
& ( U_7562 != c_Groups_Ozero__class_Ozero(U_7561)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7561),c_Groups_Ozero__class_Ozero(U_7561)),hAPP(c_Groups_Oabs__class_Oabs(U_7561),U_7562))) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_7561) ),
inference(variable_rename,[status(thm)],[f_2200_1]) ).
cnf(f_2200_3,plain,
( U_7562 != c_Groups_Ozero__class_Ozero(U_7561)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7561),c_Groups_Ozero__class_Ozero(U_7561)),hAPP(c_Groups_Oabs__class_Oabs(U_7561),U_7562)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7561) ),
inference(clausify,[status(thm)],[f_2200_2]) ).
cnf(f_2200_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7561),c_Groups_Ozero__class_Ozero(U_7561)),hAPP(c_Groups_Oabs__class_Oabs(U_7561),U_7562)))
| U_7562 = c_Groups_Ozero__class_Ozero(U_7561)
| ~ class_Groups_Oordered__ab__group__add__abs(U_7561) ),
inference(clausify,[status(thm)],[f_2200_2]) ).
fof(f_2201_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_2201_2,plain,
! [U_7564,U_7563] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7563),U_7564) = U_7564
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7563),c_Groups_Ozero__class_Ozero(U_7563)),U_7564))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7563) ),
inference(variable_rename,[status(thm)],[f_2201_1]) ).
cnf(f_2201_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7563),U_7564) = U_7564
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7563),c_Groups_Ozero__class_Ozero(U_7563)),U_7564))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7563) ),
inference(clausify,[status(thm)],[f_2201_2]) ).
fof(f_2202_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_2202_2,plain,
! [U_7567,U_7566,U_7565] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7565),hAPP(c_Groups_Oabs__class_Oabs(U_7565),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7565),U_7566),U_7567))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7565),hAPP(c_Groups_Oabs__class_Oabs(U_7565),U_7566)),hAPP(c_Groups_Oabs__class_Oabs(U_7565),U_7567))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7565) ),
inference(variable_rename,[status(thm)],[f_2202_1]) ).
cnf(f_2202_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7565),hAPP(c_Groups_Oabs__class_Oabs(U_7565),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7565),U_7566),U_7567))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7565),hAPP(c_Groups_Oabs__class_Oabs(U_7565),U_7566)),hAPP(c_Groups_Oabs__class_Oabs(U_7565),U_7567))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7565) ),
inference(clausify,[status(thm)],[f_2202_2]) ).
fof(f_2203_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_2203_2,plain,
! [U_7572,U_7571,U_7570,U_7569,U_7568] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7568),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7568),hAPP(c_Groups_Oabs__class_Oabs(U_7568),U_7569)),hAPP(c_Groups_Oabs__class_Oabs(U_7568),U_7571))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7568),U_7570),U_7572)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7568),hAPP(c_Groups_Oabs__class_Oabs(U_7568),U_7571)),U_7572))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7568),hAPP(c_Groups_Oabs__class_Oabs(U_7568),U_7569)),U_7570))
| ~ class_Rings_Olinordered__idom(U_7568) ),
inference(variable_rename,[status(thm)],[f_2203_1]) ).
cnf(f_2203_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7568),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7568),hAPP(c_Groups_Oabs__class_Oabs(U_7568),U_7569)),hAPP(c_Groups_Oabs__class_Oabs(U_7568),U_7571))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7568),U_7570),U_7572)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7568),hAPP(c_Groups_Oabs__class_Oabs(U_7568),U_7571)),U_7572))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7568),hAPP(c_Groups_Oabs__class_Oabs(U_7568),U_7569)),U_7570))
| ~ class_Rings_Olinordered__idom(U_7568) ),
inference(clausify,[status(thm)],[f_2203_2]) ).
fof(f_2204_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_2204_2,plain,
! [U_7575,U_7574,U_7573] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7573),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7573),hAPP(c_Groups_Oabs__class_Oabs(U_7573),U_7574)),hAPP(c_Groups_Oabs__class_Oabs(U_7573),U_7575))),hAPP(c_Groups_Oabs__class_Oabs(U_7573),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7573),U_7575),U_7574))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7573) ),
inference(variable_rename,[status(thm)],[f_2204_1]) ).
cnf(f_2204_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7573),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7573),hAPP(c_Groups_Oabs__class_Oabs(U_7573),U_7574)),hAPP(c_Groups_Oabs__class_Oabs(U_7573),U_7575))),hAPP(c_Groups_Oabs__class_Oabs(U_7573),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7573),U_7575),U_7574))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7573) ),
inference(clausify,[status(thm)],[f_2204_2]) ).
fof(f_2205_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_2205_2,plain,
! [U_7578,U_7577,U_7576] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7576),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7576),hAPP(c_Groups_Oabs__class_Oabs(U_7576),U_7577)),hAPP(c_Groups_Oabs__class_Oabs(U_7576),U_7578))),hAPP(c_Groups_Oabs__class_Oabs(U_7576),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7576),U_7577),U_7578))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7576) ),
inference(variable_rename,[status(thm)],[f_2205_1]) ).
cnf(f_2205_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7576),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7576),hAPP(c_Groups_Oabs__class_Oabs(U_7576),U_7577)),hAPP(c_Groups_Oabs__class_Oabs(U_7576),U_7578))),hAPP(c_Groups_Oabs__class_Oabs(U_7576),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7576),U_7577),U_7578))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7576) ),
inference(clausify,[status(thm)],[f_2205_2]) ).
fof(f_2206_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_2206_2,plain,
! [U_7581,U_7580,U_7579] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7579),hAPP(c_Groups_Oabs__class_Oabs(U_7579),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7579),hAPP(c_Groups_Oabs__class_Oabs(U_7579),U_7580)),hAPP(c_Groups_Oabs__class_Oabs(U_7579),U_7581)))),hAPP(c_Groups_Oabs__class_Oabs(U_7579),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7579),U_7580),U_7581))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7579) ),
inference(variable_rename,[status(thm)],[f_2206_1]) ).
cnf(f_2206_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7579),hAPP(c_Groups_Oabs__class_Oabs(U_7579),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7579),hAPP(c_Groups_Oabs__class_Oabs(U_7579),U_7580)),hAPP(c_Groups_Oabs__class_Oabs(U_7579),U_7581)))),hAPP(c_Groups_Oabs__class_Oabs(U_7579),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7579),U_7580),U_7581))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7579) ),
inference(clausify,[status(thm)],[f_2206_2]) ).
fof(f_2207_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_2207_2,plain,
! [U_7583,U_7582] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7582),hAPP(c_Groups_Ouminus__class_Ouminus(U_7582),U_7583)),hAPP(c_Groups_Oabs__class_Oabs(U_7582),U_7583)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7582) ),
inference(variable_rename,[status(thm)],[f_2207_1]) ).
cnf(f_2207_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7582),hAPP(c_Groups_Ouminus__class_Ouminus(U_7582),U_7583)),hAPP(c_Groups_Oabs__class_Oabs(U_7582),U_7583)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7582) ),
inference(clausify,[status(thm)],[f_2207_2]) ).
fof(f_2208_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_2208_2,plain,
! [U_7586,U_7585,U_7584] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7584),hAPP(c_Groups_Oabs__class_Oabs(U_7584),U_7585)),U_7586))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7584),hAPP(c_Groups_Ouminus__class_Ouminus(U_7584),U_7585)),U_7586))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7584),U_7585),U_7586)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7584),hAPP(c_Groups_Ouminus__class_Ouminus(U_7584),U_7585)),U_7586))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7584),U_7585),U_7586)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7584),hAPP(c_Groups_Oabs__class_Oabs(U_7584),U_7585)),U_7586)) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_7584) ),
inference(variable_rename,[status(thm)],[f_2208_1]) ).
cnf(f_2208_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7584),U_7585),U_7586))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7584),hAPP(c_Groups_Oabs__class_Oabs(U_7584),U_7585)),U_7586))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7584) ),
inference(clausify,[status(thm)],[f_2208_2]) ).
cnf(f_2208_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7584),hAPP(c_Groups_Ouminus__class_Ouminus(U_7584),U_7585)),U_7586))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7584),hAPP(c_Groups_Oabs__class_Oabs(U_7584),U_7585)),U_7586))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7584) ),
inference(clausify,[status(thm)],[f_2208_2]) ).
cnf(f_2208_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7584),hAPP(c_Groups_Oabs__class_Oabs(U_7584),U_7585)),U_7586))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7584),hAPP(c_Groups_Ouminus__class_Ouminus(U_7584),U_7585)),U_7586))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7584),U_7585),U_7586))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7584) ),
inference(clausify,[status(thm)],[f_2208_2]) ).
fof(f_2209_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_2209_2,plain,
! [U_7589,U_7588,U_7587] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7587),hAPP(c_Groups_Oabs__class_Oabs(U_7587),U_7588)),U_7589))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7587),hAPP(c_Groups_Ouminus__class_Ouminus(U_7587),U_7588)),U_7589))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7587),U_7588),U_7589))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7587) ),
inference(variable_rename,[status(thm)],[f_2209_1]) ).
cnf(f_2209_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7587),hAPP(c_Groups_Oabs__class_Oabs(U_7587),U_7588)),U_7589))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7587),hAPP(c_Groups_Ouminus__class_Ouminus(U_7587),U_7588)),U_7589))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7587),U_7588),U_7589))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7587) ),
inference(clausify,[status(thm)],[f_2209_2]) ).
fof(f_2210_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_2210_2,plain,
! [U_7592,U_7591,U_7590] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7590),hAPP(c_Groups_Ouminus__class_Ouminus(U_7590),U_7591)),U_7592))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7590),hAPP(c_Groups_Oabs__class_Oabs(U_7590),U_7591)),U_7592))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7590) ),
inference(variable_rename,[status(thm)],[f_2210_1]) ).
cnf(f_2210_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7590),hAPP(c_Groups_Ouminus__class_Ouminus(U_7590),U_7591)),U_7592))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7590),hAPP(c_Groups_Oabs__class_Oabs(U_7590),U_7591)),U_7592))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7590) ),
inference(clausify,[status(thm)],[f_2210_2]) ).
fof(f_2211_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_2211_2,plain,
! [U_7595,U_7594,U_7593] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7593),hAPP(c_Groups_Oabs__class_Oabs(U_7593),U_7594)),U_7595))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7593),hAPP(c_Groups_Ouminus__class_Ouminus(U_7593),U_7594)),U_7595))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7593),U_7594),U_7595)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7593),hAPP(c_Groups_Ouminus__class_Ouminus(U_7593),U_7594)),U_7595))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7593),U_7594),U_7595)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7593),hAPP(c_Groups_Oabs__class_Oabs(U_7593),U_7594)),U_7595)) ) )
| ~ class_Rings_Olinordered__idom(U_7593) ),
inference(variable_rename,[status(thm)],[f_2211_1]) ).
cnf(f_2211_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7593),U_7594),U_7595))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7593),hAPP(c_Groups_Oabs__class_Oabs(U_7593),U_7594)),U_7595))
| ~ class_Rings_Olinordered__idom(U_7593) ),
inference(clausify,[status(thm)],[f_2211_2]) ).
cnf(f_2211_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7593),hAPP(c_Groups_Ouminus__class_Ouminus(U_7593),U_7594)),U_7595))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7593),hAPP(c_Groups_Oabs__class_Oabs(U_7593),U_7594)),U_7595))
| ~ class_Rings_Olinordered__idom(U_7593) ),
inference(clausify,[status(thm)],[f_2211_2]) ).
cnf(f_2211_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7593),hAPP(c_Groups_Oabs__class_Oabs(U_7593),U_7594)),U_7595))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7593),hAPP(c_Groups_Ouminus__class_Ouminus(U_7593),U_7594)),U_7595))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7593),U_7594),U_7595))
| ~ class_Rings_Olinordered__idom(U_7593) ),
inference(clausify,[status(thm)],[f_2211_2]) ).
fof(f_2212_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_2212_2,plain,
! [U_7598,U_7597,U_7596] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7596),hAPP(hAPP(c_Power_Opower__class_Opower(U_7596),hAPP(c_Groups_Ouminus__class_Ouminus(U_7596),U_7597)),U_7598)) = hAPP(c_Groups_Oabs__class_Oabs(U_7596),hAPP(hAPP(c_Power_Opower__class_Opower(U_7596),U_7597),U_7598))
| ~ class_Rings_Olinordered__idom(U_7596) ),
inference(variable_rename,[status(thm)],[f_2212_1]) ).
cnf(f_2212_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7596),hAPP(hAPP(c_Power_Opower__class_Opower(U_7596),hAPP(c_Groups_Ouminus__class_Ouminus(U_7596),U_7597)),U_7598)) = hAPP(c_Groups_Oabs__class_Oabs(U_7596),hAPP(hAPP(c_Power_Opower__class_Opower(U_7596),U_7597),U_7598))
| ~ class_Rings_Olinordered__idom(U_7596) ),
inference(clausify,[status(thm)],[f_2212_2]) ).
fof(f_2213_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_2213_2,plain,
! [U_7600,U_7599] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7599) = 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_7599),U_7600)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_2213_1]) ).
cnf(f_2213_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7599) = 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_7599),U_7600)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2213_2]) ).
fof(f_2214_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_2214_2,plain,
! [U_7602,U_7601] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7601),U_7602) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7601),U_7602),c_Groups_Osgn__class_Osgn(U_7601,U_7602))
| ~ class_Rings_Olinordered__idom(U_7601) ),
inference(variable_rename,[status(thm)],[f_2214_1]) ).
cnf(f_2214_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7601),U_7602) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7601),U_7602),c_Groups_Osgn__class_Osgn(U_7601,U_7602))
| ~ class_Rings_Olinordered__idom(U_7601) ),
inference(clausify,[status(thm)],[f_2214_2]) ).
fof(f_2215_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_2215_2,plain,
! [U_7604,U_7603] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7603),c_Groups_Osgn__class_Osgn(U_7603,U_7604)),hAPP(c_Groups_Oabs__class_Oabs(U_7603),U_7604)) = U_7604
| ~ class_Rings_Olinordered__idom(U_7603) ),
inference(variable_rename,[status(thm)],[f_2215_1]) ).
cnf(f_2215_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7603),c_Groups_Osgn__class_Osgn(U_7603,U_7604)),hAPP(c_Groups_Oabs__class_Oabs(U_7603),U_7604)) = U_7604
| ~ class_Rings_Olinordered__idom(U_7603) ),
inference(clausify,[status(thm)],[f_2215_2]) ).
fof(f_2216_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_2216_2,plain,
! [U_7607,U_7606,U_7605] : hAPP(c_Finite__Set_Ofold1(U_7605,U_7606),hAPP(hAPP(c_Set_Oinsert(U_7605),U_7607),c_Orderings_Obot__class_Obot(tc_fun(U_7605,tc_HOL_Obool)))) = U_7607,
inference(variable_rename,[status(thm)],[f_2216_1]) ).
cnf(f_2216_3,plain,
hAPP(c_Finite__Set_Ofold1(U_7605,U_7606),hAPP(hAPP(c_Set_Oinsert(U_7605),U_7607),c_Orderings_Obot__class_Obot(tc_fun(U_7605,tc_HOL_Obool)))) = U_7607,
inference(clausify,[status(thm)],[f_2216_2]) ).
fof(f_2217_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_2217_2,plain,
! [U_7611,U_7610,U_7609,U_7608] :
( hAPP(U_7608,hAPP(hAPP(c_Set_Oinsert(U_7609),U_7611),c_Orderings_Obot__class_Obot(tc_fun(U_7609,tc_HOL_Obool)))) = U_7611
| U_7608 != c_Finite__Set_Ofold1(U_7609,U_7610) ),
inference(variable_rename,[status(thm)],[f_2217_1]) ).
cnf(f_2217_3,plain,
( hAPP(U_7608,hAPP(hAPP(c_Set_Oinsert(U_7609),U_7611),c_Orderings_Obot__class_Obot(tc_fun(U_7609,tc_HOL_Obool)))) = U_7611
| U_7608 != c_Finite__Set_Ofold1(U_7609,U_7610) ),
inference(clausify,[status(thm)],[f_2217_2]) ).
fof(f_2218_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_2218_2,plain,
! [U_7618,U_7617,U_7616,U_7615,U_7614,U_7613,U_7612] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7612,U_7615,U_7616,U_7617,hAPP(hAPP(c_Set_Oinsert(U_7612),U_7613),U_7614)),hAPP(hAPP(U_7616,U_7613),U_7618)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7612,U_7615,U_7616,U_7617,U_7614),U_7618))
| hBOOL(hAPP(hAPP(c_member(U_7612),U_7613),U_7614)) ),
inference(variable_rename,[status(thm)],[f_2218_1]) ).
cnf(f_2218_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7612,U_7615,U_7616,U_7617,hAPP(hAPP(c_Set_Oinsert(U_7612),U_7613),U_7614)),hAPP(hAPP(U_7616,U_7613),U_7618)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7612,U_7615,U_7616,U_7617,U_7614),U_7618))
| hBOOL(hAPP(hAPP(c_member(U_7612),U_7613),U_7614)) ),
inference(clausify,[status(thm)],[f_2218_2]) ).
fof(f_2219_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_2219_2,plain,
! [U_7621,U_7620,U_7619] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7619),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7619),U_7620),U_7621)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7619),hAPP(c_Groups_Oabs__class_Oabs(U_7619),U_7620)),hAPP(c_Groups_Oabs__class_Oabs(U_7619),U_7621))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7619),U_7621),c_Groups_Ozero__class_Ozero(U_7619)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7619),c_Groups_Ozero__class_Ozero(U_7619)),U_7621)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7619),U_7620),c_Groups_Ozero__class_Ozero(U_7619)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7619),c_Groups_Ozero__class_Ozero(U_7619)),U_7620)) )
| ~ class_Rings_Oordered__ring__abs(U_7619) ),
inference(variable_rename,[status(thm)],[f_2219_1]) ).
cnf(f_2219_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7619),c_Groups_Ozero__class_Ozero(U_7619)),U_7621))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7619),c_Groups_Ozero__class_Ozero(U_7619)),U_7620))
| hAPP(c_Groups_Oabs__class_Oabs(U_7619),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7619),U_7620),U_7621)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7619),hAPP(c_Groups_Oabs__class_Oabs(U_7619),U_7620)),hAPP(c_Groups_Oabs__class_Oabs(U_7619),U_7621))
| ~ class_Rings_Oordered__ring__abs(U_7619) ),
inference(clausify,[status(thm)],[f_2219_2]) ).
cnf(f_2219_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7619),U_7621),c_Groups_Ozero__class_Ozero(U_7619)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7619),c_Groups_Ozero__class_Ozero(U_7619)),U_7620))
| hAPP(c_Groups_Oabs__class_Oabs(U_7619),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7619),U_7620),U_7621)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7619),hAPP(c_Groups_Oabs__class_Oabs(U_7619),U_7620)),hAPP(c_Groups_Oabs__class_Oabs(U_7619),U_7621))
| ~ class_Rings_Oordered__ring__abs(U_7619) ),
inference(clausify,[status(thm)],[f_2219_2]) ).
cnf(f_2219_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7619),c_Groups_Ozero__class_Ozero(U_7619)),U_7621))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7619),U_7620),c_Groups_Ozero__class_Ozero(U_7619)))
| hAPP(c_Groups_Oabs__class_Oabs(U_7619),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7619),U_7620),U_7621)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7619),hAPP(c_Groups_Oabs__class_Oabs(U_7619),U_7620)),hAPP(c_Groups_Oabs__class_Oabs(U_7619),U_7621))
| ~ class_Rings_Oordered__ring__abs(U_7619) ),
inference(clausify,[status(thm)],[f_2219_2]) ).
cnf(f_2219_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7619),U_7621),c_Groups_Ozero__class_Ozero(U_7619)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7619),U_7620),c_Groups_Ozero__class_Ozero(U_7619)))
| hAPP(c_Groups_Oabs__class_Oabs(U_7619),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7619),U_7620),U_7621)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7619),hAPP(c_Groups_Oabs__class_Oabs(U_7619),U_7620)),hAPP(c_Groups_Oabs__class_Oabs(U_7619),U_7621))
| ~ class_Rings_Oordered__ring__abs(U_7619) ),
inference(clausify,[status(thm)],[f_2219_2]) ).
fof(f_2220_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_2220_2,plain,
! [U_7624,U_7623,U_7622] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7622),hAPP(c_Groups_Oabs__class_Oabs(U_7622),U_7624)),U_7623) = hAPP(c_Groups_Oabs__class_Oabs(U_7622),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7622),U_7624),U_7623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7622),c_Groups_Ozero__class_Ozero(U_7622)),U_7623))
| ~ class_Rings_Olinordered__idom(U_7622) ),
inference(variable_rename,[status(thm)],[f_2220_1]) ).
cnf(f_2220_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7622),hAPP(c_Groups_Oabs__class_Oabs(U_7622),U_7624)),U_7623) = hAPP(c_Groups_Oabs__class_Oabs(U_7622),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7622),U_7624),U_7623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7622),c_Groups_Ozero__class_Ozero(U_7622)),U_7623))
| ~ class_Rings_Olinordered__idom(U_7622) ),
inference(clausify,[status(thm)],[f_2220_2]) ).
fof(f_2221_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_2221_2,plain,
! [U_7629,U_7628,U_7627,U_7626,U_7625] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7625),hAPP(c_Groups_Oabs__class_Oabs(U_7625),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7625),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7625),U_7626),U_7627)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7625),U_7628),U_7629)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7625),hAPP(c_Groups_Oabs__class_Oabs(U_7625),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7625),U_7626),U_7628))),hAPP(c_Groups_Oabs__class_Oabs(U_7625),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7625),U_7627),U_7629)))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7625) ),
inference(variable_rename,[status(thm)],[f_2221_1]) ).
cnf(f_2221_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7625),hAPP(c_Groups_Oabs__class_Oabs(U_7625),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7625),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7625),U_7626),U_7627)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7625),U_7628),U_7629)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7625),hAPP(c_Groups_Oabs__class_Oabs(U_7625),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7625),U_7626),U_7628))),hAPP(c_Groups_Oabs__class_Oabs(U_7625),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7625),U_7627),U_7629)))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7625) ),
inference(clausify,[status(thm)],[f_2221_2]) ).
fof(f_2222_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_2222_2,plain,
! [U_7632,U_7631,U_7630] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7630),hAPP(c_Groups_Oabs__class_Oabs(U_7630),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7630),U_7631),U_7632))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7630),hAPP(c_Groups_Oabs__class_Oabs(U_7630),U_7631)),hAPP(c_Groups_Oabs__class_Oabs(U_7630),U_7632))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7630) ),
inference(variable_rename,[status(thm)],[f_2222_1]) ).
cnf(f_2222_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7630),hAPP(c_Groups_Oabs__class_Oabs(U_7630),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7630),U_7631),U_7632))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7630),hAPP(c_Groups_Oabs__class_Oabs(U_7630),U_7631)),hAPP(c_Groups_Oabs__class_Oabs(U_7630),U_7632))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7630) ),
inference(clausify,[status(thm)],[f_2222_2]) ).
fof(f_2223_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_2223_2,plain,
! [U_7634,U_7633] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7633),hAPP(c_Groups_Ouminus__class_Ouminus(U_7633),hAPP(c_Groups_Oabs__class_Oabs(U_7633),U_7634))),c_Groups_Ozero__class_Ozero(U_7633)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7633) ),
inference(variable_rename,[status(thm)],[f_2223_1]) ).
cnf(f_2223_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7633),hAPP(c_Groups_Ouminus__class_Ouminus(U_7633),hAPP(c_Groups_Oabs__class_Oabs(U_7633),U_7634))),c_Groups_Ozero__class_Ozero(U_7633)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7633) ),
inference(clausify,[status(thm)],[f_2223_2]) ).
fof(f_2224_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_2224_2,plain,
! [U_7636,U_7635] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7635),U_7636) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7635),U_7636)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7635),U_7636),c_Groups_Ozero__class_Ozero(U_7635)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7635) ),
inference(variable_rename,[status(thm)],[f_2224_1]) ).
cnf(f_2224_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7635),U_7636) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7635),U_7636)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7635),U_7636),c_Groups_Ozero__class_Ozero(U_7635)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7635) ),
inference(clausify,[status(thm)],[f_2224_2]) ).
fof(f_2225_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_2225_2,plain,
! [U_7638,U_7637] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7637),U_7638) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7637),U_7638)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7637),U_7638),c_Groups_Ozero__class_Ozero(U_7637)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7637) ),
inference(variable_rename,[status(thm)],[f_2225_1]) ).
cnf(f_2225_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7637),U_7638) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7637),U_7638)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7637),U_7638),c_Groups_Ozero__class_Ozero(U_7637)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_7637) ),
inference(clausify,[status(thm)],[f_2225_2]) ).
fof(f_2226_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_2226_2,plain,
! [U_7640,U_7639] :
( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_7639),U_7640) = U_7640
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7639),U_7640),c_Groups_Ozero__class_Ozero(U_7639))) )
& ( hAPP(c_Groups_Oabs__class_Oabs(U_7639),U_7640) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7639),U_7640)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7639),U_7640),c_Groups_Ozero__class_Ozero(U_7639))) ) )
| ~ class_Groups_Oabs__if(U_7639) ),
inference(variable_rename,[status(thm)],[f_2226_1]) ).
cnf(f_2226_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7639),U_7640) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7639),U_7640)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7639),U_7640),c_Groups_Ozero__class_Ozero(U_7639)))
| ~ class_Groups_Oabs__if(U_7639) ),
inference(clausify,[status(thm)],[f_2226_2]) ).
cnf(f_2226_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7639),U_7640) = U_7640
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7639),U_7640),c_Groups_Ozero__class_Ozero(U_7639)))
| ~ class_Groups_Oabs__if(U_7639) ),
inference(clausify,[status(thm)],[f_2226_2]) ).
fof(f_2227_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_2227_2,plain,
! [U_7643,U_7642,U_7641] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7641),c_Groups_Ozero__class_Ozero(U_7641)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7641),hAPP(c_Groups_Oabs__class_Oabs(U_7641),U_7642)),U_7643)))
| ~ class_Rings_Olinordered__idom(U_7641) ),
inference(variable_rename,[status(thm)],[f_2227_1]) ).
cnf(f_2227_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7641),c_Groups_Ozero__class_Ozero(U_7641)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7641),hAPP(c_Groups_Oabs__class_Oabs(U_7641),U_7642)),U_7643)))
| ~ class_Rings_Olinordered__idom(U_7641) ),
inference(clausify,[status(thm)],[f_2227_2]) ).
fof(f_2228_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_2228_2,plain,
! [U_7647,U_7646,U_7645,U_7644] :
( hAPP(U_7646,U_7647) = hAPP(c_Finite__Set_Ofold1(U_7644,U_7645),U_7647)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7644),U_7647))
| ~ c_Finite__Set_Ofolding__one(U_7644,U_7645,U_7646) ),
inference(variable_rename,[status(thm)],[f_2228_1]) ).
cnf(f_2228_3,plain,
( hAPP(U_7646,U_7647) = hAPP(c_Finite__Set_Ofold1(U_7644,U_7645),U_7647)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7644),U_7647))
| ~ c_Finite__Set_Ofolding__one(U_7644,U_7645,U_7646) ),
inference(clausify,[status(thm)],[f_2228_2]) ).
fof(f_2229_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_2229_2,plain,
! [U_7648] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7648),hAPP(c_Int_Onumber__class_Onumber__of(U_7648),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_7648)
| ~ class_Rings_Olinordered__idom(U_7648)
| ~ class_Int_Onumber__ring(U_7648) ),
inference(variable_rename,[status(thm)],[f_2229_1]) ).
cnf(f_2229_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7648),hAPP(c_Int_Onumber__class_Onumber__of(U_7648),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_7648)
| ~ class_Rings_Olinordered__idom(U_7648)
| ~ class_Int_Onumber__ring(U_7648) ),
inference(clausify,[status(thm)],[f_2229_2]) ).
fof(f_2230_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_2230_2,plain,
! [U_7649] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7649)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| U_7649 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( U_7649 = 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_7649)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_2230_1]) ).
fof(f_2230_3,plain,
( ! [U_7651] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7651)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| U_7651 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_7650] :
( U_7650 = 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_7650)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_2230_2]) ).
cnf(f_2230_4,plain,
( U_7650 = 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_7650)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2230_3]) ).
cnf(f_2230_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7651)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| U_7651 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2230_3]) ).
fof(f_2231_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_2231_2,plain,
! [U_7657,U_7656,U_7655,U_7654,U_7653,U_7652] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_7652,U_7653,U_7654),U_7655),U_7656) = U_7657
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7652,U_7653,U_7654,U_7655,U_7656),U_7657))
| ~ c_Finite__Set_Ofun__left__comm(U_7652,U_7653,U_7654) ),
inference(variable_rename,[status(thm)],[f_2231_1]) ).
cnf(f_2231_3,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_7652,U_7653,U_7654),U_7655),U_7656) = U_7657
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7652,U_7653,U_7654,U_7655,U_7656),U_7657))
| ~ c_Finite__Set_Ofun__left__comm(U_7652,U_7653,U_7654) ),
inference(clausify,[status(thm)],[f_2231_2]) ).
fof(f_2232_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_2232_2,plain,
! [U_7658] :
( ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7658) = U_7658
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7658),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7658) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7658)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7658),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_2232_1]) ).
fof(f_2232_3,plain,
( ! [U_7660] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7660) = U_7660
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7660),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_7659] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7659) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7659)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7659),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_2232_2]) ).
cnf(f_2232_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7659) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7659)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7659),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2232_3]) ).
cnf(f_2232_5,plain,
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7660) = U_7660
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7660),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2232_3]) ).
fof(f_2233_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_2233_2,plain,
! [U_7662,U_7661] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7661),U_7662))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7661))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7662))),
inference(variable_rename,[status(thm)],[f_2233_1]) ).
cnf(f_2233_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_7661),U_7662))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7661))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7662))),
inference(clausify,[status(thm)],[f_2233_2]) ).
fof(f_2234_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_2234_2,plain,
! [U_7664,U_7663] : 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_7663)),U_7664))),
inference(variable_rename,[status(thm)],[f_2234_1]) ).
cnf(f_2234_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_7663)),U_7664))),
inference(clausify,[status(thm)],[f_2234_2]) ).
fof(f_2235_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_2235_2,plain,
! [U_7669,U_7668,U_7667,U_7666,U_7665] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7665,U_7665,c_Groups_Otimes__class_Otimes(U_7665),U_7669,hAPP(hAPP(c_Set_Oinsert(U_7665),U_7666),U_7667)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7665),U_7669),U_7668)))
| hBOOL(hAPP(hAPP(c_member(U_7665),U_7666),U_7667))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7665,U_7665,c_Groups_Otimes__class_Otimes(U_7665),U_7666,U_7667),U_7668))
| ~ class_Groups_Oab__semigroup__mult(U_7665) ),
inference(variable_rename,[status(thm)],[f_2235_1]) ).
cnf(f_2235_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7665,U_7665,c_Groups_Otimes__class_Otimes(U_7665),U_7669,hAPP(hAPP(c_Set_Oinsert(U_7665),U_7666),U_7667)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7665),U_7669),U_7668)))
| hBOOL(hAPP(hAPP(c_member(U_7665),U_7666),U_7667))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7665,U_7665,c_Groups_Otimes__class_Otimes(U_7665),U_7666,U_7667),U_7668))
| ~ class_Groups_Oab__semigroup__mult(U_7665) ),
inference(clausify,[status(thm)],[f_2235_2]) ).
fof(f_2236_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_2236_2,plain,
! [U_7671,U_7670] :
( c_Big__Operators_Olattice__class_OSup__fin(U_7670,U_7671) = hAPP(c_Finite__Set_Ofold1(U_7670,c_Lattices_Osemilattice__sup__class_Osup(U_7670)),U_7671)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7670),U_7671))
| ~ class_Lattices_Olattice(U_7670) ),
inference(variable_rename,[status(thm)],[f_2236_1]) ).
cnf(f_2236_3,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_7670,U_7671) = hAPP(c_Finite__Set_Ofold1(U_7670,c_Lattices_Osemilattice__sup__class_Osup(U_7670)),U_7671)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7670),U_7671))
| ~ class_Lattices_Olattice(U_7670) ),
inference(clausify,[status(thm)],[f_2236_2]) ).
fof(f_2237_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_2237_2,plain,
! [U_7673,U_7672] :
( c_Big__Operators_Olattice__class_OInf__fin(U_7672,U_7673) = hAPP(c_Finite__Set_Ofold1(U_7672,c_Lattices_Osemilattice__inf__class_Oinf(U_7672)),U_7673)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7672),U_7673))
| ~ class_Lattices_Olattice(U_7672) ),
inference(variable_rename,[status(thm)],[f_2237_1]) ).
cnf(f_2237_3,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_7672,U_7673) = hAPP(c_Finite__Set_Ofold1(U_7672,c_Lattices_Osemilattice__inf__class_Oinf(U_7672)),U_7673)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7672),U_7673))
| ~ class_Lattices_Olattice(U_7672) ),
inference(clausify,[status(thm)],[f_2237_2]) ).
fof(f_2238_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_2238_2,plain,
! [U_7675,U_7674] :
( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_7674),hAPP(c_Int_Onumber__class_Onumber__of(U_7674),U_7675)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7674),U_7675)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7674),hAPP(c_Int_Onumber__class_Onumber__of(U_7674),U_7675)),c_Groups_Ozero__class_Ozero(U_7674))) )
& ( hAPP(c_Groups_Oabs__class_Oabs(U_7674),hAPP(c_Int_Onumber__class_Onumber__of(U_7674),U_7675)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7674),hAPP(c_Int_Onumber__class_Onumber__of(U_7674),U_7675))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7674),hAPP(c_Int_Onumber__class_Onumber__of(U_7674),U_7675)),c_Groups_Ozero__class_Ozero(U_7674))) ) )
| ~ class_Rings_Olinordered__idom(U_7674)
| ~ class_Int_Onumber__ring(U_7674) ),
inference(variable_rename,[status(thm)],[f_2238_1]) ).
cnf(f_2238_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7674),hAPP(c_Int_Onumber__class_Onumber__of(U_7674),U_7675)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7674),hAPP(c_Int_Onumber__class_Onumber__of(U_7674),U_7675))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7674),hAPP(c_Int_Onumber__class_Onumber__of(U_7674),U_7675)),c_Groups_Ozero__class_Ozero(U_7674)))
| ~ class_Rings_Olinordered__idom(U_7674)
| ~ class_Int_Onumber__ring(U_7674) ),
inference(clausify,[status(thm)],[f_2238_2]) ).
cnf(f_2238_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7674),hAPP(c_Int_Onumber__class_Onumber__of(U_7674),U_7675)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7674),U_7675)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7674),hAPP(c_Int_Onumber__class_Onumber__of(U_7674),U_7675)),c_Groups_Ozero__class_Ozero(U_7674)))
| ~ class_Rings_Olinordered__idom(U_7674)
| ~ class_Int_Onumber__ring(U_7674) ),
inference(clausify,[status(thm)],[f_2238_2]) ).
fof(f_2239_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_2239_2,plain,
! [U_7677,U_7676] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7676),hAPP(hAPP(c_Power_Opower__class_Opower(U_7676),hAPP(c_Int_Onumber__class_Onumber__of(U_7676),c_Int_OMin)),U_7677)) = c_Groups_Oone__class_Oone(U_7676)
| ~ class_Rings_Olinordered__idom(U_7676)
| ~ class_Int_Onumber__ring(U_7676) ),
inference(variable_rename,[status(thm)],[f_2239_1]) ).
cnf(f_2239_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7676),hAPP(hAPP(c_Power_Opower__class_Opower(U_7676),hAPP(c_Int_Onumber__class_Onumber__of(U_7676),c_Int_OMin)),U_7677)) = c_Groups_Oone__class_Oone(U_7676)
| ~ class_Rings_Olinordered__idom(U_7676)
| ~ class_Int_Onumber__ring(U_7676) ),
inference(clausify,[status(thm)],[f_2239_2]) ).
fof(f_2240_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_2240_2,plain,
! [U_7679,U_7678] :
( ( 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_7678)),U_7679)))
| ( U_7679 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_7678 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( U_7679 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_7678 != 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_7678)),U_7679))) ) ),
inference(variable_rename,[status(thm)],[f_2240_1]) ).
fof(f_2240_3,plain,
( ! [U_7683,U_7681] :
( 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_7681)),U_7683)))
| ( U_7683 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_7681 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_7682,U_7680] :
( U_7682 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_7680 != 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_7680)),U_7682))) ) ),
inference(miniscope,[status(thm)],[f_2240_2]) ).
cnf(f_2240_4,plain,
( U_7682 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_7680 != 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_7680)),U_7682))) ),
inference(clausify,[status(thm)],[f_2240_3]) ).
cnf(f_2240_5,plain,
( U_7681 = 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_7681)),U_7683))) ),
inference(clausify,[status(thm)],[f_2240_3]) ).
cnf(f_2240_6,plain,
( U_7683 != 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_7681)),U_7683))) ),
inference(clausify,[status(thm)],[f_2240_3]) ).
fof(f_2241_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_2241_2,plain,
! [U_7688,U_7687,U_7686,U_7685,U_7684] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7684,U_7685,U_7686,U_7688,U_7687),hAPP(hAPP(c_Finite__Set_Ofold(U_7684,U_7685,U_7686),U_7688),U_7687)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7684),U_7687))
| ~ c_Finite__Set_Ofun__left__comm(U_7684,U_7685,U_7686) ),
inference(variable_rename,[status(thm)],[f_2241_1]) ).
cnf(f_2241_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7684,U_7685,U_7686,U_7688,U_7687),hAPP(hAPP(c_Finite__Set_Ofold(U_7684,U_7685,U_7686),U_7688),U_7687)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7684),U_7687))
| ~ c_Finite__Set_Ofun__left__comm(U_7684,U_7685,U_7686) ),
inference(clausify,[status(thm)],[f_2241_2]) ).
fof(f_2242_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_2242_2,plain,
! [U_7691,U_7690,U_7689] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7689),hAPP(c_Finite__Set_Ofold1(U_7689,c_Lattices_Osemilattice__inf__class_Oinf(U_7689)),U_7690)),U_7691))
| ~ hBOOL(hAPP(hAPP(c_member(U_7689),U_7691),U_7690))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7689),U_7690))
| ~ class_Lattices_Osemilattice__inf(U_7689) ),
inference(variable_rename,[status(thm)],[f_2242_1]) ).
cnf(f_2242_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7689),hAPP(c_Finite__Set_Ofold1(U_7689,c_Lattices_Osemilattice__inf__class_Oinf(U_7689)),U_7690)),U_7691))
| ~ hBOOL(hAPP(hAPP(c_member(U_7689),U_7691),U_7690))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7689),U_7690))
| ~ class_Lattices_Osemilattice__inf(U_7689) ),
inference(clausify,[status(thm)],[f_2242_2]) ).
fof(f_2243_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_2243_2,plain,
! [U_7696,U_7695,U_7694] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7694),U_7696),hAPP(c_Finite__Set_Ofold1(U_7694,c_Lattices_Osemilattice__inf__class_Oinf(U_7694)),U_7695)))
| ? [U_7693] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7694),U_7696),U_7693))
& hBOOL(hAPP(hAPP(c_member(U_7694),U_7693),U_7695)) ) )
& ( ! [U_7692] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7694),U_7696),U_7692))
| ~ hBOOL(hAPP(hAPP(c_member(U_7694),U_7692),U_7695)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7694),U_7696),hAPP(c_Finite__Set_Ofold1(U_7694,c_Lattices_Osemilattice__inf__class_Oinf(U_7694)),U_7695))) ) )
| U_7695 = c_Orderings_Obot__class_Obot(tc_fun(U_7694,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7694),U_7695))
| ~ class_Lattices_Osemilattice__inf(U_7694) ),
inference(variable_rename,[status(thm)],[f_2243_1]) ).
fof(f_2243_3,plain,
! [U_7696,U_7695,U_7694] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7694),U_7696),hAPP(c_Finite__Set_Ofold1(U_7694,c_Lattices_Osemilattice__inf__class_Oinf(U_7694)),U_7695)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7694),U_7696),sK172(U_7696,U_7695,U_7694)))
& hBOOL(hAPP(hAPP(c_member(U_7694),sK172(U_7696,U_7695,U_7694)),U_7695)) ) )
& ( ! [U_7692] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7694),U_7696),U_7692))
| ~ hBOOL(hAPP(hAPP(c_member(U_7694),U_7692),U_7695)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7694),U_7696),hAPP(c_Finite__Set_Ofold1(U_7694,c_Lattices_Osemilattice__inf__class_Oinf(U_7694)),U_7695))) ) )
| U_7695 = c_Orderings_Obot__class_Obot(tc_fun(U_7694,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7694),U_7695))
| ~ class_Lattices_Osemilattice__inf(U_7694) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK172]),skolemize(U_7693,sK172(U_7696,U_7695,U_7694))],[f_2243_2]) ).
cnf(f_2243_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7694),U_7696),U_7692))
| ~ hBOOL(hAPP(hAPP(c_member(U_7694),U_7692),U_7695))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7694),U_7696),hAPP(c_Finite__Set_Ofold1(U_7694,c_Lattices_Osemilattice__inf__class_Oinf(U_7694)),U_7695)))
| U_7695 = c_Orderings_Obot__class_Obot(tc_fun(U_7694,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7694),U_7695))
| ~ class_Lattices_Osemilattice__inf(U_7694) ),
inference(clausify,[status(thm)],[f_2243_3]) ).
cnf(f_2243_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_7694),sK172(U_7696,U_7695,U_7694)),U_7695))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7694),U_7696),hAPP(c_Finite__Set_Ofold1(U_7694,c_Lattices_Osemilattice__inf__class_Oinf(U_7694)),U_7695)))
| U_7695 = c_Orderings_Obot__class_Obot(tc_fun(U_7694,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7694),U_7695))
| ~ class_Lattices_Osemilattice__inf(U_7694) ),
inference(clausify,[status(thm)],[f_2243_3]) ).
cnf(f_2243_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7694),U_7696),sK172(U_7696,U_7695,U_7694)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7694),U_7696),hAPP(c_Finite__Set_Ofold1(U_7694,c_Lattices_Osemilattice__inf__class_Oinf(U_7694)),U_7695)))
| U_7695 = c_Orderings_Obot__class_Obot(tc_fun(U_7694,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7694),U_7695))
| ~ class_Lattices_Osemilattice__inf(U_7694) ),
inference(clausify,[status(thm)],[f_2243_3]) ).
fof(f_2244_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_2244_2,plain,
! [U_7699,U_7698,U_7697] :
( hAPP(c_Finite__Set_Ofold1(U_7697,c_Groups_Otimes__class_Otimes(U_7697)),hAPP(hAPP(c_Set_Oinsert(U_7697),U_7699),U_7698)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7697),U_7699),hAPP(c_Finite__Set_Ofold1(U_7697,c_Groups_Otimes__class_Otimes(U_7697)),U_7698))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7697),U_7698))
| U_7698 = c_Orderings_Obot__class_Obot(tc_fun(U_7697,tc_HOL_Obool))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_7697) ),
inference(variable_rename,[status(thm)],[f_2244_1]) ).
cnf(f_2244_3,plain,
( hAPP(c_Finite__Set_Ofold1(U_7697,c_Groups_Otimes__class_Otimes(U_7697)),hAPP(hAPP(c_Set_Oinsert(U_7697),U_7699),U_7698)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7697),U_7699),hAPP(c_Finite__Set_Ofold1(U_7697,c_Groups_Otimes__class_Otimes(U_7697)),U_7698))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7697),U_7698))
| U_7698 = c_Orderings_Obot__class_Obot(tc_fun(U_7697,tc_HOL_Obool))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_7697) ),
inference(clausify,[status(thm)],[f_2244_2]) ).
fof(f_2245_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_2245_2,plain,
! [U_7702,U_7701,U_7700] :
( hAPP(c_Finite__Set_Ofold1(U_7700,c_Groups_Otimes__class_Otimes(U_7700)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7700,tc_HOL_Obool)),U_7701),U_7702)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7700),hAPP(c_Finite__Set_Ofold1(U_7700,c_Groups_Otimes__class_Otimes(U_7700)),U_7701)),hAPP(c_Finite__Set_Ofold1(U_7700,c_Groups_Otimes__class_Otimes(U_7700)),U_7702))
| U_7702 = c_Orderings_Obot__class_Obot(tc_fun(U_7700,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7700),U_7702))
| U_7701 = c_Orderings_Obot__class_Obot(tc_fun(U_7700,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7700),U_7701))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_7700) ),
inference(variable_rename,[status(thm)],[f_2245_1]) ).
cnf(f_2245_3,plain,
( hAPP(c_Finite__Set_Ofold1(U_7700,c_Groups_Otimes__class_Otimes(U_7700)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7700,tc_HOL_Obool)),U_7701),U_7702)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7700),hAPP(c_Finite__Set_Ofold1(U_7700,c_Groups_Otimes__class_Otimes(U_7700)),U_7701)),hAPP(c_Finite__Set_Ofold1(U_7700,c_Groups_Otimes__class_Otimes(U_7700)),U_7702))
| U_7702 = c_Orderings_Obot__class_Obot(tc_fun(U_7700,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7700),U_7702))
| U_7701 = c_Orderings_Obot__class_Obot(tc_fun(U_7700,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7700),U_7701))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_7700) ),
inference(clausify,[status(thm)],[f_2245_2]) ).
fof(f_2246_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_2246_2,plain,
! [U_7705,U_7704,U_7703] :
( hAPP(c_Finite__Set_Ofold1(U_7703,c_Groups_Otimes__class_Otimes(U_7703)),hAPP(hAPP(c_Set_Oinsert(U_7703),U_7705),U_7704)) = hAPP(hAPP(c_Finite__Set_Ofold(U_7703,U_7703,c_Groups_Otimes__class_Otimes(U_7703)),U_7705),U_7704)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7703),U_7704))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_7703) ),
inference(variable_rename,[status(thm)],[f_2246_1]) ).
cnf(f_2246_3,plain,
( hAPP(c_Finite__Set_Ofold1(U_7703,c_Groups_Otimes__class_Otimes(U_7703)),hAPP(hAPP(c_Set_Oinsert(U_7703),U_7705),U_7704)) = hAPP(hAPP(c_Finite__Set_Ofold(U_7703,U_7703,c_Groups_Otimes__class_Otimes(U_7703)),U_7705),U_7704)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7703),U_7704))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_7703) ),
inference(clausify,[status(thm)],[f_2246_2]) ).
fof(f_2247_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_2247_2,plain,
! [U_7707,U_7706] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7706),hAPP(hAPP(c_Power_Opower__class_Opower(U_7706),U_7707),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_7706),U_7707),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_7706) ),
inference(variable_rename,[status(thm)],[f_2247_1]) ).
cnf(f_2247_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7706),hAPP(hAPP(c_Power_Opower__class_Opower(U_7706),U_7707),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_7706),U_7707),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_7706) ),
inference(clausify,[status(thm)],[f_2247_2]) ).
fof(f_2248_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_2248_2,plain,
! [U_7709,U_7708] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7708),hAPP(c_Groups_Oabs__class_Oabs(U_7708),U_7709)),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_7708),U_7709),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_7708) ),
inference(variable_rename,[status(thm)],[f_2248_1]) ).
cnf(f_2248_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7708),hAPP(c_Groups_Oabs__class_Oabs(U_7708),U_7709)),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_7708),U_7709),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_7708) ),
inference(clausify,[status(thm)],[f_2248_2]) ).
fof(f_2249_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_2249_2,plain,
! [U_7716,U_7715,U_7714,U_7713,U_7712,U_7711,U_7710] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7710,U_7711,U_7712,U_7713,U_7714),hAPP(hAPP(U_7712,U_7715),U_7716)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7710),U_7715),U_7714))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7710,U_7711,U_7712,U_7713,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7710,tc_HOL_Obool)),U_7714),hAPP(hAPP(c_Set_Oinsert(U_7710),U_7715),c_Orderings_Obot__class_Obot(tc_fun(U_7710,tc_HOL_Obool))))),U_7716)) ),
inference(variable_rename,[status(thm)],[f_2249_1]) ).
cnf(f_2249_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7710,U_7711,U_7712,U_7713,U_7714),hAPP(hAPP(U_7712,U_7715),U_7716)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7710),U_7715),U_7714))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7710,U_7711,U_7712,U_7713,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7710,tc_HOL_Obool)),U_7714),hAPP(hAPP(c_Set_Oinsert(U_7710),U_7715),c_Orderings_Obot__class_Obot(tc_fun(U_7710,tc_HOL_Obool))))),U_7716)) ),
inference(clausify,[status(thm)],[f_2249_2]) ).
fof(f_2250_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_2250_2,plain,
! [U_7719,U_7718,U_7717] :
( hAPP(c_Finite__Set_Ofold1(U_7717,c_Groups_Otimes__class_Otimes(U_7717)),hAPP(hAPP(c_Set_Oinsert(U_7717),U_7719),U_7718)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7717),U_7719),hAPP(c_Finite__Set_Ofold1(U_7717,c_Groups_Otimes__class_Otimes(U_7717)),U_7718))
| hBOOL(hAPP(hAPP(c_member(U_7717),U_7719),U_7718))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7717),U_7718))
| U_7718 = c_Orderings_Obot__class_Obot(tc_fun(U_7717,tc_HOL_Obool))
| ~ class_Groups_Oab__semigroup__mult(U_7717) ),
inference(variable_rename,[status(thm)],[f_2250_1]) ).
cnf(f_2250_3,plain,
( hAPP(c_Finite__Set_Ofold1(U_7717,c_Groups_Otimes__class_Otimes(U_7717)),hAPP(hAPP(c_Set_Oinsert(U_7717),U_7719),U_7718)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7717),U_7719),hAPP(c_Finite__Set_Ofold1(U_7717,c_Groups_Otimes__class_Otimes(U_7717)),U_7718))
| hBOOL(hAPP(hAPP(c_member(U_7717),U_7719),U_7718))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7717),U_7718))
| U_7718 = c_Orderings_Obot__class_Obot(tc_fun(U_7717,tc_HOL_Obool))
| ~ class_Groups_Oab__semigroup__mult(U_7717) ),
inference(clausify,[status(thm)],[f_2250_2]) ).
fof(f_2251_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_2251_2,plain,
! [U_7722,U_7721,U_7720] :
( hAPP(c_Finite__Set_Ofold1(U_7720,c_Groups_Otimes__class_Otimes(U_7720)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7720,tc_HOL_Obool)),U_7721),U_7722)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7720),hAPP(c_Finite__Set_Ofold1(U_7720,c_Groups_Otimes__class_Otimes(U_7720)),U_7721)),hAPP(c_Finite__Set_Ofold1(U_7720,c_Groups_Otimes__class_Otimes(U_7720)),U_7722))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7720,tc_HOL_Obool)),U_7721),U_7722) != c_Orderings_Obot__class_Obot(tc_fun(U_7720,tc_HOL_Obool))
| U_7722 = c_Orderings_Obot__class_Obot(tc_fun(U_7720,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7720),U_7722))
| U_7721 = c_Orderings_Obot__class_Obot(tc_fun(U_7720,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7720),U_7721))
| ~ class_Groups_Oab__semigroup__mult(U_7720) ),
inference(variable_rename,[status(thm)],[f_2251_1]) ).
cnf(f_2251_3,plain,
( hAPP(c_Finite__Set_Ofold1(U_7720,c_Groups_Otimes__class_Otimes(U_7720)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7720,tc_HOL_Obool)),U_7721),U_7722)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7720),hAPP(c_Finite__Set_Ofold1(U_7720,c_Groups_Otimes__class_Otimes(U_7720)),U_7721)),hAPP(c_Finite__Set_Ofold1(U_7720,c_Groups_Otimes__class_Otimes(U_7720)),U_7722))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7720,tc_HOL_Obool)),U_7721),U_7722) != c_Orderings_Obot__class_Obot(tc_fun(U_7720,tc_HOL_Obool))
| U_7722 = c_Orderings_Obot__class_Obot(tc_fun(U_7720,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7720),U_7722))
| U_7721 = c_Orderings_Obot__class_Obot(tc_fun(U_7720,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7720),U_7721))
| ~ class_Groups_Oab__semigroup__mult(U_7720) ),
inference(clausify,[status(thm)],[f_2251_2]) ).
fof(f_2252_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_2252_2,plain,
! [U_7726,U_7725,U_7724,U_7723] :
( hAPP(U_7725,U_7726) = hAPP(c_Finite__Set_Ofold1(U_7723,U_7724),U_7726)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7723),U_7726))
| ~ c_Big__Operators_Osemilattice__big(U_7723,U_7724,U_7725) ),
inference(variable_rename,[status(thm)],[f_2252_1]) ).
cnf(f_2252_3,plain,
( hAPP(U_7725,U_7726) = hAPP(c_Finite__Set_Ofold1(U_7723,U_7724),U_7726)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7723),U_7726))
| ~ c_Big__Operators_Osemilattice__big(U_7723,U_7724,U_7725) ),
inference(clausify,[status(thm)],[f_2252_2]) ).
fof(f_2253_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_2253_2,plain,
! [U_7731,U_7730,U_7729,U_7728,U_7727] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7727,U_7728,hAPP(hAPP(c_Set_Oinsert(U_7727),U_7729),U_7730)),U_7731))
| hBOOL(hAPP(hAPP(c_member(U_7727),U_7729),U_7730))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7727,U_7727,U_7728,U_7729,U_7730),U_7731)) ),
inference(variable_rename,[status(thm)],[f_2253_1]) ).
cnf(f_2253_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7727,U_7728,hAPP(hAPP(c_Set_Oinsert(U_7727),U_7729),U_7730)),U_7731))
| hBOOL(hAPP(hAPP(c_member(U_7727),U_7729),U_7730))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7727,U_7727,U_7728,U_7729,U_7730),U_7731)) ),
inference(clausify,[status(thm)],[f_2253_2]) ).
fof(f_2254_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_2254_2,plain,
! [U_7739,U_7738,U_7737,U_7736,U_7735,U_7734,U_7733] :
( ? [U_7732] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7733,U_7734,U_7735,U_7736,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7733,tc_HOL_Obool)),U_7737),hAPP(hAPP(c_Set_Oinsert(U_7733),U_7739),c_Orderings_Obot__class_Obot(tc_fun(U_7733,tc_HOL_Obool))))),U_7732))
& U_7738 = hAPP(hAPP(U_7735,U_7739),U_7732) )
| ~ hBOOL(hAPP(hAPP(c_member(U_7733),U_7739),U_7737))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7733,U_7734,U_7735,U_7736,U_7737),U_7738))
| ~ c_Finite__Set_Ofun__left__comm(U_7733,U_7734,U_7735) ),
inference(variable_rename,[status(thm)],[f_2254_1]) ).
fof(f_2254_3,plain,
! [U_7739,U_7738,U_7737,U_7736,U_7735,U_7734,U_7733] :
( ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7733,U_7734,U_7735,U_7736,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7733,tc_HOL_Obool)),U_7737),hAPP(hAPP(c_Set_Oinsert(U_7733),U_7739),c_Orderings_Obot__class_Obot(tc_fun(U_7733,tc_HOL_Obool))))),sK173(U_7739,U_7738,U_7737,U_7736,U_7735,U_7734,U_7733)))
& U_7738 = hAPP(hAPP(U_7735,U_7739),sK173(U_7739,U_7738,U_7737,U_7736,U_7735,U_7734,U_7733)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_7733),U_7739),U_7737))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7733,U_7734,U_7735,U_7736,U_7737),U_7738))
| ~ c_Finite__Set_Ofun__left__comm(U_7733,U_7734,U_7735) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK173]),skolemize(U_7732,sK173(U_7739,U_7738,U_7737,U_7736,U_7735,U_7734,U_7733))],[f_2254_2]) ).
cnf(f_2254_4,plain,
( U_7738 = hAPP(hAPP(U_7735,U_7739),sK173(U_7739,U_7738,U_7737,U_7736,U_7735,U_7734,U_7733))
| ~ hBOOL(hAPP(hAPP(c_member(U_7733),U_7739),U_7737))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7733,U_7734,U_7735,U_7736,U_7737),U_7738))
| ~ c_Finite__Set_Ofun__left__comm(U_7733,U_7734,U_7735) ),
inference(clausify,[status(thm)],[f_2254_3]) ).
cnf(f_2254_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7733,U_7734,U_7735,U_7736,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7733,tc_HOL_Obool)),U_7737),hAPP(hAPP(c_Set_Oinsert(U_7733),U_7739),c_Orderings_Obot__class_Obot(tc_fun(U_7733,tc_HOL_Obool))))),sK173(U_7739,U_7738,U_7737,U_7736,U_7735,U_7734,U_7733)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7733),U_7739),U_7737))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7733,U_7734,U_7735,U_7736,U_7737),U_7738))
| ~ c_Finite__Set_Ofun__left__comm(U_7733,U_7734,U_7735) ),
inference(clausify,[status(thm)],[f_2254_3]) ).
fof(f_2255_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_2255_2,plain,
! [U_7743,U_7742] :
( hBOOL(hAPP(hAPP(c_member(U_7742),hAPP(c_Finite__Set_Ofold1(U_7742,c_Groups_Otimes__class_Otimes(U_7742)),U_7743)),U_7743))
| ? [U_7741,U_7740] : ~ hBOOL(hAPP(hAPP(c_member(U_7742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7742),U_7741),U_7740)),hAPP(hAPP(c_Set_Oinsert(U_7742),U_7741),hAPP(hAPP(c_Set_Oinsert(U_7742),U_7740),c_Orderings_Obot__class_Obot(tc_fun(U_7742,tc_HOL_Obool))))))
| U_7743 = c_Orderings_Obot__class_Obot(tc_fun(U_7742,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7742),U_7743))
| ~ class_Groups_Oab__semigroup__mult(U_7742) ),
inference(variable_rename,[status(thm)],[f_2255_1]) ).
fof(f_2255_3,plain,
! [U_7743,U_7742] :
( hBOOL(hAPP(hAPP(c_member(U_7742),hAPP(c_Finite__Set_Ofold1(U_7742,c_Groups_Otimes__class_Otimes(U_7742)),U_7743)),U_7743))
| ? [U_7740] : ~ hBOOL(hAPP(hAPP(c_member(U_7742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7742),sK174(U_7743,U_7742)),U_7740)),hAPP(hAPP(c_Set_Oinsert(U_7742),sK174(U_7743,U_7742)),hAPP(hAPP(c_Set_Oinsert(U_7742),U_7740),c_Orderings_Obot__class_Obot(tc_fun(U_7742,tc_HOL_Obool))))))
| U_7743 = c_Orderings_Obot__class_Obot(tc_fun(U_7742,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7742),U_7743))
| ~ class_Groups_Oab__semigroup__mult(U_7742) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK174]),skolemize(U_7741,sK174(U_7743,U_7742))],[f_2255_2]) ).
fof(f_2255_4,plain,
! [U_7743,U_7742] :
( hBOOL(hAPP(hAPP(c_member(U_7742),hAPP(c_Finite__Set_Ofold1(U_7742,c_Groups_Otimes__class_Otimes(U_7742)),U_7743)),U_7743))
| ~ hBOOL(hAPP(hAPP(c_member(U_7742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7742),sK174(U_7743,U_7742)),sK175(U_7743,U_7742))),hAPP(hAPP(c_Set_Oinsert(U_7742),sK174(U_7743,U_7742)),hAPP(hAPP(c_Set_Oinsert(U_7742),sK175(U_7743,U_7742)),c_Orderings_Obot__class_Obot(tc_fun(U_7742,tc_HOL_Obool))))))
| U_7743 = c_Orderings_Obot__class_Obot(tc_fun(U_7742,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7742),U_7743))
| ~ class_Groups_Oab__semigroup__mult(U_7742) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK175]),skolemize(U_7740,sK175(U_7743,U_7742))],[f_2255_3]) ).
cnf(f_2255_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_7742),hAPP(c_Finite__Set_Ofold1(U_7742,c_Groups_Otimes__class_Otimes(U_7742)),U_7743)),U_7743))
| ~ hBOOL(hAPP(hAPP(c_member(U_7742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7742),sK174(U_7743,U_7742)),sK175(U_7743,U_7742))),hAPP(hAPP(c_Set_Oinsert(U_7742),sK174(U_7743,U_7742)),hAPP(hAPP(c_Set_Oinsert(U_7742),sK175(U_7743,U_7742)),c_Orderings_Obot__class_Obot(tc_fun(U_7742,tc_HOL_Obool))))))
| U_7743 = c_Orderings_Obot__class_Obot(tc_fun(U_7742,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7742),U_7743))
| ~ class_Groups_Oab__semigroup__mult(U_7742) ),
inference(clausify,[status(thm)],[f_2255_4]) ).
fof(f_2256_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_2256_2,plain,
! [U_7746,U_7745,U_7744] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7744,U_7745,c_Orderings_Obot__class_Obot(tc_fun(U_7744,tc_HOL_Obool))),U_7746)),
inference(variable_rename,[status(thm)],[f_2256_1]) ).
cnf(f_2256_3,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7744,U_7745,c_Orderings_Obot__class_Obot(tc_fun(U_7744,tc_HOL_Obool))),U_7746)),
inference(clausify,[status(thm)],[f_2256_2]) ).
fof(f_2257_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_2257_2,plain,
! [U_7750,U_7749,U_7748,U_7747] :
( U_7749 != c_Orderings_Obot__class_Obot(tc_fun(U_7747,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7747,U_7748,U_7749),U_7750)) ),
inference(variable_rename,[status(thm)],[f_2257_1]) ).
cnf(f_2257_3,plain,
( U_7749 != c_Orderings_Obot__class_Obot(tc_fun(U_7747,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7747,U_7748,U_7749),U_7750)) ),
inference(clausify,[status(thm)],[f_2257_2]) ).
fof(f_2258_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_2258_2,plain,
! [U_7754,U_7753,U_7752,U_7751] :
( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7751,U_7752,hAPP(hAPP(c_Set_Oinsert(U_7751),U_7753),c_Orderings_Obot__class_Obot(tc_fun(U_7751,tc_HOL_Obool)))),U_7754))
| U_7753 != U_7754 )
& ( U_7753 = U_7754
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7751,U_7752,hAPP(hAPP(c_Set_Oinsert(U_7751),U_7753),c_Orderings_Obot__class_Obot(tc_fun(U_7751,tc_HOL_Obool)))),U_7754)) ) ),
inference(variable_rename,[status(thm)],[f_2258_1]) ).
fof(f_2258_3,plain,
( ! [U_7762,U_7760] :
( ! [U_7758,U_7756] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7756,U_7758,hAPP(hAPP(c_Set_Oinsert(U_7756),U_7760),c_Orderings_Obot__class_Obot(tc_fun(U_7756,tc_HOL_Obool)))),U_7762))
| U_7760 != U_7762 )
& ! [U_7761,U_7759] :
( ! [U_7757,U_7755] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7755,U_7757,hAPP(hAPP(c_Set_Oinsert(U_7755),U_7759),c_Orderings_Obot__class_Obot(tc_fun(U_7755,tc_HOL_Obool)))),U_7761))
| U_7759 = U_7761 ) ),
inference(miniscope,[status(thm)],[f_2258_2]) ).
cnf(f_2258_4,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7755,U_7757,hAPP(hAPP(c_Set_Oinsert(U_7755),U_7759),c_Orderings_Obot__class_Obot(tc_fun(U_7755,tc_HOL_Obool)))),U_7761))
| U_7759 = U_7761 ),
inference(clausify,[status(thm)],[f_2258_3]) ).
cnf(f_2258_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7756,U_7758,hAPP(hAPP(c_Set_Oinsert(U_7756),U_7760),c_Orderings_Obot__class_Obot(tc_fun(U_7756,tc_HOL_Obool)))),U_7762))
| U_7760 != U_7762 ),
inference(clausify,[status(thm)],[f_2258_3]) ).
fof(f_2259_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_2259_2,plain,
! [U_7767,U_7766,U_7765] :
( hAPP(U_7766,hAPP(c_Finite__Set_Ofold1(U_7765,c_Groups_Otimes__class_Otimes(U_7765)),U_7767)) = hAPP(c_Finite__Set_Ofold1(U_7765,c_Groups_Otimes__class_Otimes(U_7765)),hAPP(c_Set_Oimage(U_7765,U_7765,U_7766),U_7767))
| U_7767 = c_Orderings_Obot__class_Obot(tc_fun(U_7765,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7765),U_7767))
| ? [U_7764,U_7763] : hAPP(U_7766,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7765),U_7764),U_7763)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7765),hAPP(U_7766,U_7764)),hAPP(U_7766,U_7763))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_7765) ),
inference(variable_rename,[status(thm)],[f_2259_1]) ).
fof(f_2259_3,plain,
! [U_7767,U_7766,U_7765] :
( hAPP(U_7766,hAPP(c_Finite__Set_Ofold1(U_7765,c_Groups_Otimes__class_Otimes(U_7765)),U_7767)) = hAPP(c_Finite__Set_Ofold1(U_7765,c_Groups_Otimes__class_Otimes(U_7765)),hAPP(c_Set_Oimage(U_7765,U_7765,U_7766),U_7767))
| U_7767 = c_Orderings_Obot__class_Obot(tc_fun(U_7765,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7765),U_7767))
| ? [U_7763] : hAPP(U_7766,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7765),sK176(U_7767,U_7766,U_7765)),U_7763)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7765),hAPP(U_7766,sK176(U_7767,U_7766,U_7765))),hAPP(U_7766,U_7763))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_7765) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK176]),skolemize(U_7764,sK176(U_7767,U_7766,U_7765))],[f_2259_2]) ).
fof(f_2259_4,plain,
! [U_7767,U_7766,U_7765] :
( hAPP(U_7766,hAPP(c_Finite__Set_Ofold1(U_7765,c_Groups_Otimes__class_Otimes(U_7765)),U_7767)) = hAPP(c_Finite__Set_Ofold1(U_7765,c_Groups_Otimes__class_Otimes(U_7765)),hAPP(c_Set_Oimage(U_7765,U_7765,U_7766),U_7767))
| U_7767 = c_Orderings_Obot__class_Obot(tc_fun(U_7765,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7765),U_7767))
| hAPP(U_7766,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7765),sK176(U_7767,U_7766,U_7765)),sK177(U_7767,U_7766,U_7765))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7765),hAPP(U_7766,sK176(U_7767,U_7766,U_7765))),hAPP(U_7766,sK177(U_7767,U_7766,U_7765)))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_7765) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK177]),skolemize(U_7763,sK177(U_7767,U_7766,U_7765))],[f_2259_3]) ).
cnf(f_2259_5,plain,
( hAPP(U_7766,hAPP(c_Finite__Set_Ofold1(U_7765,c_Groups_Otimes__class_Otimes(U_7765)),U_7767)) = hAPP(c_Finite__Set_Ofold1(U_7765,c_Groups_Otimes__class_Otimes(U_7765)),hAPP(c_Set_Oimage(U_7765,U_7765,U_7766),U_7767))
| U_7767 = c_Orderings_Obot__class_Obot(tc_fun(U_7765,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7765),U_7767))
| hAPP(U_7766,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7765),sK176(U_7767,U_7766,U_7765)),sK177(U_7767,U_7766,U_7765))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7765),hAPP(U_7766,sK176(U_7767,U_7766,U_7765))),hAPP(U_7766,sK177(U_7767,U_7766,U_7765)))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_7765) ),
inference(clausify,[status(thm)],[f_2259_4]) ).
fof(f_2260_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_2260_2,plain,
! [U_7774,U_7773,U_7772,U_7771,U_7770] :
( ? [U_7769,U_7768] :
( ~ hBOOL(hAPP(hAPP(c_member(U_7770),U_7769),U_7768))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7770,U_7770,U_7771,U_7769,U_7768),U_7774))
& hAPP(hAPP(c_Set_Oinsert(U_7770),U_7772),U_7773) = hAPP(hAPP(c_Set_Oinsert(U_7770),U_7769),U_7768) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7770,U_7771,hAPP(hAPP(c_Set_Oinsert(U_7770),U_7772),U_7773)),U_7774)) ),
inference(variable_rename,[status(thm)],[f_2260_1]) ).
fof(f_2260_3,plain,
! [U_7774,U_7773,U_7772,U_7771,U_7770] :
( ? [U_7768] :
( ~ hBOOL(hAPP(hAPP(c_member(U_7770),sK178(U_7774,U_7773,U_7772,U_7771,U_7770)),U_7768))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7770,U_7770,U_7771,sK178(U_7774,U_7773,U_7772,U_7771,U_7770),U_7768),U_7774))
& hAPP(hAPP(c_Set_Oinsert(U_7770),U_7772),U_7773) = hAPP(hAPP(c_Set_Oinsert(U_7770),sK178(U_7774,U_7773,U_7772,U_7771,U_7770)),U_7768) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7770,U_7771,hAPP(hAPP(c_Set_Oinsert(U_7770),U_7772),U_7773)),U_7774)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK178]),skolemize(U_7769,sK178(U_7774,U_7773,U_7772,U_7771,U_7770))],[f_2260_2]) ).
fof(f_2260_4,plain,
! [U_7774,U_7773,U_7772,U_7771,U_7770] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_7770),sK178(U_7774,U_7773,U_7772,U_7771,U_7770)),sK179(U_7774,U_7773,U_7772,U_7771,U_7770)))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7770,U_7770,U_7771,sK178(U_7774,U_7773,U_7772,U_7771,U_7770),sK179(U_7774,U_7773,U_7772,U_7771,U_7770)),U_7774))
& hAPP(hAPP(c_Set_Oinsert(U_7770),U_7772),U_7773) = hAPP(hAPP(c_Set_Oinsert(U_7770),sK178(U_7774,U_7773,U_7772,U_7771,U_7770)),sK179(U_7774,U_7773,U_7772,U_7771,U_7770)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7770,U_7771,hAPP(hAPP(c_Set_Oinsert(U_7770),U_7772),U_7773)),U_7774)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK179]),skolemize(U_7768,sK179(U_7774,U_7773,U_7772,U_7771,U_7770))],[f_2260_3]) ).
cnf(f_2260_5,plain,
( hAPP(hAPP(c_Set_Oinsert(U_7770),U_7772),U_7773) = hAPP(hAPP(c_Set_Oinsert(U_7770),sK178(U_7774,U_7773,U_7772,U_7771,U_7770)),sK179(U_7774,U_7773,U_7772,U_7771,U_7770))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7770,U_7771,hAPP(hAPP(c_Set_Oinsert(U_7770),U_7772),U_7773)),U_7774)) ),
inference(clausify,[status(thm)],[f_2260_4]) ).
cnf(f_2260_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7770,U_7770,U_7771,sK178(U_7774,U_7773,U_7772,U_7771,U_7770),sK179(U_7774,U_7773,U_7772,U_7771,U_7770)),U_7774))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7770,U_7771,hAPP(hAPP(c_Set_Oinsert(U_7770),U_7772),U_7773)),U_7774)) ),
inference(clausify,[status(thm)],[f_2260_4]) ).
cnf(f_2260_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_7770),sK178(U_7774,U_7773,U_7772,U_7771,U_7770)),sK179(U_7774,U_7773,U_7772,U_7771,U_7770)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7770,U_7771,hAPP(hAPP(c_Set_Oinsert(U_7770),U_7772),U_7773)),U_7774)) ),
inference(clausify,[status(thm)],[f_2260_4]) ).
fof(f_2261_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_2261_2,plain,
! [U_7783,U_7782,U_7781,U_7780,U_7779] :
( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7779,U_7780,hAPP(hAPP(c_Set_Oinsert(U_7779),U_7781),U_7782)),U_7783))
| ! [U_7778,U_7777] :
( hBOOL(hAPP(hAPP(c_member(U_7779),U_7778),U_7777))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7779,U_7779,U_7780,U_7778,U_7777),U_7783))
| hAPP(hAPP(c_Set_Oinsert(U_7779),U_7781),U_7782) != hAPP(hAPP(c_Set_Oinsert(U_7779),U_7778),U_7777) ) )
& ( ? [U_7776,U_7775] :
( ~ hBOOL(hAPP(hAPP(c_member(U_7779),U_7776),U_7775))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7779,U_7779,U_7780,U_7776,U_7775),U_7783))
& hAPP(hAPP(c_Set_Oinsert(U_7779),U_7781),U_7782) = hAPP(hAPP(c_Set_Oinsert(U_7779),U_7776),U_7775) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7779,U_7780,hAPP(hAPP(c_Set_Oinsert(U_7779),U_7781),U_7782)),U_7783)) ) ),
inference(variable_rename,[status(thm)],[f_2261_1]) ).
fof(f_2261_3,plain,
( ! [U_7793,U_7791,U_7789,U_7787,U_7785] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7785,U_7787,hAPP(hAPP(c_Set_Oinsert(U_7785),U_7789),U_7791)),U_7793))
| ! [U_7778,U_7777] :
( hBOOL(hAPP(hAPP(c_member(U_7785),U_7778),U_7777))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7785,U_7785,U_7787,U_7778,U_7777),U_7793))
| hAPP(hAPP(c_Set_Oinsert(U_7785),U_7789),U_7791) != hAPP(hAPP(c_Set_Oinsert(U_7785),U_7778),U_7777) ) )
& ! [U_7792,U_7790,U_7788,U_7786,U_7784] :
( ? [U_7776,U_7775] :
( ~ hBOOL(hAPP(hAPP(c_member(U_7784),U_7776),U_7775))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7784,U_7784,U_7786,U_7776,U_7775),U_7792))
& hAPP(hAPP(c_Set_Oinsert(U_7784),U_7788),U_7790) = hAPP(hAPP(c_Set_Oinsert(U_7784),U_7776),U_7775) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7784,U_7786,hAPP(hAPP(c_Set_Oinsert(U_7784),U_7788),U_7790)),U_7792)) ) ),
inference(miniscope,[status(thm)],[f_2261_2]) ).
fof(f_2261_4,plain,
( ! [U_7793,U_7791,U_7789,U_7787,U_7785] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7785,U_7787,hAPP(hAPP(c_Set_Oinsert(U_7785),U_7789),U_7791)),U_7793))
| ! [U_7778,U_7777] :
( hBOOL(hAPP(hAPP(c_member(U_7785),U_7778),U_7777))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7785,U_7785,U_7787,U_7778,U_7777),U_7793))
| hAPP(hAPP(c_Set_Oinsert(U_7785),U_7789),U_7791) != hAPP(hAPP(c_Set_Oinsert(U_7785),U_7778),U_7777) ) )
& ! [U_7792,U_7790,U_7788,U_7786,U_7784] :
( ? [U_7775] :
( ~ hBOOL(hAPP(hAPP(c_member(U_7784),sK180(U_7792,U_7790,U_7788,U_7786,U_7784)),U_7775))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7784,U_7784,U_7786,sK180(U_7792,U_7790,U_7788,U_7786,U_7784),U_7775),U_7792))
& hAPP(hAPP(c_Set_Oinsert(U_7784),U_7788),U_7790) = hAPP(hAPP(c_Set_Oinsert(U_7784),sK180(U_7792,U_7790,U_7788,U_7786,U_7784)),U_7775) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7784,U_7786,hAPP(hAPP(c_Set_Oinsert(U_7784),U_7788),U_7790)),U_7792)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK180]),skolemize(U_7776,sK180(U_7792,U_7790,U_7788,U_7786,U_7784))],[f_2261_3]) ).
fof(f_2261_5,plain,
( ! [U_7793,U_7791,U_7789,U_7787,U_7785] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7785,U_7787,hAPP(hAPP(c_Set_Oinsert(U_7785),U_7789),U_7791)),U_7793))
| ! [U_7778,U_7777] :
( hBOOL(hAPP(hAPP(c_member(U_7785),U_7778),U_7777))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7785,U_7785,U_7787,U_7778,U_7777),U_7793))
| hAPP(hAPP(c_Set_Oinsert(U_7785),U_7789),U_7791) != hAPP(hAPP(c_Set_Oinsert(U_7785),U_7778),U_7777) ) )
& ! [U_7792,U_7790,U_7788,U_7786,U_7784] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_7784),sK180(U_7792,U_7790,U_7788,U_7786,U_7784)),sK181(U_7792,U_7790,U_7788,U_7786,U_7784)))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7784,U_7784,U_7786,sK180(U_7792,U_7790,U_7788,U_7786,U_7784),sK181(U_7792,U_7790,U_7788,U_7786,U_7784)),U_7792))
& hAPP(hAPP(c_Set_Oinsert(U_7784),U_7788),U_7790) = hAPP(hAPP(c_Set_Oinsert(U_7784),sK180(U_7792,U_7790,U_7788,U_7786,U_7784)),sK181(U_7792,U_7790,U_7788,U_7786,U_7784)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7784,U_7786,hAPP(hAPP(c_Set_Oinsert(U_7784),U_7788),U_7790)),U_7792)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK181]),skolemize(U_7775,sK181(U_7792,U_7790,U_7788,U_7786,U_7784))],[f_2261_4]) ).
cnf(f_2261_6,plain,
( hAPP(hAPP(c_Set_Oinsert(U_7784),U_7788),U_7790) = hAPP(hAPP(c_Set_Oinsert(U_7784),sK180(U_7792,U_7790,U_7788,U_7786,U_7784)),sK181(U_7792,U_7790,U_7788,U_7786,U_7784))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7784,U_7786,hAPP(hAPP(c_Set_Oinsert(U_7784),U_7788),U_7790)),U_7792)) ),
inference(clausify,[status(thm)],[f_2261_5]) ).
cnf(f_2261_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7784,U_7784,U_7786,sK180(U_7792,U_7790,U_7788,U_7786,U_7784),sK181(U_7792,U_7790,U_7788,U_7786,U_7784)),U_7792))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7784,U_7786,hAPP(hAPP(c_Set_Oinsert(U_7784),U_7788),U_7790)),U_7792)) ),
inference(clausify,[status(thm)],[f_2261_5]) ).
cnf(f_2261_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_7784),sK180(U_7792,U_7790,U_7788,U_7786,U_7784)),sK181(U_7792,U_7790,U_7788,U_7786,U_7784)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7784,U_7786,hAPP(hAPP(c_Set_Oinsert(U_7784),U_7788),U_7790)),U_7792)) ),
inference(clausify,[status(thm)],[f_2261_5]) ).
cnf(f_2261_9,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_7785,U_7787,hAPP(hAPP(c_Set_Oinsert(U_7785),U_7789),U_7791)),U_7793))
| hBOOL(hAPP(hAPP(c_member(U_7785),U_7778),U_7777))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_7785,U_7785,U_7787,U_7778,U_7777),U_7793))
| hAPP(hAPP(c_Set_Oinsert(U_7785),U_7789),U_7791) != hAPP(hAPP(c_Set_Oinsert(U_7785),U_7778),U_7777) ),
inference(clausify,[status(thm)],[f_2261_5]) ).
fof(f_2262_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_2262_2,plain,
! [U_7795,U_7794] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7794),c_Groups_Ozero__class_Ozero(U_7794)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7794),U_7795),hAPP(c_Int_Onumber__class_Onumber__of(U_7794),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7794),c_Groups_Ozero__class_Ozero(U_7794)),U_7795)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7794),c_Groups_Ozero__class_Ozero(U_7794)),U_7795))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7794),c_Groups_Ozero__class_Ozero(U_7794)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7794),U_7795),hAPP(c_Int_Onumber__class_Onumber__of(U_7794),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
| ~ class_Int_Onumber__ring(U_7794)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7794) ),
inference(variable_rename,[status(thm)],[f_2262_1]) ).
cnf(f_2262_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7794),c_Groups_Ozero__class_Ozero(U_7794)),U_7795))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7794),c_Groups_Ozero__class_Ozero(U_7794)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7794),U_7795),hAPP(c_Int_Onumber__class_Onumber__of(U_7794),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Int_Onumber__ring(U_7794)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7794) ),
inference(clausify,[status(thm)],[f_2262_2]) ).
cnf(f_2262_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7794),c_Groups_Ozero__class_Ozero(U_7794)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7794),U_7795),hAPP(c_Int_Onumber__class_Onumber__of(U_7794),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7794),c_Groups_Ozero__class_Ozero(U_7794)),U_7795))
| ~ class_Int_Onumber__ring(U_7794)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7794) ),
inference(clausify,[status(thm)],[f_2262_2]) ).
fof(f_2263_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_2263_2,plain,
! [U_7798,U_7797,U_7796] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_7796),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7796),U_7797),U_7798)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7796),hAPP(c_Groups_Ouminus__class_Ouminus(U_7796),U_7797)),U_7798)
| ~ class_Rings_Odivision__ring(U_7796) ),
inference(variable_rename,[status(thm)],[f_2263_1]) ).
cnf(f_2263_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_7796),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7796),U_7797),U_7798)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7796),hAPP(c_Groups_Ouminus__class_Ouminus(U_7796),U_7797)),U_7798)
| ~ class_Rings_Odivision__ring(U_7796) ),
inference(clausify,[status(thm)],[f_2263_2]) ).
fof(f_2264_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_2264_2,plain,
! [U_7800,U_7799] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7799),U_7800),c_Groups_Oone__class_Oone(U_7799)) = U_7800
| ~ class_Rings_Odivision__ring(U_7799) ),
inference(variable_rename,[status(thm)],[f_2264_1]) ).
cnf(f_2264_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7799),U_7800),c_Groups_Oone__class_Oone(U_7799)) = U_7800
| ~ class_Rings_Odivision__ring(U_7799) ),
inference(clausify,[status(thm)],[f_2264_2]) ).
fof(f_2265_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_2265_2,plain,
! [U_7804,U_7803,U_7802,U_7801] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7801),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7801),U_7802),U_7803)),U_7804) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7801),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7801),U_7802),U_7804)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7801),U_7803),U_7804))
| ~ class_Rings_Odivision__ring(U_7801) ),
inference(variable_rename,[status(thm)],[f_2265_1]) ).
cnf(f_2265_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7801),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7801),U_7802),U_7803)),U_7804) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7801),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7801),U_7802),U_7804)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7801),U_7803),U_7804))
| ~ class_Rings_Odivision__ring(U_7801) ),
inference(clausify,[status(thm)],[f_2265_2]) ).
fof(f_2266_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_2266_2,plain,
! [U_7808,U_7807,U_7806,U_7805] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7805),U_7806),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7805),U_7807),U_7808)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7805),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7805),U_7806),U_7807)),U_7808)
| ~ class_Rings_Odivision__ring(U_7805) ),
inference(variable_rename,[status(thm)],[f_2266_1]) ).
cnf(f_2266_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7805),U_7806),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7805),U_7807),U_7808)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7805),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7805),U_7806),U_7807)),U_7808)
| ~ class_Rings_Odivision__ring(U_7805) ),
inference(clausify,[status(thm)],[f_2266_2]) ).
fof(f_2267_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_2267_2,plain,
! [U_7812,U_7811,U_7810,U_7809] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7809),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7809),U_7810),U_7811)),U_7812) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7809),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7809),U_7810),U_7812)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7809),U_7811),U_7812))
| ~ class_Rings_Odivision__ring(U_7809) ),
inference(variable_rename,[status(thm)],[f_2267_1]) ).
cnf(f_2267_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7809),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7809),U_7810),U_7811)),U_7812) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7809),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7809),U_7810),U_7812)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7809),U_7811),U_7812))
| ~ class_Rings_Odivision__ring(U_7809) ),
inference(clausify,[status(thm)],[f_2267_2]) ).
fof(f_2268_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_2268_2,plain,
! [U_7814,U_7813] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7813),U_7814),c_Groups_Ozero__class_Ozero(U_7813)) = c_Groups_Ozero__class_Ozero(U_7813)
| ~ class_Rings_Odivision__ring__inverse__zero(U_7813) ),
inference(variable_rename,[status(thm)],[f_2268_1]) ).
cnf(f_2268_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7813),U_7814),c_Groups_Ozero__class_Ozero(U_7813)) = c_Groups_Ozero__class_Ozero(U_7813)
| ~ class_Rings_Odivision__ring__inverse__zero(U_7813) ),
inference(clausify,[status(thm)],[f_2268_2]) ).
fof(f_2269_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_2269_2,plain,
! [U_7816,U_7815] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7815),c_Groups_Ozero__class_Ozero(U_7815)),U_7816) = c_Groups_Ozero__class_Ozero(U_7815)
| ~ class_Rings_Odivision__ring(U_7815) ),
inference(variable_rename,[status(thm)],[f_2269_1]) ).
cnf(f_2269_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7815),c_Groups_Ozero__class_Ozero(U_7815)),U_7816) = c_Groups_Ozero__class_Ozero(U_7815)
| ~ class_Rings_Odivision__ring(U_7815) ),
inference(clausify,[status(thm)],[f_2269_2]) ).
fof(f_2270_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_2270_2,plain,
! [U_7820,U_7819,U_7818,U_7817] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7817),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7817),U_7818),U_7819)),U_7820) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7817),hAPP(hAPP(c_Power_Opower__class_Opower(U_7817),U_7818),U_7820)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7817),U_7819),U_7820))
| ~ class_Fields_Ofield__inverse__zero(U_7817) ),
inference(variable_rename,[status(thm)],[f_2270_1]) ).
cnf(f_2270_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7817),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7817),U_7818),U_7819)),U_7820) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7817),hAPP(hAPP(c_Power_Opower__class_Opower(U_7817),U_7818),U_7820)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7817),U_7819),U_7820))
| ~ class_Fields_Ofield__inverse__zero(U_7817) ),
inference(clausify,[status(thm)],[f_2270_2]) ).
fof(f_2271_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_2271_2,plain,
! [U_7824,U_7823,U_7822,U_7821] :
( U_7823 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7821),U_7824),U_7822)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7821),U_7823),U_7822) != U_7824
| U_7822 = c_Groups_Ozero__class_Ozero(U_7821)
| ~ class_Rings_Odivision__ring(U_7821) ),
inference(variable_rename,[status(thm)],[f_2271_1]) ).
cnf(f_2271_3,plain,
( U_7823 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7821),U_7824),U_7822)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7821),U_7823),U_7822) != U_7824
| U_7822 = c_Groups_Ozero__class_Ozero(U_7821)
| ~ class_Rings_Odivision__ring(U_7821) ),
inference(clausify,[status(thm)],[f_2271_2]) ).
fof(f_2272_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_2272_2,plain,
! [U_7828,U_7827,U_7826,U_7825] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7825),U_7827),U_7826) = U_7828
| U_7827 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7825),U_7828),U_7826)
| U_7826 = c_Groups_Ozero__class_Ozero(U_7825)
| ~ class_Rings_Odivision__ring(U_7825) ),
inference(variable_rename,[status(thm)],[f_2272_1]) ).
cnf(f_2272_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7825),U_7827),U_7826) = U_7828
| U_7827 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7825),U_7828),U_7826)
| U_7826 = c_Groups_Ozero__class_Ozero(U_7825)
| ~ class_Rings_Odivision__ring(U_7825) ),
inference(clausify,[status(thm)],[f_2272_2]) ).
fof(f_2273_1,plain,
! [V_a_2,V_b_2,V_c_2,T_b] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
| V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) )
& ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) != V_a_2 ) )
| V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
| ~ class_Rings_Odivision__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__divide__eq__eq]) ).
fof(f_2273_2,plain,
! [U_7832,U_7831,U_7830,U_7829] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7829),U_7831),U_7830) = U_7832
| U_7831 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7829),U_7832),U_7830) )
& ( U_7831 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7829),U_7832),U_7830)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7829),U_7831),U_7830) != U_7832 ) )
| U_7830 = c_Groups_Ozero__class_Ozero(U_7829)
| ~ class_Rings_Odivision__ring(U_7829) ),
inference(variable_rename,[status(thm)],[f_2273_1]) ).
cnf(f_2273_3,plain,
( U_7831 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7829),U_7832),U_7830)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7829),U_7831),U_7830) != U_7832
| U_7830 = c_Groups_Ozero__class_Ozero(U_7829)
| ~ class_Rings_Odivision__ring(U_7829) ),
inference(clausify,[status(thm)],[f_2273_2]) ).
cnf(f_2273_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7829),U_7831),U_7830) = U_7832
| U_7831 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7829),U_7832),U_7830)
| U_7830 = c_Groups_Ozero__class_Ozero(U_7829)
| ~ class_Rings_Odivision__ring(U_7829) ),
inference(clausify,[status(thm)],[f_2273_2]) ).
fof(f_2274_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) != V_b_2 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2
| V_a_2 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) ) )
| V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
| ~ class_Rings_Odivision__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__eq__divide__eq]) ).
fof(f_2274_2,plain,
! [U_7836,U_7835,U_7834,U_7833] :
( ( ( U_7835 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7833),U_7836),U_7834)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7833),U_7835),U_7834) != U_7836 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7833),U_7835),U_7834) = U_7836
| U_7835 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7833),U_7836),U_7834) ) )
| U_7834 = c_Groups_Ozero__class_Ozero(U_7833)
| ~ class_Rings_Odivision__ring(U_7833) ),
inference(variable_rename,[status(thm)],[f_2274_1]) ).
cnf(f_2274_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7833),U_7835),U_7834) = U_7836
| U_7835 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7833),U_7836),U_7834)
| U_7834 = c_Groups_Ozero__class_Ozero(U_7833)
| ~ class_Rings_Odivision__ring(U_7833) ),
inference(clausify,[status(thm)],[f_2274_2]) ).
cnf(f_2274_4,plain,
( U_7835 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7833),U_7836),U_7834)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7833),U_7835),U_7834) != U_7836
| U_7834 = c_Groups_Ozero__class_Ozero(U_7833)
| ~ class_Rings_Odivision__ring(U_7833) ),
inference(clausify,[status(thm)],[f_2274_2]) ).
fof(f_2275_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_2275_2,plain,
! [U_7838,U_7837] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7837),U_7838),U_7838) = c_Groups_Oone__class_Oone(U_7837)
| U_7838 = c_Groups_Ozero__class_Ozero(U_7837) )
& ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7837),U_7838),U_7838) = c_Groups_Ozero__class_Ozero(U_7837)
| U_7838 != c_Groups_Ozero__class_Ozero(U_7837) ) )
| ~ class_Rings_Odivision__ring__inverse__zero(U_7837) ),
inference(variable_rename,[status(thm)],[f_2275_1]) ).
cnf(f_2275_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7837),U_7838),U_7838) = c_Groups_Ozero__class_Ozero(U_7837)
| U_7838 != c_Groups_Ozero__class_Ozero(U_7837)
| ~ class_Rings_Odivision__ring__inverse__zero(U_7837) ),
inference(clausify,[status(thm)],[f_2275_2]) ).
cnf(f_2275_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7837),U_7838),U_7838) = c_Groups_Oone__class_Oone(U_7837)
| U_7838 = c_Groups_Ozero__class_Ozero(U_7837)
| ~ class_Rings_Odivision__ring__inverse__zero(U_7837) ),
inference(clausify,[status(thm)],[f_2275_2]) ).
fof(f_2276_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_2276_2,plain,
! [U_7840,U_7839] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7839),U_7840),U_7840) = c_Groups_Oone__class_Oone(U_7839)
| U_7840 = c_Groups_Ozero__class_Ozero(U_7839)
| ~ class_Rings_Odivision__ring(U_7839) ),
inference(variable_rename,[status(thm)],[f_2276_1]) ).
cnf(f_2276_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7839),U_7840),U_7840) = c_Groups_Oone__class_Oone(U_7839)
| U_7840 = c_Groups_Ozero__class_Ozero(U_7839)
| ~ class_Rings_Odivision__ring(U_7839) ),
inference(clausify,[status(thm)],[f_2276_2]) ).
fof(f_2277_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_2277_2,plain,
! [U_7843,U_7842,U_7841] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7841),U_7843),U_7842) = c_Groups_Oone__class_Oone(U_7841)
| U_7843 != U_7842 )
& ( U_7843 = U_7842
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7841),U_7843),U_7842) != c_Groups_Oone__class_Oone(U_7841) ) )
| U_7842 = c_Groups_Ozero__class_Ozero(U_7841)
| ~ class_Rings_Odivision__ring(U_7841) ),
inference(variable_rename,[status(thm)],[f_2277_1]) ).
cnf(f_2277_3,plain,
( U_7843 = U_7842
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7841),U_7843),U_7842) != c_Groups_Oone__class_Oone(U_7841)
| U_7842 = c_Groups_Ozero__class_Ozero(U_7841)
| ~ class_Rings_Odivision__ring(U_7841) ),
inference(clausify,[status(thm)],[f_2277_2]) ).
cnf(f_2277_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7841),U_7843),U_7842) = c_Groups_Oone__class_Oone(U_7841)
| U_7843 != U_7842
| U_7842 = c_Groups_Ozero__class_Ozero(U_7841)
| ~ class_Rings_Odivision__ring(U_7841) ),
inference(clausify,[status(thm)],[f_2277_2]) ).
fof(f_2278_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_2278_2,plain,
! [U_7846,U_7845,U_7844] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7844),hAPP(c_Groups_Ouminus__class_Ouminus(U_7844),U_7846)),hAPP(c_Groups_Ouminus__class_Ouminus(U_7844),U_7845)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7844),U_7846),U_7845)
| U_7845 = c_Groups_Ozero__class_Ozero(U_7844)
| ~ class_Rings_Odivision__ring(U_7844) ),
inference(variable_rename,[status(thm)],[f_2278_1]) ).
cnf(f_2278_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7844),hAPP(c_Groups_Ouminus__class_Ouminus(U_7844),U_7846)),hAPP(c_Groups_Ouminus__class_Ouminus(U_7844),U_7845)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7844),U_7846),U_7845)
| U_7845 = c_Groups_Ozero__class_Ozero(U_7844)
| ~ class_Rings_Odivision__ring(U_7844) ),
inference(clausify,[status(thm)],[f_2278_2]) ).
fof(f_2279_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_2279_2,plain,
! [U_7849,U_7848,U_7847] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_7847),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7847),U_7849),U_7848)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7847),U_7849),hAPP(c_Groups_Ouminus__class_Ouminus(U_7847),U_7848))
| U_7848 = c_Groups_Ozero__class_Ozero(U_7847)
| ~ class_Rings_Odivision__ring(U_7847) ),
inference(variable_rename,[status(thm)],[f_2279_1]) ).
cnf(f_2279_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_7847),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7847),U_7849),U_7848)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7847),U_7849),hAPP(c_Groups_Ouminus__class_Ouminus(U_7847),U_7848))
| U_7848 = c_Groups_Ozero__class_Ozero(U_7847)
| ~ class_Rings_Odivision__ring(U_7847) ),
inference(clausify,[status(thm)],[f_2279_2]) ).
fof(f_2280_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_2280_2,plain,
! [U_7853,U_7852,U_7851,U_7850] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7850),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7850),U_7852),U_7851)),U_7853) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7850),hAPP(hAPP(c_Power_Opower__class_Opower(U_7850),U_7852),U_7853)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7850),U_7851),U_7853))
| U_7851 = c_Groups_Ozero__class_Ozero(U_7850)
| ~ class_Fields_Ofield(U_7850) ),
inference(variable_rename,[status(thm)],[f_2280_1]) ).
cnf(f_2280_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7850),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7850),U_7852),U_7851)),U_7853) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7850),hAPP(hAPP(c_Power_Opower__class_Opower(U_7850),U_7852),U_7853)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7850),U_7851),U_7853))
| U_7851 = c_Groups_Ozero__class_Ozero(U_7850)
| ~ class_Fields_Ofield(U_7850) ),
inference(clausify,[status(thm)],[f_2280_2]) ).
fof(f_2281_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_2281_2,plain,
! [U_7856,U_7855,U_7854] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7854),c_Groups_Oone__class_Oone(U_7854)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7854),U_7855),U_7856)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7854),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7854),c_Groups_Oone__class_Oone(U_7854)),U_7855)),U_7856)
| ~ class_Fields_Ofield__inverse__zero(U_7854) ),
inference(variable_rename,[status(thm)],[f_2281_1]) ).
cnf(f_2281_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7854),c_Groups_Oone__class_Oone(U_7854)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7854),U_7855),U_7856)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7854),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7854),c_Groups_Oone__class_Oone(U_7854)),U_7855)),U_7856)
| ~ class_Fields_Ofield__inverse__zero(U_7854) ),
inference(clausify,[status(thm)],[f_2281_2]) ).
fof(f_2282_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_2282_2,plain,
! [U_7860,U_7859,U_7858,U_7857] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7857),U_7858),hAPP(c_Int_Onumber__class_Onumber__of(U_7857),U_7859)) = U_7860
| ( U_7860 != c_Groups_Ozero__class_Ozero(U_7857)
& hAPP(c_Int_Onumber__class_Onumber__of(U_7857),U_7859) = c_Groups_Ozero__class_Ozero(U_7857) )
| ( U_7858 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7857),U_7860),hAPP(c_Int_Onumber__class_Onumber__of(U_7857),U_7859))
& hAPP(c_Int_Onumber__class_Onumber__of(U_7857),U_7859) != c_Groups_Ozero__class_Ozero(U_7857) ) )
& ( ( ( U_7860 = c_Groups_Ozero__class_Ozero(U_7857)
| hAPP(c_Int_Onumber__class_Onumber__of(U_7857),U_7859) != c_Groups_Ozero__class_Ozero(U_7857) )
& ( U_7858 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7857),U_7860),hAPP(c_Int_Onumber__class_Onumber__of(U_7857),U_7859))
| hAPP(c_Int_Onumber__class_Onumber__of(U_7857),U_7859) = c_Groups_Ozero__class_Ozero(U_7857) ) )
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7857),U_7858),hAPP(c_Int_Onumber__class_Onumber__of(U_7857),U_7859)) != U_7860 ) )
| ~ class_Int_Onumber(U_7857)
| ~ class_Fields_Ofield__inverse__zero(U_7857) ),
inference(variable_rename,[status(thm)],[f_2282_1]) ).
cnf(f_2282_3,plain,
( U_7858 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7857),U_7860),hAPP(c_Int_Onumber__class_Onumber__of(U_7857),U_7859))
| hAPP(c_Int_Onumber__class_Onumber__of(U_7857),U_7859) = c_Groups_Ozero__class_Ozero(U_7857)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7857),U_7858),hAPP(c_Int_Onumber__class_Onumber__of(U_7857),U_7859)) != U_7860
| ~ class_Int_Onumber(U_7857)
| ~ class_Fields_Ofield__inverse__zero(U_7857) ),
inference(clausify,[status(thm)],[f_2282_2]) ).
cnf(f_2282_4,plain,
( U_7860 = c_Groups_Ozero__class_Ozero(U_7857)
| hAPP(c_Int_Onumber__class_Onumber__of(U_7857),U_7859) != c_Groups_Ozero__class_Ozero(U_7857)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7857),U_7858),hAPP(c_Int_Onumber__class_Onumber__of(U_7857),U_7859)) != U_7860
| ~ class_Int_Onumber(U_7857)
| ~ class_Fields_Ofield__inverse__zero(U_7857) ),
inference(clausify,[status(thm)],[f_2282_2]) ).
cnf(f_2282_5,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_7857),U_7859) = c_Groups_Ozero__class_Ozero(U_7857)
| hAPP(c_Int_Onumber__class_Onumber__of(U_7857),U_7859) != c_Groups_Ozero__class_Ozero(U_7857)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7857),U_7858),hAPP(c_Int_Onumber__class_Onumber__of(U_7857),U_7859)) = U_7860
| ~ class_Int_Onumber(U_7857)
| ~ class_Fields_Ofield__inverse__zero(U_7857) ),
inference(clausify,[status(thm)],[f_2282_2]) ).
cnf(f_2282_6,plain,
( U_7860 != c_Groups_Ozero__class_Ozero(U_7857)
| hAPP(c_Int_Onumber__class_Onumber__of(U_7857),U_7859) != c_Groups_Ozero__class_Ozero(U_7857)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7857),U_7858),hAPP(c_Int_Onumber__class_Onumber__of(U_7857),U_7859)) = U_7860
| ~ class_Int_Onumber(U_7857)
| ~ class_Fields_Ofield__inverse__zero(U_7857) ),
inference(clausify,[status(thm)],[f_2282_2]) ).
cnf(f_2282_7,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_7857),U_7859) = c_Groups_Ozero__class_Ozero(U_7857)
| U_7858 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7857),U_7860),hAPP(c_Int_Onumber__class_Onumber__of(U_7857),U_7859))
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7857),U_7858),hAPP(c_Int_Onumber__class_Onumber__of(U_7857),U_7859)) = U_7860
| ~ class_Int_Onumber(U_7857)
| ~ class_Fields_Ofield__inverse__zero(U_7857) ),
inference(clausify,[status(thm)],[f_2282_2]) ).
cnf(f_2282_8,plain,
( U_7860 != c_Groups_Ozero__class_Ozero(U_7857)
| U_7858 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7857),U_7860),hAPP(c_Int_Onumber__class_Onumber__of(U_7857),U_7859))
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7857),U_7858),hAPP(c_Int_Onumber__class_Onumber__of(U_7857),U_7859)) = U_7860
| ~ class_Int_Onumber(U_7857)
| ~ class_Fields_Ofield__inverse__zero(U_7857) ),
inference(clausify,[status(thm)],[f_2282_2]) ).
fof(f_2283_1,plain,
! [V_w_2,V_c_2,V_b_2,T_b] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
| ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
& V_c_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)
& V_c_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
& ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_c_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)
| V_c_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Ofield__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of]) ).
fof(f_2283_2,plain,
! [U_7864,U_7863,U_7862,U_7861] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7861),U_7862),U_7863) = hAPP(c_Int_Onumber__class_Onumber__of(U_7861),U_7864)
| ( hAPP(c_Int_Onumber__class_Onumber__of(U_7861),U_7864) != c_Groups_Ozero__class_Ozero(U_7861)
& U_7863 = c_Groups_Ozero__class_Ozero(U_7861) )
| ( U_7862 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7861),hAPP(c_Int_Onumber__class_Onumber__of(U_7861),U_7864)),U_7863)
& U_7863 != c_Groups_Ozero__class_Ozero(U_7861) ) )
& ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_7861),U_7864) = c_Groups_Ozero__class_Ozero(U_7861)
| U_7863 != c_Groups_Ozero__class_Ozero(U_7861) )
& ( U_7862 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7861),hAPP(c_Int_Onumber__class_Onumber__of(U_7861),U_7864)),U_7863)
| U_7863 = c_Groups_Ozero__class_Ozero(U_7861) ) )
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7861),U_7862),U_7863) != hAPP(c_Int_Onumber__class_Onumber__of(U_7861),U_7864) ) )
| ~ class_Int_Onumber(U_7861)
| ~ class_Fields_Ofield__inverse__zero(U_7861) ),
inference(variable_rename,[status(thm)],[f_2283_1]) ).
cnf(f_2283_3,plain,
( U_7862 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7861),hAPP(c_Int_Onumber__class_Onumber__of(U_7861),U_7864)),U_7863)
| U_7863 = c_Groups_Ozero__class_Ozero(U_7861)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7861),U_7862),U_7863) != hAPP(c_Int_Onumber__class_Onumber__of(U_7861),U_7864)
| ~ class_Int_Onumber(U_7861)
| ~ class_Fields_Ofield__inverse__zero(U_7861) ),
inference(clausify,[status(thm)],[f_2283_2]) ).
cnf(f_2283_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_7861),U_7864) = c_Groups_Ozero__class_Ozero(U_7861)
| U_7863 != c_Groups_Ozero__class_Ozero(U_7861)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7861),U_7862),U_7863) != hAPP(c_Int_Onumber__class_Onumber__of(U_7861),U_7864)
| ~ class_Int_Onumber(U_7861)
| ~ class_Fields_Ofield__inverse__zero(U_7861) ),
inference(clausify,[status(thm)],[f_2283_2]) ).
cnf(f_2283_5,plain,
( U_7863 = c_Groups_Ozero__class_Ozero(U_7861)
| U_7863 != c_Groups_Ozero__class_Ozero(U_7861)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7861),U_7862),U_7863) = hAPP(c_Int_Onumber__class_Onumber__of(U_7861),U_7864)
| ~ class_Int_Onumber(U_7861)
| ~ class_Fields_Ofield__inverse__zero(U_7861) ),
inference(clausify,[status(thm)],[f_2283_2]) ).
cnf(f_2283_6,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_7861),U_7864) != c_Groups_Ozero__class_Ozero(U_7861)
| U_7863 != c_Groups_Ozero__class_Ozero(U_7861)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7861),U_7862),U_7863) = hAPP(c_Int_Onumber__class_Onumber__of(U_7861),U_7864)
| ~ class_Int_Onumber(U_7861)
| ~ class_Fields_Ofield__inverse__zero(U_7861) ),
inference(clausify,[status(thm)],[f_2283_2]) ).
cnf(f_2283_7,plain,
( U_7863 = c_Groups_Ozero__class_Ozero(U_7861)
| U_7862 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7861),hAPP(c_Int_Onumber__class_Onumber__of(U_7861),U_7864)),U_7863)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7861),U_7862),U_7863) = hAPP(c_Int_Onumber__class_Onumber__of(U_7861),U_7864)
| ~ class_Int_Onumber(U_7861)
| ~ class_Fields_Ofield__inverse__zero(U_7861) ),
inference(clausify,[status(thm)],[f_2283_2]) ).
cnf(f_2283_8,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_7861),U_7864) != c_Groups_Ozero__class_Ozero(U_7861)
| U_7862 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7861),hAPP(c_Int_Onumber__class_Onumber__of(U_7861),U_7864)),U_7863)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7861),U_7862),U_7863) = hAPP(c_Int_Onumber__class_Onumber__of(U_7861),U_7864)
| ~ class_Int_Onumber(U_7861)
| ~ class_Fields_Ofield__inverse__zero(U_7861) ),
inference(clausify,[status(thm)],[f_2283_2]) ).
fof(f_2284_1,plain,
! [V_c_2,V_b_2,V_w_2,T_b] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
| ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
& V_c_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) != V_b_2
& V_c_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
& ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_c_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) = V_b_2
| V_c_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
| hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Ofield__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of]) ).
fof(f_2284_2,plain,
! [U_7868,U_7867,U_7866,U_7865] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_7865),U_7866) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7865),U_7867),U_7868)
| ( hAPP(c_Int_Onumber__class_Onumber__of(U_7865),U_7866) != c_Groups_Ozero__class_Ozero(U_7865)
& U_7868 = c_Groups_Ozero__class_Ozero(U_7865) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7865),hAPP(c_Int_Onumber__class_Onumber__of(U_7865),U_7866)),U_7868) != U_7867
& U_7868 != c_Groups_Ozero__class_Ozero(U_7865) ) )
& ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_7865),U_7866) = c_Groups_Ozero__class_Ozero(U_7865)
| U_7868 != c_Groups_Ozero__class_Ozero(U_7865) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7865),hAPP(c_Int_Onumber__class_Onumber__of(U_7865),U_7866)),U_7868) = U_7867
| U_7868 = c_Groups_Ozero__class_Ozero(U_7865) ) )
| hAPP(c_Int_Onumber__class_Onumber__of(U_7865),U_7866) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7865),U_7867),U_7868) ) )
| ~ class_Int_Onumber(U_7865)
| ~ class_Fields_Ofield__inverse__zero(U_7865) ),
inference(variable_rename,[status(thm)],[f_2284_1]) ).
cnf(f_2284_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7865),hAPP(c_Int_Onumber__class_Onumber__of(U_7865),U_7866)),U_7868) = U_7867
| U_7868 = c_Groups_Ozero__class_Ozero(U_7865)
| hAPP(c_Int_Onumber__class_Onumber__of(U_7865),U_7866) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7865),U_7867),U_7868)
| ~ class_Int_Onumber(U_7865)
| ~ class_Fields_Ofield__inverse__zero(U_7865) ),
inference(clausify,[status(thm)],[f_2284_2]) ).
cnf(f_2284_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_7865),U_7866) = c_Groups_Ozero__class_Ozero(U_7865)
| U_7868 != c_Groups_Ozero__class_Ozero(U_7865)
| hAPP(c_Int_Onumber__class_Onumber__of(U_7865),U_7866) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7865),U_7867),U_7868)
| ~ class_Int_Onumber(U_7865)
| ~ class_Fields_Ofield__inverse__zero(U_7865) ),
inference(clausify,[status(thm)],[f_2284_2]) ).
cnf(f_2284_5,plain,
( U_7868 = c_Groups_Ozero__class_Ozero(U_7865)
| U_7868 != c_Groups_Ozero__class_Ozero(U_7865)
| hAPP(c_Int_Onumber__class_Onumber__of(U_7865),U_7866) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7865),U_7867),U_7868)
| ~ class_Int_Onumber(U_7865)
| ~ class_Fields_Ofield__inverse__zero(U_7865) ),
inference(clausify,[status(thm)],[f_2284_2]) ).
cnf(f_2284_6,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_7865),U_7866) != c_Groups_Ozero__class_Ozero(U_7865)
| U_7868 != c_Groups_Ozero__class_Ozero(U_7865)
| hAPP(c_Int_Onumber__class_Onumber__of(U_7865),U_7866) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7865),U_7867),U_7868)
| ~ class_Int_Onumber(U_7865)
| ~ class_Fields_Ofield__inverse__zero(U_7865) ),
inference(clausify,[status(thm)],[f_2284_2]) ).
cnf(f_2284_7,plain,
( U_7868 = c_Groups_Ozero__class_Ozero(U_7865)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7865),hAPP(c_Int_Onumber__class_Onumber__of(U_7865),U_7866)),U_7868) != U_7867
| hAPP(c_Int_Onumber__class_Onumber__of(U_7865),U_7866) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7865),U_7867),U_7868)
| ~ class_Int_Onumber(U_7865)
| ~ class_Fields_Ofield__inverse__zero(U_7865) ),
inference(clausify,[status(thm)],[f_2284_2]) ).
cnf(f_2284_8,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_7865),U_7866) != c_Groups_Ozero__class_Ozero(U_7865)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7865),hAPP(c_Int_Onumber__class_Onumber__of(U_7865),U_7866)),U_7868) != U_7867
| hAPP(c_Int_Onumber__class_Onumber__of(U_7865),U_7866) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7865),U_7867),U_7868)
| ~ class_Int_Onumber(U_7865)
| ~ class_Fields_Ofield__inverse__zero(U_7865) ),
inference(clausify,[status(thm)],[f_2284_2]) ).
fof(f_2285_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_2285_2,plain,
! [U_7872,U_7871,U_7870,U_7869] :
( ( ( U_7870 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7869),U_7871),hAPP(c_Int_Onumber__class_Onumber__of(U_7869),U_7872))
| ( U_7870 != c_Groups_Ozero__class_Ozero(U_7869)
& hAPP(c_Int_Onumber__class_Onumber__of(U_7869),U_7872) = c_Groups_Ozero__class_Ozero(U_7869) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7869),U_7870),hAPP(c_Int_Onumber__class_Onumber__of(U_7869),U_7872)) != U_7871
& hAPP(c_Int_Onumber__class_Onumber__of(U_7869),U_7872) != c_Groups_Ozero__class_Ozero(U_7869) ) )
& ( ( ( U_7870 = c_Groups_Ozero__class_Ozero(U_7869)
| hAPP(c_Int_Onumber__class_Onumber__of(U_7869),U_7872) != c_Groups_Ozero__class_Ozero(U_7869) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7869),U_7870),hAPP(c_Int_Onumber__class_Onumber__of(U_7869),U_7872)) = U_7871
| hAPP(c_Int_Onumber__class_Onumber__of(U_7869),U_7872) = c_Groups_Ozero__class_Ozero(U_7869) ) )
| U_7870 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7869),U_7871),hAPP(c_Int_Onumber__class_Onumber__of(U_7869),U_7872)) ) )
| ~ class_Int_Onumber(U_7869)
| ~ class_Fields_Ofield__inverse__zero(U_7869) ),
inference(variable_rename,[status(thm)],[f_2285_1]) ).
cnf(f_2285_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7869),U_7870),hAPP(c_Int_Onumber__class_Onumber__of(U_7869),U_7872)) = U_7871
| hAPP(c_Int_Onumber__class_Onumber__of(U_7869),U_7872) = c_Groups_Ozero__class_Ozero(U_7869)
| U_7870 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7869),U_7871),hAPP(c_Int_Onumber__class_Onumber__of(U_7869),U_7872))
| ~ class_Int_Onumber(U_7869)
| ~ class_Fields_Ofield__inverse__zero(U_7869) ),
inference(clausify,[status(thm)],[f_2285_2]) ).
cnf(f_2285_4,plain,
( U_7870 = c_Groups_Ozero__class_Ozero(U_7869)
| hAPP(c_Int_Onumber__class_Onumber__of(U_7869),U_7872) != c_Groups_Ozero__class_Ozero(U_7869)
| U_7870 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7869),U_7871),hAPP(c_Int_Onumber__class_Onumber__of(U_7869),U_7872))
| ~ class_Int_Onumber(U_7869)
| ~ class_Fields_Ofield__inverse__zero(U_7869) ),
inference(clausify,[status(thm)],[f_2285_2]) ).
cnf(f_2285_5,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_7869),U_7872) = c_Groups_Ozero__class_Ozero(U_7869)
| hAPP(c_Int_Onumber__class_Onumber__of(U_7869),U_7872) != c_Groups_Ozero__class_Ozero(U_7869)
| U_7870 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7869),U_7871),hAPP(c_Int_Onumber__class_Onumber__of(U_7869),U_7872))
| ~ class_Int_Onumber(U_7869)
| ~ class_Fields_Ofield__inverse__zero(U_7869) ),
inference(clausify,[status(thm)],[f_2285_2]) ).
cnf(f_2285_6,plain,
( U_7870 != c_Groups_Ozero__class_Ozero(U_7869)
| hAPP(c_Int_Onumber__class_Onumber__of(U_7869),U_7872) != c_Groups_Ozero__class_Ozero(U_7869)
| U_7870 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7869),U_7871),hAPP(c_Int_Onumber__class_Onumber__of(U_7869),U_7872))
| ~ class_Int_Onumber(U_7869)
| ~ class_Fields_Ofield__inverse__zero(U_7869) ),
inference(clausify,[status(thm)],[f_2285_2]) ).
cnf(f_2285_7,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_7869),U_7872) = c_Groups_Ozero__class_Ozero(U_7869)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7869),U_7870),hAPP(c_Int_Onumber__class_Onumber__of(U_7869),U_7872)) != U_7871
| U_7870 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7869),U_7871),hAPP(c_Int_Onumber__class_Onumber__of(U_7869),U_7872))
| ~ class_Int_Onumber(U_7869)
| ~ class_Fields_Ofield__inverse__zero(U_7869) ),
inference(clausify,[status(thm)],[f_2285_2]) ).
cnf(f_2285_8,plain,
( U_7870 != c_Groups_Ozero__class_Ozero(U_7869)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7869),U_7870),hAPP(c_Int_Onumber__class_Onumber__of(U_7869),U_7872)) != U_7871
| U_7870 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7869),U_7871),hAPP(c_Int_Onumber__class_Onumber__of(U_7869),U_7872))
| ~ class_Int_Onumber(U_7869)
| ~ class_Fields_Ofield__inverse__zero(U_7869) ),
inference(clausify,[status(thm)],[f_2285_2]) ).
fof(f_2286_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_2286_2,plain,
! [U_7874,U_7873] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7873),U_7874),hAPP(c_Int_Onumber__class_Onumber__of(U_7873),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_7873)
| ~ class_Int_Onumber__ring(U_7873)
| ~ class_Fields_Ofield__inverse__zero(U_7873) ),
inference(variable_rename,[status(thm)],[f_2286_1]) ).
cnf(f_2286_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7873),U_7874),hAPP(c_Int_Onumber__class_Onumber__of(U_7873),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_7873)
| ~ class_Int_Onumber__ring(U_7873)
| ~ class_Fields_Ofield__inverse__zero(U_7873) ),
inference(clausify,[status(thm)],[f_2286_2]) ).
fof(f_2287_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_2287_2,plain,
! [U_7876,U_7875] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7875),U_7876),hAPP(c_Int_Onumber__class_Onumber__of(U_7875),c_Int_OBit1(c_Int_OPls))) = U_7876
| ~ class_Int_Onumber__ring(U_7875)
| ~ class_Fields_Ofield(U_7875) ),
inference(variable_rename,[status(thm)],[f_2287_1]) ).
cnf(f_2287_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7875),U_7876),hAPP(c_Int_Onumber__class_Onumber__of(U_7875),c_Int_OBit1(c_Int_OPls))) = U_7876
| ~ class_Int_Onumber__ring(U_7875)
| ~ class_Fields_Ofield(U_7875) ),
inference(clausify,[status(thm)],[f_2287_2]) ).
fof(f_2288_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_2288_2,plain,
! [U_7878,U_7877] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7877),U_7878),hAPP(c_Int_Onumber__class_Onumber__of(U_7877),c_Int_OBit1(c_Int_OPls))) = U_7878
| ~ class_Int_Onumber__ring(U_7877)
| ~ class_Fields_Ofield(U_7877) ),
inference(variable_rename,[status(thm)],[f_2288_1]) ).
cnf(f_2288_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7877),U_7878),hAPP(c_Int_Onumber__class_Onumber__of(U_7877),c_Int_OBit1(c_Int_OPls))) = U_7878
| ~ class_Int_Onumber__ring(U_7877)
| ~ class_Fields_Ofield(U_7877) ),
inference(clausify,[status(thm)],[f_2288_2]) ).
fof(f_2289_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_2289_2,plain,
! [U_7880,U_7879] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7879),U_7880),hAPP(c_Int_Onumber__class_Onumber__of(U_7879),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7879),U_7880)
| ~ class_Int_Onumber__ring(U_7879)
| ~ class_Fields_Ofield__inverse__zero(U_7879) ),
inference(variable_rename,[status(thm)],[f_2289_1]) ).
cnf(f_2289_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7879),U_7880),hAPP(c_Int_Onumber__class_Onumber__of(U_7879),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7879),U_7880)
| ~ class_Int_Onumber__ring(U_7879)
| ~ class_Fields_Ofield__inverse__zero(U_7879) ),
inference(clausify,[status(thm)],[f_2289_2]) ).
fof(f_2290_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_2290_2,plain,
! [U_7884,U_7883,U_7882,U_7881] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7881),U_7883),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7882),c_Groups_Ozero__class_Ozero(U_7881)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)),c_Groups_Ozero__class_Ozero(U_7881))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7883),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7881),U_7882),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)),c_Groups_Ozero__class_Ozero(U_7881))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),c_Groups_Ozero__class_Ozero(U_7881)),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7881),U_7882),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))),U_7883))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),c_Groups_Ozero__class_Ozero(U_7881)),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7882),c_Groups_Ozero__class_Ozero(U_7881)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)),c_Groups_Ozero__class_Ozero(U_7881))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7883),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7881),U_7882),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)),c_Groups_Ozero__class_Ozero(U_7881))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),c_Groups_Ozero__class_Ozero(U_7881)),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7881),U_7882),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))),U_7883))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),c_Groups_Ozero__class_Ozero(U_7881)),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7881),U_7883),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)))) ) )
| ~ class_Int_Onumber(U_7881)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7881) ),
inference(variable_rename,[status(thm)],[f_2290_1]) ).
cnf(f_2290_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7881),U_7882),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))),U_7883))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),c_Groups_Ozero__class_Ozero(U_7881)),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7881),U_7883),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))))
| ~ class_Int_Onumber(U_7881)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7881) ),
inference(clausify,[status(thm)],[f_2290_2]) ).
cnf(f_2290_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7883),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7881),U_7882),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)),c_Groups_Ozero__class_Ozero(U_7881)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),c_Groups_Ozero__class_Ozero(U_7881)),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7881),U_7883),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))))
| ~ class_Int_Onumber(U_7881)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7881) ),
inference(clausify,[status(thm)],[f_2290_2]) ).
cnf(f_2290_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7882),c_Groups_Ozero__class_Ozero(U_7881)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)),c_Groups_Ozero__class_Ozero(U_7881)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),c_Groups_Ozero__class_Ozero(U_7881)),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7881),U_7883),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))))
| ~ class_Int_Onumber(U_7881)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7881) ),
inference(clausify,[status(thm)],[f_2290_2]) ).
cnf(f_2290_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),c_Groups_Ozero__class_Ozero(U_7881)),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),c_Groups_Ozero__class_Ozero(U_7881)),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7881),U_7883),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))))
| ~ class_Int_Onumber(U_7881)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7881) ),
inference(clausify,[status(thm)],[f_2290_2]) ).
cnf(f_2290_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)),c_Groups_Ozero__class_Ozero(U_7881)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)),c_Groups_Ozero__class_Ozero(U_7881)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),c_Groups_Ozero__class_Ozero(U_7881)),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7881),U_7883),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))))
| ~ class_Int_Onumber(U_7881)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7881) ),
inference(clausify,[status(thm)],[f_2290_2]) ).
cnf(f_2290_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7882),c_Groups_Ozero__class_Ozero(U_7881)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)),c_Groups_Ozero__class_Ozero(U_7881)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),c_Groups_Ozero__class_Ozero(U_7881)),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7881),U_7883),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))))
| ~ class_Int_Onumber(U_7881)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7881) ),
inference(clausify,[status(thm)],[f_2290_2]) ).
cnf(f_2290_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)),c_Groups_Ozero__class_Ozero(U_7881)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7883),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7881),U_7882),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),c_Groups_Ozero__class_Ozero(U_7881)),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7881),U_7883),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))))
| ~ class_Int_Onumber(U_7881)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7881) ),
inference(clausify,[status(thm)],[f_2290_2]) ).
cnf(f_2290_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7882),c_Groups_Ozero__class_Ozero(U_7881)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7883),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7881),U_7882),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),c_Groups_Ozero__class_Ozero(U_7881)),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7881),U_7883),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))))
| ~ class_Int_Onumber(U_7881)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7881) ),
inference(clausify,[status(thm)],[f_2290_2]) ).
cnf(f_2290_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),c_Groups_Ozero__class_Ozero(U_7881)),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7881),U_7882),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))),U_7883))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7881),U_7883),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))))
| ~ class_Int_Onumber(U_7881)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7881) ),
inference(clausify,[status(thm)],[f_2290_2]) ).
cnf(f_2290_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)),c_Groups_Ozero__class_Ozero(U_7881)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)),c_Groups_Ozero__class_Ozero(U_7881)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7881),U_7882),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))),U_7883))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7881),U_7883),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))))
| ~ class_Int_Onumber(U_7881)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7881) ),
inference(clausify,[status(thm)],[f_2290_2]) ).
cnf(f_2290_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7882),c_Groups_Ozero__class_Ozero(U_7881)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)),c_Groups_Ozero__class_Ozero(U_7881)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7881),U_7882),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))),U_7883))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7881),U_7883),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))))
| ~ class_Int_Onumber(U_7881)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7881) ),
inference(clausify,[status(thm)],[f_2290_2]) ).
cnf(f_2290_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884)),c_Groups_Ozero__class_Ozero(U_7881)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7883),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7881),U_7882),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7881),U_7882),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))),U_7883))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7881),U_7883),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))))
| ~ class_Int_Onumber(U_7881)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7881) ),
inference(clausify,[status(thm)],[f_2290_2]) ).
cnf(f_2290_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7882),c_Groups_Ozero__class_Ozero(U_7881)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7883),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7881),U_7882),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7881),U_7882),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))),U_7883))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7881),U_7882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7881),U_7883),hAPP(c_Int_Onumber__class_Onumber__of(U_7881),U_7884))))
| ~ class_Int_Onumber(U_7881)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7881) ),
inference(clausify,[status(thm)],[f_2290_2]) ).
fof(f_2291_1,plain,
! [V_c_2,V_b_2,V_w_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__divide__eq__number__of]) ).
fof(f_2291_2,plain,
! [U_7888,U_7887,U_7886,U_7885] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7885),U_7887),U_7888)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),c_Groups_Ozero__class_Ozero(U_7885)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),U_7888),c_Groups_Ozero__class_Ozero(U_7885))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),U_7887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),U_7888)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),U_7888),c_Groups_Ozero__class_Ozero(U_7885))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),c_Groups_Ozero__class_Ozero(U_7885)),U_7888)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),U_7888)),U_7887))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),c_Groups_Ozero__class_Ozero(U_7885)),U_7888)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),c_Groups_Ozero__class_Ozero(U_7885)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),U_7888),c_Groups_Ozero__class_Ozero(U_7885))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),U_7887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),U_7888)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),U_7888),c_Groups_Ozero__class_Ozero(U_7885))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),c_Groups_Ozero__class_Ozero(U_7885)),U_7888)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),U_7888)),U_7887))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),c_Groups_Ozero__class_Ozero(U_7885)),U_7888)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7885),U_7887),U_7888))) ) )
| ~ class_Int_Onumber(U_7885)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7885) ),
inference(variable_rename,[status(thm)],[f_2291_1]) ).
cnf(f_2291_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),U_7888)),U_7887))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),c_Groups_Ozero__class_Ozero(U_7885)),U_7888))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7885),U_7887),U_7888)))
| ~ class_Int_Onumber(U_7885)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7885) ),
inference(clausify,[status(thm)],[f_2291_2]) ).
cnf(f_2291_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),U_7887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),U_7888)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),U_7888),c_Groups_Ozero__class_Ozero(U_7885)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),c_Groups_Ozero__class_Ozero(U_7885)),U_7888))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7885),U_7887),U_7888)))
| ~ class_Int_Onumber(U_7885)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7885) ),
inference(clausify,[status(thm)],[f_2291_2]) ).
cnf(f_2291_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),c_Groups_Ozero__class_Ozero(U_7885)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),U_7888),c_Groups_Ozero__class_Ozero(U_7885)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),c_Groups_Ozero__class_Ozero(U_7885)),U_7888))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7885),U_7887),U_7888)))
| ~ class_Int_Onumber(U_7885)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7885) ),
inference(clausify,[status(thm)],[f_2291_2]) ).
cnf(f_2291_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),c_Groups_Ozero__class_Ozero(U_7885)),U_7888))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),c_Groups_Ozero__class_Ozero(U_7885)),U_7888))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7885),U_7887),U_7888)))
| ~ class_Int_Onumber(U_7885)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7885) ),
inference(clausify,[status(thm)],[f_2291_2]) ).
cnf(f_2291_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),U_7888),c_Groups_Ozero__class_Ozero(U_7885)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),U_7888),c_Groups_Ozero__class_Ozero(U_7885)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),c_Groups_Ozero__class_Ozero(U_7885)),U_7888))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7885),U_7887),U_7888)))
| ~ class_Int_Onumber(U_7885)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7885) ),
inference(clausify,[status(thm)],[f_2291_2]) ).
cnf(f_2291_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),c_Groups_Ozero__class_Ozero(U_7885)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),U_7888),c_Groups_Ozero__class_Ozero(U_7885)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),c_Groups_Ozero__class_Ozero(U_7885)),U_7888))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7885),U_7887),U_7888)))
| ~ class_Int_Onumber(U_7885)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7885) ),
inference(clausify,[status(thm)],[f_2291_2]) ).
cnf(f_2291_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),U_7888),c_Groups_Ozero__class_Ozero(U_7885)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),U_7887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),U_7888)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),c_Groups_Ozero__class_Ozero(U_7885)),U_7888))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7885),U_7887),U_7888)))
| ~ class_Int_Onumber(U_7885)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7885) ),
inference(clausify,[status(thm)],[f_2291_2]) ).
cnf(f_2291_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),c_Groups_Ozero__class_Ozero(U_7885)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),U_7887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),U_7888)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),c_Groups_Ozero__class_Ozero(U_7885)),U_7888))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7885),U_7887),U_7888)))
| ~ class_Int_Onumber(U_7885)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7885) ),
inference(clausify,[status(thm)],[f_2291_2]) ).
cnf(f_2291_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),c_Groups_Ozero__class_Ozero(U_7885)),U_7888))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),U_7888)),U_7887))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7885),U_7887),U_7888)))
| ~ class_Int_Onumber(U_7885)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7885) ),
inference(clausify,[status(thm)],[f_2291_2]) ).
cnf(f_2291_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),U_7888),c_Groups_Ozero__class_Ozero(U_7885)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),U_7888),c_Groups_Ozero__class_Ozero(U_7885)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),U_7888)),U_7887))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7885),U_7887),U_7888)))
| ~ class_Int_Onumber(U_7885)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7885) ),
inference(clausify,[status(thm)],[f_2291_2]) ).
cnf(f_2291_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),c_Groups_Ozero__class_Ozero(U_7885)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),U_7888),c_Groups_Ozero__class_Ozero(U_7885)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),U_7888)),U_7887))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7885),U_7887),U_7888)))
| ~ class_Int_Onumber(U_7885)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7885) ),
inference(clausify,[status(thm)],[f_2291_2]) ).
cnf(f_2291_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),U_7888),c_Groups_Ozero__class_Ozero(U_7885)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),U_7887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),U_7888)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),U_7888)),U_7887))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7885),U_7887),U_7888)))
| ~ class_Int_Onumber(U_7885)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7885) ),
inference(clausify,[status(thm)],[f_2291_2]) ).
cnf(f_2291_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),c_Groups_Ozero__class_Ozero(U_7885)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),U_7887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),U_7888)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),U_7888)),U_7887))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7885),hAPP(c_Int_Onumber__class_Onumber__of(U_7885),U_7886)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7885),U_7887),U_7888)))
| ~ class_Int_Onumber(U_7885)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7885) ),
inference(clausify,[status(thm)],[f_2291_2]) ).
fof(f_2292_1,plain,
! [V_w_2,V_c_2,V_b_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__less__eq__number__of]) ).
fof(f_2292_2,plain,
! [U_7892,U_7891,U_7890,U_7889] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7889),U_7890),U_7891)),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),c_Groups_Ozero__class_Ozero(U_7889)),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),U_7891),c_Groups_Ozero__class_Ozero(U_7889))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7889),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)),U_7891)),U_7890))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),U_7891),c_Groups_Ozero__class_Ozero(U_7889))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),c_Groups_Ozero__class_Ozero(U_7889)),U_7891)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),U_7890),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7889),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)),U_7891)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),c_Groups_Ozero__class_Ozero(U_7889)),U_7891)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),c_Groups_Ozero__class_Ozero(U_7889)),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),U_7891),c_Groups_Ozero__class_Ozero(U_7889))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7889),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)),U_7891)),U_7890))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),U_7891),c_Groups_Ozero__class_Ozero(U_7889))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),c_Groups_Ozero__class_Ozero(U_7889)),U_7891)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),U_7890),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7889),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)),U_7891)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),c_Groups_Ozero__class_Ozero(U_7889)),U_7891)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7889),U_7890),U_7891)),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892))) ) )
| ~ class_Int_Onumber(U_7889)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7889) ),
inference(variable_rename,[status(thm)],[f_2292_1]) ).
cnf(f_2292_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),U_7890),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7889),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)),U_7891)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),c_Groups_Ozero__class_Ozero(U_7889)),U_7891))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7889),U_7890),U_7891)),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)))
| ~ class_Int_Onumber(U_7889)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7889) ),
inference(clausify,[status(thm)],[f_2292_2]) ).
cnf(f_2292_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7889),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)),U_7891)),U_7890))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),U_7891),c_Groups_Ozero__class_Ozero(U_7889)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),c_Groups_Ozero__class_Ozero(U_7889)),U_7891))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7889),U_7890),U_7891)),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)))
| ~ class_Int_Onumber(U_7889)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7889) ),
inference(clausify,[status(thm)],[f_2292_2]) ).
cnf(f_2292_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),c_Groups_Ozero__class_Ozero(U_7889)),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),U_7891),c_Groups_Ozero__class_Ozero(U_7889)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),c_Groups_Ozero__class_Ozero(U_7889)),U_7891))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7889),U_7890),U_7891)),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)))
| ~ class_Int_Onumber(U_7889)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7889) ),
inference(clausify,[status(thm)],[f_2292_2]) ).
cnf(f_2292_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),c_Groups_Ozero__class_Ozero(U_7889)),U_7891))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),c_Groups_Ozero__class_Ozero(U_7889)),U_7891))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7889),U_7890),U_7891)),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)))
| ~ class_Int_Onumber(U_7889)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7889) ),
inference(clausify,[status(thm)],[f_2292_2]) ).
cnf(f_2292_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),U_7891),c_Groups_Ozero__class_Ozero(U_7889)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),U_7891),c_Groups_Ozero__class_Ozero(U_7889)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),c_Groups_Ozero__class_Ozero(U_7889)),U_7891))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7889),U_7890),U_7891)),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)))
| ~ class_Int_Onumber(U_7889)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7889) ),
inference(clausify,[status(thm)],[f_2292_2]) ).
cnf(f_2292_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),c_Groups_Ozero__class_Ozero(U_7889)),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),U_7891),c_Groups_Ozero__class_Ozero(U_7889)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),c_Groups_Ozero__class_Ozero(U_7889)),U_7891))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7889),U_7890),U_7891)),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)))
| ~ class_Int_Onumber(U_7889)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7889) ),
inference(clausify,[status(thm)],[f_2292_2]) ).
cnf(f_2292_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),U_7891),c_Groups_Ozero__class_Ozero(U_7889)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7889),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)),U_7891)),U_7890))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),c_Groups_Ozero__class_Ozero(U_7889)),U_7891))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7889),U_7890),U_7891)),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)))
| ~ class_Int_Onumber(U_7889)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7889) ),
inference(clausify,[status(thm)],[f_2292_2]) ).
cnf(f_2292_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),c_Groups_Ozero__class_Ozero(U_7889)),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7889),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)),U_7891)),U_7890))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),c_Groups_Ozero__class_Ozero(U_7889)),U_7891))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7889),U_7890),U_7891)),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)))
| ~ class_Int_Onumber(U_7889)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7889) ),
inference(clausify,[status(thm)],[f_2292_2]) ).
cnf(f_2292_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),c_Groups_Ozero__class_Ozero(U_7889)),U_7891))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),U_7890),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7889),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)),U_7891)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7889),U_7890),U_7891)),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)))
| ~ class_Int_Onumber(U_7889)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7889) ),
inference(clausify,[status(thm)],[f_2292_2]) ).
cnf(f_2292_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),U_7891),c_Groups_Ozero__class_Ozero(U_7889)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),U_7891),c_Groups_Ozero__class_Ozero(U_7889)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),U_7890),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7889),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)),U_7891)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7889),U_7890),U_7891)),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)))
| ~ class_Int_Onumber(U_7889)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7889) ),
inference(clausify,[status(thm)],[f_2292_2]) ).
cnf(f_2292_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),c_Groups_Ozero__class_Ozero(U_7889)),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),U_7891),c_Groups_Ozero__class_Ozero(U_7889)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),U_7890),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7889),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)),U_7891)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7889),U_7890),U_7891)),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)))
| ~ class_Int_Onumber(U_7889)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7889) ),
inference(clausify,[status(thm)],[f_2292_2]) ).
cnf(f_2292_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),U_7891),c_Groups_Ozero__class_Ozero(U_7889)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7889),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)),U_7891)),U_7890))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),U_7890),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7889),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)),U_7891)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7889),U_7890),U_7891)),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)))
| ~ class_Int_Onumber(U_7889)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7889) ),
inference(clausify,[status(thm)],[f_2292_2]) ).
cnf(f_2292_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),c_Groups_Ozero__class_Ozero(U_7889)),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7889),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)),U_7891)),U_7890))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),U_7890),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7889),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)),U_7891)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7889),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7889),U_7890),U_7891)),hAPP(c_Int_Onumber__class_Onumber__of(U_7889),U_7892)))
| ~ class_Int_Onumber(U_7889)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7889) ),
inference(clausify,[status(thm)],[f_2292_2]) ).
fof(f_2293_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_2293_2,plain,
! [U_7896,U_7895,U_7894,U_7893] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7893),U_7894),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))),U_7896))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),c_Groups_Ozero__class_Ozero(U_7893)),U_7896))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895)),c_Groups_Ozero__class_Ozero(U_7893))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7893),U_7896),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))),U_7894))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895)),c_Groups_Ozero__class_Ozero(U_7893))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),c_Groups_Ozero__class_Ozero(U_7893)),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),U_7894),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7893),U_7896),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),c_Groups_Ozero__class_Ozero(U_7893)),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),c_Groups_Ozero__class_Ozero(U_7893)),U_7896))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895)),c_Groups_Ozero__class_Ozero(U_7893))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7893),U_7896),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))),U_7894))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895)),c_Groups_Ozero__class_Ozero(U_7893))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),c_Groups_Ozero__class_Ozero(U_7893)),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),U_7894),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7893),U_7896),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),c_Groups_Ozero__class_Ozero(U_7893)),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7893),U_7894),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))),U_7896)) ) )
| ~ class_Int_Onumber(U_7893)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7893) ),
inference(variable_rename,[status(thm)],[f_2293_1]) ).
cnf(f_2293_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),U_7894),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7893),U_7896),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),c_Groups_Ozero__class_Ozero(U_7893)),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7893),U_7894),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))),U_7896))
| ~ class_Int_Onumber(U_7893)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7893) ),
inference(clausify,[status(thm)],[f_2293_2]) ).
cnf(f_2293_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7893),U_7896),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))),U_7894))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895)),c_Groups_Ozero__class_Ozero(U_7893)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),c_Groups_Ozero__class_Ozero(U_7893)),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7893),U_7894),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))),U_7896))
| ~ class_Int_Onumber(U_7893)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7893) ),
inference(clausify,[status(thm)],[f_2293_2]) ).
cnf(f_2293_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),c_Groups_Ozero__class_Ozero(U_7893)),U_7896))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895)),c_Groups_Ozero__class_Ozero(U_7893)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),c_Groups_Ozero__class_Ozero(U_7893)),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7893),U_7894),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))),U_7896))
| ~ class_Int_Onumber(U_7893)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7893) ),
inference(clausify,[status(thm)],[f_2293_2]) ).
cnf(f_2293_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),c_Groups_Ozero__class_Ozero(U_7893)),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),c_Groups_Ozero__class_Ozero(U_7893)),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7893),U_7894),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))),U_7896))
| ~ class_Int_Onumber(U_7893)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7893) ),
inference(clausify,[status(thm)],[f_2293_2]) ).
cnf(f_2293_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895)),c_Groups_Ozero__class_Ozero(U_7893)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895)),c_Groups_Ozero__class_Ozero(U_7893)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),c_Groups_Ozero__class_Ozero(U_7893)),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7893),U_7894),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))),U_7896))
| ~ class_Int_Onumber(U_7893)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7893) ),
inference(clausify,[status(thm)],[f_2293_2]) ).
cnf(f_2293_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),c_Groups_Ozero__class_Ozero(U_7893)),U_7896))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895)),c_Groups_Ozero__class_Ozero(U_7893)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),c_Groups_Ozero__class_Ozero(U_7893)),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7893),U_7894),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))),U_7896))
| ~ class_Int_Onumber(U_7893)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7893) ),
inference(clausify,[status(thm)],[f_2293_2]) ).
cnf(f_2293_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895)),c_Groups_Ozero__class_Ozero(U_7893)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7893),U_7896),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))),U_7894))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),c_Groups_Ozero__class_Ozero(U_7893)),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7893),U_7894),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))),U_7896))
| ~ class_Int_Onumber(U_7893)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7893) ),
inference(clausify,[status(thm)],[f_2293_2]) ).
cnf(f_2293_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),c_Groups_Ozero__class_Ozero(U_7893)),U_7896))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7893),U_7896),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))),U_7894))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),c_Groups_Ozero__class_Ozero(U_7893)),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7893),U_7894),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))),U_7896))
| ~ class_Int_Onumber(U_7893)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7893) ),
inference(clausify,[status(thm)],[f_2293_2]) ).
cnf(f_2293_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),c_Groups_Ozero__class_Ozero(U_7893)),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),U_7894),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7893),U_7896),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7893),U_7894),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))),U_7896))
| ~ class_Int_Onumber(U_7893)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7893) ),
inference(clausify,[status(thm)],[f_2293_2]) ).
cnf(f_2293_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895)),c_Groups_Ozero__class_Ozero(U_7893)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895)),c_Groups_Ozero__class_Ozero(U_7893)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),U_7894),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7893),U_7896),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7893),U_7894),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))),U_7896))
| ~ class_Int_Onumber(U_7893)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7893) ),
inference(clausify,[status(thm)],[f_2293_2]) ).
cnf(f_2293_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),c_Groups_Ozero__class_Ozero(U_7893)),U_7896))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895)),c_Groups_Ozero__class_Ozero(U_7893)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),U_7894),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7893),U_7896),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7893),U_7894),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))),U_7896))
| ~ class_Int_Onumber(U_7893)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7893) ),
inference(clausify,[status(thm)],[f_2293_2]) ).
cnf(f_2293_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895)),c_Groups_Ozero__class_Ozero(U_7893)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7893),U_7896),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))),U_7894))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),U_7894),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7893),U_7896),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7893),U_7894),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))),U_7896))
| ~ class_Int_Onumber(U_7893)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7893) ),
inference(clausify,[status(thm)],[f_2293_2]) ).
cnf(f_2293_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),c_Groups_Ozero__class_Ozero(U_7893)),U_7896))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7893),U_7896),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))),U_7894))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),U_7894),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7893),U_7896),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7893),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7893),U_7894),hAPP(c_Int_Onumber__class_Onumber__of(U_7893),U_7895))),U_7896))
| ~ class_Int_Onumber(U_7893)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7893) ),
inference(clausify,[status(thm)],[f_2293_2]) ).
fof(f_2294_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_2294_2,plain,
! [U_7900,U_7899,U_7898,U_7897] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7897),U_7898),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7900),U_7899)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7897),hAPP(hAPP(c_Power_Opower__class_Opower(U_7897),U_7898),U_7900)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7897),U_7898),U_7899))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7899),U_7900))
| U_7898 = c_Groups_Ozero__class_Ozero(U_7897)
| ~ class_Fields_Ofield(U_7897) ),
inference(variable_rename,[status(thm)],[f_2294_1]) ).
cnf(f_2294_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7897),U_7898),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7900),U_7899)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7897),hAPP(hAPP(c_Power_Opower__class_Opower(U_7897),U_7898),U_7900)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7897),U_7898),U_7899))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7899),U_7900))
| U_7898 = c_Groups_Ozero__class_Ozero(U_7897)
| ~ class_Fields_Ofield(U_7897) ),
inference(clausify,[status(thm)],[f_2294_2]) ).
fof(f_2295_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_2295_2,plain,
! [U_7902,U_7901] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7901),hAPP(c_Int_Onumber__class_Onumber__of(U_7901),c_Int_OMin)),U_7902) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7901),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7901),c_Groups_Oone__class_Oone(U_7901)),U_7902))
| ~ class_Int_Onumber__ring(U_7901)
| ~ class_Fields_Ofield__inverse__zero(U_7901) ),
inference(variable_rename,[status(thm)],[f_2295_1]) ).
cnf(f_2295_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7901),hAPP(c_Int_Onumber__class_Onumber__of(U_7901),c_Int_OMin)),U_7902) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7901),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7901),c_Groups_Oone__class_Oone(U_7901)),U_7902))
| ~ class_Int_Onumber__ring(U_7901)
| ~ class_Fields_Ofield__inverse__zero(U_7901) ),
inference(clausify,[status(thm)],[f_2295_2]) ).
fof(f_2296_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_2296_2,plain,
! [U_7906,U_7905,U_7904,U_7903] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7903),U_7904),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))),U_7906))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),c_Groups_Ozero__class_Ozero(U_7903)),U_7906))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905)),c_Groups_Ozero__class_Ozero(U_7903))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7903),U_7906),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))),U_7904))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905)),c_Groups_Ozero__class_Ozero(U_7903))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),c_Groups_Ozero__class_Ozero(U_7903)),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),U_7904),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7903),U_7906),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),c_Groups_Ozero__class_Ozero(U_7903)),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),c_Groups_Ozero__class_Ozero(U_7903)),U_7906))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905)),c_Groups_Ozero__class_Ozero(U_7903))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7903),U_7906),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))),U_7904))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905)),c_Groups_Ozero__class_Ozero(U_7903))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),c_Groups_Ozero__class_Ozero(U_7903)),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),U_7904),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7903),U_7906),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),c_Groups_Ozero__class_Ozero(U_7903)),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7903),U_7904),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))),U_7906)) ) )
| ~ class_Int_Onumber(U_7903)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7903) ),
inference(variable_rename,[status(thm)],[f_2296_1]) ).
cnf(f_2296_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),U_7904),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7903),U_7906),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),c_Groups_Ozero__class_Ozero(U_7903)),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7903),U_7904),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))),U_7906))
| ~ class_Int_Onumber(U_7903)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7903) ),
inference(clausify,[status(thm)],[f_2296_2]) ).
cnf(f_2296_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7903),U_7906),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))),U_7904))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905)),c_Groups_Ozero__class_Ozero(U_7903)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),c_Groups_Ozero__class_Ozero(U_7903)),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7903),U_7904),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))),U_7906))
| ~ class_Int_Onumber(U_7903)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7903) ),
inference(clausify,[status(thm)],[f_2296_2]) ).
cnf(f_2296_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),c_Groups_Ozero__class_Ozero(U_7903)),U_7906))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905)),c_Groups_Ozero__class_Ozero(U_7903)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),c_Groups_Ozero__class_Ozero(U_7903)),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7903),U_7904),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))),U_7906))
| ~ class_Int_Onumber(U_7903)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7903) ),
inference(clausify,[status(thm)],[f_2296_2]) ).
cnf(f_2296_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),c_Groups_Ozero__class_Ozero(U_7903)),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),c_Groups_Ozero__class_Ozero(U_7903)),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7903),U_7904),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))),U_7906))
| ~ class_Int_Onumber(U_7903)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7903) ),
inference(clausify,[status(thm)],[f_2296_2]) ).
cnf(f_2296_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905)),c_Groups_Ozero__class_Ozero(U_7903)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905)),c_Groups_Ozero__class_Ozero(U_7903)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),c_Groups_Ozero__class_Ozero(U_7903)),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7903),U_7904),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))),U_7906))
| ~ class_Int_Onumber(U_7903)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7903) ),
inference(clausify,[status(thm)],[f_2296_2]) ).
cnf(f_2296_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),c_Groups_Ozero__class_Ozero(U_7903)),U_7906))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905)),c_Groups_Ozero__class_Ozero(U_7903)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),c_Groups_Ozero__class_Ozero(U_7903)),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7903),U_7904),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))),U_7906))
| ~ class_Int_Onumber(U_7903)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7903) ),
inference(clausify,[status(thm)],[f_2296_2]) ).
cnf(f_2296_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905)),c_Groups_Ozero__class_Ozero(U_7903)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7903),U_7906),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))),U_7904))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),c_Groups_Ozero__class_Ozero(U_7903)),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7903),U_7904),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))),U_7906))
| ~ class_Int_Onumber(U_7903)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7903) ),
inference(clausify,[status(thm)],[f_2296_2]) ).
cnf(f_2296_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),c_Groups_Ozero__class_Ozero(U_7903)),U_7906))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7903),U_7906),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))),U_7904))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),c_Groups_Ozero__class_Ozero(U_7903)),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7903),U_7904),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))),U_7906))
| ~ class_Int_Onumber(U_7903)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7903) ),
inference(clausify,[status(thm)],[f_2296_2]) ).
cnf(f_2296_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),c_Groups_Ozero__class_Ozero(U_7903)),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),U_7904),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7903),U_7906),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7903),U_7904),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))),U_7906))
| ~ class_Int_Onumber(U_7903)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7903) ),
inference(clausify,[status(thm)],[f_2296_2]) ).
cnf(f_2296_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905)),c_Groups_Ozero__class_Ozero(U_7903)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905)),c_Groups_Ozero__class_Ozero(U_7903)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),U_7904),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7903),U_7906),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7903),U_7904),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))),U_7906))
| ~ class_Int_Onumber(U_7903)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7903) ),
inference(clausify,[status(thm)],[f_2296_2]) ).
cnf(f_2296_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),c_Groups_Ozero__class_Ozero(U_7903)),U_7906))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905)),c_Groups_Ozero__class_Ozero(U_7903)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),U_7904),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7903),U_7906),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7903),U_7904),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))),U_7906))
| ~ class_Int_Onumber(U_7903)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7903) ),
inference(clausify,[status(thm)],[f_2296_2]) ).
cnf(f_2296_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7903),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905)),c_Groups_Ozero__class_Ozero(U_7903)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7903),U_7906),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))),U_7904))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),U_7904),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7903),U_7906),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7903),U_7904),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))),U_7906))
| ~ class_Int_Onumber(U_7903)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7903) ),
inference(clausify,[status(thm)],[f_2296_2]) ).
cnf(f_2296_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),c_Groups_Ozero__class_Ozero(U_7903)),U_7906))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7903),U_7906),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))),U_7904))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),U_7904),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7903),U_7906),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7903),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7903),U_7904),hAPP(c_Int_Onumber__class_Onumber__of(U_7903),U_7905))),U_7906))
| ~ class_Int_Onumber(U_7903)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7903) ),
inference(clausify,[status(thm)],[f_2296_2]) ).
fof(f_2297_1,plain,
! [V_w_2,V_c_2,V_b_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__le__eq__number__of]) ).
fof(f_2297_2,plain,
! [U_7910,U_7909,U_7908,U_7907] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7907),U_7908),U_7909)),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),c_Groups_Ozero__class_Ozero(U_7907)),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),U_7909),c_Groups_Ozero__class_Ozero(U_7907))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7907),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)),U_7909)),U_7908))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),U_7909),c_Groups_Ozero__class_Ozero(U_7907))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),c_Groups_Ozero__class_Ozero(U_7907)),U_7909)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),U_7908),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7907),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)),U_7909)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),c_Groups_Ozero__class_Ozero(U_7907)),U_7909)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),c_Groups_Ozero__class_Ozero(U_7907)),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),U_7909),c_Groups_Ozero__class_Ozero(U_7907))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7907),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)),U_7909)),U_7908))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),U_7909),c_Groups_Ozero__class_Ozero(U_7907))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),c_Groups_Ozero__class_Ozero(U_7907)),U_7909)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),U_7908),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7907),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)),U_7909)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),c_Groups_Ozero__class_Ozero(U_7907)),U_7909)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7907),U_7908),U_7909)),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910))) ) )
| ~ class_Int_Onumber(U_7907)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7907) ),
inference(variable_rename,[status(thm)],[f_2297_1]) ).
cnf(f_2297_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),U_7908),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7907),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)),U_7909)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),c_Groups_Ozero__class_Ozero(U_7907)),U_7909))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7907),U_7908),U_7909)),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)))
| ~ class_Int_Onumber(U_7907)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7907) ),
inference(clausify,[status(thm)],[f_2297_2]) ).
cnf(f_2297_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7907),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)),U_7909)),U_7908))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),U_7909),c_Groups_Ozero__class_Ozero(U_7907)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),c_Groups_Ozero__class_Ozero(U_7907)),U_7909))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7907),U_7908),U_7909)),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)))
| ~ class_Int_Onumber(U_7907)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7907) ),
inference(clausify,[status(thm)],[f_2297_2]) ).
cnf(f_2297_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),c_Groups_Ozero__class_Ozero(U_7907)),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),U_7909),c_Groups_Ozero__class_Ozero(U_7907)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),c_Groups_Ozero__class_Ozero(U_7907)),U_7909))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7907),U_7908),U_7909)),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)))
| ~ class_Int_Onumber(U_7907)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7907) ),
inference(clausify,[status(thm)],[f_2297_2]) ).
cnf(f_2297_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),c_Groups_Ozero__class_Ozero(U_7907)),U_7909))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),c_Groups_Ozero__class_Ozero(U_7907)),U_7909))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7907),U_7908),U_7909)),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)))
| ~ class_Int_Onumber(U_7907)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7907) ),
inference(clausify,[status(thm)],[f_2297_2]) ).
cnf(f_2297_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),U_7909),c_Groups_Ozero__class_Ozero(U_7907)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),U_7909),c_Groups_Ozero__class_Ozero(U_7907)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),c_Groups_Ozero__class_Ozero(U_7907)),U_7909))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7907),U_7908),U_7909)),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)))
| ~ class_Int_Onumber(U_7907)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7907) ),
inference(clausify,[status(thm)],[f_2297_2]) ).
cnf(f_2297_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),c_Groups_Ozero__class_Ozero(U_7907)),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),U_7909),c_Groups_Ozero__class_Ozero(U_7907)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),c_Groups_Ozero__class_Ozero(U_7907)),U_7909))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7907),U_7908),U_7909)),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)))
| ~ class_Int_Onumber(U_7907)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7907) ),
inference(clausify,[status(thm)],[f_2297_2]) ).
cnf(f_2297_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),U_7909),c_Groups_Ozero__class_Ozero(U_7907)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7907),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)),U_7909)),U_7908))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),c_Groups_Ozero__class_Ozero(U_7907)),U_7909))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7907),U_7908),U_7909)),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)))
| ~ class_Int_Onumber(U_7907)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7907) ),
inference(clausify,[status(thm)],[f_2297_2]) ).
cnf(f_2297_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),c_Groups_Ozero__class_Ozero(U_7907)),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7907),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)),U_7909)),U_7908))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),c_Groups_Ozero__class_Ozero(U_7907)),U_7909))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7907),U_7908),U_7909)),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)))
| ~ class_Int_Onumber(U_7907)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7907) ),
inference(clausify,[status(thm)],[f_2297_2]) ).
cnf(f_2297_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),c_Groups_Ozero__class_Ozero(U_7907)),U_7909))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),U_7908),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7907),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)),U_7909)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7907),U_7908),U_7909)),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)))
| ~ class_Int_Onumber(U_7907)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7907) ),
inference(clausify,[status(thm)],[f_2297_2]) ).
cnf(f_2297_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),U_7909),c_Groups_Ozero__class_Ozero(U_7907)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),U_7909),c_Groups_Ozero__class_Ozero(U_7907)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),U_7908),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7907),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)),U_7909)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7907),U_7908),U_7909)),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)))
| ~ class_Int_Onumber(U_7907)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7907) ),
inference(clausify,[status(thm)],[f_2297_2]) ).
cnf(f_2297_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),c_Groups_Ozero__class_Ozero(U_7907)),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),U_7909),c_Groups_Ozero__class_Ozero(U_7907)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),U_7908),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7907),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)),U_7909)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7907),U_7908),U_7909)),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)))
| ~ class_Int_Onumber(U_7907)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7907) ),
inference(clausify,[status(thm)],[f_2297_2]) ).
cnf(f_2297_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7907),U_7909),c_Groups_Ozero__class_Ozero(U_7907)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7907),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)),U_7909)),U_7908))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),U_7908),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7907),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)),U_7909)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7907),U_7908),U_7909)),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)))
| ~ class_Int_Onumber(U_7907)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7907) ),
inference(clausify,[status(thm)],[f_2297_2]) ).
cnf(f_2297_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),c_Groups_Ozero__class_Ozero(U_7907)),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7907),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)),U_7909)),U_7908))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),U_7908),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7907),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)),U_7909)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7907),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7907),U_7908),U_7909)),hAPP(c_Int_Onumber__class_Onumber__of(U_7907),U_7910)))
| ~ class_Int_Onumber(U_7907)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7907) ),
inference(clausify,[status(thm)],[f_2297_2]) ).
fof(f_2298_1,plain,
! [V_c_2,V_b_2,V_w_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__divide__eq__number__of]) ).
fof(f_2298_2,plain,
! [U_7914,U_7913,U_7912,U_7911] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7911),U_7913),U_7914)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),c_Groups_Ozero__class_Ozero(U_7911)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),U_7914),c_Groups_Ozero__class_Ozero(U_7911))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),U_7913),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),U_7914)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),U_7914),c_Groups_Ozero__class_Ozero(U_7911))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),c_Groups_Ozero__class_Ozero(U_7911)),U_7914)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),U_7914)),U_7913))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),c_Groups_Ozero__class_Ozero(U_7911)),U_7914)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),c_Groups_Ozero__class_Ozero(U_7911)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),U_7914),c_Groups_Ozero__class_Ozero(U_7911))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),U_7913),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),U_7914)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),U_7914),c_Groups_Ozero__class_Ozero(U_7911))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),c_Groups_Ozero__class_Ozero(U_7911)),U_7914)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),U_7914)),U_7913))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),c_Groups_Ozero__class_Ozero(U_7911)),U_7914)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7911),U_7913),U_7914))) ) )
| ~ class_Int_Onumber(U_7911)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7911) ),
inference(variable_rename,[status(thm)],[f_2298_1]) ).
cnf(f_2298_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),U_7914)),U_7913))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),c_Groups_Ozero__class_Ozero(U_7911)),U_7914))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7911),U_7913),U_7914)))
| ~ class_Int_Onumber(U_7911)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7911) ),
inference(clausify,[status(thm)],[f_2298_2]) ).
cnf(f_2298_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),U_7913),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),U_7914)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),U_7914),c_Groups_Ozero__class_Ozero(U_7911)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),c_Groups_Ozero__class_Ozero(U_7911)),U_7914))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7911),U_7913),U_7914)))
| ~ class_Int_Onumber(U_7911)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7911) ),
inference(clausify,[status(thm)],[f_2298_2]) ).
cnf(f_2298_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),c_Groups_Ozero__class_Ozero(U_7911)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),U_7914),c_Groups_Ozero__class_Ozero(U_7911)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),c_Groups_Ozero__class_Ozero(U_7911)),U_7914))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7911),U_7913),U_7914)))
| ~ class_Int_Onumber(U_7911)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7911) ),
inference(clausify,[status(thm)],[f_2298_2]) ).
cnf(f_2298_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),c_Groups_Ozero__class_Ozero(U_7911)),U_7914))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),c_Groups_Ozero__class_Ozero(U_7911)),U_7914))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7911),U_7913),U_7914)))
| ~ class_Int_Onumber(U_7911)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7911) ),
inference(clausify,[status(thm)],[f_2298_2]) ).
cnf(f_2298_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),U_7914),c_Groups_Ozero__class_Ozero(U_7911)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),U_7914),c_Groups_Ozero__class_Ozero(U_7911)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),c_Groups_Ozero__class_Ozero(U_7911)),U_7914))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7911),U_7913),U_7914)))
| ~ class_Int_Onumber(U_7911)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7911) ),
inference(clausify,[status(thm)],[f_2298_2]) ).
cnf(f_2298_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),c_Groups_Ozero__class_Ozero(U_7911)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),U_7914),c_Groups_Ozero__class_Ozero(U_7911)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),c_Groups_Ozero__class_Ozero(U_7911)),U_7914))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7911),U_7913),U_7914)))
| ~ class_Int_Onumber(U_7911)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7911) ),
inference(clausify,[status(thm)],[f_2298_2]) ).
cnf(f_2298_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),U_7914),c_Groups_Ozero__class_Ozero(U_7911)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),U_7913),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),U_7914)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),c_Groups_Ozero__class_Ozero(U_7911)),U_7914))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7911),U_7913),U_7914)))
| ~ class_Int_Onumber(U_7911)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7911) ),
inference(clausify,[status(thm)],[f_2298_2]) ).
cnf(f_2298_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),c_Groups_Ozero__class_Ozero(U_7911)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),U_7913),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),U_7914)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),c_Groups_Ozero__class_Ozero(U_7911)),U_7914))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7911),U_7913),U_7914)))
| ~ class_Int_Onumber(U_7911)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7911) ),
inference(clausify,[status(thm)],[f_2298_2]) ).
cnf(f_2298_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),c_Groups_Ozero__class_Ozero(U_7911)),U_7914))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),U_7914)),U_7913))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7911),U_7913),U_7914)))
| ~ class_Int_Onumber(U_7911)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7911) ),
inference(clausify,[status(thm)],[f_2298_2]) ).
cnf(f_2298_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),U_7914),c_Groups_Ozero__class_Ozero(U_7911)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),U_7914),c_Groups_Ozero__class_Ozero(U_7911)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),U_7914)),U_7913))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7911),U_7913),U_7914)))
| ~ class_Int_Onumber(U_7911)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7911) ),
inference(clausify,[status(thm)],[f_2298_2]) ).
cnf(f_2298_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),c_Groups_Ozero__class_Ozero(U_7911)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),U_7914),c_Groups_Ozero__class_Ozero(U_7911)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),U_7914)),U_7913))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7911),U_7913),U_7914)))
| ~ class_Int_Onumber(U_7911)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7911) ),
inference(clausify,[status(thm)],[f_2298_2]) ).
cnf(f_2298_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7911),U_7914),c_Groups_Ozero__class_Ozero(U_7911)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),U_7913),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),U_7914)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),U_7914)),U_7913))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7911),U_7913),U_7914)))
| ~ class_Int_Onumber(U_7911)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7911) ),
inference(clausify,[status(thm)],[f_2298_2]) ).
cnf(f_2298_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),c_Groups_Ozero__class_Ozero(U_7911)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),U_7913),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),U_7914)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),U_7914)),U_7913))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7911),hAPP(c_Int_Onumber__class_Onumber__of(U_7911),U_7912)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7911),U_7913),U_7914)))
| ~ class_Int_Onumber(U_7911)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7911) ),
inference(clausify,[status(thm)],[f_2298_2]) ).
fof(f_2299_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_2299_2,plain,
! [U_7918,U_7917,U_7916,U_7915] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7916),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7915),U_7917),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7916),c_Groups_Ozero__class_Ozero(U_7915)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)),c_Groups_Ozero__class_Ozero(U_7915))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7917),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7915),U_7916),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)),c_Groups_Ozero__class_Ozero(U_7915))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),c_Groups_Ozero__class_Ozero(U_7915)),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7915),U_7916),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))),U_7917))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),c_Groups_Ozero__class_Ozero(U_7915)),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7916),c_Groups_Ozero__class_Ozero(U_7915)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)),c_Groups_Ozero__class_Ozero(U_7915))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7917),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7915),U_7916),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)),c_Groups_Ozero__class_Ozero(U_7915))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),c_Groups_Ozero__class_Ozero(U_7915)),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7915),U_7916),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))),U_7917))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),c_Groups_Ozero__class_Ozero(U_7915)),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7916),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7915),U_7917),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)))) ) )
| ~ class_Int_Onumber(U_7915)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7915) ),
inference(variable_rename,[status(thm)],[f_2299_1]) ).
cnf(f_2299_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7915),U_7916),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))),U_7917))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),c_Groups_Ozero__class_Ozero(U_7915)),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7916),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7915),U_7917),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))))
| ~ class_Int_Onumber(U_7915)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7915) ),
inference(clausify,[status(thm)],[f_2299_2]) ).
cnf(f_2299_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7917),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7915),U_7916),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)),c_Groups_Ozero__class_Ozero(U_7915)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),c_Groups_Ozero__class_Ozero(U_7915)),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7916),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7915),U_7917),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))))
| ~ class_Int_Onumber(U_7915)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7915) ),
inference(clausify,[status(thm)],[f_2299_2]) ).
cnf(f_2299_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7916),c_Groups_Ozero__class_Ozero(U_7915)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)),c_Groups_Ozero__class_Ozero(U_7915)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),c_Groups_Ozero__class_Ozero(U_7915)),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7916),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7915),U_7917),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))))
| ~ class_Int_Onumber(U_7915)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7915) ),
inference(clausify,[status(thm)],[f_2299_2]) ).
cnf(f_2299_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),c_Groups_Ozero__class_Ozero(U_7915)),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),c_Groups_Ozero__class_Ozero(U_7915)),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7916),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7915),U_7917),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))))
| ~ class_Int_Onumber(U_7915)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7915) ),
inference(clausify,[status(thm)],[f_2299_2]) ).
cnf(f_2299_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)),c_Groups_Ozero__class_Ozero(U_7915)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)),c_Groups_Ozero__class_Ozero(U_7915)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),c_Groups_Ozero__class_Ozero(U_7915)),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7916),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7915),U_7917),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))))
| ~ class_Int_Onumber(U_7915)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7915) ),
inference(clausify,[status(thm)],[f_2299_2]) ).
cnf(f_2299_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7916),c_Groups_Ozero__class_Ozero(U_7915)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)),c_Groups_Ozero__class_Ozero(U_7915)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),c_Groups_Ozero__class_Ozero(U_7915)),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7916),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7915),U_7917),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))))
| ~ class_Int_Onumber(U_7915)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7915) ),
inference(clausify,[status(thm)],[f_2299_2]) ).
cnf(f_2299_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)),c_Groups_Ozero__class_Ozero(U_7915)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7917),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7915),U_7916),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),c_Groups_Ozero__class_Ozero(U_7915)),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7916),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7915),U_7917),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))))
| ~ class_Int_Onumber(U_7915)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7915) ),
inference(clausify,[status(thm)],[f_2299_2]) ).
cnf(f_2299_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7916),c_Groups_Ozero__class_Ozero(U_7915)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7917),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7915),U_7916),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),c_Groups_Ozero__class_Ozero(U_7915)),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7916),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7915),U_7917),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))))
| ~ class_Int_Onumber(U_7915)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7915) ),
inference(clausify,[status(thm)],[f_2299_2]) ).
cnf(f_2299_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),c_Groups_Ozero__class_Ozero(U_7915)),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7915),U_7916),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))),U_7917))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7916),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7915),U_7917),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))))
| ~ class_Int_Onumber(U_7915)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7915) ),
inference(clausify,[status(thm)],[f_2299_2]) ).
cnf(f_2299_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)),c_Groups_Ozero__class_Ozero(U_7915)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)),c_Groups_Ozero__class_Ozero(U_7915)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7915),U_7916),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))),U_7917))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7916),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7915),U_7917),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))))
| ~ class_Int_Onumber(U_7915)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7915) ),
inference(clausify,[status(thm)],[f_2299_2]) ).
cnf(f_2299_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7916),c_Groups_Ozero__class_Ozero(U_7915)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)),c_Groups_Ozero__class_Ozero(U_7915)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7915),U_7916),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))),U_7917))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7916),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7915),U_7917),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))))
| ~ class_Int_Onumber(U_7915)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7915) ),
inference(clausify,[status(thm)],[f_2299_2]) ).
cnf(f_2299_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7915),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918)),c_Groups_Ozero__class_Ozero(U_7915)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7917),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7915),U_7916),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7915),U_7916),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))),U_7917))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7916),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7915),U_7917),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))))
| ~ class_Int_Onumber(U_7915)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7915) ),
inference(clausify,[status(thm)],[f_2299_2]) ).
cnf(f_2299_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7916),c_Groups_Ozero__class_Ozero(U_7915)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7917),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7915),U_7916),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7915),U_7916),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))),U_7917))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7915),U_7916),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7915),U_7917),hAPP(c_Int_Onumber__class_Onumber__of(U_7915),U_7918))))
| ~ class_Int_Onumber(U_7915)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7915) ),
inference(clausify,[status(thm)],[f_2299_2]) ).
fof(f_2300_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_2300_2,plain,
! [U_7920,U_7919] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7919),c_Groups_Ozero__class_Ozero(U_7919)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7919),U_7920),hAPP(c_Int_Onumber__class_Onumber__of(U_7919),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7919),c_Groups_Ozero__class_Ozero(U_7919)),U_7920))
| ~ class_Int_Onumber__ring(U_7919)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7919) ),
inference(variable_rename,[status(thm)],[f_2300_1]) ).
cnf(f_2300_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7919),c_Groups_Ozero__class_Ozero(U_7919)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7919),U_7920),hAPP(c_Int_Onumber__class_Onumber__of(U_7919),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7919),c_Groups_Ozero__class_Ozero(U_7919)),U_7920))
| ~ class_Int_Onumber__ring(U_7919)
| ~ class_Fields_Olinordered__field__inverse__zero(U_7919) ),
inference(clausify,[status(thm)],[f_2300_2]) ).
fof(f_2301_1,plain,
! [V_c_2,V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__divide__eq]) ).
fof(f_2301_2,plain,
! [U_7924,U_7923,U_7922,U_7921] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7922),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7921),U_7923),U_7924)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7922),c_Groups_Ozero__class_Ozero(U_7921)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),U_7924),c_Groups_Ozero__class_Ozero(U_7921))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7923),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7921),U_7922),U_7924)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),U_7924),c_Groups_Ozero__class_Ozero(U_7921))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),c_Groups_Ozero__class_Ozero(U_7921)),U_7924)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7921),U_7922),U_7924)),U_7923))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),c_Groups_Ozero__class_Ozero(U_7921)),U_7924)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7922),c_Groups_Ozero__class_Ozero(U_7921)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),U_7924),c_Groups_Ozero__class_Ozero(U_7921))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7923),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7921),U_7922),U_7924)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),U_7924),c_Groups_Ozero__class_Ozero(U_7921))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),c_Groups_Ozero__class_Ozero(U_7921)),U_7924)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7921),U_7922),U_7924)),U_7923))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),c_Groups_Ozero__class_Ozero(U_7921)),U_7924)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7922),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7921),U_7923),U_7924))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_7921) ),
inference(variable_rename,[status(thm)],[f_2301_1]) ).
cnf(f_2301_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7921),U_7922),U_7924)),U_7923))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),c_Groups_Ozero__class_Ozero(U_7921)),U_7924))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7922),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7921),U_7923),U_7924)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7921) ),
inference(clausify,[status(thm)],[f_2301_2]) ).
cnf(f_2301_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7923),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7921),U_7922),U_7924)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),U_7924),c_Groups_Ozero__class_Ozero(U_7921)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),c_Groups_Ozero__class_Ozero(U_7921)),U_7924))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7922),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7921),U_7923),U_7924)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7921) ),
inference(clausify,[status(thm)],[f_2301_2]) ).
cnf(f_2301_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7922),c_Groups_Ozero__class_Ozero(U_7921)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),U_7924),c_Groups_Ozero__class_Ozero(U_7921)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),c_Groups_Ozero__class_Ozero(U_7921)),U_7924))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7922),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7921),U_7923),U_7924)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7921) ),
inference(clausify,[status(thm)],[f_2301_2]) ).
cnf(f_2301_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),c_Groups_Ozero__class_Ozero(U_7921)),U_7924))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),c_Groups_Ozero__class_Ozero(U_7921)),U_7924))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7922),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7921),U_7923),U_7924)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7921) ),
inference(clausify,[status(thm)],[f_2301_2]) ).
cnf(f_2301_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),U_7924),c_Groups_Ozero__class_Ozero(U_7921)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),U_7924),c_Groups_Ozero__class_Ozero(U_7921)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),c_Groups_Ozero__class_Ozero(U_7921)),U_7924))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7922),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7921),U_7923),U_7924)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7921) ),
inference(clausify,[status(thm)],[f_2301_2]) ).
cnf(f_2301_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7922),c_Groups_Ozero__class_Ozero(U_7921)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),U_7924),c_Groups_Ozero__class_Ozero(U_7921)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),c_Groups_Ozero__class_Ozero(U_7921)),U_7924))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7922),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7921),U_7923),U_7924)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7921) ),
inference(clausify,[status(thm)],[f_2301_2]) ).
cnf(f_2301_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),U_7924),c_Groups_Ozero__class_Ozero(U_7921)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7923),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7921),U_7922),U_7924)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),c_Groups_Ozero__class_Ozero(U_7921)),U_7924))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7922),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7921),U_7923),U_7924)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7921) ),
inference(clausify,[status(thm)],[f_2301_2]) ).
cnf(f_2301_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7922),c_Groups_Ozero__class_Ozero(U_7921)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7923),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7921),U_7922),U_7924)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),c_Groups_Ozero__class_Ozero(U_7921)),U_7924))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7922),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7921),U_7923),U_7924)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7921) ),
inference(clausify,[status(thm)],[f_2301_2]) ).
cnf(f_2301_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),c_Groups_Ozero__class_Ozero(U_7921)),U_7924))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7921),U_7922),U_7924)),U_7923))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7922),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7921),U_7923),U_7924)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7921) ),
inference(clausify,[status(thm)],[f_2301_2]) ).
cnf(f_2301_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),U_7924),c_Groups_Ozero__class_Ozero(U_7921)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),U_7924),c_Groups_Ozero__class_Ozero(U_7921)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7921),U_7922),U_7924)),U_7923))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7922),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7921),U_7923),U_7924)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7921) ),
inference(clausify,[status(thm)],[f_2301_2]) ).
cnf(f_2301_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7922),c_Groups_Ozero__class_Ozero(U_7921)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),U_7924),c_Groups_Ozero__class_Ozero(U_7921)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7921),U_7922),U_7924)),U_7923))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7922),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7921),U_7923),U_7924)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7921) ),
inference(clausify,[status(thm)],[f_2301_2]) ).
cnf(f_2301_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7921),U_7924),c_Groups_Ozero__class_Ozero(U_7921)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7923),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7921),U_7922),U_7924)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7921),U_7922),U_7924)),U_7923))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7922),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7921),U_7923),U_7924)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7921) ),
inference(clausify,[status(thm)],[f_2301_2]) ).
cnf(f_2301_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7922),c_Groups_Ozero__class_Ozero(U_7921)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7923),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7921),U_7922),U_7924)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7921),U_7922),U_7924)),U_7923))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7921),U_7922),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7921),U_7923),U_7924)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7921) ),
inference(clausify,[status(thm)],[f_2301_2]) ).
fof(f_2302_1,plain,
! [V_a_2,V_c_2,V_b_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__le__eq]) ).
fof(f_2302_2,plain,
! [U_7928,U_7927,U_7926,U_7925] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7925),U_7926),U_7927)),U_7928))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),c_Groups_Ozero__class_Ozero(U_7925)),U_7928))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),U_7927),c_Groups_Ozero__class_Ozero(U_7925))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7925),U_7928),U_7927)),U_7926))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),U_7927),c_Groups_Ozero__class_Ozero(U_7925))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),c_Groups_Ozero__class_Ozero(U_7925)),U_7927)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),U_7926),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7925),U_7928),U_7927)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),c_Groups_Ozero__class_Ozero(U_7925)),U_7927)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),c_Groups_Ozero__class_Ozero(U_7925)),U_7928))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),U_7927),c_Groups_Ozero__class_Ozero(U_7925))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7925),U_7928),U_7927)),U_7926))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),U_7927),c_Groups_Ozero__class_Ozero(U_7925))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),c_Groups_Ozero__class_Ozero(U_7925)),U_7927)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),U_7926),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7925),U_7928),U_7927)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),c_Groups_Ozero__class_Ozero(U_7925)),U_7927)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7925),U_7926),U_7927)),U_7928)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_7925) ),
inference(variable_rename,[status(thm)],[f_2302_1]) ).
cnf(f_2302_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),U_7926),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7925),U_7928),U_7927)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),c_Groups_Ozero__class_Ozero(U_7925)),U_7927))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7925),U_7926),U_7927)),U_7928))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7925) ),
inference(clausify,[status(thm)],[f_2302_2]) ).
cnf(f_2302_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7925),U_7928),U_7927)),U_7926))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),U_7927),c_Groups_Ozero__class_Ozero(U_7925)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),c_Groups_Ozero__class_Ozero(U_7925)),U_7927))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7925),U_7926),U_7927)),U_7928))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7925) ),
inference(clausify,[status(thm)],[f_2302_2]) ).
cnf(f_2302_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),c_Groups_Ozero__class_Ozero(U_7925)),U_7928))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),U_7927),c_Groups_Ozero__class_Ozero(U_7925)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),c_Groups_Ozero__class_Ozero(U_7925)),U_7927))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7925),U_7926),U_7927)),U_7928))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7925) ),
inference(clausify,[status(thm)],[f_2302_2]) ).
cnf(f_2302_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),c_Groups_Ozero__class_Ozero(U_7925)),U_7927))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),c_Groups_Ozero__class_Ozero(U_7925)),U_7927))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7925),U_7926),U_7927)),U_7928))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7925) ),
inference(clausify,[status(thm)],[f_2302_2]) ).
cnf(f_2302_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),U_7927),c_Groups_Ozero__class_Ozero(U_7925)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),U_7927),c_Groups_Ozero__class_Ozero(U_7925)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),c_Groups_Ozero__class_Ozero(U_7925)),U_7927))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7925),U_7926),U_7927)),U_7928))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7925) ),
inference(clausify,[status(thm)],[f_2302_2]) ).
cnf(f_2302_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),c_Groups_Ozero__class_Ozero(U_7925)),U_7928))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),U_7927),c_Groups_Ozero__class_Ozero(U_7925)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),c_Groups_Ozero__class_Ozero(U_7925)),U_7927))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7925),U_7926),U_7927)),U_7928))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7925) ),
inference(clausify,[status(thm)],[f_2302_2]) ).
cnf(f_2302_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),U_7927),c_Groups_Ozero__class_Ozero(U_7925)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7925),U_7928),U_7927)),U_7926))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),c_Groups_Ozero__class_Ozero(U_7925)),U_7927))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7925),U_7926),U_7927)),U_7928))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7925) ),
inference(clausify,[status(thm)],[f_2302_2]) ).
cnf(f_2302_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),c_Groups_Ozero__class_Ozero(U_7925)),U_7928))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7925),U_7928),U_7927)),U_7926))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),c_Groups_Ozero__class_Ozero(U_7925)),U_7927))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7925),U_7926),U_7927)),U_7928))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7925) ),
inference(clausify,[status(thm)],[f_2302_2]) ).
cnf(f_2302_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),c_Groups_Ozero__class_Ozero(U_7925)),U_7927))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),U_7926),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7925),U_7928),U_7927)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7925),U_7926),U_7927)),U_7928))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7925) ),
inference(clausify,[status(thm)],[f_2302_2]) ).
cnf(f_2302_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),U_7927),c_Groups_Ozero__class_Ozero(U_7925)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),U_7927),c_Groups_Ozero__class_Ozero(U_7925)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),U_7926),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7925),U_7928),U_7927)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7925),U_7926),U_7927)),U_7928))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7925) ),
inference(clausify,[status(thm)],[f_2302_2]) ).
cnf(f_2302_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),c_Groups_Ozero__class_Ozero(U_7925)),U_7928))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),U_7927),c_Groups_Ozero__class_Ozero(U_7925)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),U_7926),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7925),U_7928),U_7927)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7925),U_7926),U_7927)),U_7928))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7925) ),
inference(clausify,[status(thm)],[f_2302_2]) ).
cnf(f_2302_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7925),U_7927),c_Groups_Ozero__class_Ozero(U_7925)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7925),U_7928),U_7927)),U_7926))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),U_7926),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7925),U_7928),U_7927)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7925),U_7926),U_7927)),U_7928))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7925) ),
inference(clausify,[status(thm)],[f_2302_2]) ).
cnf(f_2302_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),c_Groups_Ozero__class_Ozero(U_7925)),U_7928))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7925),U_7928),U_7927)),U_7926))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),U_7926),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7925),U_7928),U_7927)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7925),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7925),U_7926),U_7927)),U_7928))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7925) ),
inference(clausify,[status(thm)],[f_2302_2]) ).
fof(f_2303_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_pos__le__divide__eq]) ).
fof(f_2303_2,plain,
! [U_7932,U_7931,U_7930,U_7929] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7929),U_7931),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7929),U_7932),U_7930)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7929),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7929),U_7931),U_7930)),U_7932)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7929),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7929),U_7931),U_7930)),U_7932))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7929),U_7931),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7929),U_7932),U_7930))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7929),c_Groups_Ozero__class_Ozero(U_7929)),U_7930))
| ~ class_Fields_Olinordered__field(U_7929) ),
inference(variable_rename,[status(thm)],[f_2303_1]) ).
cnf(f_2303_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7929),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7929),U_7931),U_7930)),U_7932))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7929),U_7931),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7929),U_7932),U_7930)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7929),c_Groups_Ozero__class_Ozero(U_7929)),U_7930))
| ~ class_Fields_Olinordered__field(U_7929) ),
inference(clausify,[status(thm)],[f_2303_2]) ).
cnf(f_2303_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7929),U_7931),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7929),U_7932),U_7930)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7929),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7929),U_7931),U_7930)),U_7932))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7929),c_Groups_Ozero__class_Ozero(U_7929)),U_7930))
| ~ class_Fields_Olinordered__field(U_7929) ),
inference(clausify,[status(thm)],[f_2303_2]) ).
fof(f_2304_1,plain,
! [V_a_2,V_b_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_pos__divide__le__eq]) ).
fof(f_2304_2,plain,
! [U_7936,U_7935,U_7934,U_7933] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7933),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7933),U_7935),U_7934)),U_7936))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7933),U_7935),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7933),U_7936),U_7934))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7933),U_7935),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7933),U_7936),U_7934)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7933),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7933),U_7935),U_7934)),U_7936)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7933),c_Groups_Ozero__class_Ozero(U_7933)),U_7934))
| ~ class_Fields_Olinordered__field(U_7933) ),
inference(variable_rename,[status(thm)],[f_2304_1]) ).
cnf(f_2304_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7933),U_7935),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7933),U_7936),U_7934)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7933),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7933),U_7935),U_7934)),U_7936))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7933),c_Groups_Ozero__class_Ozero(U_7933)),U_7934))
| ~ class_Fields_Olinordered__field(U_7933) ),
inference(clausify,[status(thm)],[f_2304_2]) ).
cnf(f_2304_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7933),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7933),U_7935),U_7934)),U_7936))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7933),U_7935),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7933),U_7936),U_7934)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7933),c_Groups_Ozero__class_Ozero(U_7933)),U_7934))
| ~ class_Fields_Olinordered__field(U_7933) ),
inference(clausify,[status(thm)],[f_2304_2]) ).
fof(f_2305_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_2305_2,plain,
! [U_7941,U_7940,U_7939,U_7938,U_7937] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7937),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7937),U_7938),U_7939)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7937),U_7940),U_7941)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7937),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7937),U_7938),U_7940)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7937),U_7939),U_7941))
| ~ class_Fields_Ofield__inverse__zero(U_7937) ),
inference(variable_rename,[status(thm)],[f_2305_1]) ).
cnf(f_2305_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7937),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7937),U_7938),U_7939)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7937),U_7940),U_7941)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7937),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7937),U_7938),U_7940)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7937),U_7939),U_7941))
| ~ class_Fields_Ofield__inverse__zero(U_7937) ),
inference(clausify,[status(thm)],[f_2305_2]) ).
fof(f_2306_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_2306_2,plain,
! [U_7944,U_7943,U_7942] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_7942),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7942),U_7943),U_7944)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7942),U_7943),hAPP(c_Groups_Ouminus__class_Ouminus(U_7942),U_7944))
| ~ class_Fields_Ofield__inverse__zero(U_7942) ),
inference(variable_rename,[status(thm)],[f_2306_1]) ).
cnf(f_2306_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_7942),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7942),U_7943),U_7944)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7942),U_7943),hAPP(c_Groups_Ouminus__class_Ouminus(U_7942),U_7944))
| ~ class_Fields_Ofield__inverse__zero(U_7942) ),
inference(clausify,[status(thm)],[f_2306_2]) ).
fof(f_2307_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_2307_2,plain,
! [U_7947,U_7946,U_7945] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7945),hAPP(c_Groups_Ouminus__class_Ouminus(U_7945),U_7946)),hAPP(c_Groups_Ouminus__class_Ouminus(U_7945),U_7947)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7945),U_7946),U_7947)
| ~ class_Fields_Ofield__inverse__zero(U_7945) ),
inference(variable_rename,[status(thm)],[f_2307_1]) ).
cnf(f_2307_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7945),hAPP(c_Groups_Ouminus__class_Ouminus(U_7945),U_7946)),hAPP(c_Groups_Ouminus__class_Ouminus(U_7945),U_7947)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7945),U_7946),U_7947)
| ~ class_Fields_Ofield__inverse__zero(U_7945) ),
inference(clausify,[status(thm)],[f_2307_2]) ).
fof(f_2308_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_2308_2,plain,
! [U_7950,U_7949,U_7948] :
( hAPP(c_Groups_Oabs__class_Oabs(U_7948),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7948),U_7949),U_7950)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7948),hAPP(c_Groups_Oabs__class_Oabs(U_7948),U_7949)),hAPP(c_Groups_Oabs__class_Oabs(U_7948),U_7950))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7948) ),
inference(variable_rename,[status(thm)],[f_2308_1]) ).
cnf(f_2308_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_7948),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7948),U_7949),U_7950)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7948),hAPP(c_Groups_Oabs__class_Oabs(U_7948),U_7949)),hAPP(c_Groups_Oabs__class_Oabs(U_7948),U_7950))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7948) ),
inference(clausify,[status(thm)],[f_2308_2]) ).
fof(f_2309_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_2309_2,plain,
! [U_7953,U_7952,U_7951] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),c_Groups_Ozero__class_Ozero(U_7951)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7951),U_7952),U_7953)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),U_7953),c_Groups_Ozero__class_Ozero(U_7951)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),U_7952),c_Groups_Ozero__class_Ozero(U_7951))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),c_Groups_Ozero__class_Ozero(U_7951)),U_7953))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),c_Groups_Ozero__class_Ozero(U_7951)),U_7952)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),U_7953),c_Groups_Ozero__class_Ozero(U_7951)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),U_7952),c_Groups_Ozero__class_Ozero(U_7951))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),c_Groups_Ozero__class_Ozero(U_7951)),U_7953))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),c_Groups_Ozero__class_Ozero(U_7951)),U_7952)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),c_Groups_Ozero__class_Ozero(U_7951)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7951),U_7952),U_7953))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_7951) ),
inference(variable_rename,[status(thm)],[f_2309_1]) ).
cnf(f_2309_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),U_7952),c_Groups_Ozero__class_Ozero(U_7951)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),c_Groups_Ozero__class_Ozero(U_7951)),U_7952))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),c_Groups_Ozero__class_Ozero(U_7951)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7951),U_7952),U_7953)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7951) ),
inference(clausify,[status(thm)],[f_2309_2]) ).
cnf(f_2309_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),U_7953),c_Groups_Ozero__class_Ozero(U_7951)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),c_Groups_Ozero__class_Ozero(U_7951)),U_7952))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),c_Groups_Ozero__class_Ozero(U_7951)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7951),U_7952),U_7953)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7951) ),
inference(clausify,[status(thm)],[f_2309_2]) ).
cnf(f_2309_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),U_7952),c_Groups_Ozero__class_Ozero(U_7951)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),c_Groups_Ozero__class_Ozero(U_7951)),U_7953))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),c_Groups_Ozero__class_Ozero(U_7951)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7951),U_7952),U_7953)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7951) ),
inference(clausify,[status(thm)],[f_2309_2]) ).
cnf(f_2309_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),U_7953),c_Groups_Ozero__class_Ozero(U_7951)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),c_Groups_Ozero__class_Ozero(U_7951)),U_7953))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),c_Groups_Ozero__class_Ozero(U_7951)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7951),U_7952),U_7953)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7951) ),
inference(clausify,[status(thm)],[f_2309_2]) ).
cnf(f_2309_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),c_Groups_Ozero__class_Ozero(U_7951)),U_7953))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),c_Groups_Ozero__class_Ozero(U_7951)),U_7952))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),c_Groups_Ozero__class_Ozero(U_7951)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7951),U_7952),U_7953)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7951) ),
inference(clausify,[status(thm)],[f_2309_2]) ).
cnf(f_2309_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),U_7953),c_Groups_Ozero__class_Ozero(U_7951)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),U_7952),c_Groups_Ozero__class_Ozero(U_7951)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7951),c_Groups_Ozero__class_Ozero(U_7951)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7951),U_7952),U_7953)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7951) ),
inference(clausify,[status(thm)],[f_2309_2]) ).
fof(f_2310_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_2310_2,plain,
! [U_7956,U_7955,U_7954] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7954),U_7955),U_7956)),c_Groups_Ozero__class_Ozero(U_7954)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),c_Groups_Ozero__class_Ozero(U_7954)),U_7956))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),U_7955),c_Groups_Ozero__class_Ozero(U_7954))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),U_7956),c_Groups_Ozero__class_Ozero(U_7954)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),c_Groups_Ozero__class_Ozero(U_7954)),U_7955)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),c_Groups_Ozero__class_Ozero(U_7954)),U_7956))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),U_7955),c_Groups_Ozero__class_Ozero(U_7954))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),U_7956),c_Groups_Ozero__class_Ozero(U_7954)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),c_Groups_Ozero__class_Ozero(U_7954)),U_7955)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7954),U_7955),U_7956)),c_Groups_Ozero__class_Ozero(U_7954))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_7954) ),
inference(variable_rename,[status(thm)],[f_2310_1]) ).
cnf(f_2310_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),U_7955),c_Groups_Ozero__class_Ozero(U_7954)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),c_Groups_Ozero__class_Ozero(U_7954)),U_7955))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7954),U_7955),U_7956)),c_Groups_Ozero__class_Ozero(U_7954)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7954) ),
inference(clausify,[status(thm)],[f_2310_2]) ).
cnf(f_2310_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),c_Groups_Ozero__class_Ozero(U_7954)),U_7956))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),c_Groups_Ozero__class_Ozero(U_7954)),U_7955))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7954),U_7955),U_7956)),c_Groups_Ozero__class_Ozero(U_7954)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7954) ),
inference(clausify,[status(thm)],[f_2310_2]) ).
cnf(f_2310_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),U_7955),c_Groups_Ozero__class_Ozero(U_7954)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),U_7956),c_Groups_Ozero__class_Ozero(U_7954)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7954),U_7955),U_7956)),c_Groups_Ozero__class_Ozero(U_7954)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7954) ),
inference(clausify,[status(thm)],[f_2310_2]) ).
cnf(f_2310_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),c_Groups_Ozero__class_Ozero(U_7954)),U_7956))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),U_7956),c_Groups_Ozero__class_Ozero(U_7954)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7954),U_7955),U_7956)),c_Groups_Ozero__class_Ozero(U_7954)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7954) ),
inference(clausify,[status(thm)],[f_2310_2]) ).
cnf(f_2310_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),U_7956),c_Groups_Ozero__class_Ozero(U_7954)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),c_Groups_Ozero__class_Ozero(U_7954)),U_7955))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7954),U_7955),U_7956)),c_Groups_Ozero__class_Ozero(U_7954)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7954) ),
inference(clausify,[status(thm)],[f_2310_2]) ).
cnf(f_2310_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),c_Groups_Ozero__class_Ozero(U_7954)),U_7956))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),U_7955),c_Groups_Ozero__class_Ozero(U_7954)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7954),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7954),U_7955),U_7956)),c_Groups_Ozero__class_Ozero(U_7954)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7954) ),
inference(clausify,[status(thm)],[f_2310_2]) ).
fof(f_2311_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_2311_2,plain,
! [U_7960,U_7959,U_7958,U_7957] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7957),U_7958),U_7960)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7957),U_7959),U_7960)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7957),c_Groups_Ozero__class_Ozero(U_7957)),U_7960))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7957),U_7958),U_7959))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7957) ),
inference(variable_rename,[status(thm)],[f_2311_1]) ).
cnf(f_2311_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7957),U_7958),U_7960)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7957),U_7959),U_7960)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7957),c_Groups_Ozero__class_Ozero(U_7957)),U_7960))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7957),U_7958),U_7959))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7957) ),
inference(clausify,[status(thm)],[f_2311_2]) ).
fof(f_2312_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_2312_2,plain,
! [U_7964,U_7963,U_7962,U_7961] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7961),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7961),U_7963),U_7964)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7961),U_7962),U_7964)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7961),U_7964),c_Groups_Ozero__class_Ozero(U_7961)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7961),U_7962),U_7963))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7961) ),
inference(variable_rename,[status(thm)],[f_2312_1]) ).
cnf(f_2312_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7961),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7961),U_7963),U_7964)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7961),U_7962),U_7964)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7961),U_7964),c_Groups_Ozero__class_Ozero(U_7961)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7961),U_7962),U_7963))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7961) ),
inference(clausify,[status(thm)],[f_2312_2]) ).
fof(f_2313_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_2313_2,plain,
! [U_7968,U_7967,U_7966,U_7965] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7965),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7965),U_7967),U_7968)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7965),U_7966),U_7968)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7965),U_7968),c_Groups_Ozero__class_Ozero(U_7965)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7965),U_7966),U_7967))
| ~ class_Fields_Olinordered__field(U_7965) ),
inference(variable_rename,[status(thm)],[f_2313_1]) ).
cnf(f_2313_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7965),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7965),U_7967),U_7968)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7965),U_7966),U_7968)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7965),U_7968),c_Groups_Ozero__class_Ozero(U_7965)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7965),U_7966),U_7967))
| ~ class_Fields_Olinordered__field(U_7965) ),
inference(clausify,[status(thm)],[f_2313_2]) ).
fof(f_2314_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_2314_2,plain,
! [U_7972,U_7971,U_7970,U_7969] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7969),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7969),U_7970),U_7972)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7969),U_7971),U_7972)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7969),c_Groups_Ozero__class_Ozero(U_7969)),U_7972))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7969),U_7970),U_7971))
| ~ class_Fields_Olinordered__field(U_7969) ),
inference(variable_rename,[status(thm)],[f_2314_1]) ).
cnf(f_2314_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7969),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7969),U_7970),U_7972)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7969),U_7971),U_7972)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7969),c_Groups_Ozero__class_Ozero(U_7969)),U_7972))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7969),U_7970),U_7971))
| ~ class_Fields_Olinordered__field(U_7969) ),
inference(clausify,[status(thm)],[f_2314_2]) ).
fof(f_2315_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_2315_2,plain,
! [U_7975,U_7974,U_7973] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7973),c_Groups_Ozero__class_Ozero(U_7973)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7973),U_7974),U_7975)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7973),U_7975),c_Groups_Ozero__class_Ozero(U_7973)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7973),U_7974),c_Groups_Ozero__class_Ozero(U_7973)))
| ~ class_Fields_Olinordered__field(U_7973) ),
inference(variable_rename,[status(thm)],[f_2315_1]) ).
cnf(f_2315_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7973),c_Groups_Ozero__class_Ozero(U_7973)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7973),U_7974),U_7975)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7973),U_7975),c_Groups_Ozero__class_Ozero(U_7973)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7973),U_7974),c_Groups_Ozero__class_Ozero(U_7973)))
| ~ class_Fields_Olinordered__field(U_7973) ),
inference(clausify,[status(thm)],[f_2315_2]) ).
fof(f_2316_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_2316_2,plain,
! [U_7978,U_7977,U_7976] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7976),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7976),U_7977),U_7978)),c_Groups_Ozero__class_Ozero(U_7976)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7976),c_Groups_Ozero__class_Ozero(U_7976)),U_7978))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7976),U_7977),c_Groups_Ozero__class_Ozero(U_7976)))
| ~ class_Fields_Olinordered__field(U_7976) ),
inference(variable_rename,[status(thm)],[f_2316_1]) ).
cnf(f_2316_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7976),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7976),U_7977),U_7978)),c_Groups_Ozero__class_Ozero(U_7976)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7976),c_Groups_Ozero__class_Ozero(U_7976)),U_7978))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7976),U_7977),c_Groups_Ozero__class_Ozero(U_7976)))
| ~ class_Fields_Olinordered__field(U_7976) ),
inference(clausify,[status(thm)],[f_2316_2]) ).
fof(f_2317_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_2317_2,plain,
! [U_7981,U_7980,U_7979] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7979),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7979),U_7980),U_7981)),c_Groups_Ozero__class_Ozero(U_7979)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7979),U_7981),c_Groups_Ozero__class_Ozero(U_7979)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7979),c_Groups_Ozero__class_Ozero(U_7979)),U_7980))
| ~ class_Fields_Olinordered__field(U_7979) ),
inference(variable_rename,[status(thm)],[f_2317_1]) ).
cnf(f_2317_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7979),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7979),U_7980),U_7981)),c_Groups_Ozero__class_Ozero(U_7979)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7979),U_7981),c_Groups_Ozero__class_Ozero(U_7979)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7979),c_Groups_Ozero__class_Ozero(U_7979)),U_7980))
| ~ class_Fields_Olinordered__field(U_7979) ),
inference(clausify,[status(thm)],[f_2317_2]) ).
fof(f_2318_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_2318_2,plain,
! [U_7984,U_7983,U_7982] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7982),c_Groups_Ozero__class_Ozero(U_7982)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7982),U_7983),U_7984)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7982),c_Groups_Ozero__class_Ozero(U_7982)),U_7984))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7982),c_Groups_Ozero__class_Ozero(U_7982)),U_7983))
| ~ class_Fields_Olinordered__field(U_7982) ),
inference(variable_rename,[status(thm)],[f_2318_1]) ).
cnf(f_2318_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7982),c_Groups_Ozero__class_Ozero(U_7982)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7982),U_7983),U_7984)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7982),c_Groups_Ozero__class_Ozero(U_7982)),U_7984))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7982),c_Groups_Ozero__class_Ozero(U_7982)),U_7983))
| ~ class_Fields_Olinordered__field(U_7982) ),
inference(clausify,[status(thm)],[f_2318_2]) ).
fof(f_2319_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_2319_2,plain,
! [U_7987,U_7986,U_7985] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7985),U_7986),U_7987)),c_Groups_Ozero__class_Ozero(U_7985)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),c_Groups_Ozero__class_Ozero(U_7985)),U_7987))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),U_7986),c_Groups_Ozero__class_Ozero(U_7985))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),U_7987),c_Groups_Ozero__class_Ozero(U_7985)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),c_Groups_Ozero__class_Ozero(U_7985)),U_7986)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),c_Groups_Ozero__class_Ozero(U_7985)),U_7987))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),U_7986),c_Groups_Ozero__class_Ozero(U_7985))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),U_7987),c_Groups_Ozero__class_Ozero(U_7985)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),c_Groups_Ozero__class_Ozero(U_7985)),U_7986)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7985),U_7986),U_7987)),c_Groups_Ozero__class_Ozero(U_7985))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_7985) ),
inference(variable_rename,[status(thm)],[f_2319_1]) ).
cnf(f_2319_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),U_7986),c_Groups_Ozero__class_Ozero(U_7985)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),c_Groups_Ozero__class_Ozero(U_7985)),U_7986))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7985),U_7986),U_7987)),c_Groups_Ozero__class_Ozero(U_7985)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7985) ),
inference(clausify,[status(thm)],[f_2319_2]) ).
cnf(f_2319_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),c_Groups_Ozero__class_Ozero(U_7985)),U_7987))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),c_Groups_Ozero__class_Ozero(U_7985)),U_7986))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7985),U_7986),U_7987)),c_Groups_Ozero__class_Ozero(U_7985)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7985) ),
inference(clausify,[status(thm)],[f_2319_2]) ).
cnf(f_2319_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),U_7986),c_Groups_Ozero__class_Ozero(U_7985)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),U_7987),c_Groups_Ozero__class_Ozero(U_7985)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7985),U_7986),U_7987)),c_Groups_Ozero__class_Ozero(U_7985)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7985) ),
inference(clausify,[status(thm)],[f_2319_2]) ).
cnf(f_2319_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),c_Groups_Ozero__class_Ozero(U_7985)),U_7987))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),U_7987),c_Groups_Ozero__class_Ozero(U_7985)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7985),U_7986),U_7987)),c_Groups_Ozero__class_Ozero(U_7985)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7985) ),
inference(clausify,[status(thm)],[f_2319_2]) ).
cnf(f_2319_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),U_7987),c_Groups_Ozero__class_Ozero(U_7985)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),c_Groups_Ozero__class_Ozero(U_7985)),U_7986))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7985),U_7986),U_7987)),c_Groups_Ozero__class_Ozero(U_7985)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7985) ),
inference(clausify,[status(thm)],[f_2319_2]) ).
cnf(f_2319_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),c_Groups_Ozero__class_Ozero(U_7985)),U_7987))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),U_7986),c_Groups_Ozero__class_Ozero(U_7985)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7985),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7985),U_7986),U_7987)),c_Groups_Ozero__class_Ozero(U_7985)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7985) ),
inference(clausify,[status(thm)],[f_2319_2]) ).
fof(f_2320_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_2320_2,plain,
! [U_7990,U_7989,U_7988] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),c_Groups_Ozero__class_Ozero(U_7988)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7988),U_7989),U_7990)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),U_7990),c_Groups_Ozero__class_Ozero(U_7988)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),U_7989),c_Groups_Ozero__class_Ozero(U_7988))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),c_Groups_Ozero__class_Ozero(U_7988)),U_7990))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),c_Groups_Ozero__class_Ozero(U_7988)),U_7989)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),U_7990),c_Groups_Ozero__class_Ozero(U_7988)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),U_7989),c_Groups_Ozero__class_Ozero(U_7988))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),c_Groups_Ozero__class_Ozero(U_7988)),U_7990))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),c_Groups_Ozero__class_Ozero(U_7988)),U_7989)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),c_Groups_Ozero__class_Ozero(U_7988)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7988),U_7989),U_7990))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_7988) ),
inference(variable_rename,[status(thm)],[f_2320_1]) ).
cnf(f_2320_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),U_7989),c_Groups_Ozero__class_Ozero(U_7988)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),c_Groups_Ozero__class_Ozero(U_7988)),U_7989))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),c_Groups_Ozero__class_Ozero(U_7988)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7988),U_7989),U_7990)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7988) ),
inference(clausify,[status(thm)],[f_2320_2]) ).
cnf(f_2320_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),U_7990),c_Groups_Ozero__class_Ozero(U_7988)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),c_Groups_Ozero__class_Ozero(U_7988)),U_7989))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),c_Groups_Ozero__class_Ozero(U_7988)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7988),U_7989),U_7990)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7988) ),
inference(clausify,[status(thm)],[f_2320_2]) ).
cnf(f_2320_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),U_7989),c_Groups_Ozero__class_Ozero(U_7988)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),c_Groups_Ozero__class_Ozero(U_7988)),U_7990))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),c_Groups_Ozero__class_Ozero(U_7988)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7988),U_7989),U_7990)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7988) ),
inference(clausify,[status(thm)],[f_2320_2]) ).
cnf(f_2320_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),U_7990),c_Groups_Ozero__class_Ozero(U_7988)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),c_Groups_Ozero__class_Ozero(U_7988)),U_7990))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),c_Groups_Ozero__class_Ozero(U_7988)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7988),U_7989),U_7990)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7988) ),
inference(clausify,[status(thm)],[f_2320_2]) ).
cnf(f_2320_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),c_Groups_Ozero__class_Ozero(U_7988)),U_7990))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),c_Groups_Ozero__class_Ozero(U_7988)),U_7989))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),c_Groups_Ozero__class_Ozero(U_7988)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7988),U_7989),U_7990)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7988) ),
inference(clausify,[status(thm)],[f_2320_2]) ).
cnf(f_2320_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),U_7990),c_Groups_Ozero__class_Ozero(U_7988)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),U_7989),c_Groups_Ozero__class_Ozero(U_7988)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7988),c_Groups_Ozero__class_Ozero(U_7988)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7988),U_7989),U_7990)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_7988) ),
inference(clausify,[status(thm)],[f_2320_2]) ).
fof(f_2321_1,plain,
! [V_c_2,V_b_2,V_a_2,T_b] :
( ( ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
| ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
& V_c_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) != V_b_2
& V_c_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
& ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| V_c_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2
| V_c_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
| V_a_2 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) ) )
| ~ class_Fields_Ofield__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__divide__eq]) ).
fof(f_2321_2,plain,
! [U_7994,U_7993,U_7992,U_7991] :
( ( ( U_7992 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7991),U_7993),U_7994)
| ( U_7992 != c_Groups_Ozero__class_Ozero(U_7991)
& U_7994 = c_Groups_Ozero__class_Ozero(U_7991) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7991),U_7992),U_7994) != U_7993
& U_7994 != c_Groups_Ozero__class_Ozero(U_7991) ) )
& ( ( ( U_7992 = c_Groups_Ozero__class_Ozero(U_7991)
| U_7994 != c_Groups_Ozero__class_Ozero(U_7991) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7991),U_7992),U_7994) = U_7993
| U_7994 = c_Groups_Ozero__class_Ozero(U_7991) ) )
| U_7992 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7991),U_7993),U_7994) ) )
| ~ class_Fields_Ofield__inverse__zero(U_7991) ),
inference(variable_rename,[status(thm)],[f_2321_1]) ).
cnf(f_2321_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7991),U_7992),U_7994) = U_7993
| U_7994 = c_Groups_Ozero__class_Ozero(U_7991)
| U_7992 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7991),U_7993),U_7994)
| ~ class_Fields_Ofield__inverse__zero(U_7991) ),
inference(clausify,[status(thm)],[f_2321_2]) ).
cnf(f_2321_4,plain,
( U_7992 = c_Groups_Ozero__class_Ozero(U_7991)
| U_7994 != c_Groups_Ozero__class_Ozero(U_7991)
| U_7992 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7991),U_7993),U_7994)
| ~ class_Fields_Ofield__inverse__zero(U_7991) ),
inference(clausify,[status(thm)],[f_2321_2]) ).
cnf(f_2321_5,plain,
( U_7994 = c_Groups_Ozero__class_Ozero(U_7991)
| U_7994 != c_Groups_Ozero__class_Ozero(U_7991)
| U_7992 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7991),U_7993),U_7994)
| ~ class_Fields_Ofield__inverse__zero(U_7991) ),
inference(clausify,[status(thm)],[f_2321_2]) ).
cnf(f_2321_6,plain,
( U_7992 != c_Groups_Ozero__class_Ozero(U_7991)
| U_7994 != c_Groups_Ozero__class_Ozero(U_7991)
| U_7992 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7991),U_7993),U_7994)
| ~ class_Fields_Ofield__inverse__zero(U_7991) ),
inference(clausify,[status(thm)],[f_2321_2]) ).
cnf(f_2321_7,plain,
( U_7994 = c_Groups_Ozero__class_Ozero(U_7991)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7991),U_7992),U_7994) != U_7993
| U_7992 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7991),U_7993),U_7994)
| ~ class_Fields_Ofield__inverse__zero(U_7991) ),
inference(clausify,[status(thm)],[f_2321_2]) ).
cnf(f_2321_8,plain,
( U_7992 != c_Groups_Ozero__class_Ozero(U_7991)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7991),U_7992),U_7994) != U_7993
| U_7992 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7991),U_7993),U_7994)
| ~ class_Fields_Ofield__inverse__zero(U_7991) ),
inference(clausify,[status(thm)],[f_2321_2]) ).
fof(f_2322_1,plain,
! [V_a_2,V_c_2,V_b_2,T_b] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
| ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
& V_c_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)
& V_c_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
& ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| V_c_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)
| V_c_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) != V_a_2 ) )
| ~ class_Fields_Ofield__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__eq__eq]) ).
fof(f_2322_2,plain,
! [U_7998,U_7997,U_7996,U_7995] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7995),U_7996),U_7997) = U_7998
| ( U_7998 != c_Groups_Ozero__class_Ozero(U_7995)
& U_7997 = c_Groups_Ozero__class_Ozero(U_7995) )
| ( U_7996 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7995),U_7998),U_7997)
& U_7997 != c_Groups_Ozero__class_Ozero(U_7995) ) )
& ( ( ( U_7998 = c_Groups_Ozero__class_Ozero(U_7995)
| U_7997 != c_Groups_Ozero__class_Ozero(U_7995) )
& ( U_7996 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7995),U_7998),U_7997)
| U_7997 = c_Groups_Ozero__class_Ozero(U_7995) ) )
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7995),U_7996),U_7997) != U_7998 ) )
| ~ class_Fields_Ofield__inverse__zero(U_7995) ),
inference(variable_rename,[status(thm)],[f_2322_1]) ).
cnf(f_2322_3,plain,
( U_7996 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7995),U_7998),U_7997)
| U_7997 = c_Groups_Ozero__class_Ozero(U_7995)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7995),U_7996),U_7997) != U_7998
| ~ class_Fields_Ofield__inverse__zero(U_7995) ),
inference(clausify,[status(thm)],[f_2322_2]) ).
cnf(f_2322_4,plain,
( U_7998 = c_Groups_Ozero__class_Ozero(U_7995)
| U_7997 != c_Groups_Ozero__class_Ozero(U_7995)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7995),U_7996),U_7997) != U_7998
| ~ class_Fields_Ofield__inverse__zero(U_7995) ),
inference(clausify,[status(thm)],[f_2322_2]) ).
cnf(f_2322_5,plain,
( U_7997 = c_Groups_Ozero__class_Ozero(U_7995)
| U_7997 != c_Groups_Ozero__class_Ozero(U_7995)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7995),U_7996),U_7997) = U_7998
| ~ class_Fields_Ofield__inverse__zero(U_7995) ),
inference(clausify,[status(thm)],[f_2322_2]) ).
cnf(f_2322_6,plain,
( U_7998 != c_Groups_Ozero__class_Ozero(U_7995)
| U_7997 != c_Groups_Ozero__class_Ozero(U_7995)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7995),U_7996),U_7997) = U_7998
| ~ class_Fields_Ofield__inverse__zero(U_7995) ),
inference(clausify,[status(thm)],[f_2322_2]) ).
cnf(f_2322_7,plain,
( U_7997 = c_Groups_Ozero__class_Ozero(U_7995)
| U_7996 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7995),U_7998),U_7997)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7995),U_7996),U_7997) = U_7998
| ~ class_Fields_Ofield__inverse__zero(U_7995) ),
inference(clausify,[status(thm)],[f_2322_2]) ).
cnf(f_2322_8,plain,
( U_7998 != c_Groups_Ozero__class_Ozero(U_7995)
| U_7996 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7995),U_7998),U_7997)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7995),U_7996),U_7997) = U_7998
| ~ class_Fields_Ofield__inverse__zero(U_7995) ),
inference(clausify,[status(thm)],[f_2322_2]) ).
fof(f_2323_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_2323_2,plain,
! [U_8002,U_8001,U_8000,U_7999] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7999),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7999),U_8001),U_8000)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7999),U_8002),U_8000)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7999),U_8001),U_8002)
| U_8000 = c_Groups_Ozero__class_Ozero(U_7999)
| ~ class_Fields_Ofield__inverse__zero(U_7999) ),
inference(variable_rename,[status(thm)],[f_2323_1]) ).
cnf(f_2323_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7999),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7999),U_8001),U_8000)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7999),U_8002),U_8000)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7999),U_8001),U_8002)
| U_8000 = c_Groups_Ozero__class_Ozero(U_7999)
| ~ class_Fields_Ofield__inverse__zero(U_7999) ),
inference(clausify,[status(thm)],[f_2323_2]) ).
fof(f_2324_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_2324_2,plain,
! [U_8006,U_8005,U_8004,U_8003] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8003),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8003),U_8004),U_8005)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8003),U_8004),U_8006)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8003),U_8005),U_8006)
| U_8004 = c_Groups_Ozero__class_Ozero(U_8003)
| ~ class_Fields_Ofield__inverse__zero(U_8003) ),
inference(variable_rename,[status(thm)],[f_2324_1]) ).
cnf(f_2324_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8003),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8003),U_8004),U_8005)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8003),U_8004),U_8006)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8003),U_8005),U_8006)
| U_8004 = c_Groups_Ozero__class_Ozero(U_8003)
| ~ class_Fields_Ofield__inverse__zero(U_8003) ),
inference(clausify,[status(thm)],[f_2324_2]) ).
fof(f_2325_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_2325_2,plain,
! [U_8011,U_8010,U_8009,U_8008,U_8007] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8007),U_8010),U_8008) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8007),U_8011),U_8009)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8007),U_8010),U_8009) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8007),U_8011),U_8008) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8007),U_8010),U_8009) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8007),U_8011),U_8008)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8007),U_8010),U_8008) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8007),U_8011),U_8009) ) )
| U_8009 = c_Groups_Ozero__class_Ozero(U_8007)
| U_8008 = c_Groups_Ozero__class_Ozero(U_8007)
| ~ class_Fields_Ofield(U_8007) ),
inference(variable_rename,[status(thm)],[f_2325_1]) ).
cnf(f_2325_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8007),U_8010),U_8009) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8007),U_8011),U_8008)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8007),U_8010),U_8008) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8007),U_8011),U_8009)
| U_8009 = c_Groups_Ozero__class_Ozero(U_8007)
| U_8008 = c_Groups_Ozero__class_Ozero(U_8007)
| ~ class_Fields_Ofield(U_8007) ),
inference(clausify,[status(thm)],[f_2325_2]) ).
cnf(f_2325_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8007),U_8010),U_8008) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8007),U_8011),U_8009)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8007),U_8010),U_8009) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8007),U_8011),U_8008)
| U_8009 = c_Groups_Ozero__class_Ozero(U_8007)
| U_8008 = c_Groups_Ozero__class_Ozero(U_8007)
| ~ class_Fields_Ofield(U_8007) ),
inference(clausify,[status(thm)],[f_2325_2]) ).
fof(f_2326_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_2326_2,plain,
! [U_8014,U_8013,U_8012] :
( hAPP(c_Groups_Oabs__class_Oabs(U_8012),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8012),U_8014),U_8013)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8012),hAPP(c_Groups_Oabs__class_Oabs(U_8012),U_8014)),hAPP(c_Groups_Oabs__class_Oabs(U_8012),U_8013))
| U_8013 = c_Groups_Ozero__class_Ozero(U_8012)
| ~ class_Fields_Olinordered__field(U_8012) ),
inference(variable_rename,[status(thm)],[f_2326_1]) ).
cnf(f_2326_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_8012),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8012),U_8014),U_8013)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8012),hAPP(c_Groups_Oabs__class_Oabs(U_8012),U_8014)),hAPP(c_Groups_Oabs__class_Oabs(U_8012),U_8013))
| U_8013 = c_Groups_Ozero__class_Ozero(U_8012)
| ~ class_Fields_Olinordered__field(U_8012) ),
inference(clausify,[status(thm)],[f_2326_2]) ).
fof(f_2327_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_2327_2,plain,
! [U_8017,U_8016,U_8015] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8015),c_Groups_Ozero__class_Ozero(U_8015)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8015),U_8016),U_8017)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8015),U_8017),c_Groups_Ozero__class_Ozero(U_8015)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8015),U_8016),c_Groups_Ozero__class_Ozero(U_8015)))
| ~ class_Fields_Olinordered__field(U_8015) ),
inference(variable_rename,[status(thm)],[f_2327_1]) ).
cnf(f_2327_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8015),c_Groups_Ozero__class_Ozero(U_8015)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8015),U_8016),U_8017)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8015),U_8017),c_Groups_Ozero__class_Ozero(U_8015)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8015),U_8016),c_Groups_Ozero__class_Ozero(U_8015)))
| ~ class_Fields_Olinordered__field(U_8015) ),
inference(clausify,[status(thm)],[f_2327_2]) ).
fof(f_2328_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_2328_2,plain,
! [U_8020,U_8019,U_8018] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8018),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8018),U_8019),U_8020)),c_Groups_Ozero__class_Ozero(U_8018)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8018),c_Groups_Ozero__class_Ozero(U_8018)),U_8020))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8018),U_8019),c_Groups_Ozero__class_Ozero(U_8018)))
| ~ class_Fields_Olinordered__field(U_8018) ),
inference(variable_rename,[status(thm)],[f_2328_1]) ).
cnf(f_2328_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8018),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8018),U_8019),U_8020)),c_Groups_Ozero__class_Ozero(U_8018)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8018),c_Groups_Ozero__class_Ozero(U_8018)),U_8020))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8018),U_8019),c_Groups_Ozero__class_Ozero(U_8018)))
| ~ class_Fields_Olinordered__field(U_8018) ),
inference(clausify,[status(thm)],[f_2328_2]) ).
fof(f_2329_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_2329_2,plain,
! [U_8025,U_8024,U_8023,U_8022,U_8021] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8021),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8021),U_8022),U_8025)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8021),U_8023),U_8024)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8021),U_8024),U_8025))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8021),c_Groups_Ozero__class_Ozero(U_8021)),U_8024))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8021),U_8022),U_8023))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8021),c_Groups_Ozero__class_Ozero(U_8021)),U_8022))
| ~ class_Fields_Olinordered__field(U_8021) ),
inference(variable_rename,[status(thm)],[f_2329_1]) ).
cnf(f_2329_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8021),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8021),U_8022),U_8025)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8021),U_8023),U_8024)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8021),U_8024),U_8025))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8021),c_Groups_Ozero__class_Ozero(U_8021)),U_8024))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8021),U_8022),U_8023))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8021),c_Groups_Ozero__class_Ozero(U_8021)),U_8022))
| ~ class_Fields_Olinordered__field(U_8021) ),
inference(clausify,[status(thm)],[f_2329_2]) ).
fof(f_2330_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_2330_2,plain,
! [U_8030,U_8029,U_8028,U_8027,U_8026] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8026),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8026),U_8027),U_8030)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8026),U_8028),U_8029)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8026),U_8029),U_8030))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8026),c_Groups_Ozero__class_Ozero(U_8026)),U_8029))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8026),U_8027),U_8028))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8026),c_Groups_Ozero__class_Ozero(U_8026)),U_8027))
| ~ class_Fields_Olinordered__field(U_8026) ),
inference(variable_rename,[status(thm)],[f_2330_1]) ).
cnf(f_2330_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8026),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8026),U_8027),U_8030)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8026),U_8028),U_8029)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8026),U_8029),U_8030))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8026),c_Groups_Ozero__class_Ozero(U_8026)),U_8029))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8026),U_8027),U_8028))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8026),c_Groups_Ozero__class_Ozero(U_8026)),U_8027))
| ~ class_Fields_Olinordered__field(U_8026) ),
inference(clausify,[status(thm)],[f_2330_2]) ).
fof(f_2331_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_2331_2,plain,
! [U_8035,U_8034,U_8033,U_8032,U_8031] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8031),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8031),U_8032),U_8035)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8031),U_8033),U_8034)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8031),U_8034),U_8035))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8031),c_Groups_Ozero__class_Ozero(U_8031)),U_8034))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8031),U_8032),U_8033))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8031),c_Groups_Ozero__class_Ozero(U_8031)),U_8032))
| ~ class_Fields_Olinordered__field(U_8031) ),
inference(variable_rename,[status(thm)],[f_2331_1]) ).
cnf(f_2331_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8031),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8031),U_8032),U_8035)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8031),U_8033),U_8034)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8031),U_8034),U_8035))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8031),c_Groups_Ozero__class_Ozero(U_8031)),U_8034))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8031),U_8032),U_8033))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8031),c_Groups_Ozero__class_Ozero(U_8031)),U_8032))
| ~ class_Fields_Olinordered__field(U_8031) ),
inference(clausify,[status(thm)],[f_2331_2]) ).
fof(f_2332_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_2332_2,plain,
! [U_8038,U_8037,U_8036] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8036),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8036),U_8037),U_8038)),c_Groups_Ozero__class_Ozero(U_8036)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8036),U_8038),c_Groups_Ozero__class_Ozero(U_8036)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8036),c_Groups_Ozero__class_Ozero(U_8036)),U_8037))
| ~ class_Fields_Olinordered__field(U_8036) ),
inference(variable_rename,[status(thm)],[f_2332_1]) ).
cnf(f_2332_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8036),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8036),U_8037),U_8038)),c_Groups_Ozero__class_Ozero(U_8036)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8036),U_8038),c_Groups_Ozero__class_Ozero(U_8036)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8036),c_Groups_Ozero__class_Ozero(U_8036)),U_8037))
| ~ class_Fields_Olinordered__field(U_8036) ),
inference(clausify,[status(thm)],[f_2332_2]) ).
fof(f_2333_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_2333_2,plain,
! [U_8041,U_8040,U_8039] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8039),c_Groups_Ozero__class_Ozero(U_8039)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8039),U_8040),U_8041)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8039),c_Groups_Ozero__class_Ozero(U_8039)),U_8041))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8039),c_Groups_Ozero__class_Ozero(U_8039)),U_8040))
| ~ class_Fields_Olinordered__field(U_8039) ),
inference(variable_rename,[status(thm)],[f_2333_1]) ).
cnf(f_2333_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8039),c_Groups_Ozero__class_Ozero(U_8039)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8039),U_8040),U_8041)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8039),c_Groups_Ozero__class_Ozero(U_8039)),U_8041))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8039),c_Groups_Ozero__class_Ozero(U_8039)),U_8040))
| ~ class_Fields_Olinordered__field(U_8039) ),
inference(clausify,[status(thm)],[f_2333_2]) ).
fof(f_2334_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_2334_2,plain,
! [U_8045,U_8044,U_8043,U_8042] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8042),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8042),U_8045),U_8043)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8042),U_8045),U_8044)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8042),c_Groups_Ozero__class_Ozero(U_8042)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8042),U_8043),U_8044)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8042),U_8045),c_Groups_Ozero__class_Ozero(U_8042)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8042),U_8043),U_8044))
| ~ class_Fields_Olinordered__field(U_8042) ),
inference(variable_rename,[status(thm)],[f_2334_1]) ).
cnf(f_2334_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8042),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8042),U_8045),U_8043)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8042),U_8045),U_8044)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8042),c_Groups_Ozero__class_Ozero(U_8042)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8042),U_8043),U_8044)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8042),U_8045),c_Groups_Ozero__class_Ozero(U_8042)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8042),U_8043),U_8044))
| ~ class_Fields_Olinordered__field(U_8042) ),
inference(clausify,[status(thm)],[f_2334_2]) ).
fof(f_2335_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_2335_2,plain,
! [U_8049,U_8048,U_8047,U_8046] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8046),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8046),U_8049),U_8048)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8046),U_8049),U_8047)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8046),c_Groups_Ozero__class_Ozero(U_8046)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8046),U_8048),U_8047)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8046),c_Groups_Ozero__class_Ozero(U_8046)),U_8049))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8046),U_8047),U_8048))
| ~ class_Fields_Olinordered__field(U_8046) ),
inference(variable_rename,[status(thm)],[f_2335_1]) ).
cnf(f_2335_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8046),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8046),U_8049),U_8048)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8046),U_8049),U_8047)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8046),c_Groups_Ozero__class_Ozero(U_8046)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8046),U_8048),U_8047)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8046),c_Groups_Ozero__class_Ozero(U_8046)),U_8049))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8046),U_8047),U_8048))
| ~ class_Fields_Olinordered__field(U_8046) ),
inference(clausify,[status(thm)],[f_2335_2]) ).
fof(f_2336_1,plain,
! [V_a_2,V_b_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__divide__less__eq]) ).
fof(f_2336_2,plain,
! [U_8053,U_8052,U_8051,U_8050] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8050),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8050),U_8052),U_8051)),U_8053))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8050),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8050),U_8053),U_8051)),U_8052)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8050),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8050),U_8053),U_8051)),U_8052))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8050),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8050),U_8052),U_8051)),U_8053)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8050),U_8051),c_Groups_Ozero__class_Ozero(U_8050)))
| ~ class_Fields_Olinordered__field(U_8050) ),
inference(variable_rename,[status(thm)],[f_2336_1]) ).
cnf(f_2336_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8050),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8050),U_8053),U_8051)),U_8052))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8050),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8050),U_8052),U_8051)),U_8053))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8050),U_8051),c_Groups_Ozero__class_Ozero(U_8050)))
| ~ class_Fields_Olinordered__field(U_8050) ),
inference(clausify,[status(thm)],[f_2336_2]) ).
cnf(f_2336_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8050),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8050),U_8052),U_8051)),U_8053))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8050),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8050),U_8053),U_8051)),U_8052))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8050),U_8051),c_Groups_Ozero__class_Ozero(U_8050)))
| ~ class_Fields_Olinordered__field(U_8050) ),
inference(clausify,[status(thm)],[f_2336_2]) ).
fof(f_2337_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__divide__eq]) ).
fof(f_2337_2,plain,
! [U_8057,U_8056,U_8055,U_8054] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8054),U_8056),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8054),U_8057),U_8055)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8054),U_8057),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8054),U_8056),U_8055))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8054),U_8057),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8054),U_8056),U_8055)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8054),U_8056),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8054),U_8057),U_8055))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8054),U_8055),c_Groups_Ozero__class_Ozero(U_8054)))
| ~ class_Fields_Olinordered__field(U_8054) ),
inference(variable_rename,[status(thm)],[f_2337_1]) ).
cnf(f_2337_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8054),U_8057),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8054),U_8056),U_8055)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8054),U_8056),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8054),U_8057),U_8055)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8054),U_8055),c_Groups_Ozero__class_Ozero(U_8054)))
| ~ class_Fields_Olinordered__field(U_8054) ),
inference(clausify,[status(thm)],[f_2337_2]) ).
cnf(f_2337_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8054),U_8056),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8054),U_8057),U_8055)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8054),U_8057),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8054),U_8056),U_8055)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8054),U_8055),c_Groups_Ozero__class_Ozero(U_8054)))
| ~ class_Fields_Olinordered__field(U_8054) ),
inference(clausify,[status(thm)],[f_2337_2]) ).
fof(f_2338_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_2338_2,plain,
! [U_8061,U_8060,U_8059,U_8058] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8058),U_8060),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8058),U_8061),U_8059)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8058),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8058),U_8060),U_8059)),U_8061))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8058),c_Groups_Ozero__class_Ozero(U_8058)),U_8059))
| ~ class_Fields_Olinordered__field(U_8058) ),
inference(variable_rename,[status(thm)],[f_2338_1]) ).
cnf(f_2338_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8058),U_8060),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8058),U_8061),U_8059)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8058),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8058),U_8060),U_8059)),U_8061))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8058),c_Groups_Ozero__class_Ozero(U_8058)),U_8059))
| ~ class_Fields_Olinordered__field(U_8058) ),
inference(clausify,[status(thm)],[f_2338_2]) ).
fof(f_2339_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_2339_2,plain,
! [U_8065,U_8064,U_8063,U_8062] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8062),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8062),U_8064),U_8063)),U_8065))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8062),U_8064),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8062),U_8065),U_8063)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8062),c_Groups_Ozero__class_Ozero(U_8062)),U_8063))
| ~ class_Fields_Olinordered__field(U_8062) ),
inference(variable_rename,[status(thm)],[f_2339_1]) ).
cnf(f_2339_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8062),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8062),U_8064),U_8063)),U_8065))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8062),U_8064),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8062),U_8065),U_8063)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8062),c_Groups_Ozero__class_Ozero(U_8062)),U_8063))
| ~ class_Fields_Olinordered__field(U_8062) ),
inference(clausify,[status(thm)],[f_2339_2]) ).
fof(f_2340_1,plain,
! [V_a_2,V_b_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_pos__divide__less__eq]) ).
fof(f_2340_2,plain,
! [U_8069,U_8068,U_8067,U_8066] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8066),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8066),U_8068),U_8067)),U_8069))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8066),U_8068),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8066),U_8069),U_8067))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8066),U_8068),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8066),U_8069),U_8067)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8066),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8066),U_8068),U_8067)),U_8069)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8066),c_Groups_Ozero__class_Ozero(U_8066)),U_8067))
| ~ class_Fields_Olinordered__field(U_8066) ),
inference(variable_rename,[status(thm)],[f_2340_1]) ).
cnf(f_2340_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8066),U_8068),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8066),U_8069),U_8067)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8066),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8066),U_8068),U_8067)),U_8069))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8066),c_Groups_Ozero__class_Ozero(U_8066)),U_8067))
| ~ class_Fields_Olinordered__field(U_8066) ),
inference(clausify,[status(thm)],[f_2340_2]) ).
cnf(f_2340_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8066),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8066),U_8068),U_8067)),U_8069))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8066),U_8068),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8066),U_8069),U_8067)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8066),c_Groups_Ozero__class_Ozero(U_8066)),U_8067))
| ~ class_Fields_Olinordered__field(U_8066) ),
inference(clausify,[status(thm)],[f_2340_2]) ).
fof(f_2341_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_pos__less__divide__eq]) ).
fof(f_2341_2,plain,
! [U_8073,U_8072,U_8071,U_8070] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8070),U_8072),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8070),U_8073),U_8071)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8070),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8070),U_8072),U_8071)),U_8073)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8070),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8070),U_8072),U_8071)),U_8073))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8070),U_8072),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8070),U_8073),U_8071))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8070),c_Groups_Ozero__class_Ozero(U_8070)),U_8071))
| ~ class_Fields_Olinordered__field(U_8070) ),
inference(variable_rename,[status(thm)],[f_2341_1]) ).
cnf(f_2341_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8070),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8070),U_8072),U_8071)),U_8073))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8070),U_8072),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8070),U_8073),U_8071)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8070),c_Groups_Ozero__class_Ozero(U_8070)),U_8071))
| ~ class_Fields_Olinordered__field(U_8070) ),
inference(clausify,[status(thm)],[f_2341_2]) ).
cnf(f_2341_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8070),U_8072),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8070),U_8073),U_8071)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8070),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8070),U_8072),U_8071)),U_8073))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8070),c_Groups_Ozero__class_Ozero(U_8070)),U_8071))
| ~ class_Fields_Olinordered__field(U_8070) ),
inference(clausify,[status(thm)],[f_2341_2]) ).
fof(f_2342_1,plain,
! [V_a_2,V_c_2,V_b_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__less__eq]) ).
fof(f_2342_2,plain,
! [U_8077,U_8076,U_8075,U_8074] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8074),U_8075),U_8076)),U_8077))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),c_Groups_Ozero__class_Ozero(U_8074)),U_8077))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),U_8076),c_Groups_Ozero__class_Ozero(U_8074))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8074),U_8077),U_8076)),U_8075))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),U_8076),c_Groups_Ozero__class_Ozero(U_8074))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),c_Groups_Ozero__class_Ozero(U_8074)),U_8076)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),U_8075),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8074),U_8077),U_8076)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),c_Groups_Ozero__class_Ozero(U_8074)),U_8076)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),c_Groups_Ozero__class_Ozero(U_8074)),U_8077))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),U_8076),c_Groups_Ozero__class_Ozero(U_8074))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8074),U_8077),U_8076)),U_8075))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),U_8076),c_Groups_Ozero__class_Ozero(U_8074))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),c_Groups_Ozero__class_Ozero(U_8074)),U_8076)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),U_8075),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8074),U_8077),U_8076)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),c_Groups_Ozero__class_Ozero(U_8074)),U_8076)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8074),U_8075),U_8076)),U_8077)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_8074) ),
inference(variable_rename,[status(thm)],[f_2342_1]) ).
cnf(f_2342_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),U_8075),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8074),U_8077),U_8076)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),c_Groups_Ozero__class_Ozero(U_8074)),U_8076))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8074),U_8075),U_8076)),U_8077))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8074) ),
inference(clausify,[status(thm)],[f_2342_2]) ).
cnf(f_2342_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8074),U_8077),U_8076)),U_8075))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),U_8076),c_Groups_Ozero__class_Ozero(U_8074)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),c_Groups_Ozero__class_Ozero(U_8074)),U_8076))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8074),U_8075),U_8076)),U_8077))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8074) ),
inference(clausify,[status(thm)],[f_2342_2]) ).
cnf(f_2342_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),c_Groups_Ozero__class_Ozero(U_8074)),U_8077))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),U_8076),c_Groups_Ozero__class_Ozero(U_8074)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),c_Groups_Ozero__class_Ozero(U_8074)),U_8076))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8074),U_8075),U_8076)),U_8077))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8074) ),
inference(clausify,[status(thm)],[f_2342_2]) ).
cnf(f_2342_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),c_Groups_Ozero__class_Ozero(U_8074)),U_8076))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),c_Groups_Ozero__class_Ozero(U_8074)),U_8076))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8074),U_8075),U_8076)),U_8077))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8074) ),
inference(clausify,[status(thm)],[f_2342_2]) ).
cnf(f_2342_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),U_8076),c_Groups_Ozero__class_Ozero(U_8074)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),U_8076),c_Groups_Ozero__class_Ozero(U_8074)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),c_Groups_Ozero__class_Ozero(U_8074)),U_8076))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8074),U_8075),U_8076)),U_8077))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8074) ),
inference(clausify,[status(thm)],[f_2342_2]) ).
cnf(f_2342_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),c_Groups_Ozero__class_Ozero(U_8074)),U_8077))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),U_8076),c_Groups_Ozero__class_Ozero(U_8074)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),c_Groups_Ozero__class_Ozero(U_8074)),U_8076))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8074),U_8075),U_8076)),U_8077))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8074) ),
inference(clausify,[status(thm)],[f_2342_2]) ).
cnf(f_2342_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),U_8076),c_Groups_Ozero__class_Ozero(U_8074)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8074),U_8077),U_8076)),U_8075))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),c_Groups_Ozero__class_Ozero(U_8074)),U_8076))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8074),U_8075),U_8076)),U_8077))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8074) ),
inference(clausify,[status(thm)],[f_2342_2]) ).
cnf(f_2342_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),c_Groups_Ozero__class_Ozero(U_8074)),U_8077))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8074),U_8077),U_8076)),U_8075))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),c_Groups_Ozero__class_Ozero(U_8074)),U_8076))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8074),U_8075),U_8076)),U_8077))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8074) ),
inference(clausify,[status(thm)],[f_2342_2]) ).
cnf(f_2342_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),c_Groups_Ozero__class_Ozero(U_8074)),U_8076))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),U_8075),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8074),U_8077),U_8076)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8074),U_8075),U_8076)),U_8077))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8074) ),
inference(clausify,[status(thm)],[f_2342_2]) ).
cnf(f_2342_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),U_8076),c_Groups_Ozero__class_Ozero(U_8074)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),U_8076),c_Groups_Ozero__class_Ozero(U_8074)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),U_8075),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8074),U_8077),U_8076)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8074),U_8075),U_8076)),U_8077))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8074) ),
inference(clausify,[status(thm)],[f_2342_2]) ).
cnf(f_2342_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),c_Groups_Ozero__class_Ozero(U_8074)),U_8077))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),U_8076),c_Groups_Ozero__class_Ozero(U_8074)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),U_8075),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8074),U_8077),U_8076)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8074),U_8075),U_8076)),U_8077))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8074) ),
inference(clausify,[status(thm)],[f_2342_2]) ).
cnf(f_2342_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),U_8076),c_Groups_Ozero__class_Ozero(U_8074)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8074),U_8077),U_8076)),U_8075))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),U_8075),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8074),U_8077),U_8076)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8074),U_8075),U_8076)),U_8077))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8074) ),
inference(clausify,[status(thm)],[f_2342_2]) ).
cnf(f_2342_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),c_Groups_Ozero__class_Ozero(U_8074)),U_8077))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8074),U_8077),U_8076)),U_8075))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),U_8075),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8074),U_8077),U_8076)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8074),U_8075),U_8076)),U_8077))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8074) ),
inference(clausify,[status(thm)],[f_2342_2]) ).
fof(f_2343_1,plain,
! [V_c_2,V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__divide__eq]) ).
fof(f_2343_2,plain,
! [U_8081,U_8080,U_8079,U_8078] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8079),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8078),U_8080),U_8081)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8079),c_Groups_Ozero__class_Ozero(U_8078)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8081),c_Groups_Ozero__class_Ozero(U_8078))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8078),U_8079),U_8081)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8081),c_Groups_Ozero__class_Ozero(U_8078))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),c_Groups_Ozero__class_Ozero(U_8078)),U_8081)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8078),U_8079),U_8081)),U_8080))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),c_Groups_Ozero__class_Ozero(U_8078)),U_8081)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8079),c_Groups_Ozero__class_Ozero(U_8078)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8081),c_Groups_Ozero__class_Ozero(U_8078))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8078),U_8079),U_8081)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8081),c_Groups_Ozero__class_Ozero(U_8078))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),c_Groups_Ozero__class_Ozero(U_8078)),U_8081)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8078),U_8079),U_8081)),U_8080))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),c_Groups_Ozero__class_Ozero(U_8078)),U_8081)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8079),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8078),U_8080),U_8081))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_8078) ),
inference(variable_rename,[status(thm)],[f_2343_1]) ).
cnf(f_2343_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8078),U_8079),U_8081)),U_8080))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),c_Groups_Ozero__class_Ozero(U_8078)),U_8081))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8079),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8078),U_8080),U_8081)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8078) ),
inference(clausify,[status(thm)],[f_2343_2]) ).
cnf(f_2343_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8078),U_8079),U_8081)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8081),c_Groups_Ozero__class_Ozero(U_8078)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),c_Groups_Ozero__class_Ozero(U_8078)),U_8081))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8079),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8078),U_8080),U_8081)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8078) ),
inference(clausify,[status(thm)],[f_2343_2]) ).
cnf(f_2343_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8079),c_Groups_Ozero__class_Ozero(U_8078)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8081),c_Groups_Ozero__class_Ozero(U_8078)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),c_Groups_Ozero__class_Ozero(U_8078)),U_8081))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8079),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8078),U_8080),U_8081)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8078) ),
inference(clausify,[status(thm)],[f_2343_2]) ).
cnf(f_2343_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),c_Groups_Ozero__class_Ozero(U_8078)),U_8081))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),c_Groups_Ozero__class_Ozero(U_8078)),U_8081))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8079),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8078),U_8080),U_8081)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8078) ),
inference(clausify,[status(thm)],[f_2343_2]) ).
cnf(f_2343_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8081),c_Groups_Ozero__class_Ozero(U_8078)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8081),c_Groups_Ozero__class_Ozero(U_8078)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),c_Groups_Ozero__class_Ozero(U_8078)),U_8081))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8079),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8078),U_8080),U_8081)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8078) ),
inference(clausify,[status(thm)],[f_2343_2]) ).
cnf(f_2343_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8079),c_Groups_Ozero__class_Ozero(U_8078)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8081),c_Groups_Ozero__class_Ozero(U_8078)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),c_Groups_Ozero__class_Ozero(U_8078)),U_8081))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8079),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8078),U_8080),U_8081)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8078) ),
inference(clausify,[status(thm)],[f_2343_2]) ).
cnf(f_2343_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8081),c_Groups_Ozero__class_Ozero(U_8078)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8078),U_8079),U_8081)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),c_Groups_Ozero__class_Ozero(U_8078)),U_8081))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8079),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8078),U_8080),U_8081)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8078) ),
inference(clausify,[status(thm)],[f_2343_2]) ).
cnf(f_2343_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8079),c_Groups_Ozero__class_Ozero(U_8078)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8078),U_8079),U_8081)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),c_Groups_Ozero__class_Ozero(U_8078)),U_8081))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8079),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8078),U_8080),U_8081)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8078) ),
inference(clausify,[status(thm)],[f_2343_2]) ).
cnf(f_2343_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),c_Groups_Ozero__class_Ozero(U_8078)),U_8081))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8078),U_8079),U_8081)),U_8080))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8079),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8078),U_8080),U_8081)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8078) ),
inference(clausify,[status(thm)],[f_2343_2]) ).
cnf(f_2343_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8081),c_Groups_Ozero__class_Ozero(U_8078)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8081),c_Groups_Ozero__class_Ozero(U_8078)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8078),U_8079),U_8081)),U_8080))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8079),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8078),U_8080),U_8081)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8078) ),
inference(clausify,[status(thm)],[f_2343_2]) ).
cnf(f_2343_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8079),c_Groups_Ozero__class_Ozero(U_8078)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8081),c_Groups_Ozero__class_Ozero(U_8078)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8078),U_8079),U_8081)),U_8080))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8079),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8078),U_8080),U_8081)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8078) ),
inference(clausify,[status(thm)],[f_2343_2]) ).
cnf(f_2343_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8081),c_Groups_Ozero__class_Ozero(U_8078)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8078),U_8079),U_8081)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8078),U_8079),U_8081)),U_8080))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8079),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8078),U_8080),U_8081)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8078) ),
inference(clausify,[status(thm)],[f_2343_2]) ).
cnf(f_2343_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8079),c_Groups_Ozero__class_Ozero(U_8078)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8078),U_8079),U_8081)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8078),U_8079),U_8081)),U_8080))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8078),U_8079),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8078),U_8080),U_8081)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8078) ),
inference(clausify,[status(thm)],[f_2343_2]) ).
fof(f_2344_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_2344_2,plain,
! [U_8085,U_8084,U_8083,U_8082] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8082),U_8084),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8082),U_8085),U_8083)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8082),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8082),U_8085),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8082),U_8084),U_8083))),U_8083)
| U_8083 = c_Groups_Ozero__class_Ozero(U_8082)
| ~ class_Fields_Ofield__inverse__zero(U_8082) ),
inference(variable_rename,[status(thm)],[f_2344_1]) ).
cnf(f_2344_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8082),U_8084),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8082),U_8085),U_8083)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8082),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8082),U_8085),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8082),U_8084),U_8083))),U_8083)
| U_8083 = c_Groups_Ozero__class_Ozero(U_8082)
| ~ class_Fields_Ofield__inverse__zero(U_8082) ),
inference(clausify,[status(thm)],[f_2344_2]) ).
fof(f_2345_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_2345_2,plain,
! [U_8089,U_8088,U_8087,U_8086] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8086),U_8088),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8086),U_8089),U_8087)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8086),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8086),U_8087),U_8088)),U_8089)),U_8087)
| U_8087 = c_Groups_Ozero__class_Ozero(U_8086)
| ~ class_Fields_Ofield(U_8086) ),
inference(variable_rename,[status(thm)],[f_2345_1]) ).
cnf(f_2345_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8086),U_8088),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8086),U_8089),U_8087)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8086),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8086),U_8087),U_8088)),U_8089)),U_8087)
| U_8087 = c_Groups_Ozero__class_Ozero(U_8086)
| ~ class_Fields_Ofield(U_8086) ),
inference(clausify,[status(thm)],[f_2345_2]) ).
fof(f_2346_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_2346_2,plain,
! [U_8093,U_8092,U_8091,U_8090] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8090),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8090),U_8092),U_8091)),U_8093) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8090),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8090),U_8092),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8090),U_8093),U_8091))),U_8091)
| U_8091 = c_Groups_Ozero__class_Ozero(U_8090)
| ~ class_Fields_Ofield__inverse__zero(U_8090) ),
inference(variable_rename,[status(thm)],[f_2346_1]) ).
cnf(f_2346_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8090),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8090),U_8092),U_8091)),U_8093) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8090),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8090),U_8092),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8090),U_8093),U_8091))),U_8091)
| U_8091 = c_Groups_Ozero__class_Ozero(U_8090)
| ~ class_Fields_Ofield__inverse__zero(U_8090) ),
inference(clausify,[status(thm)],[f_2346_2]) ).
fof(f_2347_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_2347_2,plain,
! [U_8097,U_8096,U_8095,U_8094] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8094),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8094),U_8096),U_8095)),U_8097) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8094),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8094),U_8096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8094),U_8095),U_8097))),U_8095)
| U_8095 = c_Groups_Ozero__class_Ozero(U_8094)
| ~ class_Fields_Ofield(U_8094) ),
inference(variable_rename,[status(thm)],[f_2347_1]) ).
cnf(f_2347_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8094),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8094),U_8096),U_8095)),U_8097) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8094),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8094),U_8096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8094),U_8095),U_8097))),U_8095)
| U_8095 = c_Groups_Ozero__class_Ozero(U_8094)
| ~ class_Fields_Ofield(U_8094) ),
inference(clausify,[status(thm)],[f_2347_2]) ).
fof(f_2348_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_2348_2,plain,
! [U_8102,U_8101,U_8100,U_8099,U_8098] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8098),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8098),U_8101),U_8099)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8098),U_8102),U_8100)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8098),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8098),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8098),U_8101),U_8100)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8098),U_8102),U_8099))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8098),U_8099),U_8100))
| U_8100 = c_Groups_Ozero__class_Ozero(U_8098)
| U_8099 = c_Groups_Ozero__class_Ozero(U_8098)
| ~ class_Fields_Ofield(U_8098) ),
inference(variable_rename,[status(thm)],[f_2348_1]) ).
cnf(f_2348_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8098),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8098),U_8101),U_8099)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8098),U_8102),U_8100)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8098),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8098),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8098),U_8101),U_8100)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8098),U_8102),U_8099))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8098),U_8099),U_8100))
| U_8100 = c_Groups_Ozero__class_Ozero(U_8098)
| U_8099 = c_Groups_Ozero__class_Ozero(U_8098)
| ~ class_Fields_Ofield(U_8098) ),
inference(clausify,[status(thm)],[f_2348_2]) ).
fof(f_2349_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_2349_2,plain,
! [U_8106,U_8105,U_8104,U_8103] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8103),U_8105),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8103),U_8106),U_8104)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8103),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8103),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8103),U_8104),U_8105)),U_8106)),U_8104)
| U_8104 = c_Groups_Ozero__class_Ozero(U_8103)
| ~ class_Fields_Ofield(U_8103) ),
inference(variable_rename,[status(thm)],[f_2349_1]) ).
cnf(f_2349_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8103),U_8105),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8103),U_8106),U_8104)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8103),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8103),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8103),U_8104),U_8105)),U_8106)),U_8104)
| U_8104 = c_Groups_Ozero__class_Ozero(U_8103)
| ~ class_Fields_Ofield(U_8103) ),
inference(clausify,[status(thm)],[f_2349_2]) ).
fof(f_2350_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_2350_2,plain,
! [U_8110,U_8109,U_8108,U_8107] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8107),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8107),U_8109),U_8108)),U_8110) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8107),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8107),U_8109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8107),U_8108),U_8110))),U_8108)
| U_8108 = c_Groups_Ozero__class_Ozero(U_8107)
| ~ class_Fields_Ofield(U_8107) ),
inference(variable_rename,[status(thm)],[f_2350_1]) ).
cnf(f_2350_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8107),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8107),U_8109),U_8108)),U_8110) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8107),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8107),U_8109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8107),U_8108),U_8110))),U_8108)
| U_8108 = c_Groups_Ozero__class_Ozero(U_8107)
| ~ class_Fields_Ofield(U_8107) ),
inference(clausify,[status(thm)],[f_2350_2]) ).
fof(f_2351_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_2351_2,plain,
! [U_8115,U_8114,U_8113,U_8112,U_8111] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8111),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8111),U_8114),U_8112)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8111),U_8115),U_8113)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8111),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8111),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8111),U_8114),U_8113)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8111),U_8115),U_8112))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8111),U_8112),U_8113))
| U_8113 = c_Groups_Ozero__class_Ozero(U_8111)
| U_8112 = c_Groups_Ozero__class_Ozero(U_8111)
| ~ class_Fields_Ofield(U_8111) ),
inference(variable_rename,[status(thm)],[f_2351_1]) ).
cnf(f_2351_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8111),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8111),U_8114),U_8112)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8111),U_8115),U_8113)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8111),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8111),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8111),U_8114),U_8113)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8111),U_8115),U_8112))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8111),U_8112),U_8113))
| U_8113 = c_Groups_Ozero__class_Ozero(U_8111)
| U_8112 = c_Groups_Ozero__class_Ozero(U_8111)
| ~ class_Fields_Ofield(U_8111) ),
inference(clausify,[status(thm)],[f_2351_2]) ).
fof(f_2352_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_2352_2,plain,
! [U_8118,U_8117,U_8116] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8116),U_8117),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8116),U_8117),U_8118)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8116),c_Groups_Oone__class_Oone(U_8116)),c_Groups_Oone__class_Oone(U_8116)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8116),U_8117),U_8118))
| ~ class_Fields_Olinordered__field(U_8116) ),
inference(variable_rename,[status(thm)],[f_2352_1]) ).
cnf(f_2352_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8116),U_8117),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8116),U_8117),U_8118)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8116),c_Groups_Oone__class_Oone(U_8116)),c_Groups_Oone__class_Oone(U_8116)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8116),U_8117),U_8118))
| ~ class_Fields_Olinordered__field(U_8116) ),
inference(clausify,[status(thm)],[f_2352_2]) ).
fof(f_2353_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_2353_2,plain,
! [U_8121,U_8120,U_8119] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8119),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8119),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8119),U_8120),U_8121)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8119),c_Groups_Oone__class_Oone(U_8119)),c_Groups_Oone__class_Oone(U_8119)))),U_8121))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8119),U_8120),U_8121))
| ~ class_Fields_Olinordered__field(U_8119) ),
inference(variable_rename,[status(thm)],[f_2353_1]) ).
cnf(f_2353_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8119),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8119),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8119),U_8120),U_8121)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8119),c_Groups_Oone__class_Oone(U_8119)),c_Groups_Oone__class_Oone(U_8119)))),U_8121))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8119),U_8120),U_8121))
| ~ class_Fields_Olinordered__field(U_8119) ),
inference(clausify,[status(thm)],[f_2353_2]) ).
fof(f_2354_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_2354_2,plain,
! [U_8124,U_8123,U_8122] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8122),hAPP(c_Groups_Oabs__class_Oabs(U_8122),U_8124)),U_8123) = hAPP(c_Groups_Oabs__class_Oabs(U_8122),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8122),U_8124),U_8123))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8122),c_Groups_Ozero__class_Ozero(U_8122)),U_8123))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8122) ),
inference(variable_rename,[status(thm)],[f_2354_1]) ).
cnf(f_2354_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8122),hAPP(c_Groups_Oabs__class_Oabs(U_8122),U_8124)),U_8123) = hAPP(c_Groups_Oabs__class_Oabs(U_8122),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8122),U_8124),U_8123))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8122),c_Groups_Ozero__class_Ozero(U_8122)),U_8123))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8122) ),
inference(clausify,[status(thm)],[f_2354_2]) ).
fof(f_2355_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_2355_2,plain,
! [U_8128,U_8127,U_8126,U_8125] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8125),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8125),U_8128),U_8126)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8125),U_8128),U_8127)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8125),c_Groups_Ozero__class_Ozero(U_8125)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8125),U_8126),U_8127)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8125),U_8128),c_Groups_Ozero__class_Ozero(U_8125)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8125),U_8126),U_8127))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8125) ),
inference(variable_rename,[status(thm)],[f_2355_1]) ).
cnf(f_2355_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8125),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8125),U_8128),U_8126)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8125),U_8128),U_8127)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8125),c_Groups_Ozero__class_Ozero(U_8125)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8125),U_8126),U_8127)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8125),U_8128),c_Groups_Ozero__class_Ozero(U_8125)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8125),U_8126),U_8127))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8125) ),
inference(clausify,[status(thm)],[f_2355_2]) ).
fof(f_2356_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_2356_2,plain,
! [U_8132,U_8131,U_8130,U_8129] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8129),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8129),U_8132),U_8131)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8129),U_8132),U_8130)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8129),c_Groups_Ozero__class_Ozero(U_8129)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8129),U_8131),U_8130)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8129),c_Groups_Ozero__class_Ozero(U_8129)),U_8132))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8129),U_8130),U_8131))
| ~ class_Fields_Olinordered__field(U_8129) ),
inference(variable_rename,[status(thm)],[f_2356_1]) ).
cnf(f_2356_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8129),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8129),U_8132),U_8131)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8129),U_8132),U_8130)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8129),c_Groups_Ozero__class_Ozero(U_8129)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8129),U_8131),U_8130)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8129),c_Groups_Ozero__class_Ozero(U_8129)),U_8132))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8129),U_8130),U_8131))
| ~ class_Fields_Olinordered__field(U_8129) ),
inference(clausify,[status(thm)],[f_2356_2]) ).
fof(f_2357_1,plain,
! [V_a_2,V_b_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__divide__le__eq]) ).
fof(f_2357_2,plain,
! [U_8136,U_8135,U_8134,U_8133] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8133),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8133),U_8135),U_8134)),U_8136))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8133),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8133),U_8136),U_8134)),U_8135)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8133),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8133),U_8136),U_8134)),U_8135))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8133),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8133),U_8135),U_8134)),U_8136)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8133),U_8134),c_Groups_Ozero__class_Ozero(U_8133)))
| ~ class_Fields_Olinordered__field(U_8133) ),
inference(variable_rename,[status(thm)],[f_2357_1]) ).
cnf(f_2357_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8133),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8133),U_8136),U_8134)),U_8135))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8133),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8133),U_8135),U_8134)),U_8136))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8133),U_8134),c_Groups_Ozero__class_Ozero(U_8133)))
| ~ class_Fields_Olinordered__field(U_8133) ),
inference(clausify,[status(thm)],[f_2357_2]) ).
cnf(f_2357_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8133),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8133),U_8135),U_8134)),U_8136))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8133),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8133),U_8136),U_8134)),U_8135))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8133),U_8134),c_Groups_Ozero__class_Ozero(U_8133)))
| ~ class_Fields_Olinordered__field(U_8133) ),
inference(clausify,[status(thm)],[f_2357_2]) ).
fof(f_2358_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__le__divide__eq]) ).
fof(f_2358_2,plain,
! [U_8140,U_8139,U_8138,U_8137] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8137),U_8139),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8137),U_8140),U_8138)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8137),U_8140),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8137),U_8139),U_8138))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8137),U_8140),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8137),U_8139),U_8138)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8137),U_8139),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8137),U_8140),U_8138))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8137),U_8138),c_Groups_Ozero__class_Ozero(U_8137)))
| ~ class_Fields_Olinordered__field(U_8137) ),
inference(variable_rename,[status(thm)],[f_2358_1]) ).
cnf(f_2358_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8137),U_8140),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8137),U_8139),U_8138)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8137),U_8139),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8137),U_8140),U_8138)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8137),U_8138),c_Groups_Ozero__class_Ozero(U_8137)))
| ~ class_Fields_Olinordered__field(U_8137) ),
inference(clausify,[status(thm)],[f_2358_2]) ).
cnf(f_2358_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8137),U_8139),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8137),U_8140),U_8138)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8137),U_8140),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8137),U_8139),U_8138)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8137),U_8138),c_Groups_Ozero__class_Ozero(U_8137)))
| ~ class_Fields_Olinordered__field(U_8137) ),
inference(clausify,[status(thm)],[f_2358_2]) ).
fof(f_2359_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_2359_2,plain,
! [U_8144,U_8143,U_8142,U_8141] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8141),U_8143),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8141),U_8144),U_8142)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8141),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8141),U_8143),U_8142)),U_8144))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8141),c_Groups_Ozero__class_Ozero(U_8141)),U_8142))
| ~ class_Fields_Olinordered__field(U_8141) ),
inference(variable_rename,[status(thm)],[f_2359_1]) ).
cnf(f_2359_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8141),U_8143),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8141),U_8144),U_8142)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8141),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8141),U_8143),U_8142)),U_8144))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8141),c_Groups_Ozero__class_Ozero(U_8141)),U_8142))
| ~ class_Fields_Olinordered__field(U_8141) ),
inference(clausify,[status(thm)],[f_2359_2]) ).
fof(f_2360_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_2360_2,plain,
! [U_8148,U_8147,U_8146,U_8145] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8145),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8145),U_8147),U_8146)),U_8148))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8145),U_8147),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8145),U_8148),U_8146)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8145),c_Groups_Ozero__class_Ozero(U_8145)),U_8146))
| ~ class_Fields_Olinordered__field(U_8145) ),
inference(variable_rename,[status(thm)],[f_2360_1]) ).
cnf(f_2360_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8145),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8145),U_8147),U_8146)),U_8148))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8145),U_8147),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8145),U_8148),U_8146)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8145),c_Groups_Ozero__class_Ozero(U_8145)),U_8146))
| ~ class_Fields_Olinordered__field(U_8145) ),
inference(clausify,[status(thm)],[f_2360_2]) ).
fof(f_2361_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_2361_2,plain,
! [U_8153,U_8152,U_8151,U_8150,U_8149] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8150,U_8149),U_8152),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8150,tc_HOL_Obool)),U_8151),hAPP(hAPP(c_Set_Oinsert(U_8150),U_8153),c_Orderings_Obot__class_Obot(tc_fun(U_8150,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8150,U_8149),U_8152),U_8151)
| hBOOL(hAPP(hAPP(c_member(U_8150),U_8153),U_8151)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8150,U_8149),U_8152),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8150,tc_HOL_Obool)),U_8151),hAPP(hAPP(c_Set_Oinsert(U_8150),U_8153),c_Orderings_Obot__class_Obot(tc_fun(U_8150,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8149),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8150,U_8149),U_8152),U_8151)),hAPP(U_8152,U_8153))
| ~ hBOOL(hAPP(hAPP(c_member(U_8150),U_8153),U_8151)) ) )
| hAPP(U_8152,U_8153) = c_Groups_Ozero__class_Ozero(U_8149)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8150),U_8151))
| ~ class_Fields_Ofield(U_8149) ),
inference(variable_rename,[status(thm)],[f_2361_1]) ).
cnf(f_2361_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8150,U_8149),U_8152),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8150,tc_HOL_Obool)),U_8151),hAPP(hAPP(c_Set_Oinsert(U_8150),U_8153),c_Orderings_Obot__class_Obot(tc_fun(U_8150,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8149),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8150,U_8149),U_8152),U_8151)),hAPP(U_8152,U_8153))
| ~ hBOOL(hAPP(hAPP(c_member(U_8150),U_8153),U_8151))
| hAPP(U_8152,U_8153) = c_Groups_Ozero__class_Ozero(U_8149)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8150),U_8151))
| ~ class_Fields_Ofield(U_8149) ),
inference(clausify,[status(thm)],[f_2361_2]) ).
cnf(f_2361_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8150,U_8149),U_8152),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8150,tc_HOL_Obool)),U_8151),hAPP(hAPP(c_Set_Oinsert(U_8150),U_8153),c_Orderings_Obot__class_Obot(tc_fun(U_8150,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8150,U_8149),U_8152),U_8151)
| hBOOL(hAPP(hAPP(c_member(U_8150),U_8153),U_8151))
| hAPP(U_8152,U_8153) = c_Groups_Ozero__class_Ozero(U_8149)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8150),U_8151))
| ~ class_Fields_Ofield(U_8149) ),
inference(clausify,[status(thm)],[f_2361_2]) ).
fof(f_2362_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_2362_2,plain,
! [U_8157,U_8156,U_8155] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8155),U_8156),U_8157))
| ? [U_8154] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8155),U_8154),U_8156)),U_8157))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8155),U_8154),c_Groups_Oone__class_Oone(U_8155)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8155),c_Groups_Ozero__class_Ozero(U_8155)),U_8154)) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_8155) ),
inference(variable_rename,[status(thm)],[f_2362_1]) ).
fof(f_2362_3,plain,
! [U_8157,U_8156,U_8155] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8155),U_8156),U_8157))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8155),sK182(U_8157,U_8156,U_8155)),U_8156)),U_8157))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8155),sK182(U_8157,U_8156,U_8155)),c_Groups_Oone__class_Oone(U_8155)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8155),c_Groups_Ozero__class_Ozero(U_8155)),sK182(U_8157,U_8156,U_8155))) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_8155) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK182]),skolemize(U_8154,sK182(U_8157,U_8156,U_8155))],[f_2362_2]) ).
cnf(f_2362_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8155),c_Groups_Ozero__class_Ozero(U_8155)),sK182(U_8157,U_8156,U_8155)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8155),U_8156),U_8157))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8155) ),
inference(clausify,[status(thm)],[f_2362_3]) ).
cnf(f_2362_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8155),sK182(U_8157,U_8156,U_8155)),c_Groups_Oone__class_Oone(U_8155)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8155),U_8156),U_8157))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8155) ),
inference(clausify,[status(thm)],[f_2362_3]) ).
cnf(f_2362_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8155),sK182(U_8157,U_8156,U_8155)),U_8156)),U_8157))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8155),U_8156),U_8157))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8155) ),
inference(clausify,[status(thm)],[f_2362_3]) ).
fof(f_2363_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_2363_2,plain,
! [U_8162,U_8161,U_8160] :
( ? [U_8159] :
( hAPP(U_8161,U_8159) = U_8162
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8159),U_8160)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8162),hAPP(U_8161,U_8160)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8161,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8162))
| ? [U_8158] :
( ~ 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_8161,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8158),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8161,U_8158)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8158),U_8160)) ) ),
inference(variable_rename,[status(thm)],[f_2363_1]) ).
fof(f_2363_3,plain,
! [U_8162,U_8161,U_8160] :
( ? [U_8159] :
( hAPP(U_8161,U_8159) = U_8162
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8159),U_8160)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8162),hAPP(U_8161,U_8160)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8161,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8162))
| ( ~ 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_8161,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK183(U_8162,U_8161,U_8160)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8161,sK183(U_8162,U_8161,U_8160))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK183(U_8162,U_8161,U_8160)),U_8160)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK183]),skolemize(U_8158,sK183(U_8162,U_8161,U_8160))],[f_2363_2]) ).
fof(f_2363_4,plain,
! [U_8162,U_8161,U_8160] :
( ( hAPP(U_8161,sK184(U_8162,U_8161,U_8160)) = U_8162
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK184(U_8162,U_8161,U_8160)),U_8160)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8162),hAPP(U_8161,U_8160)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8161,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8162))
| ( ~ 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_8161,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK183(U_8162,U_8161,U_8160)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8161,sK183(U_8162,U_8161,U_8160))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK183(U_8162,U_8161,U_8160)),U_8160)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK184]),skolemize(U_8159,sK184(U_8162,U_8161,U_8160))],[f_2363_3]) ).
cnf(f_2363_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK184(U_8162,U_8161,U_8160)),U_8160))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8162),hAPP(U_8161,U_8160)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8161,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8162))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK183(U_8162,U_8161,U_8160)),U_8160)) ),
inference(clausify,[status(thm)],[f_2363_4]) ).
cnf(f_2363_6,plain,
( hAPP(U_8161,sK184(U_8162,U_8161,U_8160)) = U_8162
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8162),hAPP(U_8161,U_8160)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8161,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8162))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK183(U_8162,U_8161,U_8160)),U_8160)) ),
inference(clausify,[status(thm)],[f_2363_4]) ).
cnf(f_2363_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK184(U_8162,U_8161,U_8160)),U_8160))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8162),hAPP(U_8161,U_8160)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8161,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8162))
| ~ 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_8161,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK183(U_8162,U_8161,U_8160)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8161,sK183(U_8162,U_8161,U_8160))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2363_4]) ).
cnf(f_2363_8,plain,
( hAPP(U_8161,sK184(U_8162,U_8161,U_8160)) = U_8162
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8162),hAPP(U_8161,U_8160)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8161,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8162))
| ~ 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_8161,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK183(U_8162,U_8161,U_8160)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8161,sK183(U_8162,U_8161,U_8160))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2363_4]) ).
fof(f_2364_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_2364_2,plain,
! [U_8167,U_8166,U_8165] :
( ? [U_8164] :
( hAPP(U_8166,U_8164) = U_8167
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8164),U_8165)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8167),hAPP(U_8166,U_8165)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8166,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8167))
| ? [U_8163] :
( ~ 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_8166,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8163),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8166,U_8163)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8163),U_8165)) ) ),
inference(variable_rename,[status(thm)],[f_2364_1]) ).
fof(f_2364_3,plain,
! [U_8167,U_8166,U_8165] :
( ? [U_8164] :
( hAPP(U_8166,U_8164) = U_8167
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8164),U_8165)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8167),hAPP(U_8166,U_8165)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8166,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8167))
| ( ~ 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_8166,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK185(U_8167,U_8166,U_8165)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8166,sK185(U_8167,U_8166,U_8165))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK185(U_8167,U_8166,U_8165)),U_8165)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK185]),skolemize(U_8163,sK185(U_8167,U_8166,U_8165))],[f_2364_2]) ).
fof(f_2364_4,plain,
! [U_8167,U_8166,U_8165] :
( ( hAPP(U_8166,sK186(U_8167,U_8166,U_8165)) = U_8167
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK186(U_8167,U_8166,U_8165)),U_8165)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8167),hAPP(U_8166,U_8165)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8166,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8167))
| ( ~ 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_8166,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK185(U_8167,U_8166,U_8165)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8166,sK185(U_8167,U_8166,U_8165))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK185(U_8167,U_8166,U_8165)),U_8165)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK186]),skolemize(U_8164,sK186(U_8167,U_8166,U_8165))],[f_2364_3]) ).
cnf(f_2364_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK186(U_8167,U_8166,U_8165)),U_8165))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8167),hAPP(U_8166,U_8165)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8166,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8167))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK185(U_8167,U_8166,U_8165)),U_8165)) ),
inference(clausify,[status(thm)],[f_2364_4]) ).
cnf(f_2364_6,plain,
( hAPP(U_8166,sK186(U_8167,U_8166,U_8165)) = U_8167
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8167),hAPP(U_8166,U_8165)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8166,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8167))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK185(U_8167,U_8166,U_8165)),U_8165)) ),
inference(clausify,[status(thm)],[f_2364_4]) ).
cnf(f_2364_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK186(U_8167,U_8166,U_8165)),U_8165))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8167),hAPP(U_8166,U_8165)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8166,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8167))
| ~ 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_8166,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK185(U_8167,U_8166,U_8165)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8166,sK185(U_8167,U_8166,U_8165))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2364_4]) ).
cnf(f_2364_8,plain,
( hAPP(U_8166,sK186(U_8167,U_8166,U_8165)) = U_8167
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8167),hAPP(U_8166,U_8165)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8166,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8167))
| ~ 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_8166,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK185(U_8167,U_8166,U_8165)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8166,sK185(U_8167,U_8166,U_8165))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2364_4]) ).
fof(f_2365_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_2365_2,plain,
! [U_8173,U_8172,U_8171,U_8170] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8171,U_8170),U_8173),U_8172) = c_Groups_Ozero__class_Ozero(U_8170)
| ! [U_8169] :
( hAPP(U_8173,U_8169) != c_Groups_Ozero__class_Ozero(U_8170)
| ~ hBOOL(hAPP(hAPP(c_member(U_8171),U_8169),U_8172)) ) )
& ( ? [U_8168] :
( hAPP(U_8173,U_8168) = c_Groups_Ozero__class_Ozero(U_8170)
& hBOOL(hAPP(hAPP(c_member(U_8171),U_8168),U_8172)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8171,U_8170),U_8173),U_8172) != c_Groups_Ozero__class_Ozero(U_8170) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8171),U_8172))
| ~ class_Rings_Ono__zero__divisors(U_8170)
| ~ class_Rings_Ocomm__semiring__1(U_8170) ),
inference(variable_rename,[status(thm)],[f_2365_1]) ).
fof(f_2365_3,plain,
! [U_8173,U_8172,U_8171,U_8170] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8171,U_8170),U_8173),U_8172) = c_Groups_Ozero__class_Ozero(U_8170)
| ! [U_8169] :
( hAPP(U_8173,U_8169) != c_Groups_Ozero__class_Ozero(U_8170)
| ~ hBOOL(hAPP(hAPP(c_member(U_8171),U_8169),U_8172)) ) )
& ( ( hAPP(U_8173,sK187(U_8173,U_8172,U_8171,U_8170)) = c_Groups_Ozero__class_Ozero(U_8170)
& hBOOL(hAPP(hAPP(c_member(U_8171),sK187(U_8173,U_8172,U_8171,U_8170)),U_8172)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8171,U_8170),U_8173),U_8172) != c_Groups_Ozero__class_Ozero(U_8170) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8171),U_8172))
| ~ class_Rings_Ono__zero__divisors(U_8170)
| ~ class_Rings_Ocomm__semiring__1(U_8170) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK187]),skolemize(U_8168,sK187(U_8173,U_8172,U_8171,U_8170))],[f_2365_2]) ).
cnf(f_2365_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8171),sK187(U_8173,U_8172,U_8171,U_8170)),U_8172))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8171,U_8170),U_8173),U_8172) != c_Groups_Ozero__class_Ozero(U_8170)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8171),U_8172))
| ~ class_Rings_Ono__zero__divisors(U_8170)
| ~ class_Rings_Ocomm__semiring__1(U_8170) ),
inference(clausify,[status(thm)],[f_2365_3]) ).
cnf(f_2365_5,plain,
( hAPP(U_8173,sK187(U_8173,U_8172,U_8171,U_8170)) = c_Groups_Ozero__class_Ozero(U_8170)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8171,U_8170),U_8173),U_8172) != c_Groups_Ozero__class_Ozero(U_8170)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8171),U_8172))
| ~ class_Rings_Ono__zero__divisors(U_8170)
| ~ class_Rings_Ocomm__semiring__1(U_8170) ),
inference(clausify,[status(thm)],[f_2365_3]) ).
cnf(f_2365_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8171,U_8170),U_8173),U_8172) = c_Groups_Ozero__class_Ozero(U_8170)
| hAPP(U_8173,U_8169) != c_Groups_Ozero__class_Ozero(U_8170)
| ~ hBOOL(hAPP(hAPP(c_member(U_8171),U_8169),U_8172))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8171),U_8172))
| ~ class_Rings_Ono__zero__divisors(U_8170)
| ~ class_Rings_Ocomm__semiring__1(U_8170) ),
inference(clausify,[status(thm)],[f_2365_3]) ).
fof(f_2366_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_2366_2,plain,
! [U_8178,U_8177,U_8176,U_8175] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8176,U_8175),U_8178),U_8177) = c_Groups_Ozero__class_Ozero(U_8175)
| ! [U_8174] :
( hAPP(U_8178,U_8174) != c_Groups_Ozero__class_Ozero(U_8175)
| ~ hBOOL(hAPP(hAPP(c_member(U_8176),U_8174),U_8177)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8176),U_8177))
| ~ class_Rings_Ocomm__semiring__1(U_8175) ),
inference(variable_rename,[status(thm)],[f_2366_1]) ).
cnf(f_2366_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8176,U_8175),U_8178),U_8177) = c_Groups_Ozero__class_Ozero(U_8175)
| hAPP(U_8178,U_8174) != c_Groups_Ozero__class_Ozero(U_8175)
| ~ hBOOL(hAPP(hAPP(c_member(U_8176),U_8174),U_8177))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8176),U_8177))
| ~ class_Rings_Ocomm__semiring__1(U_8175) ),
inference(clausify,[status(thm)],[f_2366_2]) ).
fof(f_2367_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_2367_2,plain,
! [U_8181,U_8180,U_8179] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8180,U_8179),U_8181),c_Orderings_Obot__class_Obot(tc_fun(U_8180,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_8179)
| ~ class_Groups_Ocomm__monoid__mult(U_8179) ),
inference(variable_rename,[status(thm)],[f_2367_1]) ).
cnf(f_2367_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8180,U_8179),U_8181),c_Orderings_Obot__class_Obot(tc_fun(U_8180,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_8179)
| ~ class_Groups_Ocomm__monoid__mult(U_8179) ),
inference(clausify,[status(thm)],[f_2367_2]) ).
fof(f_2368_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_2368_2,plain,
! [U_8184,U_8183,U_8182] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8183,U_8182),U_8184),c_Orderings_Obot__class_Obot(tc_fun(U_8183,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_8182)
| ~ class_Groups_Ocomm__monoid__mult(U_8182) ),
inference(variable_rename,[status(thm)],[f_2368_1]) ).
cnf(f_2368_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8183,U_8182),U_8184),c_Orderings_Obot__class_Obot(tc_fun(U_8183,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_8182)
| ~ class_Groups_Ocomm__monoid__mult(U_8182) ),
inference(clausify,[status(thm)],[f_2368_2]) ).
fof(f_2369_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_2369_2,plain,
! [U_8188,U_8187,U_8186,U_8185] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8186,U_8185),U_8188),U_8187) = c_Groups_Oone__class_Oone(U_8185)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_8186),U_8187))
| ~ class_Groups_Ocomm__monoid__mult(U_8185) ),
inference(variable_rename,[status(thm)],[f_2369_1]) ).
cnf(f_2369_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8186,U_8185),U_8188),U_8187) = c_Groups_Oone__class_Oone(U_8185)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_8186),U_8187))
| ~ class_Groups_Ocomm__monoid__mult(U_8185) ),
inference(clausify,[status(thm)],[f_2369_2]) ).
fof(f_2370_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_2370_2,plain,
! [U_8192,U_8191,U_8190,U_8189] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8190,U_8189),U_8192),U_8191) = c_Groups_Oone__class_Oone(U_8189)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_8190),U_8191))
| ~ class_Groups_Ocomm__monoid__mult(U_8189) ),
inference(variable_rename,[status(thm)],[f_2370_1]) ).
cnf(f_2370_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8190,U_8189),U_8192),U_8191) = c_Groups_Oone__class_Oone(U_8189)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_8190),U_8191))
| ~ class_Groups_Ocomm__monoid__mult(U_8189) ),
inference(clausify,[status(thm)],[f_2370_2]) ).
fof(f_2371_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_2371_2,plain,
! [U_8197,U_8196,U_8195] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8195,tc_Nat_Onat),U_8197),U_8196) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ? [U_8194] :
( hAPP(U_8197,U_8194) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_8195),U_8194),U_8196)) ) )
& ( ! [U_8193] :
( hAPP(U_8197,U_8193) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_8195),U_8193),U_8196)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8195,tc_Nat_Onat),U_8197),U_8196) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8195),U_8196)) ),
inference(variable_rename,[status(thm)],[f_2371_1]) ).
fof(f_2371_3,plain,
! [U_8197,U_8196,U_8195] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8195,tc_Nat_Onat),U_8197),U_8196) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ( hAPP(U_8197,sK188(U_8197,U_8196,U_8195)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_8195),sK188(U_8197,U_8196,U_8195)),U_8196)) ) )
& ( ! [U_8193] :
( hAPP(U_8197,U_8193) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_8195),U_8193),U_8196)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8195,tc_Nat_Onat),U_8197),U_8196) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8195),U_8196)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK188]),skolemize(U_8194,sK188(U_8197,U_8196,U_8195))],[f_2371_2]) ).
cnf(f_2371_4,plain,
( hAPP(U_8197,U_8193) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_8195),U_8193),U_8196))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8195,tc_Nat_Onat),U_8197),U_8196) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8195),U_8196)) ),
inference(clausify,[status(thm)],[f_2371_3]) ).
cnf(f_2371_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_8195),sK188(U_8197,U_8196,U_8195)),U_8196))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8195,tc_Nat_Onat),U_8197),U_8196) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8195),U_8196)) ),
inference(clausify,[status(thm)],[f_2371_3]) ).
cnf(f_2371_6,plain,
( hAPP(U_8197,sK188(U_8197,U_8196,U_8195)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8195,tc_Nat_Onat),U_8197),U_8196) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8195),U_8196)) ),
inference(clausify,[status(thm)],[f_2371_3]) ).
fof(f_2372_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_2372_2,plain,
! [U_8202,U_8201,U_8200] :
( ( ( 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_8200,tc_Nat_Onat),U_8202),U_8201)))
| ? [U_8199] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_8202,U_8199)))
& hBOOL(hAPP(hAPP(c_member(U_8200),U_8199),U_8201)) ) )
& ( ! [U_8198] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_8202,U_8198)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8200),U_8198),U_8201)) )
| ~ 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_8200,tc_Nat_Onat),U_8202),U_8201))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8200),U_8201)) ),
inference(variable_rename,[status(thm)],[f_2372_1]) ).
fof(f_2372_3,plain,
! [U_8202,U_8201,U_8200] :
( ( ( 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_8200,tc_Nat_Onat),U_8202),U_8201)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_8202,sK189(U_8202,U_8201,U_8200))))
& hBOOL(hAPP(hAPP(c_member(U_8200),sK189(U_8202,U_8201,U_8200)),U_8201)) ) )
& ( ! [U_8198] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_8202,U_8198)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8200),U_8198),U_8201)) )
| ~ 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_8200,tc_Nat_Onat),U_8202),U_8201))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8200),U_8201)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK189]),skolemize(U_8199,sK189(U_8202,U_8201,U_8200))],[f_2372_2]) ).
cnf(f_2372_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_8202,U_8198)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8200),U_8198),U_8201))
| ~ 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_8200,tc_Nat_Onat),U_8202),U_8201)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8200),U_8201)) ),
inference(clausify,[status(thm)],[f_2372_3]) ).
cnf(f_2372_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_8200),sK189(U_8202,U_8201,U_8200)),U_8201))
| 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_8200,tc_Nat_Onat),U_8202),U_8201)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8200),U_8201)) ),
inference(clausify,[status(thm)],[f_2372_3]) ).
cnf(f_2372_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_8202,sK189(U_8202,U_8201,U_8200))))
| 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_8200,tc_Nat_Onat),U_8202),U_8201)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8200),U_8201)) ),
inference(clausify,[status(thm)],[f_2372_3]) ).
fof(f_2373_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_2373_2,plain,
! [U_8207,U_8206,U_8205,U_8204,U_8203] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8204,U_8203),U_8207),hAPP(hAPP(c_Set_Oinsert(U_8204),U_8206),U_8205)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8203),hAPP(U_8207,U_8206)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8204,U_8203),U_8207),U_8205))
| hBOOL(hAPP(hAPP(c_member(U_8204),U_8206),U_8205))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8204),U_8205))
| ~ class_Groups_Ocomm__monoid__mult(U_8203) ),
inference(variable_rename,[status(thm)],[f_2373_1]) ).
cnf(f_2373_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8204,U_8203),U_8207),hAPP(hAPP(c_Set_Oinsert(U_8204),U_8206),U_8205)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8203),hAPP(U_8207,U_8206)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8204,U_8203),U_8207),U_8205))
| hBOOL(hAPP(hAPP(c_member(U_8204),U_8206),U_8205))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8204),U_8205))
| ~ class_Groups_Ocomm__monoid__mult(U_8203) ),
inference(clausify,[status(thm)],[f_2373_2]) ).
fof(f_2374_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_2374_2,plain,
! [U_8212,U_8211,U_8210,U_8209,U_8208] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8209,U_8208),U_8212),hAPP(hAPP(c_Set_Oinsert(U_8209),U_8211),U_8210)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8208),hAPP(U_8212,U_8211)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8209,U_8208),U_8212),U_8210))
| hBOOL(hAPP(hAPP(c_member(U_8209),U_8211),U_8210))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8209),U_8210))
| ~ class_Groups_Ocomm__monoid__mult(U_8208) ),
inference(variable_rename,[status(thm)],[f_2374_1]) ).
cnf(f_2374_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8209,U_8208),U_8212),hAPP(hAPP(c_Set_Oinsert(U_8209),U_8211),U_8210)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8208),hAPP(U_8212,U_8211)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8209,U_8208),U_8212),U_8210))
| hBOOL(hAPP(hAPP(c_member(U_8209),U_8211),U_8210))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8209),U_8210))
| ~ class_Groups_Ocomm__monoid__mult(U_8208) ),
inference(clausify,[status(thm)],[f_2374_2]) ).
fof(f_2375_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_2375_2,plain,
! [U_8217,U_8216,U_8215,U_8214,U_8213] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8213),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8214,U_8213),U_8217),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8214,tc_HOL_Obool)),U_8215),U_8216))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8214,U_8213),U_8217),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8214,tc_HOL_Obool)),U_8215),U_8216))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8213),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8214,U_8213),U_8217),U_8215)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8214,U_8213),U_8217),U_8216))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8214),U_8216))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8214),U_8215))
| ~ class_Groups_Ocomm__monoid__mult(U_8213) ),
inference(variable_rename,[status(thm)],[f_2375_1]) ).
cnf(f_2375_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8213),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8214,U_8213),U_8217),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8214,tc_HOL_Obool)),U_8215),U_8216))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8214,U_8213),U_8217),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8214,tc_HOL_Obool)),U_8215),U_8216))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8213),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8214,U_8213),U_8217),U_8215)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8214,U_8213),U_8217),U_8216))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8214),U_8216))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8214),U_8215))
| ~ class_Groups_Ocomm__monoid__mult(U_8213) ),
inference(clausify,[status(thm)],[f_2375_2]) ).
fof(f_2376_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_2376_2,plain,
! [U_8222,U_8221,U_8220,U_8219,U_8218] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8218),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8219,U_8218),U_8222),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8219,tc_HOL_Obool)),U_8220),U_8221))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8219,U_8218),U_8222),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8219,tc_HOL_Obool)),U_8220),U_8221))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8218),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8219,U_8218),U_8222),U_8220)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8219,U_8218),U_8222),U_8221))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8219),U_8221))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8219),U_8220))
| ~ class_Groups_Ocomm__monoid__mult(U_8218) ),
inference(variable_rename,[status(thm)],[f_2376_1]) ).
cnf(f_2376_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8218),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8219,U_8218),U_8222),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8219,tc_HOL_Obool)),U_8220),U_8221))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8219,U_8218),U_8222),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8219,tc_HOL_Obool)),U_8220),U_8221))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8218),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8219,U_8218),U_8222),U_8220)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8219,U_8218),U_8222),U_8221))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8219),U_8221))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8219),U_8220))
| ~ class_Groups_Ocomm__monoid__mult(U_8218) ),
inference(clausify,[status(thm)],[f_2376_2]) ).
fof(f_2377_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_2377_2,plain,
! [U_8226,U_8225,U_8224,U_8223] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8224,U_8223),U_8226),U_8225) = c_Groups_Oone__class_Oone(U_8223)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_8224),U_8225)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8224,U_8223),U_8226),U_8225) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_8223,U_8224,c_Groups_Otimes__class_Otimes(U_8223)),U_8226),c_Groups_Oone__class_Oone(U_8223)),U_8225)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8224),U_8225)) ) )
| ~ class_Groups_Ocomm__monoid__mult(U_8223) ),
inference(variable_rename,[status(thm)],[f_2377_1]) ).
cnf(f_2377_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8224,U_8223),U_8226),U_8225) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_8223,U_8224,c_Groups_Otimes__class_Otimes(U_8223)),U_8226),c_Groups_Oone__class_Oone(U_8223)),U_8225)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8224),U_8225))
| ~ class_Groups_Ocomm__monoid__mult(U_8223) ),
inference(clausify,[status(thm)],[f_2377_2]) ).
cnf(f_2377_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8224,U_8223),U_8226),U_8225) = c_Groups_Oone__class_Oone(U_8223)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_8224),U_8225))
| ~ class_Groups_Ocomm__monoid__mult(U_8223) ),
inference(clausify,[status(thm)],[f_2377_2]) ).
fof(f_2378_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_2378_2,plain,
! [U_8230,U_8229,U_8228,U_8227] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8228,U_8227),U_8230),U_8229) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_8227,U_8228,c_Groups_Otimes__class_Otimes(U_8227)),U_8230),c_Groups_Oone__class_Oone(U_8227)),U_8229)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8228),U_8229))
| ~ class_Groups_Ocomm__monoid__mult(U_8227) ),
inference(variable_rename,[status(thm)],[f_2378_1]) ).
cnf(f_2378_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8228,U_8227),U_8230),U_8229) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_8227,U_8228,c_Groups_Otimes__class_Otimes(U_8227)),U_8230),c_Groups_Oone__class_Oone(U_8227)),U_8229)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8228),U_8229))
| ~ class_Groups_Ocomm__monoid__mult(U_8227) ),
inference(clausify,[status(thm)],[f_2378_2]) ).
fof(f_2379_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_2379_2,plain,
! [U_8235,U_8234,U_8233,U_8232,U_8231] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8232,U_8231),U_8234),hAPP(hAPP(c_Set_Oinsert(U_8232),U_8235),U_8233)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8231),hAPP(U_8234,U_8235)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8232,U_8231),U_8234),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8232,tc_HOL_Obool)),U_8233),hAPP(hAPP(c_Set_Oinsert(U_8232),U_8235),c_Orderings_Obot__class_Obot(tc_fun(U_8232,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8232),U_8233))
| ~ class_Groups_Ocomm__monoid__mult(U_8231) ),
inference(variable_rename,[status(thm)],[f_2379_1]) ).
cnf(f_2379_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8232,U_8231),U_8234),hAPP(hAPP(c_Set_Oinsert(U_8232),U_8235),U_8233)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8231),hAPP(U_8234,U_8235)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8232,U_8231),U_8234),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8232,tc_HOL_Obool)),U_8233),hAPP(hAPP(c_Set_Oinsert(U_8232),U_8235),c_Orderings_Obot__class_Obot(tc_fun(U_8232,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8232),U_8233))
| ~ class_Groups_Ocomm__monoid__mult(U_8231) ),
inference(clausify,[status(thm)],[f_2379_2]) ).
fof(f_2380_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_2380_2,plain,
! [U_8240,U_8239,U_8238,U_8237,U_8236] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8237,U_8236),U_8240),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8237,tc_HOL_Obool)),U_8238),U_8239)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8236),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8237,U_8236),U_8240),U_8238)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8237,U_8236),U_8240),U_8239))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8237,tc_HOL_Obool)),U_8238),U_8239) != c_Orderings_Obot__class_Obot(tc_fun(U_8237,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8237),U_8239))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8237),U_8238))
| ~ class_Groups_Ocomm__monoid__mult(U_8236) ),
inference(variable_rename,[status(thm)],[f_2380_1]) ).
cnf(f_2380_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8237,U_8236),U_8240),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8237,tc_HOL_Obool)),U_8238),U_8239)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8236),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8237,U_8236),U_8240),U_8238)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8237,U_8236),U_8240),U_8239))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8237,tc_HOL_Obool)),U_8238),U_8239) != c_Orderings_Obot__class_Obot(tc_fun(U_8237,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8237),U_8239))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8237),U_8238))
| ~ class_Groups_Ocomm__monoid__mult(U_8236) ),
inference(clausify,[status(thm)],[f_2380_2]) ).
fof(f_2381_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_2381_2,plain,
! [U_8245,U_8244,U_8243,U_8242,U_8241] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8242,U_8241),U_8245),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8242,tc_HOL_Obool)),U_8243),U_8244)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8241),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8242,U_8241),U_8245),U_8243)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8242,U_8241),U_8245),U_8244))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8242,tc_HOL_Obool)),U_8243),U_8244) != c_Orderings_Obot__class_Obot(tc_fun(U_8242,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8242),U_8244))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8242),U_8243))
| ~ class_Groups_Ocomm__monoid__mult(U_8241) ),
inference(variable_rename,[status(thm)],[f_2381_1]) ).
cnf(f_2381_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8242,U_8241),U_8245),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8242,tc_HOL_Obool)),U_8243),U_8244)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8241),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8242,U_8241),U_8245),U_8243)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8242,U_8241),U_8245),U_8244))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8242,tc_HOL_Obool)),U_8243),U_8244) != c_Orderings_Obot__class_Obot(tc_fun(U_8242,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8242),U_8244))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8242),U_8243))
| ~ class_Groups_Ocomm__monoid__mult(U_8241) ),
inference(clausify,[status(thm)],[f_2381_2]) ).
fof(f_2382_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_2382_2,plain,
! [U_8250,U_8249,U_8248,U_8247,U_8246] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8247,U_8246),U_8250),U_8248) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8246),hAPP(U_8250,U_8249)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8247,U_8246),U_8250),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8247,tc_HOL_Obool)),U_8248),hAPP(hAPP(c_Set_Oinsert(U_8247),U_8249),c_Orderings_Obot__class_Obot(tc_fun(U_8247,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_8247),U_8249),U_8248))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8247),U_8248))
| ~ class_Groups_Ocomm__monoid__mult(U_8246) ),
inference(variable_rename,[status(thm)],[f_2382_1]) ).
cnf(f_2382_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8247,U_8246),U_8250),U_8248) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8246),hAPP(U_8250,U_8249)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8247,U_8246),U_8250),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8247,tc_HOL_Obool)),U_8248),hAPP(hAPP(c_Set_Oinsert(U_8247),U_8249),c_Orderings_Obot__class_Obot(tc_fun(U_8247,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_8247),U_8249),U_8248))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8247),U_8248))
| ~ class_Groups_Ocomm__monoid__mult(U_8246) ),
inference(clausify,[status(thm)],[f_2382_2]) ).
fof(f_2383_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_2383_2,plain,
! [U_8256,U_8255,U_8254,U_8253,U_8252] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8253,U_8252),U_8256),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8253,tc_HOL_Obool)),U_8254),U_8255)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8252),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8252),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8253,U_8252),U_8256),U_8254)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8253,U_8252),U_8256),U_8255))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8253,U_8252),U_8256),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8253,tc_HOL_Obool)),U_8254),U_8255)))
| ? [U_8251] :
( hAPP(U_8256,U_8251) = c_Groups_Ozero__class_Ozero(U_8252)
& hBOOL(hAPP(hAPP(c_member(U_8253),U_8251),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8253,tc_HOL_Obool)),U_8254),U_8255))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8253),U_8255))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8253),U_8254))
| ~ class_Fields_Ofield(U_8252) ),
inference(variable_rename,[status(thm)],[f_2383_1]) ).
fof(f_2383_3,plain,
! [U_8256,U_8255,U_8254,U_8253,U_8252] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8253,U_8252),U_8256),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8253,tc_HOL_Obool)),U_8254),U_8255)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8252),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8252),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8253,U_8252),U_8256),U_8254)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8253,U_8252),U_8256),U_8255))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8253,U_8252),U_8256),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8253,tc_HOL_Obool)),U_8254),U_8255)))
| ( hAPP(U_8256,sK190(U_8256,U_8255,U_8254,U_8253,U_8252)) = c_Groups_Ozero__class_Ozero(U_8252)
& hBOOL(hAPP(hAPP(c_member(U_8253),sK190(U_8256,U_8255,U_8254,U_8253,U_8252)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8253,tc_HOL_Obool)),U_8254),U_8255))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8253),U_8255))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8253),U_8254))
| ~ class_Fields_Ofield(U_8252) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK190]),skolemize(U_8251,sK190(U_8256,U_8255,U_8254,U_8253,U_8252))],[f_2383_2]) ).
cnf(f_2383_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8253),sK190(U_8256,U_8255,U_8254,U_8253,U_8252)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8253,tc_HOL_Obool)),U_8254),U_8255)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8253,U_8252),U_8256),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8253,tc_HOL_Obool)),U_8254),U_8255)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8252),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8252),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8253,U_8252),U_8256),U_8254)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8253,U_8252),U_8256),U_8255))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8253,U_8252),U_8256),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8253,tc_HOL_Obool)),U_8254),U_8255)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8253),U_8255))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8253),U_8254))
| ~ class_Fields_Ofield(U_8252) ),
inference(clausify,[status(thm)],[f_2383_3]) ).
cnf(f_2383_5,plain,
( hAPP(U_8256,sK190(U_8256,U_8255,U_8254,U_8253,U_8252)) = c_Groups_Ozero__class_Ozero(U_8252)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8253,U_8252),U_8256),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8253,tc_HOL_Obool)),U_8254),U_8255)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8252),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8252),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8253,U_8252),U_8256),U_8254)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8253,U_8252),U_8256),U_8255))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8253,U_8252),U_8256),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8253,tc_HOL_Obool)),U_8254),U_8255)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8253),U_8255))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8253),U_8254))
| ~ class_Fields_Ofield(U_8252) ),
inference(clausify,[status(thm)],[f_2383_3]) ).
fof(f_2384_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_2384_2,plain,
! [U_8262,U_8261,U_8260,U_8259,U_8258] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8259,U_8258),U_8262),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8259,tc_HOL_Obool)),U_8260),U_8261)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8258),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8259,U_8258),U_8262),U_8260)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8259,U_8258),U_8262),U_8261))
| ? [U_8257] :
( hAPP(U_8262,U_8257) != c_Groups_Oone__class_Oone(U_8258)
& hBOOL(hAPP(hAPP(c_member(U_8259),U_8257),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8259,tc_HOL_Obool)),U_8260),U_8261))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8259),U_8261))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8259),U_8260))
| ~ class_Groups_Ocomm__monoid__mult(U_8258) ),
inference(variable_rename,[status(thm)],[f_2384_1]) ).
fof(f_2384_3,plain,
! [U_8262,U_8261,U_8260,U_8259,U_8258] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8259,U_8258),U_8262),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8259,tc_HOL_Obool)),U_8260),U_8261)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8258),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8259,U_8258),U_8262),U_8260)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8259,U_8258),U_8262),U_8261))
| ( hAPP(U_8262,sK191(U_8262,U_8261,U_8260,U_8259,U_8258)) != c_Groups_Oone__class_Oone(U_8258)
& hBOOL(hAPP(hAPP(c_member(U_8259),sK191(U_8262,U_8261,U_8260,U_8259,U_8258)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8259,tc_HOL_Obool)),U_8260),U_8261))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8259),U_8261))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8259),U_8260))
| ~ class_Groups_Ocomm__monoid__mult(U_8258) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK191]),skolemize(U_8257,sK191(U_8262,U_8261,U_8260,U_8259,U_8258))],[f_2384_2]) ).
cnf(f_2384_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8259),sK191(U_8262,U_8261,U_8260,U_8259,U_8258)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8259,tc_HOL_Obool)),U_8260),U_8261)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8259,U_8258),U_8262),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8259,tc_HOL_Obool)),U_8260),U_8261)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8258),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8259,U_8258),U_8262),U_8260)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8259,U_8258),U_8262),U_8261))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8259),U_8261))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8259),U_8260))
| ~ class_Groups_Ocomm__monoid__mult(U_8258) ),
inference(clausify,[status(thm)],[f_2384_3]) ).
cnf(f_2384_5,plain,
( hAPP(U_8262,sK191(U_8262,U_8261,U_8260,U_8259,U_8258)) != c_Groups_Oone__class_Oone(U_8258)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8259,U_8258),U_8262),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8259,tc_HOL_Obool)),U_8260),U_8261)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8258),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8259,U_8258),U_8262),U_8260)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8259,U_8258),U_8262),U_8261))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8259),U_8261))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8259),U_8260))
| ~ class_Groups_Ocomm__monoid__mult(U_8258) ),
inference(clausify,[status(thm)],[f_2384_3]) ).
fof(f_2385_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_2385_2,plain,
! [U_8268,U_8267,U_8266,U_8265,U_8264] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8265,U_8264),U_8268),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8265,tc_HOL_Obool)),U_8266),U_8267)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8264),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8265,U_8264),U_8268),U_8266)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8265,U_8264),U_8268),U_8267))
| ? [U_8263] :
( hAPP(U_8268,U_8263) != c_Groups_Oone__class_Oone(U_8264)
& hBOOL(hAPP(hAPP(c_member(U_8265),U_8263),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8265,tc_HOL_Obool)),U_8266),U_8267))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8265),U_8267))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8265),U_8266))
| ~ class_Groups_Ocomm__monoid__mult(U_8264) ),
inference(variable_rename,[status(thm)],[f_2385_1]) ).
fof(f_2385_3,plain,
! [U_8268,U_8267,U_8266,U_8265,U_8264] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8265,U_8264),U_8268),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8265,tc_HOL_Obool)),U_8266),U_8267)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8264),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8265,U_8264),U_8268),U_8266)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8265,U_8264),U_8268),U_8267))
| ( hAPP(U_8268,sK192(U_8268,U_8267,U_8266,U_8265,U_8264)) != c_Groups_Oone__class_Oone(U_8264)
& hBOOL(hAPP(hAPP(c_member(U_8265),sK192(U_8268,U_8267,U_8266,U_8265,U_8264)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8265,tc_HOL_Obool)),U_8266),U_8267))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8265),U_8267))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8265),U_8266))
| ~ class_Groups_Ocomm__monoid__mult(U_8264) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK192]),skolemize(U_8263,sK192(U_8268,U_8267,U_8266,U_8265,U_8264))],[f_2385_2]) ).
cnf(f_2385_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8265),sK192(U_8268,U_8267,U_8266,U_8265,U_8264)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8265,tc_HOL_Obool)),U_8266),U_8267)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8265,U_8264),U_8268),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8265,tc_HOL_Obool)),U_8266),U_8267)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8264),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8265,U_8264),U_8268),U_8266)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8265,U_8264),U_8268),U_8267))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8265),U_8267))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8265),U_8266))
| ~ class_Groups_Ocomm__monoid__mult(U_8264) ),
inference(clausify,[status(thm)],[f_2385_3]) ).
cnf(f_2385_5,plain,
( hAPP(U_8268,sK192(U_8268,U_8267,U_8266,U_8265,U_8264)) != c_Groups_Oone__class_Oone(U_8264)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8265,U_8264),U_8268),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8265,tc_HOL_Obool)),U_8266),U_8267)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8264),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8265,U_8264),U_8268),U_8266)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8265,U_8264),U_8268),U_8267))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8265),U_8267))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8265),U_8266))
| ~ class_Groups_Ocomm__monoid__mult(U_8264) ),
inference(clausify,[status(thm)],[f_2385_3]) ).
fof(f_2386_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_2386_2,plain,
! [U_8274,U_8273,U_8272,U_8271,U_8270] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8271,U_8270),U_8274),U_8273) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8271,U_8270),U_8274),U_8272)
| ? [U_8269] :
( hAPP(U_8274,U_8269) != c_Groups_Oone__class_Oone(U_8270)
& hBOOL(hAPP(hAPP(c_member(U_8271),U_8269),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8271,tc_HOL_Obool)),U_8272),U_8273))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8271,tc_HOL_Obool)),U_8273),U_8272))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8271),U_8272))
| ~ class_Groups_Ocomm__monoid__mult(U_8270) ),
inference(variable_rename,[status(thm)],[f_2386_1]) ).
fof(f_2386_3,plain,
! [U_8274,U_8273,U_8272,U_8271,U_8270] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8271,U_8270),U_8274),U_8273) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8271,U_8270),U_8274),U_8272)
| ( hAPP(U_8274,sK193(U_8274,U_8273,U_8272,U_8271,U_8270)) != c_Groups_Oone__class_Oone(U_8270)
& hBOOL(hAPP(hAPP(c_member(U_8271),sK193(U_8274,U_8273,U_8272,U_8271,U_8270)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8271,tc_HOL_Obool)),U_8272),U_8273))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8271,tc_HOL_Obool)),U_8273),U_8272))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8271),U_8272))
| ~ class_Groups_Ocomm__monoid__mult(U_8270) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK193]),skolemize(U_8269,sK193(U_8274,U_8273,U_8272,U_8271,U_8270))],[f_2386_2]) ).
cnf(f_2386_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8271),sK193(U_8274,U_8273,U_8272,U_8271,U_8270)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8271,tc_HOL_Obool)),U_8272),U_8273)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8271,U_8270),U_8274),U_8273) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8271,U_8270),U_8274),U_8272)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8271,tc_HOL_Obool)),U_8273),U_8272))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8271),U_8272))
| ~ class_Groups_Ocomm__monoid__mult(U_8270) ),
inference(clausify,[status(thm)],[f_2386_3]) ).
cnf(f_2386_5,plain,
( hAPP(U_8274,sK193(U_8274,U_8273,U_8272,U_8271,U_8270)) != c_Groups_Oone__class_Oone(U_8270)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8271,U_8270),U_8274),U_8273) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8271,U_8270),U_8274),U_8272)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8271,tc_HOL_Obool)),U_8273),U_8272))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8271),U_8272))
| ~ class_Groups_Ocomm__monoid__mult(U_8270) ),
inference(clausify,[status(thm)],[f_2386_3]) ).
fof(f_2387_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_2387_2,plain,
! [U_8280,U_8279,U_8278,U_8277,U_8276] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8277,U_8276),U_8280),U_8278) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8277,U_8276),U_8280),U_8279)
| ? [U_8275] :
( hAPP(U_8280,U_8275) != c_Groups_Oone__class_Oone(U_8276)
& hBOOL(hAPP(hAPP(c_member(U_8277),U_8275),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8277,tc_HOL_Obool)),U_8278),U_8279))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8277,tc_HOL_Obool)),U_8279),U_8278))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8277),U_8278))
| ~ class_Groups_Ocomm__monoid__mult(U_8276) ),
inference(variable_rename,[status(thm)],[f_2387_1]) ).
fof(f_2387_3,plain,
! [U_8280,U_8279,U_8278,U_8277,U_8276] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8277,U_8276),U_8280),U_8278) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8277,U_8276),U_8280),U_8279)
| ( hAPP(U_8280,sK194(U_8280,U_8279,U_8278,U_8277,U_8276)) != c_Groups_Oone__class_Oone(U_8276)
& hBOOL(hAPP(hAPP(c_member(U_8277),sK194(U_8280,U_8279,U_8278,U_8277,U_8276)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8277,tc_HOL_Obool)),U_8278),U_8279))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8277,tc_HOL_Obool)),U_8279),U_8278))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8277),U_8278))
| ~ class_Groups_Ocomm__monoid__mult(U_8276) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK194]),skolemize(U_8275,sK194(U_8280,U_8279,U_8278,U_8277,U_8276))],[f_2387_2]) ).
cnf(f_2387_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8277),sK194(U_8280,U_8279,U_8278,U_8277,U_8276)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8277,tc_HOL_Obool)),U_8278),U_8279)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8277,U_8276),U_8280),U_8278) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8277,U_8276),U_8280),U_8279)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8277,tc_HOL_Obool)),U_8279),U_8278))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8277),U_8278))
| ~ class_Groups_Ocomm__monoid__mult(U_8276) ),
inference(clausify,[status(thm)],[f_2387_3]) ).
cnf(f_2387_5,plain,
( hAPP(U_8280,sK194(U_8280,U_8279,U_8278,U_8277,U_8276)) != c_Groups_Oone__class_Oone(U_8276)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8277,U_8276),U_8280),U_8278) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8277,U_8276),U_8280),U_8279)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8277,tc_HOL_Obool)),U_8279),U_8278))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8277),U_8278))
| ~ class_Groups_Ocomm__monoid__mult(U_8276) ),
inference(clausify,[status(thm)],[f_2387_3]) ).
fof(f_2388_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_2388_2,plain,
! [U_8284,U_8283,U_8282] :
( 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_8282,tc_Nat_Onat),U_8284),U_8283)))
| ? [U_8281] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_8284,U_8281)))
& hBOOL(hAPP(hAPP(c_member(U_8282),U_8281),U_8283)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8282),U_8283)) ),
inference(variable_rename,[status(thm)],[f_2388_1]) ).
fof(f_2388_3,plain,
! [U_8284,U_8283,U_8282] :
( 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_8282,tc_Nat_Onat),U_8284),U_8283)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_8284,sK195(U_8284,U_8283,U_8282))))
& hBOOL(hAPP(hAPP(c_member(U_8282),sK195(U_8284,U_8283,U_8282)),U_8283)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8282),U_8283)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK195]),skolemize(U_8281,sK195(U_8284,U_8283,U_8282))],[f_2388_2]) ).
cnf(f_2388_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8282),sK195(U_8284,U_8283,U_8282)),U_8283))
| 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_8282,tc_Nat_Onat),U_8284),U_8283)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8282),U_8283)) ),
inference(clausify,[status(thm)],[f_2388_3]) ).
cnf(f_2388_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_8284,sK195(U_8284,U_8283,U_8282))))
| 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_8282,tc_Nat_Onat),U_8284),U_8283)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8282),U_8283)) ),
inference(clausify,[status(thm)],[f_2388_3]) ).
fof(f_2389_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_2389_2,plain,
! [U_8292,U_8291,U_8290,U_8289,U_8288,U_8287,U_8286] :
( ? [U_8285] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_8286,U_8287,U_8288,U_8289,U_8291),U_8285))
& U_8292 = hAPP(hAPP(U_8288,U_8290),U_8285) )
| hBOOL(hAPP(hAPP(c_member(U_8286),U_8290),U_8291))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_8286,U_8287,U_8288,U_8289,hAPP(hAPP(c_Set_Oinsert(U_8286),U_8290),U_8291)),U_8292))
| ~ c_Finite__Set_Ofun__left__comm(U_8286,U_8287,U_8288) ),
inference(variable_rename,[status(thm)],[f_2389_1]) ).
fof(f_2389_3,plain,
! [U_8292,U_8291,U_8290,U_8289,U_8288,U_8287,U_8286] :
( ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_8286,U_8287,U_8288,U_8289,U_8291),sK196(U_8292,U_8291,U_8290,U_8289,U_8288,U_8287,U_8286)))
& U_8292 = hAPP(hAPP(U_8288,U_8290),sK196(U_8292,U_8291,U_8290,U_8289,U_8288,U_8287,U_8286)) )
| hBOOL(hAPP(hAPP(c_member(U_8286),U_8290),U_8291))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_8286,U_8287,U_8288,U_8289,hAPP(hAPP(c_Set_Oinsert(U_8286),U_8290),U_8291)),U_8292))
| ~ c_Finite__Set_Ofun__left__comm(U_8286,U_8287,U_8288) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK196]),skolemize(U_8285,sK196(U_8292,U_8291,U_8290,U_8289,U_8288,U_8287,U_8286))],[f_2389_2]) ).
cnf(f_2389_4,plain,
( U_8292 = hAPP(hAPP(U_8288,U_8290),sK196(U_8292,U_8291,U_8290,U_8289,U_8288,U_8287,U_8286))
| hBOOL(hAPP(hAPP(c_member(U_8286),U_8290),U_8291))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_8286,U_8287,U_8288,U_8289,hAPP(hAPP(c_Set_Oinsert(U_8286),U_8290),U_8291)),U_8292))
| ~ c_Finite__Set_Ofun__left__comm(U_8286,U_8287,U_8288) ),
inference(clausify,[status(thm)],[f_2389_3]) ).
cnf(f_2389_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_8286,U_8287,U_8288,U_8289,U_8291),sK196(U_8292,U_8291,U_8290,U_8289,U_8288,U_8287,U_8286)))
| hBOOL(hAPP(hAPP(c_member(U_8286),U_8290),U_8291))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_8286,U_8287,U_8288,U_8289,hAPP(hAPP(c_Set_Oinsert(U_8286),U_8290),U_8291)),U_8292))
| ~ c_Finite__Set_Ofun__left__comm(U_8286,U_8287,U_8288) ),
inference(clausify,[status(thm)],[f_2389_3]) ).
fof(f_2390_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_2390_2,plain,
! [U_8298,U_8297,U_8296,U_8295,U_8294,U_8293] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_8293,U_8294,U_8295),U_8297),hAPP(hAPP(c_Set_Oinsert(U_8293),U_8298),U_8296)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8293,U_8294,U_8295),hAPP(hAPP(U_8295,U_8298),U_8297)),U_8296)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8293),U_8296))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_8293,U_8294,U_8295) ),
inference(variable_rename,[status(thm)],[f_2390_1]) ).
cnf(f_2390_3,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_8293,U_8294,U_8295),U_8297),hAPP(hAPP(c_Set_Oinsert(U_8293),U_8298),U_8296)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8293,U_8294,U_8295),hAPP(hAPP(U_8295,U_8298),U_8297)),U_8296)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8293),U_8296))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_8293,U_8294,U_8295) ),
inference(clausify,[status(thm)],[f_2390_2]) ).
fof(f_2391_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_2391_2,plain,
! [U_8303,U_8302,U_8301,U_8300,U_8299] :
( hAPP(hAPP(U_8301,U_8302),hAPP(hAPP(U_8301,U_8302),U_8303)) = hAPP(hAPP(U_8301,U_8302),U_8303)
| ~ c_Finite__Set_Ofun__left__comm__idem(U_8299,U_8300,U_8301) ),
inference(variable_rename,[status(thm)],[f_2391_1]) ).
fof(f_2391_3,plain,
! [U_8303,U_8302,U_8301] :
( ! [U_8300,U_8299] : ~ c_Finite__Set_Ofun__left__comm__idem(U_8299,U_8300,U_8301)
| hAPP(hAPP(U_8301,U_8302),hAPP(hAPP(U_8301,U_8302),U_8303)) = hAPP(hAPP(U_8301,U_8302),U_8303) ),
inference(miniscope,[status(thm)],[f_2391_2]) ).
cnf(f_2391_4,plain,
( ~ c_Finite__Set_Ofun__left__comm__idem(U_8299,U_8300,U_8301)
| hAPP(hAPP(U_8301,U_8302),hAPP(hAPP(U_8301,U_8302),U_8303)) = hAPP(hAPP(U_8301,U_8302),U_8303) ),
inference(clausify,[status(thm)],[f_2391_3]) ).
fof(f_2392_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_2392_2,plain,
! [U_8304] : c_Finite__Set_Ofun__left__comm__idem(U_8304,tc_fun(U_8304,tc_HOL_Obool),c_Set_Oinsert(U_8304)),
inference(variable_rename,[status(thm)],[f_2392_1]) ).
cnf(f_2392_3,plain,
c_Finite__Set_Ofun__left__comm__idem(U_8304,tc_fun(U_8304,tc_HOL_Obool),c_Set_Oinsert(U_8304)),
inference(clausify,[status(thm)],[f_2392_2]) ).
fof(f_2393_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_2393_2,plain,
! [U_8305] :
( c_Finite__Set_Ofun__left__comm__idem(U_8305,U_8305,c_Groups_Otimes__class_Otimes(U_8305))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_8305) ),
inference(variable_rename,[status(thm)],[f_2393_1]) ).
cnf(f_2393_3,plain,
( c_Finite__Set_Ofun__left__comm__idem(U_8305,U_8305,c_Groups_Otimes__class_Otimes(U_8305))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_8305) ),
inference(clausify,[status(thm)],[f_2393_2]) ).
fof(f_2394_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_2394_2,plain,
! [U_8306] :
( c_Finite__Set_Ofun__left__comm__idem(U_8306,U_8306,c_Lattices_Osemilattice__sup__class_Osup(U_8306))
| ~ class_Lattices_Osemilattice__sup(U_8306) ),
inference(variable_rename,[status(thm)],[f_2394_1]) ).
cnf(f_2394_3,plain,
( c_Finite__Set_Ofun__left__comm__idem(U_8306,U_8306,c_Lattices_Osemilattice__sup__class_Osup(U_8306))
| ~ class_Lattices_Osemilattice__sup(U_8306) ),
inference(clausify,[status(thm)],[f_2394_2]) ).
fof(f_2395_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_2395_2,plain,
! [U_8307] :
( c_Finite__Set_Ofun__left__comm__idem(U_8307,U_8307,c_Lattices_Osemilattice__inf__class_Oinf(U_8307))
| ~ class_Lattices_Osemilattice__inf(U_8307) ),
inference(variable_rename,[status(thm)],[f_2395_1]) ).
cnf(f_2395_3,plain,
( c_Finite__Set_Ofun__left__comm__idem(U_8307,U_8307,c_Lattices_Osemilattice__inf__class_Oinf(U_8307))
| ~ class_Lattices_Osemilattice__inf(U_8307) ),
inference(clausify,[status(thm)],[f_2395_2]) ).
fof(f_2396_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_2396_2,plain,
! [U_8313,U_8312,U_8311,U_8310,U_8309,U_8308] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_8308,U_8309,U_8310),U_8312),hAPP(hAPP(c_Set_Oinsert(U_8308),U_8313),U_8311)) = hAPP(hAPP(U_8310,U_8313),hAPP(hAPP(c_Finite__Set_Ofold(U_8308,U_8309,U_8310),U_8312),U_8311))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8308),U_8311))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_8308,U_8309,U_8310) ),
inference(variable_rename,[status(thm)],[f_2396_1]) ).
cnf(f_2396_3,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_8308,U_8309,U_8310),U_8312),hAPP(hAPP(c_Set_Oinsert(U_8308),U_8313),U_8311)) = hAPP(hAPP(U_8310,U_8313),hAPP(hAPP(c_Finite__Set_Ofold(U_8308,U_8309,U_8310),U_8312),U_8311))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8308),U_8311))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_8308,U_8309,U_8310) ),
inference(clausify,[status(thm)],[f_2396_2]) ).
fof(f_2397_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_2397_2,plain,
! [U_8317,U_8316,U_8315] :
( ? [U_8314] : U_8315 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8316),U_8314))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8317),U_8315))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8315,U_8316) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8317,U_8316) ),
inference(variable_rename,[status(thm)],[f_2397_1]) ).
fof(f_2397_3,plain,
! [U_8317,U_8316,U_8315] :
( U_8315 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8316),sK197(U_8317,U_8316,U_8315)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8317),U_8315))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8315,U_8316) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8317,U_8316) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK197]),skolemize(U_8314,sK197(U_8317,U_8316,U_8315))],[f_2397_2]) ).
cnf(f_2397_4,plain,
( U_8315 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8316),sK197(U_8317,U_8316,U_8315)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8317),U_8315))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8315,U_8316) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8317,U_8316) ),
inference(clausify,[status(thm)],[f_2397_3]) ).
fof(f_2398_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_2398_2,plain,
! [U_8322,U_8321,U_8320,U_8319] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_8319,U_8320,c_Groups_Otimes__class_Otimes(U_8319)),U_8322),c_Groups_Oone__class_Oone(U_8319)),U_8321) = c_Groups_Oone__class_Oone(U_8319)
| ? [U_8318] :
( hAPP(U_8322,U_8318) != c_Groups_Oone__class_Oone(U_8319)
& hBOOL(hAPP(hAPP(c_member(U_8320),U_8318),U_8321)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8320),U_8321))
| ~ class_Groups_Ocomm__monoid__mult(U_8319) ),
inference(variable_rename,[status(thm)],[f_2398_1]) ).
fof(f_2398_3,plain,
! [U_8322,U_8321,U_8320,U_8319] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_8319,U_8320,c_Groups_Otimes__class_Otimes(U_8319)),U_8322),c_Groups_Oone__class_Oone(U_8319)),U_8321) = c_Groups_Oone__class_Oone(U_8319)
| ( hAPP(U_8322,sK198(U_8322,U_8321,U_8320,U_8319)) != c_Groups_Oone__class_Oone(U_8319)
& hBOOL(hAPP(hAPP(c_member(U_8320),sK198(U_8322,U_8321,U_8320,U_8319)),U_8321)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8320),U_8321))
| ~ class_Groups_Ocomm__monoid__mult(U_8319) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK198]),skolemize(U_8318,sK198(U_8322,U_8321,U_8320,U_8319))],[f_2398_2]) ).
cnf(f_2398_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8320),sK198(U_8322,U_8321,U_8320,U_8319)),U_8321))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_8319,U_8320,c_Groups_Otimes__class_Otimes(U_8319)),U_8322),c_Groups_Oone__class_Oone(U_8319)),U_8321) = c_Groups_Oone__class_Oone(U_8319)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8320),U_8321))
| ~ class_Groups_Ocomm__monoid__mult(U_8319) ),
inference(clausify,[status(thm)],[f_2398_3]) ).
cnf(f_2398_5,plain,
( hAPP(U_8322,sK198(U_8322,U_8321,U_8320,U_8319)) != c_Groups_Oone__class_Oone(U_8319)
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_8319,U_8320,c_Groups_Otimes__class_Otimes(U_8319)),U_8322),c_Groups_Oone__class_Oone(U_8319)),U_8321) = c_Groups_Oone__class_Oone(U_8319)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8320),U_8321))
| ~ class_Groups_Ocomm__monoid__mult(U_8319) ),
inference(clausify,[status(thm)],[f_2398_3]) ).
fof(f_2399_1,plain,
! [V_i_2,V_P_2,V_p_2] :
( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
| ~ hBOOL(hAPP(V_P_2,V_i_2))
| ? [B_i] :
( ~ hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2)))
& hBOOL(hAPP(V_P_2,B_i))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_mod__induct__0]) ).
fof(f_2399_2,plain,
! [U_8326,U_8325,U_8324] :
( hBOOL(hAPP(U_8325,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8326),U_8324))
| ~ hBOOL(hAPP(U_8325,U_8326))
| ? [U_8323] :
( ~ hBOOL(hAPP(U_8325,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8323),U_8324)))
& hBOOL(hAPP(U_8325,U_8323))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8323),U_8324)) ) ),
inference(variable_rename,[status(thm)],[f_2399_1]) ).
fof(f_2399_3,plain,
! [U_8326,U_8325,U_8324] :
( hBOOL(hAPP(U_8325,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8326),U_8324))
| ~ hBOOL(hAPP(U_8325,U_8326))
| ( ~ hBOOL(hAPP(U_8325,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK199(U_8326,U_8325,U_8324)),U_8324)))
& hBOOL(hAPP(U_8325,sK199(U_8326,U_8325,U_8324)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK199(U_8326,U_8325,U_8324)),U_8324)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK199]),skolemize(U_8323,sK199(U_8326,U_8325,U_8324))],[f_2399_2]) ).
cnf(f_2399_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK199(U_8326,U_8325,U_8324)),U_8324))
| hBOOL(hAPP(U_8325,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8326),U_8324))
| ~ hBOOL(hAPP(U_8325,U_8326)) ),
inference(clausify,[status(thm)],[f_2399_3]) ).
cnf(f_2399_5,plain,
( hBOOL(hAPP(U_8325,sK199(U_8326,U_8325,U_8324)))
| hBOOL(hAPP(U_8325,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8326),U_8324))
| ~ hBOOL(hAPP(U_8325,U_8326)) ),
inference(clausify,[status(thm)],[f_2399_3]) ).
cnf(f_2399_6,plain,
( ~ hBOOL(hAPP(U_8325,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK199(U_8326,U_8325,U_8324)),U_8324)))
| hBOOL(hAPP(U_8325,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8326),U_8324))
| ~ hBOOL(hAPP(U_8325,U_8326)) ),
inference(clausify,[status(thm)],[f_2399_3]) ).
fof(f_2400_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_2400_2,plain,
! [U_8333,U_8332,U_8331,U_8330,U_8329,U_8328] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_8328,U_8329,c_Groups_Otimes__class_Otimes(U_8328)),U_8331),U_8333),U_8330) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_8328,U_8329,c_Groups_Otimes__class_Otimes(U_8328)),U_8332),U_8333),U_8330)
| ? [U_8327] :
( hAPP(U_8331,U_8327) != hAPP(U_8332,U_8327)
& hBOOL(hAPP(hAPP(c_member(U_8329),U_8327),U_8330)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8329),U_8330))
| ~ class_Groups_Oab__semigroup__mult(U_8328) ),
inference(variable_rename,[status(thm)],[f_2400_1]) ).
fof(f_2400_3,plain,
! [U_8333,U_8332,U_8331,U_8330,U_8329,U_8328] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_8328,U_8329,c_Groups_Otimes__class_Otimes(U_8328)),U_8331),U_8333),U_8330) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_8328,U_8329,c_Groups_Otimes__class_Otimes(U_8328)),U_8332),U_8333),U_8330)
| ( hAPP(U_8331,sK200(U_8333,U_8332,U_8331,U_8330,U_8329,U_8328)) != hAPP(U_8332,sK200(U_8333,U_8332,U_8331,U_8330,U_8329,U_8328))
& hBOOL(hAPP(hAPP(c_member(U_8329),sK200(U_8333,U_8332,U_8331,U_8330,U_8329,U_8328)),U_8330)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8329),U_8330))
| ~ class_Groups_Oab__semigroup__mult(U_8328) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK200]),skolemize(U_8327,sK200(U_8333,U_8332,U_8331,U_8330,U_8329,U_8328))],[f_2400_2]) ).
cnf(f_2400_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8329),sK200(U_8333,U_8332,U_8331,U_8330,U_8329,U_8328)),U_8330))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_8328,U_8329,c_Groups_Otimes__class_Otimes(U_8328)),U_8331),U_8333),U_8330) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_8328,U_8329,c_Groups_Otimes__class_Otimes(U_8328)),U_8332),U_8333),U_8330)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8329),U_8330))
| ~ class_Groups_Oab__semigroup__mult(U_8328) ),
inference(clausify,[status(thm)],[f_2400_3]) ).
cnf(f_2400_5,plain,
( hAPP(U_8331,sK200(U_8333,U_8332,U_8331,U_8330,U_8329,U_8328)) != hAPP(U_8332,sK200(U_8333,U_8332,U_8331,U_8330,U_8329,U_8328))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_8328,U_8329,c_Groups_Otimes__class_Otimes(U_8328)),U_8331),U_8333),U_8330) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_8328,U_8329,c_Groups_Otimes__class_Otimes(U_8328)),U_8332),U_8333),U_8330)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8329),U_8330))
| ~ class_Groups_Oab__semigroup__mult(U_8328) ),
inference(clausify,[status(thm)],[f_2400_3]) ).
fof(f_2401_1,plain,
! [V_c_2,V_b_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_c_2),V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Osemilattice__inf(T_b) ),
inference(fof_nnf,[status(thm)],[fact_inf__le__fold__inf]) ).
fof(f_2401_2,plain,
! [U_8338,U_8337,U_8336,U_8335] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8335),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_8335),U_8337),U_8338)),hAPP(hAPP(c_Finite__Set_Ofold(U_8335,U_8335,c_Lattices_Osemilattice__inf__class_Oinf(U_8335)),U_8338),U_8336)))
| ? [U_8334] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8335),U_8337),U_8334))
& hBOOL(hAPP(hAPP(c_member(U_8335),U_8334),U_8336)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8335),U_8336))
| ~ class_Lattices_Osemilattice__inf(U_8335) ),
inference(variable_rename,[status(thm)],[f_2401_1]) ).
fof(f_2401_3,plain,
! [U_8338,U_8337,U_8336,U_8335] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8335),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_8335),U_8337),U_8338)),hAPP(hAPP(c_Finite__Set_Ofold(U_8335,U_8335,c_Lattices_Osemilattice__inf__class_Oinf(U_8335)),U_8338),U_8336)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8335),U_8337),sK201(U_8338,U_8337,U_8336,U_8335)))
& hBOOL(hAPP(hAPP(c_member(U_8335),sK201(U_8338,U_8337,U_8336,U_8335)),U_8336)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8335),U_8336))
| ~ class_Lattices_Osemilattice__inf(U_8335) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK201]),skolemize(U_8334,sK201(U_8338,U_8337,U_8336,U_8335))],[f_2401_2]) ).
cnf(f_2401_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8335),sK201(U_8338,U_8337,U_8336,U_8335)),U_8336))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8335),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_8335),U_8337),U_8338)),hAPP(hAPP(c_Finite__Set_Ofold(U_8335,U_8335,c_Lattices_Osemilattice__inf__class_Oinf(U_8335)),U_8338),U_8336)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8335),U_8336))
| ~ class_Lattices_Osemilattice__inf(U_8335) ),
inference(clausify,[status(thm)],[f_2401_3]) ).
cnf(f_2401_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8335),U_8337),sK201(U_8338,U_8337,U_8336,U_8335)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8335),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_8335),U_8337),U_8338)),hAPP(hAPP(c_Finite__Set_Ofold(U_8335,U_8335,c_Lattices_Osemilattice__inf__class_Oinf(U_8335)),U_8338),U_8336)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8335),U_8336))
| ~ class_Lattices_Osemilattice__inf(U_8335) ),
inference(clausify,[status(thm)],[f_2401_3]) ).
fof(f_2402_1,plain,
! [V_c_2,V_b_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_c_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Osemilattice__sup(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold__sup__le__sup]) ).
fof(f_2402_2,plain,
! [U_8343,U_8342,U_8341,U_8340] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8340),hAPP(hAPP(c_Finite__Set_Ofold(U_8340,U_8340,c_Lattices_Osemilattice__sup__class_Osup(U_8340)),U_8343),U_8341)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8340),U_8342),U_8343)))
| ? [U_8339] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8340),U_8339),U_8342))
& hBOOL(hAPP(hAPP(c_member(U_8340),U_8339),U_8341)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8340),U_8341))
| ~ class_Lattices_Osemilattice__sup(U_8340) ),
inference(variable_rename,[status(thm)],[f_2402_1]) ).
fof(f_2402_3,plain,
! [U_8343,U_8342,U_8341,U_8340] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8340),hAPP(hAPP(c_Finite__Set_Ofold(U_8340,U_8340,c_Lattices_Osemilattice__sup__class_Osup(U_8340)),U_8343),U_8341)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8340),U_8342),U_8343)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8340),sK202(U_8343,U_8342,U_8341,U_8340)),U_8342))
& hBOOL(hAPP(hAPP(c_member(U_8340),sK202(U_8343,U_8342,U_8341,U_8340)),U_8341)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8340),U_8341))
| ~ class_Lattices_Osemilattice__sup(U_8340) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK202]),skolemize(U_8339,sK202(U_8343,U_8342,U_8341,U_8340))],[f_2402_2]) ).
cnf(f_2402_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8340),sK202(U_8343,U_8342,U_8341,U_8340)),U_8341))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8340),hAPP(hAPP(c_Finite__Set_Ofold(U_8340,U_8340,c_Lattices_Osemilattice__sup__class_Osup(U_8340)),U_8343),U_8341)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8340),U_8342),U_8343)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8340),U_8341))
| ~ class_Lattices_Osemilattice__sup(U_8340) ),
inference(clausify,[status(thm)],[f_2402_3]) ).
cnf(f_2402_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8340),sK202(U_8343,U_8342,U_8341,U_8340)),U_8342))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8340),hAPP(hAPP(c_Finite__Set_Ofold(U_8340,U_8340,c_Lattices_Osemilattice__sup__class_Osup(U_8340)),U_8343),U_8341)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8340),U_8342),U_8343)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8340),U_8341))
| ~ class_Lattices_Osemilattice__sup(U_8340) ),
inference(clausify,[status(thm)],[f_2402_3]) ).
fof(f_2403_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_2403_2,plain,
! [U_8349,U_8348,U_8347,U_8346] :
( ? [U_8345] :
( hAPP(U_8348,U_8345) = U_8349
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8345),U_8347))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8346),U_8345)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8349),hAPP(U_8348,U_8347)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8348,U_8346)),U_8349))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8346),U_8347))
| ? [U_8344] :
( ~ 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_8348,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8344),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8348,U_8344)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8344),U_8347))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8346),U_8344)) ) ),
inference(variable_rename,[status(thm)],[f_2403_1]) ).
fof(f_2403_3,plain,
! [U_8349,U_8348,U_8347,U_8346] :
( ? [U_8345] :
( hAPP(U_8348,U_8345) = U_8349
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8345),U_8347))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8346),U_8345)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8349),hAPP(U_8348,U_8347)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8348,U_8346)),U_8349))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8346),U_8347))
| ( ~ 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_8348,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK203(U_8349,U_8348,U_8347,U_8346)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8348,sK203(U_8349,U_8348,U_8347,U_8346))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK203(U_8349,U_8348,U_8347,U_8346)),U_8347))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8346),sK203(U_8349,U_8348,U_8347,U_8346))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK203]),skolemize(U_8344,sK203(U_8349,U_8348,U_8347,U_8346))],[f_2403_2]) ).
fof(f_2403_4,plain,
! [U_8349,U_8348,U_8347,U_8346] :
( ( hAPP(U_8348,sK204(U_8349,U_8348,U_8347,U_8346)) = U_8349
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK204(U_8349,U_8348,U_8347,U_8346)),U_8347))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8346),sK204(U_8349,U_8348,U_8347,U_8346))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8349),hAPP(U_8348,U_8347)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8348,U_8346)),U_8349))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8346),U_8347))
| ( ~ 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_8348,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK203(U_8349,U_8348,U_8347,U_8346)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8348,sK203(U_8349,U_8348,U_8347,U_8346))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK203(U_8349,U_8348,U_8347,U_8346)),U_8347))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8346),sK203(U_8349,U_8348,U_8347,U_8346))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK204]),skolemize(U_8345,sK204(U_8349,U_8348,U_8347,U_8346))],[f_2403_3]) ).
cnf(f_2403_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8346),sK204(U_8349,U_8348,U_8347,U_8346)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8349),hAPP(U_8348,U_8347)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8348,U_8346)),U_8349))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8346),U_8347))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8346),sK203(U_8349,U_8348,U_8347,U_8346))) ),
inference(clausify,[status(thm)],[f_2403_4]) ).
cnf(f_2403_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK204(U_8349,U_8348,U_8347,U_8346)),U_8347))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8349),hAPP(U_8348,U_8347)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8348,U_8346)),U_8349))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8346),U_8347))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8346),sK203(U_8349,U_8348,U_8347,U_8346))) ),
inference(clausify,[status(thm)],[f_2403_4]) ).
cnf(f_2403_7,plain,
( hAPP(U_8348,sK204(U_8349,U_8348,U_8347,U_8346)) = U_8349
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8349),hAPP(U_8348,U_8347)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8348,U_8346)),U_8349))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8346),U_8347))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8346),sK203(U_8349,U_8348,U_8347,U_8346))) ),
inference(clausify,[status(thm)],[f_2403_4]) ).
cnf(f_2403_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8346),sK204(U_8349,U_8348,U_8347,U_8346)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8349),hAPP(U_8348,U_8347)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8348,U_8346)),U_8349))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8346),U_8347))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK203(U_8349,U_8348,U_8347,U_8346)),U_8347)) ),
inference(clausify,[status(thm)],[f_2403_4]) ).
cnf(f_2403_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK204(U_8349,U_8348,U_8347,U_8346)),U_8347))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8349),hAPP(U_8348,U_8347)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8348,U_8346)),U_8349))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8346),U_8347))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK203(U_8349,U_8348,U_8347,U_8346)),U_8347)) ),
inference(clausify,[status(thm)],[f_2403_4]) ).
cnf(f_2403_10,plain,
( hAPP(U_8348,sK204(U_8349,U_8348,U_8347,U_8346)) = U_8349
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8349),hAPP(U_8348,U_8347)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8348,U_8346)),U_8349))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8346),U_8347))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK203(U_8349,U_8348,U_8347,U_8346)),U_8347)) ),
inference(clausify,[status(thm)],[f_2403_4]) ).
cnf(f_2403_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8346),sK204(U_8349,U_8348,U_8347,U_8346)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8349),hAPP(U_8348,U_8347)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8348,U_8346)),U_8349))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8346),U_8347))
| ~ 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_8348,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK203(U_8349,U_8348,U_8347,U_8346)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8348,sK203(U_8349,U_8348,U_8347,U_8346))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2403_4]) ).
cnf(f_2403_12,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK204(U_8349,U_8348,U_8347,U_8346)),U_8347))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8349),hAPP(U_8348,U_8347)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8348,U_8346)),U_8349))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8346),U_8347))
| ~ 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_8348,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK203(U_8349,U_8348,U_8347,U_8346)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8348,sK203(U_8349,U_8348,U_8347,U_8346))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2403_4]) ).
cnf(f_2403_13,plain,
( hAPP(U_8348,sK204(U_8349,U_8348,U_8347,U_8346)) = U_8349
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8349),hAPP(U_8348,U_8347)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8348,U_8346)),U_8349))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8346),U_8347))
| ~ 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_8348,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK203(U_8349,U_8348,U_8347,U_8346)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8348,sK203(U_8349,U_8348,U_8347,U_8346))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2403_4]) ).
fof(f_2404_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_2404_2,plain,
! [U_8351,U_8350] :
( ( c_Random_Olog(U_8350,U_8351) = 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_8350,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_8351),U_8350)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8351),U_8350))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_8350),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
& ( c_Random_Olog(U_8350,U_8351) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8351),U_8350))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_8350),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ) ) ),
inference(variable_rename,[status(thm)],[f_2404_1]) ).
fof(f_2404_3,plain,
( ! [U_8355,U_8353] :
( c_Random_Olog(U_8353,U_8355) = 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_8353,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_8355),U_8353)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8355),U_8353))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_8353),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
& ! [U_8354,U_8352] :
( c_Random_Olog(U_8352,U_8354) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8354),U_8352))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_8352),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ) ) ),
inference(miniscope,[status(thm)],[f_2404_2]) ).
cnf(f_2404_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_8352),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
| c_Random_Olog(U_8352,U_8354) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_2404_3]) ).
cnf(f_2404_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8354),U_8352))
| c_Random_Olog(U_8352,U_8354) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_2404_3]) ).
cnf(f_2404_6,plain,
( c_Random_Olog(U_8353,U_8355) = 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_8353,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_8355),U_8353)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8355),U_8353))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_8353),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ),
inference(clausify,[status(thm)],[f_2404_3]) ).
fof(f_2405_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_2405_2,plain,
! [U_8358,U_8357,U_8356] :
( ( c_Random_Ominus__shift(U_8358,U_8356,U_8357) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_8356),U_8357)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8356),U_8357)) )
& ( c_Random_Ominus__shift(U_8358,U_8356,U_8357) = 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_8358),U_8356)),U_8357)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8356),U_8357)) ) ),
inference(variable_rename,[status(thm)],[f_2405_1]) ).
fof(f_2405_3,plain,
( ! [U_8364,U_8362,U_8360] :
( c_Random_Ominus__shift(U_8364,U_8360,U_8362) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_8360),U_8362)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8360),U_8362)) )
& ! [U_8363,U_8361,U_8359] :
( c_Random_Ominus__shift(U_8363,U_8359,U_8361) = 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_8363),U_8359)),U_8361)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8359),U_8361)) ) ),
inference(miniscope,[status(thm)],[f_2405_2]) ).
cnf(f_2405_4,plain,
( c_Random_Ominus__shift(U_8363,U_8359,U_8361) = 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_8363),U_8359)),U_8361)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8359),U_8361)) ),
inference(clausify,[status(thm)],[f_2405_3]) ).
cnf(f_2405_5,plain,
( c_Random_Ominus__shift(U_8364,U_8360,U_8362) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_8360),U_8362)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8360),U_8362)) ),
inference(clausify,[status(thm)],[f_2405_3]) ).
fof(f_2406_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_2406_2,plain,
! [U_8366,U_8365] :
( ( c_Random_Oinc__shift(U_8365,U_8366) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_8366),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
| U_8365 = U_8366 )
& ( c_Random_Oinc__shift(U_8365,U_8366) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| U_8365 != U_8366 ) ),
inference(variable_rename,[status(thm)],[f_2406_1]) ).
fof(f_2406_3,plain,
( ! [U_8370,U_8368] :
( c_Random_Oinc__shift(U_8368,U_8370) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_8370),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
| U_8368 = U_8370 )
& ! [U_8369,U_8367] :
( c_Random_Oinc__shift(U_8367,U_8369) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| U_8367 != U_8369 ) ),
inference(miniscope,[status(thm)],[f_2406_2]) ).
cnf(f_2406_4,plain,
( c_Random_Oinc__shift(U_8367,U_8369) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| U_8367 != U_8369 ),
inference(clausify,[status(thm)],[f_2406_3]) ).
cnf(f_2406_5,plain,
( c_Random_Oinc__shift(U_8368,U_8370) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_8370),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
| U_8368 = U_8370 ),
inference(clausify,[status(thm)],[f_2406_3]) ).
fof(f_2407_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_2407_2,plain,
! [U_8373,U_8372,U_8371] :
( U_8372 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8371),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8371),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_8371),U_8372),U_8373)),U_8373)),c_Divides_Odiv__class_Omod(U_8371,U_8372,U_8373))
| ~ class_Divides_Osemiring__div(U_8371) ),
inference(variable_rename,[status(thm)],[f_2407_1]) ).
cnf(f_2407_3,plain,
( U_8372 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8371),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8371),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_8371),U_8372),U_8373)),U_8373)),c_Divides_Odiv__class_Omod(U_8371,U_8372,U_8373))
| ~ class_Divides_Osemiring__div(U_8371) ),
inference(clausify,[status(thm)],[f_2407_2]) ).
fof(f_2408_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_2408_2,plain,
! [U_8378,U_8377,U_8376,U_8375] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8375),c_Groups_Ozero__class_Ozero(U_8375)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8376,U_8375),U_8378),U_8377)))
| ? [U_8374] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8375),c_Groups_Ozero__class_Ozero(U_8375)),hAPP(U_8378,U_8374)))
& hBOOL(hAPP(hAPP(c_member(U_8376),U_8374),U_8377)) )
| ~ class_Rings_Olinordered__semidom(U_8375) ),
inference(variable_rename,[status(thm)],[f_2408_1]) ).
fof(f_2408_3,plain,
! [U_8378,U_8377,U_8376,U_8375] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8375),c_Groups_Ozero__class_Ozero(U_8375)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8376,U_8375),U_8378),U_8377)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8375),c_Groups_Ozero__class_Ozero(U_8375)),hAPP(U_8378,sK205(U_8378,U_8377,U_8376,U_8375))))
& hBOOL(hAPP(hAPP(c_member(U_8376),sK205(U_8378,U_8377,U_8376,U_8375)),U_8377)) )
| ~ class_Rings_Olinordered__semidom(U_8375) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK205]),skolemize(U_8374,sK205(U_8378,U_8377,U_8376,U_8375))],[f_2408_2]) ).
cnf(f_2408_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8376),sK205(U_8378,U_8377,U_8376,U_8375)),U_8377))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8375),c_Groups_Ozero__class_Ozero(U_8375)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8376,U_8375),U_8378),U_8377)))
| ~ class_Rings_Olinordered__semidom(U_8375) ),
inference(clausify,[status(thm)],[f_2408_3]) ).
cnf(f_2408_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8375),c_Groups_Ozero__class_Ozero(U_8375)),hAPP(U_8378,sK205(U_8378,U_8377,U_8376,U_8375))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8375),c_Groups_Ozero__class_Ozero(U_8375)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8376,U_8375),U_8378),U_8377)))
| ~ class_Rings_Olinordered__semidom(U_8375) ),
inference(clausify,[status(thm)],[f_2408_3]) ).
fof(f_2409_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_2409_2,plain,
! [U_8383,U_8382,U_8381,U_8380] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8380),c_Groups_Ozero__class_Ozero(U_8380)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8381,U_8380),U_8383),U_8382)))
| ? [U_8379] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8380),c_Groups_Ozero__class_Ozero(U_8380)),hAPP(U_8383,U_8379)))
& hBOOL(hAPP(hAPP(c_member(U_8381),U_8379),U_8382)) )
| ~ class_Rings_Olinordered__semidom(U_8380) ),
inference(variable_rename,[status(thm)],[f_2409_1]) ).
fof(f_2409_3,plain,
! [U_8383,U_8382,U_8381,U_8380] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8380),c_Groups_Ozero__class_Ozero(U_8380)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8381,U_8380),U_8383),U_8382)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8380),c_Groups_Ozero__class_Ozero(U_8380)),hAPP(U_8383,sK206(U_8383,U_8382,U_8381,U_8380))))
& hBOOL(hAPP(hAPP(c_member(U_8381),sK206(U_8383,U_8382,U_8381,U_8380)),U_8382)) )
| ~ class_Rings_Olinordered__semidom(U_8380) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK206]),skolemize(U_8379,sK206(U_8383,U_8382,U_8381,U_8380))],[f_2409_2]) ).
cnf(f_2409_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8381),sK206(U_8383,U_8382,U_8381,U_8380)),U_8382))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8380),c_Groups_Ozero__class_Ozero(U_8380)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8381,U_8380),U_8383),U_8382)))
| ~ class_Rings_Olinordered__semidom(U_8380) ),
inference(clausify,[status(thm)],[f_2409_3]) ).
cnf(f_2409_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8380),c_Groups_Ozero__class_Ozero(U_8380)),hAPP(U_8383,sK206(U_8383,U_8382,U_8381,U_8380))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8380),c_Groups_Ozero__class_Ozero(U_8380)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8381,U_8380),U_8383),U_8382)))
| ~ class_Rings_Olinordered__semidom(U_8380) ),
inference(clausify,[status(thm)],[f_2409_3]) ).
fof(f_2410_1,plain,
! [V_P_2,V_F_2,T_b] :
( hBOOL(hAPP(V_P_2,V_F_2))
| ? [B_x,B_F] :
( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F)))
& hBOOL(hAPP(V_P_2,B_F))
& ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F)) )
| ~ hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__induct]) ).
fof(f_2410_2,plain,
! [U_8388,U_8387,U_8386] :
( hBOOL(hAPP(U_8388,U_8387))
| ? [U_8385,U_8384] :
( ~ hBOOL(hAPP(U_8388,hAPP(hAPP(c_Set_Oinsert(U_8386),U_8385),U_8384)))
& hBOOL(hAPP(U_8388,U_8384))
& ~ hBOOL(hAPP(hAPP(c_member(U_8386),U_8385),U_8384))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_8386),U_8384)) )
| ~ hBOOL(hAPP(U_8388,c_Orderings_Obot__class_Obot(tc_fun(U_8386,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8386),U_8387)) ),
inference(variable_rename,[status(thm)],[f_2410_1]) ).
fof(f_2410_3,plain,
! [U_8388,U_8387,U_8386] :
( hBOOL(hAPP(U_8388,U_8387))
| ? [U_8384] :
( ~ hBOOL(hAPP(U_8388,hAPP(hAPP(c_Set_Oinsert(U_8386),sK207(U_8388,U_8387,U_8386)),U_8384)))
& hBOOL(hAPP(U_8388,U_8384))
& ~ hBOOL(hAPP(hAPP(c_member(U_8386),sK207(U_8388,U_8387,U_8386)),U_8384))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_8386),U_8384)) )
| ~ hBOOL(hAPP(U_8388,c_Orderings_Obot__class_Obot(tc_fun(U_8386,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8386),U_8387)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK207]),skolemize(U_8385,sK207(U_8388,U_8387,U_8386))],[f_2410_2]) ).
fof(f_2410_4,plain,
! [U_8388,U_8387,U_8386] :
( hBOOL(hAPP(U_8388,U_8387))
| ( ~ hBOOL(hAPP(U_8388,hAPP(hAPP(c_Set_Oinsert(U_8386),sK207(U_8388,U_8387,U_8386)),sK208(U_8388,U_8387,U_8386))))
& hBOOL(hAPP(U_8388,sK208(U_8388,U_8387,U_8386)))
& ~ hBOOL(hAPP(hAPP(c_member(U_8386),sK207(U_8388,U_8387,U_8386)),sK208(U_8388,U_8387,U_8386)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_8386),sK208(U_8388,U_8387,U_8386))) )
| ~ hBOOL(hAPP(U_8388,c_Orderings_Obot__class_Obot(tc_fun(U_8386,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8386),U_8387)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK208]),skolemize(U_8384,sK208(U_8388,U_8387,U_8386))],[f_2410_3]) ).
cnf(f_2410_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8386),sK208(U_8388,U_8387,U_8386)))
| hBOOL(hAPP(U_8388,U_8387))
| ~ hBOOL(hAPP(U_8388,c_Orderings_Obot__class_Obot(tc_fun(U_8386,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8386),U_8387)) ),
inference(clausify,[status(thm)],[f_2410_4]) ).
cnf(f_2410_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8386),sK207(U_8388,U_8387,U_8386)),sK208(U_8388,U_8387,U_8386)))
| hBOOL(hAPP(U_8388,U_8387))
| ~ hBOOL(hAPP(U_8388,c_Orderings_Obot__class_Obot(tc_fun(U_8386,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8386),U_8387)) ),
inference(clausify,[status(thm)],[f_2410_4]) ).
cnf(f_2410_7,plain,
( hBOOL(hAPP(U_8388,sK208(U_8388,U_8387,U_8386)))
| hBOOL(hAPP(U_8388,U_8387))
| ~ hBOOL(hAPP(U_8388,c_Orderings_Obot__class_Obot(tc_fun(U_8386,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8386),U_8387)) ),
inference(clausify,[status(thm)],[f_2410_4]) ).
cnf(f_2410_8,plain,
( ~ hBOOL(hAPP(U_8388,hAPP(hAPP(c_Set_Oinsert(U_8386),sK207(U_8388,U_8387,U_8386)),sK208(U_8388,U_8387,U_8386))))
| hBOOL(hAPP(U_8388,U_8387))
| ~ hBOOL(hAPP(U_8388,c_Orderings_Obot__class_Obot(tc_fun(U_8386,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8386),U_8387)) ),
inference(clausify,[status(thm)],[f_2410_4]) ).
fof(f_2411_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_2411_2,plain,
! [U_8395,U_8394,U_8393,U_8392,U_8391,U_8390,U_8389] :
( c_Nitpick_Ofold__graph_H(U_8389,U_8392,U_8393,U_8394,U_8391,hAPP(hAPP(U_8393,U_8390),U_8395))
| ~ c_Nitpick_Ofold__graph_H(U_8389,U_8392,U_8393,U_8394,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8389,tc_HOL_Obool)),U_8391),hAPP(hAPP(c_Set_Oinsert(U_8389),U_8390),c_Orderings_Obot__class_Obot(tc_fun(U_8389,tc_HOL_Obool)))),U_8395)
| ~ hBOOL(hAPP(hAPP(c_member(U_8389),U_8390),U_8391)) ),
inference(variable_rename,[status(thm)],[f_2411_1]) ).
cnf(f_2411_3,plain,
( c_Nitpick_Ofold__graph_H(U_8389,U_8392,U_8393,U_8394,U_8391,hAPP(hAPP(U_8393,U_8390),U_8395))
| ~ c_Nitpick_Ofold__graph_H(U_8389,U_8392,U_8393,U_8394,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8389,tc_HOL_Obool)),U_8391),hAPP(hAPP(c_Set_Oinsert(U_8389),U_8390),c_Orderings_Obot__class_Obot(tc_fun(U_8389,tc_HOL_Obool)))),U_8395)
| ~ hBOOL(hAPP(hAPP(c_member(U_8389),U_8390),U_8391)) ),
inference(clausify,[status(thm)],[f_2411_2]) ).
fof(f_2412_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_2412_2,plain,
! [U_8398,U_8397,U_8396] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8396),hAPP(c_Finite__Set_Ofold1(U_8396,c_Orderings_Oord__class_Omin(U_8396)),U_8398)),hAPP(c_Finite__Set_Ofold1(U_8396,c_Orderings_Oord__class_Omin(U_8396)),U_8397)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8396),U_8398))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8396,tc_HOL_Obool)),U_8397),U_8398))
| U_8397 = c_Orderings_Obot__class_Obot(tc_fun(U_8396,tc_HOL_Obool))
| ~ class_Orderings_Olinorder(U_8396) ),
inference(variable_rename,[status(thm)],[f_2412_1]) ).
cnf(f_2412_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8396),hAPP(c_Finite__Set_Ofold1(U_8396,c_Orderings_Oord__class_Omin(U_8396)),U_8398)),hAPP(c_Finite__Set_Ofold1(U_8396,c_Orderings_Oord__class_Omin(U_8396)),U_8397)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8396),U_8398))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8396,tc_HOL_Obool)),U_8397),U_8398))
| U_8397 = c_Orderings_Obot__class_Obot(tc_fun(U_8396,tc_HOL_Obool))
| ~ class_Orderings_Olinorder(U_8396) ),
inference(clausify,[status(thm)],[f_2412_2]) ).
fof(f_2413_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_2413_2,plain,
! [U_8399] :
( c_Finite__Set_Ofun__left__comm__idem(U_8399,U_8399,c_Orderings_Oord__class_Omin(U_8399))
| ~ class_Orderings_Olinorder(U_8399) ),
inference(variable_rename,[status(thm)],[f_2413_1]) ).
cnf(f_2413_3,plain,
( c_Finite__Set_Ofun__left__comm__idem(U_8399,U_8399,c_Orderings_Oord__class_Omin(U_8399))
| ~ class_Orderings_Olinorder(U_8399) ),
inference(clausify,[status(thm)],[f_2413_2]) ).
fof(f_2414_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_2414_2,plain,
! [U_8400] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_8400) = c_Orderings_Oord__class_Omin(U_8400)
| ~ class_Orderings_Olinorder(U_8400)
| ~ class_Lattices_Osemilattice__inf(U_8400) ),
inference(variable_rename,[status(thm)],[f_2414_1]) ).
cnf(f_2414_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_8400) = c_Orderings_Oord__class_Omin(U_8400)
| ~ class_Orderings_Olinorder(U_8400)
| ~ class_Lattices_Osemilattice__inf(U_8400) ),
inference(clausify,[status(thm)],[f_2414_2]) ).
fof(f_2415_1,plain,
! [V_n_2,V_m_2,V_f_2,T_b,T_c] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,V_n_2)) = hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_m_2),V_n_2))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__of__mono]) ).
fof(f_2415_2,plain,
! [U_8405,U_8404,U_8403,U_8402,U_8401] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8401),hAPP(U_8403,U_8404)),hAPP(U_8403,U_8405)) = hAPP(U_8403,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8402),U_8404),U_8405))
| ~ c_Orderings_Oorder__class_Omono(U_8402,U_8401,U_8403)
| ~ class_Orderings_Olinorder(U_8402)
| ~ class_Orderings_Olinorder(U_8401) ),
inference(variable_rename,[status(thm)],[f_2415_1]) ).
cnf(f_2415_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8401),hAPP(U_8403,U_8404)),hAPP(U_8403,U_8405)) = hAPP(U_8403,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8402),U_8404),U_8405))
| ~ c_Orderings_Oorder__class_Omono(U_8402,U_8401,U_8403)
| ~ class_Orderings_Olinorder(U_8402)
| ~ class_Orderings_Olinorder(U_8401) ),
inference(clausify,[status(thm)],[f_2415_2]) ).
fof(f_2416_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_2416_2,plain,
! [U_8406] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_8406),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_2416_1]) ).
cnf(f_2416_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_8406),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_2416_2]) ).
fof(f_2417_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_2417_2,plain,
! [U_8407] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8407) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_2417_1]) ).
cnf(f_2417_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8407) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_2417_2]) ).
fof(f_2418_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_2418_2,plain,
! [U_8409,U_8408] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8408),U_8409),U_8409) = U_8409
| ~ class_Orderings_Olinorder(U_8408) ),
inference(variable_rename,[status(thm)],[f_2418_1]) ).
cnf(f_2418_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8408),U_8409),U_8409) = U_8409
| ~ class_Orderings_Olinorder(U_8408) ),
inference(clausify,[status(thm)],[f_2418_2]) ).
fof(f_2419_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_2419_2,plain,
! [U_8412,U_8411,U_8410] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8410),U_8411),U_8412) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8410),U_8412),U_8411)
| ~ class_Orderings_Olinorder(U_8410) ),
inference(variable_rename,[status(thm)],[f_2419_1]) ).
cnf(f_2419_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8410),U_8411),U_8412) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8410),U_8412),U_8411)
| ~ class_Orderings_Olinorder(U_8410) ),
inference(clausify,[status(thm)],[f_2419_2]) ).
fof(f_2420_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_2420_2,plain,
! [U_8415,U_8414,U_8413] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8413),U_8414),U_8415) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8413),U_8415),U_8414)
| ~ class_Orderings_Olinorder(U_8413) ),
inference(variable_rename,[status(thm)],[f_2420_1]) ).
cnf(f_2420_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8413),U_8414),U_8415) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8413),U_8415),U_8414)
| ~ class_Orderings_Olinorder(U_8413) ),
inference(clausify,[status(thm)],[f_2420_2]) ).
fof(f_2421_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_2421_2,plain,
! [U_8418,U_8417,U_8416] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8416),U_8417),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8416),U_8417),U_8418)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8416),U_8417),U_8418)
| ~ class_Orderings_Olinorder(U_8416) ),
inference(variable_rename,[status(thm)],[f_2421_1]) ).
cnf(f_2421_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8416),U_8417),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8416),U_8417),U_8418)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8416),U_8417),U_8418)
| ~ class_Orderings_Olinorder(U_8416) ),
inference(clausify,[status(thm)],[f_2421_2]) ).
fof(f_2422_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_2422_2,plain,
! [U_8421,U_8420,U_8419] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8419),U_8420),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8419),U_8420),U_8421)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8419),U_8420),U_8421)
| ~ class_Orderings_Olinorder(U_8419) ),
inference(variable_rename,[status(thm)],[f_2422_1]) ).
cnf(f_2422_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8419),U_8420),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8419),U_8420),U_8421)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8419),U_8420),U_8421)
| ~ class_Orderings_Olinorder(U_8419) ),
inference(clausify,[status(thm)],[f_2422_2]) ).
fof(f_2423_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_2423_2,plain,
! [U_8425,U_8424,U_8423,U_8422] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8422),U_8423),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8422),U_8424),U_8425)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8422),U_8424),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8422),U_8423),U_8425))
| ~ class_Orderings_Olinorder(U_8422) ),
inference(variable_rename,[status(thm)],[f_2423_1]) ).
cnf(f_2423_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8422),U_8423),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8422),U_8424),U_8425)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8422),U_8424),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8422),U_8423),U_8425))
| ~ class_Orderings_Olinorder(U_8422) ),
inference(clausify,[status(thm)],[f_2423_2]) ).
fof(f_2424_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_2424_2,plain,
! [U_8429,U_8428,U_8427,U_8426] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8426),U_8427),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8426),U_8428),U_8429)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8426),U_8428),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8426),U_8427),U_8429))
| ~ class_Orderings_Olinorder(U_8426) ),
inference(variable_rename,[status(thm)],[f_2424_1]) ).
cnf(f_2424_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8426),U_8427),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8426),U_8428),U_8429)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8426),U_8428),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8426),U_8427),U_8429))
| ~ class_Orderings_Olinorder(U_8426) ),
inference(clausify,[status(thm)],[f_2424_2]) ).
fof(f_2425_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_2425_2,plain,
! [U_8433,U_8432,U_8431,U_8430] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8430),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8430),U_8431),U_8432)),U_8433) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8430),U_8431),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8430),U_8432),U_8433))
| ~ class_Orderings_Olinorder(U_8430) ),
inference(variable_rename,[status(thm)],[f_2425_1]) ).
cnf(f_2425_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8430),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8430),U_8431),U_8432)),U_8433) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8430),U_8431),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8430),U_8432),U_8433))
| ~ class_Orderings_Olinorder(U_8430) ),
inference(clausify,[status(thm)],[f_2425_2]) ).
fof(f_2426_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_2426_2,plain,
! [U_8437,U_8436,U_8435,U_8434] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8434),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8434),U_8435),U_8436)),U_8437) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8434),U_8435),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8434),U_8436),U_8437))
| ~ class_Orderings_Olinorder(U_8434) ),
inference(variable_rename,[status(thm)],[f_2426_1]) ).
cnf(f_2426_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8434),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8434),U_8435),U_8436)),U_8437) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8434),U_8435),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8434),U_8436),U_8437))
| ~ class_Orderings_Olinorder(U_8434) ),
inference(clausify,[status(thm)],[f_2426_2]) ).
fof(f_2427_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_2427_2,plain,
! [U_8439,U_8438] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8438),U_8439),U_8439) = U_8439
| ~ class_Orderings_Olinorder(U_8438) ),
inference(variable_rename,[status(thm)],[f_2427_1]) ).
cnf(f_2427_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8438),U_8439),U_8439) = U_8439
| ~ class_Orderings_Olinorder(U_8438) ),
inference(clausify,[status(thm)],[f_2427_2]) ).
fof(f_2428_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_2428_2,plain,
! [U_8443,U_8442,U_8441,U_8440] : c_Nitpick_Ofold__graph_H(U_8440,U_8441,U_8442,U_8443,c_Orderings_Obot__class_Obot(tc_fun(U_8440,tc_HOL_Obool)),U_8443),
inference(variable_rename,[status(thm)],[f_2428_1]) ).
cnf(f_2428_3,plain,
c_Nitpick_Ofold__graph_H(U_8440,U_8441,U_8442,U_8443,c_Orderings_Obot__class_Obot(tc_fun(U_8440,tc_HOL_Obool)),U_8443),
inference(clausify,[status(thm)],[f_2428_2]) ).
fof(f_2429_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_2429_2,plain,
! [U_8447,U_8446,U_8445,U_8444] : c_Nitpick_Ofold__graph_H(U_8444,U_8445,U_8446,U_8447,c_Orderings_Obot__class_Obot(tc_fun(U_8444,tc_HOL_Obool)),U_8447),
inference(variable_rename,[status(thm)],[f_2429_1]) ).
cnf(f_2429_3,plain,
c_Nitpick_Ofold__graph_H(U_8444,U_8445,U_8446,U_8447,c_Orderings_Obot__class_Obot(tc_fun(U_8444,tc_HOL_Obool)),U_8447),
inference(clausify,[status(thm)],[f_2429_2]) ).
fof(f_2430_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_2430_2,plain,
! [U_8451,U_8450,U_8449,U_8448] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8448),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8448),U_8449),U_8450)),U_8451) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8448),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8448),U_8449),U_8451)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8448),U_8450),U_8451))
| ~ class_Groups_Oordered__ab__group__add(U_8448) ),
inference(variable_rename,[status(thm)],[f_2430_1]) ).
cnf(f_2430_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8448),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8448),U_8449),U_8450)),U_8451) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8448),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8448),U_8449),U_8451)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8448),U_8450),U_8451))
| ~ class_Groups_Oordered__ab__group__add(U_8448) ),
inference(clausify,[status(thm)],[f_2430_2]) ).
fof(f_2431_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_2431_2,plain,
! [U_8454,U_8453,U_8452] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8452),U_8453)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8454),U_8453)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_8452),U_8454)),U_8453),
inference(variable_rename,[status(thm)],[f_2431_1]) ).
cnf(f_2431_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8452),U_8453)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8454),U_8453)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_8452),U_8454)),U_8453),
inference(clausify,[status(thm)],[f_2431_2]) ).
fof(f_2432_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_2432_2,plain,
! [U_8456,U_8455] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8455)),hAPP(c_Nat_OSuc,U_8456)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_8455),U_8456)),
inference(variable_rename,[status(thm)],[f_2432_1]) ).
cnf(f_2432_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8455)),hAPP(c_Nat_OSuc,U_8456)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_8455),U_8456)),
inference(clausify,[status(thm)],[f_2432_2]) ).
fof(f_2433_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_2433_2,plain,
! [U_8460,U_8459,U_8458,U_8457] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8457),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8457),U_8458),U_8459)),U_8460))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8457),U_8459),U_8460))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8457),U_8458),U_8460)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8457),U_8459),U_8460))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8457),U_8458),U_8460))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8457),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8457),U_8458),U_8459)),U_8460)) ) )
| ~ class_Orderings_Olinorder(U_8457) ),
inference(variable_rename,[status(thm)],[f_2433_1]) ).
cnf(f_2433_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8457),U_8459),U_8460))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8457),U_8458),U_8460))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8457),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8457),U_8458),U_8459)),U_8460))
| ~ class_Orderings_Olinorder(U_8457) ),
inference(clausify,[status(thm)],[f_2433_2]) ).
cnf(f_2433_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8457),U_8458),U_8460))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8457),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8457),U_8458),U_8459)),U_8460))
| ~ class_Orderings_Olinorder(U_8457) ),
inference(clausify,[status(thm)],[f_2433_2]) ).
cnf(f_2433_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8457),U_8459),U_8460))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8457),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8457),U_8458),U_8459)),U_8460))
| ~ class_Orderings_Olinorder(U_8457) ),
inference(clausify,[status(thm)],[f_2433_2]) ).
fof(f_2434_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_2434_2,plain,
! [U_8463,U_8462,U_8461] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8461),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8461),U_8462),U_8463)),U_8462))
| ~ class_Orderings_Olinorder(U_8461) ),
inference(variable_rename,[status(thm)],[f_2434_1]) ).
cnf(f_2434_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8461),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8461),U_8462),U_8463)),U_8462))
| ~ class_Orderings_Olinorder(U_8461) ),
inference(clausify,[status(thm)],[f_2434_2]) ).
fof(f_2435_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_2435_2,plain,
! [U_8466,U_8465,U_8464] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8464),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8464),U_8465),U_8466)),U_8466))
| ~ class_Orderings_Olinorder(U_8464) ),
inference(variable_rename,[status(thm)],[f_2435_1]) ).
cnf(f_2435_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8464),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8464),U_8465),U_8466)),U_8466))
| ~ class_Orderings_Olinorder(U_8464) ),
inference(clausify,[status(thm)],[f_2435_2]) ).
fof(f_2436_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_2436_2,plain,
! [U_8469,U_8468,U_8467] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8467),U_8468),U_8469))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8467),U_8468),U_8469) != U_8468 )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8467),U_8468),U_8469) = U_8468
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8467),U_8468),U_8469)) ) )
| ~ class_Orderings_Olinorder(U_8467) ),
inference(variable_rename,[status(thm)],[f_2436_1]) ).
cnf(f_2436_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8467),U_8468),U_8469) = U_8468
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8467),U_8468),U_8469))
| ~ class_Orderings_Olinorder(U_8467) ),
inference(clausify,[status(thm)],[f_2436_2]) ).
cnf(f_2436_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8467),U_8468),U_8469))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8467),U_8468),U_8469) != U_8468
| ~ class_Orderings_Olinorder(U_8467) ),
inference(clausify,[status(thm)],[f_2436_2]) ).
fof(f_2437_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_2437_2,plain,
! [U_8473,U_8472,U_8471,U_8470] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8470),U_8471),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8470),U_8472),U_8473)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8470),U_8471),U_8473))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8470),U_8471),U_8472)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8470),U_8471),U_8473))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8470),U_8471),U_8472)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8470),U_8471),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8470),U_8472),U_8473))) ) )
| ~ class_Orderings_Olinorder(U_8470) ),
inference(variable_rename,[status(thm)],[f_2437_1]) ).
cnf(f_2437_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8470),U_8471),U_8472))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8470),U_8471),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8470),U_8472),U_8473)))
| ~ class_Orderings_Olinorder(U_8470) ),
inference(clausify,[status(thm)],[f_2437_2]) ).
cnf(f_2437_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8470),U_8471),U_8473))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8470),U_8471),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8470),U_8472),U_8473)))
| ~ class_Orderings_Olinorder(U_8470) ),
inference(clausify,[status(thm)],[f_2437_2]) ).
cnf(f_2437_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8470),U_8471),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8470),U_8472),U_8473)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8470),U_8471),U_8473))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8470),U_8471),U_8472))
| ~ class_Orderings_Olinorder(U_8470) ),
inference(clausify,[status(thm)],[f_2437_2]) ).
fof(f_2438_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_2438_2,plain,
! [U_8477,U_8476,U_8475,U_8474] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8474),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8474),U_8475),U_8477)),U_8476))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8474),U_8475),U_8476))
| ~ class_Orderings_Olinorder(U_8474) ),
inference(variable_rename,[status(thm)],[f_2438_1]) ).
cnf(f_2438_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8474),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8474),U_8475),U_8477)),U_8476))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8474),U_8475),U_8476))
| ~ class_Orderings_Olinorder(U_8474) ),
inference(clausify,[status(thm)],[f_2438_2]) ).
fof(f_2439_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_2439_2,plain,
! [U_8481,U_8480,U_8479,U_8478] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8478),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8478),U_8481),U_8479)),U_8480))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8478),U_8479),U_8480))
| ~ class_Orderings_Olinorder(U_8478) ),
inference(variable_rename,[status(thm)],[f_2439_1]) ).
cnf(f_2439_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8478),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8478),U_8481),U_8479)),U_8480))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8478),U_8479),U_8480))
| ~ class_Orderings_Olinorder(U_8478) ),
inference(clausify,[status(thm)],[f_2439_2]) ).
fof(f_2440_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_2440_2,plain,
! [U_8484,U_8483,U_8482] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8482),U_8483),U_8484) = U_8483
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8482),U_8483),U_8484))
| ~ class_Orderings_Olinorder(U_8482) ),
inference(variable_rename,[status(thm)],[f_2440_1]) ).
cnf(f_2440_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8482),U_8483),U_8484) = U_8483
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8482),U_8483),U_8484))
| ~ class_Orderings_Olinorder(U_8482) ),
inference(clausify,[status(thm)],[f_2440_2]) ).
fof(f_2441_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_2441_2,plain,
! [U_8487,U_8486,U_8485] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8485),U_8487),U_8486) = U_8486
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8485),U_8486),U_8487))
| ~ class_Orderings_Olinorder(U_8485) ),
inference(variable_rename,[status(thm)],[f_2441_1]) ).
cnf(f_2441_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8485),U_8487),U_8486) = U_8486
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8485),U_8486),U_8487))
| ~ class_Orderings_Olinorder(U_8485) ),
inference(clausify,[status(thm)],[f_2441_2]) ).
fof(f_2442_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_2442_2,plain,
! [U_8491,U_8490,U_8489,U_8488] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8488),U_8489),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8488),U_8490),U_8491)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8488),U_8489),U_8491))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8488),U_8489),U_8490))
| ~ class_Orderings_Olinorder(U_8488) ),
inference(variable_rename,[status(thm)],[f_2442_1]) ).
cnf(f_2442_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8488),U_8489),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8488),U_8490),U_8491)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8488),U_8489),U_8491))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8488),U_8489),U_8490))
| ~ class_Orderings_Olinorder(U_8488) ),
inference(clausify,[status(thm)],[f_2442_2]) ).
fof(f_2443_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_2443_2,plain,
! [U_8495,U_8494,U_8493,U_8492] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8492),U_8493),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8492),U_8494),U_8495)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8492),U_8493),U_8495))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8492),U_8493),U_8494))
| ~ class_Orderings_Olinorder(U_8492) ),
inference(variable_rename,[status(thm)],[f_2443_1]) ).
cnf(f_2443_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8492),U_8493),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8492),U_8494),U_8495)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8492),U_8493),U_8495))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8492),U_8493),U_8494))
| ~ class_Orderings_Olinorder(U_8492) ),
inference(clausify,[status(thm)],[f_2443_2]) ).
fof(f_2444_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_2444_2,plain,
! [U_8500,U_8499,U_8498,U_8497,U_8496] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8496),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8496),U_8497),U_8499)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8496),U_8498),U_8500)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8496),U_8499),U_8500))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8496),U_8497),U_8498))
| ~ class_Orderings_Olinorder(U_8496) ),
inference(variable_rename,[status(thm)],[f_2444_1]) ).
cnf(f_2444_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8496),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8496),U_8497),U_8499)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8496),U_8498),U_8500)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8496),U_8499),U_8500))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8496),U_8497),U_8498))
| ~ class_Orderings_Olinorder(U_8496) ),
inference(clausify,[status(thm)],[f_2444_2]) ).
fof(f_2445_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_2445_2,plain,
! [U_8504,U_8503,U_8502,U_8501] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8501),U_8502),U_8504))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8501),U_8502),U_8503)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8501),U_8502),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8501),U_8503),U_8504)))
| ~ class_Orderings_Olinorder(U_8501) ),
inference(variable_rename,[status(thm)],[f_2445_1]) ).
cnf(f_2445_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8501),U_8502),U_8503))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8501),U_8502),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8501),U_8503),U_8504)))
| ~ class_Orderings_Olinorder(U_8501) ),
inference(clausify,[status(thm)],[f_2445_2]) ).
cnf(f_2445_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8501),U_8502),U_8504))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8501),U_8502),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8501),U_8503),U_8504)))
| ~ class_Orderings_Olinorder(U_8501) ),
inference(clausify,[status(thm)],[f_2445_2]) ).
fof(f_2446_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_2446_2,plain,
! [U_8508,U_8507,U_8506,U_8505] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8505),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8505),U_8506),U_8508)),U_8507))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8505),U_8506),U_8507))
| ~ class_Orderings_Olinorder(U_8505) ),
inference(variable_rename,[status(thm)],[f_2446_1]) ).
cnf(f_2446_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8505),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8505),U_8506),U_8508)),U_8507))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8505),U_8506),U_8507))
| ~ class_Orderings_Olinorder(U_8505) ),
inference(clausify,[status(thm)],[f_2446_2]) ).
fof(f_2447_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_2447_2,plain,
! [U_8512,U_8511,U_8510,U_8509] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8509),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8509),U_8512),U_8510)),U_8511))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8509),U_8510),U_8511))
| ~ class_Orderings_Olinorder(U_8509) ),
inference(variable_rename,[status(thm)],[f_2447_1]) ).
cnf(f_2447_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8509),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8509),U_8512),U_8510)),U_8511))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8509),U_8510),U_8511))
| ~ class_Orderings_Olinorder(U_8509) ),
inference(clausify,[status(thm)],[f_2447_2]) ).
fof(f_2448_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_2448_2,plain,
! [U_8516,U_8515,U_8514,U_8513] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8513),U_8514),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8513),U_8515),U_8516)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8513),U_8514),U_8516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8513),U_8514),U_8515)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8513),U_8514),U_8516))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8513),U_8514),U_8515)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8513),U_8514),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8513),U_8515),U_8516))) ) )
| ~ class_Orderings_Olinorder(U_8513) ),
inference(variable_rename,[status(thm)],[f_2448_1]) ).
cnf(f_2448_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8513),U_8514),U_8515))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8513),U_8514),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8513),U_8515),U_8516)))
| ~ class_Orderings_Olinorder(U_8513) ),
inference(clausify,[status(thm)],[f_2448_2]) ).
cnf(f_2448_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8513),U_8514),U_8516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8513),U_8514),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8513),U_8515),U_8516)))
| ~ class_Orderings_Olinorder(U_8513) ),
inference(clausify,[status(thm)],[f_2448_2]) ).
cnf(f_2448_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8513),U_8514),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8513),U_8515),U_8516)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8513),U_8514),U_8516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8513),U_8514),U_8515))
| ~ class_Orderings_Olinorder(U_8513) ),
inference(clausify,[status(thm)],[f_2448_2]) ).
fof(f_2449_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_2449_2,plain,
! [U_8520,U_8519,U_8518,U_8517] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8517),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8517),U_8518),U_8519)),U_8520))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8517),U_8519),U_8520))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8517),U_8518),U_8520)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8517),U_8519),U_8520))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8517),U_8518),U_8520))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8517),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8517),U_8518),U_8519)),U_8520)) ) )
| ~ class_Orderings_Olinorder(U_8517) ),
inference(variable_rename,[status(thm)],[f_2449_1]) ).
cnf(f_2449_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8517),U_8519),U_8520))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8517),U_8518),U_8520))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8517),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8517),U_8518),U_8519)),U_8520))
| ~ class_Orderings_Olinorder(U_8517) ),
inference(clausify,[status(thm)],[f_2449_2]) ).
cnf(f_2449_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8517),U_8518),U_8520))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8517),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8517),U_8518),U_8519)),U_8520))
| ~ class_Orderings_Olinorder(U_8517) ),
inference(clausify,[status(thm)],[f_2449_2]) ).
cnf(f_2449_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8517),U_8519),U_8520))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8517),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8517),U_8518),U_8519)),U_8520))
| ~ class_Orderings_Olinorder(U_8517) ),
inference(clausify,[status(thm)],[f_2449_2]) ).
fof(f_2450_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_2450_2,plain,
! [U_8524,U_8523,U_8522,U_8521] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8521),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8521),U_8522),U_8523)),U_8524) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8521),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8521),U_8522),U_8524)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8521),U_8523),U_8524))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_8521) ),
inference(variable_rename,[status(thm)],[f_2450_1]) ).
cnf(f_2450_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8521),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8521),U_8522),U_8523)),U_8524) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8521),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8521),U_8522),U_8524)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8521),U_8523),U_8524))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_8521) ),
inference(clausify,[status(thm)],[f_2450_2]) ).
fof(f_2451_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_2451_2,plain,
! [U_8527,U_8526,U_8525] :
( ( ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8525),hAPP(c_Int_Onumber__class_Onumber__of(U_8525),U_8526)),hAPP(c_Int_Onumber__class_Onumber__of(U_8525),U_8527)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8525),U_8527)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8525),hAPP(c_Int_Onumber__class_Onumber__of(U_8525),U_8526)),hAPP(c_Int_Onumber__class_Onumber__of(U_8525),U_8527))) )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8525),hAPP(c_Int_Onumber__class_Onumber__of(U_8525),U_8526)),hAPP(c_Int_Onumber__class_Onumber__of(U_8525),U_8527)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8525),U_8526)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8525),hAPP(c_Int_Onumber__class_Onumber__of(U_8525),U_8526)),hAPP(c_Int_Onumber__class_Onumber__of(U_8525),U_8527))) ) )
| ~ class_Orderings_Oord(U_8525)
| ~ class_Int_Onumber(U_8525) ),
inference(variable_rename,[status(thm)],[f_2451_1]) ).
cnf(f_2451_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8525),hAPP(c_Int_Onumber__class_Onumber__of(U_8525),U_8526)),hAPP(c_Int_Onumber__class_Onumber__of(U_8525),U_8527)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8525),U_8526)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8525),hAPP(c_Int_Onumber__class_Onumber__of(U_8525),U_8526)),hAPP(c_Int_Onumber__class_Onumber__of(U_8525),U_8527)))
| ~ class_Orderings_Oord(U_8525)
| ~ class_Int_Onumber(U_8525) ),
inference(clausify,[status(thm)],[f_2451_2]) ).
cnf(f_2451_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8525),hAPP(c_Int_Onumber__class_Onumber__of(U_8525),U_8526)),hAPP(c_Int_Onumber__class_Onumber__of(U_8525),U_8527)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8525),U_8527)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8525),hAPP(c_Int_Onumber__class_Onumber__of(U_8525),U_8526)),hAPP(c_Int_Onumber__class_Onumber__of(U_8525),U_8527)))
| ~ class_Orderings_Oord(U_8525)
| ~ class_Int_Onumber(U_8525) ),
inference(clausify,[status(thm)],[f_2451_2]) ).
fof(f_2452_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_2452_2,plain,
! [U_8531,U_8530,U_8529,U_8528] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_8528,U_8528,c_Orderings_Oord__class_Omin(U_8528)),U_8530),hAPP(hAPP(c_Set_Oinsert(U_8528),U_8531),U_8529)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8528),U_8531),hAPP(hAPP(c_Finite__Set_Ofold(U_8528,U_8528,c_Orderings_Oord__class_Omin(U_8528)),U_8530),U_8529))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8528),U_8529))
| ~ class_Orderings_Olinorder(U_8528) ),
inference(variable_rename,[status(thm)],[f_2452_1]) ).
cnf(f_2452_3,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_8528,U_8528,c_Orderings_Oord__class_Omin(U_8528)),U_8530),hAPP(hAPP(c_Set_Oinsert(U_8528),U_8531),U_8529)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8528),U_8531),hAPP(hAPP(c_Finite__Set_Ofold(U_8528,U_8528,c_Orderings_Oord__class_Omin(U_8528)),U_8530),U_8529))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8528),U_8529))
| ~ class_Orderings_Olinorder(U_8528) ),
inference(clausify,[status(thm)],[f_2452_2]) ).
fof(f_2453_1,plain,
! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Lattices_Osemilattice__inf(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Omono__inf]) ).
fof(f_2453_2,plain,
! [U_8536,U_8535,U_8534,U_8533,U_8532] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8532),hAPP(U_8534,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8533),U_8535),U_8536))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_8532),hAPP(U_8534,U_8535)),hAPP(U_8534,U_8536))))
| ~ c_Orderings_Oorder__class_Omono(U_8533,U_8532,U_8534)
| ~ class_Orderings_Olinorder(U_8533)
| ~ class_Lattices_Osemilattice__inf(U_8532) ),
inference(variable_rename,[status(thm)],[f_2453_1]) ).
cnf(f_2453_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8532),hAPP(U_8534,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8533),U_8535),U_8536))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_8532),hAPP(U_8534,U_8535)),hAPP(U_8534,U_8536))))
| ~ c_Orderings_Oorder__class_Omono(U_8533,U_8532,U_8534)
| ~ class_Orderings_Olinorder(U_8533)
| ~ class_Lattices_Osemilattice__inf(U_8532) ),
inference(clausify,[status(thm)],[f_2453_2]) ).
fof(f_2454_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_2454_2,plain,
! [U_8540,U_8539,U_8538,U_8537] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8537,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8537,U_8538,U_8539)),hAPP(c_SetInterval_Oord__class_OatMost(U_8537),U_8540)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8537,U_8538,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8537),U_8539),U_8540))
| ~ class_Orderings_Olinorder(U_8537) ),
inference(variable_rename,[status(thm)],[f_2454_1]) ).
cnf(f_2454_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8537,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8537,U_8538,U_8539)),hAPP(c_SetInterval_Oord__class_OatMost(U_8537),U_8540)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8537,U_8538,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8537),U_8539),U_8540))
| ~ class_Orderings_Olinorder(U_8537) ),
inference(clausify,[status(thm)],[f_2454_2]) ).
fof(f_2455_1,plain,
! [V_d_2,V_c_2,V_b_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR1]) ).
fof(f_2455_2,plain,
! [U_8544,U_8543,U_8542,U_8541] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8541,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8541),U_8542)),c_SetInterval_Oord__class_OatLeastAtMost(U_8541,U_8543,U_8544)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8541,U_8543,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8541),U_8542),U_8544))
| ~ class_Orderings_Olinorder(U_8541) ),
inference(variable_rename,[status(thm)],[f_2455_1]) ).
cnf(f_2455_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8541,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8541),U_8542)),c_SetInterval_Oord__class_OatLeastAtMost(U_8541,U_8543,U_8544)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8541,U_8543,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8541),U_8542),U_8544))
| ~ class_Orderings_Olinorder(U_8541) ),
inference(clausify,[status(thm)],[f_2455_2]) ).
fof(f_2456_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_2456_2,plain,
! [U_8548,U_8547,U_8546,U_8545] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8545),hAPP(hAPP(c_Finite__Set_Ofold(U_8545,U_8545,c_Orderings_Oord__class_Omin(U_8545)),U_8548),U_8546)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8545),U_8547),U_8548)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8545),U_8547),U_8546))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8545),U_8546))
| ~ class_Orderings_Olinorder(U_8545) ),
inference(variable_rename,[status(thm)],[f_2456_1]) ).
cnf(f_2456_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8545),hAPP(hAPP(c_Finite__Set_Ofold(U_8545,U_8545,c_Orderings_Oord__class_Omin(U_8545)),U_8548),U_8546)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8545),U_8547),U_8548)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8545),U_8547),U_8546))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8545),U_8546))
| ~ class_Orderings_Olinorder(U_8545) ),
inference(clausify,[status(thm)],[f_2456_2]) ).
fof(f_2457_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_2457_2,plain,
! [U_8551,U_8550,U_8549] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8549),hAPP(c_Finite__Set_Ofold1(U_8549,c_Orderings_Oord__class_Omin(U_8549)),U_8550)),U_8551))
| ~ hBOOL(hAPP(hAPP(c_member(U_8549),U_8551),U_8550))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8549),U_8550))
| ~ class_Orderings_Olinorder(U_8549) ),
inference(variable_rename,[status(thm)],[f_2457_1]) ).
cnf(f_2457_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8549),hAPP(c_Finite__Set_Ofold1(U_8549,c_Orderings_Oord__class_Omin(U_8549)),U_8550)),U_8551))
| ~ hBOOL(hAPP(hAPP(c_member(U_8549),U_8551),U_8550))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8549),U_8550))
| ~ class_Orderings_Olinorder(U_8549) ),
inference(clausify,[status(thm)],[f_2457_2]) ).
fof(f_2458_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_2458_2,plain,
! [U_8556,U_8555,U_8554] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8554),U_8556),hAPP(c_Finite__Set_Ofold1(U_8554,c_Orderings_Oord__class_Omin(U_8554)),U_8555)))
| ? [U_8553] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8554),U_8556),U_8553))
& hBOOL(hAPP(hAPP(c_member(U_8554),U_8553),U_8555)) ) )
& ( ! [U_8552] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8554),U_8556),U_8552))
| ~ hBOOL(hAPP(hAPP(c_member(U_8554),U_8552),U_8555)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8554),U_8556),hAPP(c_Finite__Set_Ofold1(U_8554,c_Orderings_Oord__class_Omin(U_8554)),U_8555))) ) )
| U_8555 = c_Orderings_Obot__class_Obot(tc_fun(U_8554,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8554),U_8555))
| ~ class_Orderings_Olinorder(U_8554) ),
inference(variable_rename,[status(thm)],[f_2458_1]) ).
fof(f_2458_3,plain,
! [U_8556,U_8555,U_8554] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8554),U_8556),hAPP(c_Finite__Set_Ofold1(U_8554,c_Orderings_Oord__class_Omin(U_8554)),U_8555)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8554),U_8556),sK209(U_8556,U_8555,U_8554)))
& hBOOL(hAPP(hAPP(c_member(U_8554),sK209(U_8556,U_8555,U_8554)),U_8555)) ) )
& ( ! [U_8552] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8554),U_8556),U_8552))
| ~ hBOOL(hAPP(hAPP(c_member(U_8554),U_8552),U_8555)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8554),U_8556),hAPP(c_Finite__Set_Ofold1(U_8554,c_Orderings_Oord__class_Omin(U_8554)),U_8555))) ) )
| U_8555 = c_Orderings_Obot__class_Obot(tc_fun(U_8554,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8554),U_8555))
| ~ class_Orderings_Olinorder(U_8554) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK209]),skolemize(U_8553,sK209(U_8556,U_8555,U_8554))],[f_2458_2]) ).
cnf(f_2458_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8554),U_8556),U_8552))
| ~ hBOOL(hAPP(hAPP(c_member(U_8554),U_8552),U_8555))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8554),U_8556),hAPP(c_Finite__Set_Ofold1(U_8554,c_Orderings_Oord__class_Omin(U_8554)),U_8555)))
| U_8555 = c_Orderings_Obot__class_Obot(tc_fun(U_8554,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8554),U_8555))
| ~ class_Orderings_Olinorder(U_8554) ),
inference(clausify,[status(thm)],[f_2458_3]) ).
cnf(f_2458_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_8554),sK209(U_8556,U_8555,U_8554)),U_8555))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8554),U_8556),hAPP(c_Finite__Set_Ofold1(U_8554,c_Orderings_Oord__class_Omin(U_8554)),U_8555)))
| U_8555 = c_Orderings_Obot__class_Obot(tc_fun(U_8554,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8554),U_8555))
| ~ class_Orderings_Olinorder(U_8554) ),
inference(clausify,[status(thm)],[f_2458_3]) ).
cnf(f_2458_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8554),U_8556),sK209(U_8556,U_8555,U_8554)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8554),U_8556),hAPP(c_Finite__Set_Ofold1(U_8554,c_Orderings_Oord__class_Omin(U_8554)),U_8555)))
| U_8555 = c_Orderings_Obot__class_Obot(tc_fun(U_8554,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8554),U_8555))
| ~ class_Orderings_Olinorder(U_8554) ),
inference(clausify,[status(thm)],[f_2458_3]) ).
fof(f_2459_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_2459_2,plain,
! [U_8561,U_8560,U_8559] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8559),hAPP(c_Finite__Set_Ofold1(U_8559,c_Orderings_Oord__class_Omin(U_8559)),U_8560)),U_8561))
| ! [U_8558] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8559),U_8558),U_8561))
| ~ hBOOL(hAPP(hAPP(c_member(U_8559),U_8558),U_8560)) ) )
& ( ? [U_8557] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8559),U_8557),U_8561))
& hBOOL(hAPP(hAPP(c_member(U_8559),U_8557),U_8560)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8559),hAPP(c_Finite__Set_Ofold1(U_8559,c_Orderings_Oord__class_Omin(U_8559)),U_8560)),U_8561)) ) )
| U_8560 = c_Orderings_Obot__class_Obot(tc_fun(U_8559,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8559),U_8560))
| ~ class_Orderings_Olinorder(U_8559) ),
inference(variable_rename,[status(thm)],[f_2459_1]) ).
fof(f_2459_3,plain,
! [U_8561,U_8560,U_8559] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8559),hAPP(c_Finite__Set_Ofold1(U_8559,c_Orderings_Oord__class_Omin(U_8559)),U_8560)),U_8561))
| ! [U_8558] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8559),U_8558),U_8561))
| ~ hBOOL(hAPP(hAPP(c_member(U_8559),U_8558),U_8560)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8559),sK210(U_8561,U_8560,U_8559)),U_8561))
& hBOOL(hAPP(hAPP(c_member(U_8559),sK210(U_8561,U_8560,U_8559)),U_8560)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8559),hAPP(c_Finite__Set_Ofold1(U_8559,c_Orderings_Oord__class_Omin(U_8559)),U_8560)),U_8561)) ) )
| U_8560 = c_Orderings_Obot__class_Obot(tc_fun(U_8559,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8559),U_8560))
| ~ class_Orderings_Olinorder(U_8559) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK210]),skolemize(U_8557,sK210(U_8561,U_8560,U_8559))],[f_2459_2]) ).
cnf(f_2459_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8559),sK210(U_8561,U_8560,U_8559)),U_8560))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8559),hAPP(c_Finite__Set_Ofold1(U_8559,c_Orderings_Oord__class_Omin(U_8559)),U_8560)),U_8561))
| U_8560 = c_Orderings_Obot__class_Obot(tc_fun(U_8559,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8559),U_8560))
| ~ class_Orderings_Olinorder(U_8559) ),
inference(clausify,[status(thm)],[f_2459_3]) ).
cnf(f_2459_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8559),sK210(U_8561,U_8560,U_8559)),U_8561))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8559),hAPP(c_Finite__Set_Ofold1(U_8559,c_Orderings_Oord__class_Omin(U_8559)),U_8560)),U_8561))
| U_8560 = c_Orderings_Obot__class_Obot(tc_fun(U_8559,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8559),U_8560))
| ~ class_Orderings_Olinorder(U_8559) ),
inference(clausify,[status(thm)],[f_2459_3]) ).
cnf(f_2459_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8559),hAPP(c_Finite__Set_Ofold1(U_8559,c_Orderings_Oord__class_Omin(U_8559)),U_8560)),U_8561))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8559),U_8558),U_8561))
| ~ hBOOL(hAPP(hAPP(c_member(U_8559),U_8558),U_8560))
| U_8560 = c_Orderings_Obot__class_Obot(tc_fun(U_8559,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8559),U_8560))
| ~ class_Orderings_Olinorder(U_8559) ),
inference(clausify,[status(thm)],[f_2459_3]) ).
fof(f_2460_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_2460_2,plain,
! [U_8566,U_8565,U_8564] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8564),hAPP(c_Finite__Set_Ofold1(U_8564,c_Orderings_Oord__class_Omin(U_8564)),U_8565)),U_8566))
| ! [U_8563] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8564),U_8563),U_8566))
| ~ hBOOL(hAPP(hAPP(c_member(U_8564),U_8563),U_8565)) ) )
& ( ? [U_8562] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8564),U_8562),U_8566))
& hBOOL(hAPP(hAPP(c_member(U_8564),U_8562),U_8565)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8564),hAPP(c_Finite__Set_Ofold1(U_8564,c_Orderings_Oord__class_Omin(U_8564)),U_8565)),U_8566)) ) )
| U_8565 = c_Orderings_Obot__class_Obot(tc_fun(U_8564,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8564),U_8565))
| ~ class_Orderings_Olinorder(U_8564) ),
inference(variable_rename,[status(thm)],[f_2460_1]) ).
fof(f_2460_3,plain,
! [U_8566,U_8565,U_8564] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8564),hAPP(c_Finite__Set_Ofold1(U_8564,c_Orderings_Oord__class_Omin(U_8564)),U_8565)),U_8566))
| ! [U_8563] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8564),U_8563),U_8566))
| ~ hBOOL(hAPP(hAPP(c_member(U_8564),U_8563),U_8565)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8564),sK211(U_8566,U_8565,U_8564)),U_8566))
& hBOOL(hAPP(hAPP(c_member(U_8564),sK211(U_8566,U_8565,U_8564)),U_8565)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8564),hAPP(c_Finite__Set_Ofold1(U_8564,c_Orderings_Oord__class_Omin(U_8564)),U_8565)),U_8566)) ) )
| U_8565 = c_Orderings_Obot__class_Obot(tc_fun(U_8564,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8564),U_8565))
| ~ class_Orderings_Olinorder(U_8564) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK211]),skolemize(U_8562,sK211(U_8566,U_8565,U_8564))],[f_2460_2]) ).
cnf(f_2460_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8564),sK211(U_8566,U_8565,U_8564)),U_8565))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8564),hAPP(c_Finite__Set_Ofold1(U_8564,c_Orderings_Oord__class_Omin(U_8564)),U_8565)),U_8566))
| U_8565 = c_Orderings_Obot__class_Obot(tc_fun(U_8564,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8564),U_8565))
| ~ class_Orderings_Olinorder(U_8564) ),
inference(clausify,[status(thm)],[f_2460_3]) ).
cnf(f_2460_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8564),sK211(U_8566,U_8565,U_8564)),U_8566))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8564),hAPP(c_Finite__Set_Ofold1(U_8564,c_Orderings_Oord__class_Omin(U_8564)),U_8565)),U_8566))
| U_8565 = c_Orderings_Obot__class_Obot(tc_fun(U_8564,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8564),U_8565))
| ~ class_Orderings_Olinorder(U_8564) ),
inference(clausify,[status(thm)],[f_2460_3]) ).
cnf(f_2460_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8564),hAPP(c_Finite__Set_Ofold1(U_8564,c_Orderings_Oord__class_Omin(U_8564)),U_8565)),U_8566))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8564),U_8563),U_8566))
| ~ hBOOL(hAPP(hAPP(c_member(U_8564),U_8563),U_8565))
| U_8565 = c_Orderings_Obot__class_Obot(tc_fun(U_8564,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8564),U_8565))
| ~ class_Orderings_Olinorder(U_8564) ),
inference(clausify,[status(thm)],[f_2460_3]) ).
fof(f_2461_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_2461_2,plain,
! [U_8571,U_8570,U_8569] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8569),U_8571),hAPP(c_Finite__Set_Ofold1(U_8569,c_Orderings_Oord__class_Omin(U_8569)),U_8570)))
| ? [U_8568] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8569),U_8571),U_8568))
& hBOOL(hAPP(hAPP(c_member(U_8569),U_8568),U_8570)) ) )
& ( ! [U_8567] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8569),U_8571),U_8567))
| ~ hBOOL(hAPP(hAPP(c_member(U_8569),U_8567),U_8570)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8569),U_8571),hAPP(c_Finite__Set_Ofold1(U_8569,c_Orderings_Oord__class_Omin(U_8569)),U_8570))) ) )
| U_8570 = c_Orderings_Obot__class_Obot(tc_fun(U_8569,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8569),U_8570))
| ~ class_Orderings_Olinorder(U_8569) ),
inference(variable_rename,[status(thm)],[f_2461_1]) ).
fof(f_2461_3,plain,
! [U_8571,U_8570,U_8569] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8569),U_8571),hAPP(c_Finite__Set_Ofold1(U_8569,c_Orderings_Oord__class_Omin(U_8569)),U_8570)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8569),U_8571),sK212(U_8571,U_8570,U_8569)))
& hBOOL(hAPP(hAPP(c_member(U_8569),sK212(U_8571,U_8570,U_8569)),U_8570)) ) )
& ( ! [U_8567] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8569),U_8571),U_8567))
| ~ hBOOL(hAPP(hAPP(c_member(U_8569),U_8567),U_8570)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8569),U_8571),hAPP(c_Finite__Set_Ofold1(U_8569,c_Orderings_Oord__class_Omin(U_8569)),U_8570))) ) )
| U_8570 = c_Orderings_Obot__class_Obot(tc_fun(U_8569,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8569),U_8570))
| ~ class_Orderings_Olinorder(U_8569) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK212]),skolemize(U_8568,sK212(U_8571,U_8570,U_8569))],[f_2461_2]) ).
cnf(f_2461_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8569),U_8571),U_8567))
| ~ hBOOL(hAPP(hAPP(c_member(U_8569),U_8567),U_8570))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8569),U_8571),hAPP(c_Finite__Set_Ofold1(U_8569,c_Orderings_Oord__class_Omin(U_8569)),U_8570)))
| U_8570 = c_Orderings_Obot__class_Obot(tc_fun(U_8569,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8569),U_8570))
| ~ class_Orderings_Olinorder(U_8569) ),
inference(clausify,[status(thm)],[f_2461_3]) ).
cnf(f_2461_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_8569),sK212(U_8571,U_8570,U_8569)),U_8570))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8569),U_8571),hAPP(c_Finite__Set_Ofold1(U_8569,c_Orderings_Oord__class_Omin(U_8569)),U_8570)))
| U_8570 = c_Orderings_Obot__class_Obot(tc_fun(U_8569,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8569),U_8570))
| ~ class_Orderings_Olinorder(U_8569) ),
inference(clausify,[status(thm)],[f_2461_3]) ).
cnf(f_2461_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8569),U_8571),sK212(U_8571,U_8570,U_8569)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8569),U_8571),hAPP(c_Finite__Set_Ofold1(U_8569,c_Orderings_Oord__class_Omin(U_8569)),U_8570)))
| U_8570 = c_Orderings_Obot__class_Obot(tc_fun(U_8569,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8569),U_8570))
| ~ class_Orderings_Olinorder(U_8569) ),
inference(clausify,[status(thm)],[f_2461_3]) ).
fof(f_2462_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_2462_2,plain,
! [U_8572] :
( c_Orderings_Oord__class_Omin(U_8572) = c_Orderings_Oord_Omin(U_8572,c_Orderings_Oord__class_Oless__eq(U_8572))
| ~ class_Orderings_Oord(U_8572) ),
inference(variable_rename,[status(thm)],[f_2462_1]) ).
cnf(f_2462_3,plain,
( c_Orderings_Oord__class_Omin(U_8572) = c_Orderings_Oord_Omin(U_8572,c_Orderings_Oord__class_Oless__eq(U_8572))
| ~ class_Orderings_Oord(U_8572) ),
inference(clausify,[status(thm)],[f_2462_2]) ).
fof(f_2463_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_2463_2,plain,
! [U_8575,U_8574,U_8573] :
( ( ( c_Big__Operators_Olinorder__class_OMin(U_8573,U_8574) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8573),U_8575),c_Big__Operators_Olinorder__class_OMin(U_8573,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8573,tc_HOL_Obool)),U_8574),hAPP(hAPP(c_Set_Oinsert(U_8573),U_8575),c_Orderings_Obot__class_Obot(tc_fun(U_8573,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8573,tc_HOL_Obool)),U_8574),hAPP(hAPP(c_Set_Oinsert(U_8573),U_8575),c_Orderings_Obot__class_Obot(tc_fun(U_8573,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8573,tc_HOL_Obool)) )
& ( c_Big__Operators_Olinorder__class_OMin(U_8573,U_8574) = U_8575
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8573,tc_HOL_Obool)),U_8574),hAPP(hAPP(c_Set_Oinsert(U_8573),U_8575),c_Orderings_Obot__class_Obot(tc_fun(U_8573,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8573,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_8573),U_8575),U_8574))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8573),U_8574))
| ~ class_Orderings_Olinorder(U_8573) ),
inference(variable_rename,[status(thm)],[f_2463_1]) ).
cnf(f_2463_3,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8573,U_8574) = U_8575
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8573,tc_HOL_Obool)),U_8574),hAPP(hAPP(c_Set_Oinsert(U_8573),U_8575),c_Orderings_Obot__class_Obot(tc_fun(U_8573,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8573,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_8573),U_8575),U_8574))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8573),U_8574))
| ~ class_Orderings_Olinorder(U_8573) ),
inference(clausify,[status(thm)],[f_2463_2]) ).
cnf(f_2463_4,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8573,U_8574) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8573),U_8575),c_Big__Operators_Olinorder__class_OMin(U_8573,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8573,tc_HOL_Obool)),U_8574),hAPP(hAPP(c_Set_Oinsert(U_8573),U_8575),c_Orderings_Obot__class_Obot(tc_fun(U_8573,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8573,tc_HOL_Obool)),U_8574),hAPP(hAPP(c_Set_Oinsert(U_8573),U_8575),c_Orderings_Obot__class_Obot(tc_fun(U_8573,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8573,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_8573),U_8575),U_8574))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8573),U_8574))
| ~ class_Orderings_Olinorder(U_8573) ),
inference(clausify,[status(thm)],[f_2463_2]) ).
fof(f_2464_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_2464_2,plain,
! [U_8586,U_8585,U_8584,U_8583,U_8582,U_8581,U_8580] :
( ( c_Nitpick_Ofold__graph_H(U_8580,U_8581,U_8582,U_8583,U_8584,hAPP(hAPP(U_8582,U_8585),U_8586))
| ( ! [U_8579,U_8578] :
( ~ c_Nitpick_Ofold__graph_H(U_8580,U_8581,U_8582,U_8583,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8580,tc_HOL_Obool)),U_8584),hAPP(hAPP(c_Set_Oinsert(U_8580),U_8579),c_Orderings_Obot__class_Obot(tc_fun(U_8580,tc_HOL_Obool)))),U_8578)
| ~ hBOOL(hAPP(hAPP(c_member(U_8580),U_8579),U_8584))
| hAPP(hAPP(U_8582,U_8585),U_8586) != hAPP(hAPP(U_8582,U_8579),U_8578) )
& ( hAPP(hAPP(U_8582,U_8585),U_8586) != U_8583
| U_8584 != c_Orderings_Obot__class_Obot(tc_fun(U_8580,tc_HOL_Obool)) ) ) )
& ( ? [U_8577,U_8576] :
( c_Nitpick_Ofold__graph_H(U_8580,U_8581,U_8582,U_8583,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8580,tc_HOL_Obool)),U_8584),hAPP(hAPP(c_Set_Oinsert(U_8580),U_8577),c_Orderings_Obot__class_Obot(tc_fun(U_8580,tc_HOL_Obool)))),U_8576)
& hBOOL(hAPP(hAPP(c_member(U_8580),U_8577),U_8584))
& hAPP(hAPP(U_8582,U_8585),U_8586) = hAPP(hAPP(U_8582,U_8577),U_8576) )
| ( hAPP(hAPP(U_8582,U_8585),U_8586) = U_8583
& U_8584 = c_Orderings_Obot__class_Obot(tc_fun(U_8580,tc_HOL_Obool)) )
| ~ c_Nitpick_Ofold__graph_H(U_8580,U_8581,U_8582,U_8583,U_8584,hAPP(hAPP(U_8582,U_8585),U_8586)) ) ),
inference(variable_rename,[status(thm)],[f_2464_1]) ).
fof(f_2464_3,plain,
( ! [U_8600,U_8598,U_8596,U_8594,U_8592,U_8590,U_8588] :
( c_Nitpick_Ofold__graph_H(U_8588,U_8590,U_8592,U_8594,U_8596,hAPP(hAPP(U_8592,U_8598),U_8600))
| ( ! [U_8579] :
( ! [U_8578] :
( ~ c_Nitpick_Ofold__graph_H(U_8588,U_8590,U_8592,U_8594,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8588,tc_HOL_Obool)),U_8596),hAPP(hAPP(c_Set_Oinsert(U_8588),U_8579),c_Orderings_Obot__class_Obot(tc_fun(U_8588,tc_HOL_Obool)))),U_8578)
| hAPP(hAPP(U_8592,U_8598),U_8600) != hAPP(hAPP(U_8592,U_8579),U_8578) )
| ~ hBOOL(hAPP(hAPP(c_member(U_8588),U_8579),U_8596)) )
& ( hAPP(hAPP(U_8592,U_8598),U_8600) != U_8594
| U_8596 != c_Orderings_Obot__class_Obot(tc_fun(U_8588,tc_HOL_Obool)) ) ) )
& ! [U_8599,U_8597,U_8595,U_8593,U_8591,U_8589,U_8587] :
( ? [U_8577] :
( ? [U_8576] :
( c_Nitpick_Ofold__graph_H(U_8587,U_8589,U_8591,U_8593,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8587,tc_HOL_Obool)),U_8595),hAPP(hAPP(c_Set_Oinsert(U_8587),U_8577),c_Orderings_Obot__class_Obot(tc_fun(U_8587,tc_HOL_Obool)))),U_8576)
& hAPP(hAPP(U_8591,U_8597),U_8599) = hAPP(hAPP(U_8591,U_8577),U_8576) )
& hBOOL(hAPP(hAPP(c_member(U_8587),U_8577),U_8595)) )
| ( hAPP(hAPP(U_8591,U_8597),U_8599) = U_8593
& U_8595 = c_Orderings_Obot__class_Obot(tc_fun(U_8587,tc_HOL_Obool)) )
| ~ c_Nitpick_Ofold__graph_H(U_8587,U_8589,U_8591,U_8593,U_8595,hAPP(hAPP(U_8591,U_8597),U_8599)) ) ),
inference(miniscope,[status(thm)],[f_2464_2]) ).
fof(f_2464_4,plain,
( ! [U_8600,U_8598,U_8596,U_8594,U_8592,U_8590,U_8588] :
( c_Nitpick_Ofold__graph_H(U_8588,U_8590,U_8592,U_8594,U_8596,hAPP(hAPP(U_8592,U_8598),U_8600))
| ( ! [U_8579] :
( ! [U_8578] :
( ~ c_Nitpick_Ofold__graph_H(U_8588,U_8590,U_8592,U_8594,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8588,tc_HOL_Obool)),U_8596),hAPP(hAPP(c_Set_Oinsert(U_8588),U_8579),c_Orderings_Obot__class_Obot(tc_fun(U_8588,tc_HOL_Obool)))),U_8578)
| hAPP(hAPP(U_8592,U_8598),U_8600) != hAPP(hAPP(U_8592,U_8579),U_8578) )
| ~ hBOOL(hAPP(hAPP(c_member(U_8588),U_8579),U_8596)) )
& ( hAPP(hAPP(U_8592,U_8598),U_8600) != U_8594
| U_8596 != c_Orderings_Obot__class_Obot(tc_fun(U_8588,tc_HOL_Obool)) ) ) )
& ! [U_8599,U_8597,U_8595,U_8593,U_8591,U_8589,U_8587] :
( ( ? [U_8576] :
( c_Nitpick_Ofold__graph_H(U_8587,U_8589,U_8591,U_8593,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8587,tc_HOL_Obool)),U_8595),hAPP(hAPP(c_Set_Oinsert(U_8587),sK213(U_8599,U_8597,U_8595,U_8593,U_8591,U_8589,U_8587)),c_Orderings_Obot__class_Obot(tc_fun(U_8587,tc_HOL_Obool)))),U_8576)
& hAPP(hAPP(U_8591,U_8597),U_8599) = hAPP(hAPP(U_8591,sK213(U_8599,U_8597,U_8595,U_8593,U_8591,U_8589,U_8587)),U_8576) )
& hBOOL(hAPP(hAPP(c_member(U_8587),sK213(U_8599,U_8597,U_8595,U_8593,U_8591,U_8589,U_8587)),U_8595)) )
| ( hAPP(hAPP(U_8591,U_8597),U_8599) = U_8593
& U_8595 = c_Orderings_Obot__class_Obot(tc_fun(U_8587,tc_HOL_Obool)) )
| ~ c_Nitpick_Ofold__graph_H(U_8587,U_8589,U_8591,U_8593,U_8595,hAPP(hAPP(U_8591,U_8597),U_8599)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK213]),skolemize(U_8577,sK213(U_8599,U_8597,U_8595,U_8593,U_8591,U_8589,U_8587))],[f_2464_3]) ).
fof(f_2464_5,plain,
( ! [U_8600,U_8598,U_8596,U_8594,U_8592,U_8590,U_8588] :
( c_Nitpick_Ofold__graph_H(U_8588,U_8590,U_8592,U_8594,U_8596,hAPP(hAPP(U_8592,U_8598),U_8600))
| ( ! [U_8579] :
( ! [U_8578] :
( ~ c_Nitpick_Ofold__graph_H(U_8588,U_8590,U_8592,U_8594,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8588,tc_HOL_Obool)),U_8596),hAPP(hAPP(c_Set_Oinsert(U_8588),U_8579),c_Orderings_Obot__class_Obot(tc_fun(U_8588,tc_HOL_Obool)))),U_8578)
| hAPP(hAPP(U_8592,U_8598),U_8600) != hAPP(hAPP(U_8592,U_8579),U_8578) )
| ~ hBOOL(hAPP(hAPP(c_member(U_8588),U_8579),U_8596)) )
& ( hAPP(hAPP(U_8592,U_8598),U_8600) != U_8594
| U_8596 != c_Orderings_Obot__class_Obot(tc_fun(U_8588,tc_HOL_Obool)) ) ) )
& ! [U_8599,U_8597,U_8595,U_8593,U_8591,U_8589,U_8587] :
( ( c_Nitpick_Ofold__graph_H(U_8587,U_8589,U_8591,U_8593,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8587,tc_HOL_Obool)),U_8595),hAPP(hAPP(c_Set_Oinsert(U_8587),sK213(U_8599,U_8597,U_8595,U_8593,U_8591,U_8589,U_8587)),c_Orderings_Obot__class_Obot(tc_fun(U_8587,tc_HOL_Obool)))),sK214(U_8599,U_8597,U_8595,U_8593,U_8591,U_8589,U_8587))
& hAPP(hAPP(U_8591,U_8597),U_8599) = hAPP(hAPP(U_8591,sK213(U_8599,U_8597,U_8595,U_8593,U_8591,U_8589,U_8587)),sK214(U_8599,U_8597,U_8595,U_8593,U_8591,U_8589,U_8587))
& hBOOL(hAPP(hAPP(c_member(U_8587),sK213(U_8599,U_8597,U_8595,U_8593,U_8591,U_8589,U_8587)),U_8595)) )
| ( hAPP(hAPP(U_8591,U_8597),U_8599) = U_8593
& U_8595 = c_Orderings_Obot__class_Obot(tc_fun(U_8587,tc_HOL_Obool)) )
| ~ c_Nitpick_Ofold__graph_H(U_8587,U_8589,U_8591,U_8593,U_8595,hAPP(hAPP(U_8591,U_8597),U_8599)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK214]),skolemize(U_8576,sK214(U_8599,U_8597,U_8595,U_8593,U_8591,U_8589,U_8587))],[f_2464_4]) ).
cnf(f_2464_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8587),sK213(U_8599,U_8597,U_8595,U_8593,U_8591,U_8589,U_8587)),U_8595))
| U_8595 = c_Orderings_Obot__class_Obot(tc_fun(U_8587,tc_HOL_Obool))
| ~ c_Nitpick_Ofold__graph_H(U_8587,U_8589,U_8591,U_8593,U_8595,hAPP(hAPP(U_8591,U_8597),U_8599)) ),
inference(clausify,[status(thm)],[f_2464_5]) ).
cnf(f_2464_7,plain,
( hAPP(hAPP(U_8591,U_8597),U_8599) = hAPP(hAPP(U_8591,sK213(U_8599,U_8597,U_8595,U_8593,U_8591,U_8589,U_8587)),sK214(U_8599,U_8597,U_8595,U_8593,U_8591,U_8589,U_8587))
| U_8595 = c_Orderings_Obot__class_Obot(tc_fun(U_8587,tc_HOL_Obool))
| ~ c_Nitpick_Ofold__graph_H(U_8587,U_8589,U_8591,U_8593,U_8595,hAPP(hAPP(U_8591,U_8597),U_8599)) ),
inference(clausify,[status(thm)],[f_2464_5]) ).
cnf(f_2464_8,plain,
( c_Nitpick_Ofold__graph_H(U_8587,U_8589,U_8591,U_8593,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8587,tc_HOL_Obool)),U_8595),hAPP(hAPP(c_Set_Oinsert(U_8587),sK213(U_8599,U_8597,U_8595,U_8593,U_8591,U_8589,U_8587)),c_Orderings_Obot__class_Obot(tc_fun(U_8587,tc_HOL_Obool)))),sK214(U_8599,U_8597,U_8595,U_8593,U_8591,U_8589,U_8587))
| U_8595 = c_Orderings_Obot__class_Obot(tc_fun(U_8587,tc_HOL_Obool))
| ~ c_Nitpick_Ofold__graph_H(U_8587,U_8589,U_8591,U_8593,U_8595,hAPP(hAPP(U_8591,U_8597),U_8599)) ),
inference(clausify,[status(thm)],[f_2464_5]) ).
cnf(f_2464_9,plain,
( hBOOL(hAPP(hAPP(c_member(U_8587),sK213(U_8599,U_8597,U_8595,U_8593,U_8591,U_8589,U_8587)),U_8595))
| hAPP(hAPP(U_8591,U_8597),U_8599) = U_8593
| ~ c_Nitpick_Ofold__graph_H(U_8587,U_8589,U_8591,U_8593,U_8595,hAPP(hAPP(U_8591,U_8597),U_8599)) ),
inference(clausify,[status(thm)],[f_2464_5]) ).
cnf(f_2464_10,plain,
( hAPP(hAPP(U_8591,U_8597),U_8599) = hAPP(hAPP(U_8591,sK213(U_8599,U_8597,U_8595,U_8593,U_8591,U_8589,U_8587)),sK214(U_8599,U_8597,U_8595,U_8593,U_8591,U_8589,U_8587))
| hAPP(hAPP(U_8591,U_8597),U_8599) = U_8593
| ~ c_Nitpick_Ofold__graph_H(U_8587,U_8589,U_8591,U_8593,U_8595,hAPP(hAPP(U_8591,U_8597),U_8599)) ),
inference(clausify,[status(thm)],[f_2464_5]) ).
cnf(f_2464_11,plain,
( c_Nitpick_Ofold__graph_H(U_8587,U_8589,U_8591,U_8593,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8587,tc_HOL_Obool)),U_8595),hAPP(hAPP(c_Set_Oinsert(U_8587),sK213(U_8599,U_8597,U_8595,U_8593,U_8591,U_8589,U_8587)),c_Orderings_Obot__class_Obot(tc_fun(U_8587,tc_HOL_Obool)))),sK214(U_8599,U_8597,U_8595,U_8593,U_8591,U_8589,U_8587))
| hAPP(hAPP(U_8591,U_8597),U_8599) = U_8593
| ~ c_Nitpick_Ofold__graph_H(U_8587,U_8589,U_8591,U_8593,U_8595,hAPP(hAPP(U_8591,U_8597),U_8599)) ),
inference(clausify,[status(thm)],[f_2464_5]) ).
cnf(f_2464_12,plain,
( hAPP(hAPP(U_8592,U_8598),U_8600) != U_8594
| U_8596 != c_Orderings_Obot__class_Obot(tc_fun(U_8588,tc_HOL_Obool))
| c_Nitpick_Ofold__graph_H(U_8588,U_8590,U_8592,U_8594,U_8596,hAPP(hAPP(U_8592,U_8598),U_8600)) ),
inference(clausify,[status(thm)],[f_2464_5]) ).
cnf(f_2464_13,plain,
( ~ c_Nitpick_Ofold__graph_H(U_8588,U_8590,U_8592,U_8594,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8588,tc_HOL_Obool)),U_8596),hAPP(hAPP(c_Set_Oinsert(U_8588),U_8579),c_Orderings_Obot__class_Obot(tc_fun(U_8588,tc_HOL_Obool)))),U_8578)
| hAPP(hAPP(U_8592,U_8598),U_8600) != hAPP(hAPP(U_8592,U_8579),U_8578)
| ~ hBOOL(hAPP(hAPP(c_member(U_8588),U_8579),U_8596))
| c_Nitpick_Ofold__graph_H(U_8588,U_8590,U_8592,U_8594,U_8596,hAPP(hAPP(U_8592,U_8598),U_8600)) ),
inference(clausify,[status(thm)],[f_2464_5]) ).
fof(f_2465_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_2465_2,plain,
! [U_8603,U_8602,U_8601] :
( ( ( c_Big__Operators_Olattice_OInf__fin(U_8601,c_Orderings_Oord__class_Omin(U_8601),U_8602) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8601),U_8603),c_Big__Operators_Olattice_OInf__fin(U_8601,c_Orderings_Oord__class_Omin(U_8601),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8601,tc_HOL_Obool)),U_8602),hAPP(hAPP(c_Set_Oinsert(U_8601),U_8603),c_Orderings_Obot__class_Obot(tc_fun(U_8601,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8601,tc_HOL_Obool)),U_8602),hAPP(hAPP(c_Set_Oinsert(U_8601),U_8603),c_Orderings_Obot__class_Obot(tc_fun(U_8601,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8601,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice_OInf__fin(U_8601,c_Orderings_Oord__class_Omin(U_8601),U_8602) = U_8603
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8601,tc_HOL_Obool)),U_8602),hAPP(hAPP(c_Set_Oinsert(U_8601),U_8603),c_Orderings_Obot__class_Obot(tc_fun(U_8601,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8601,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_8601),U_8603),U_8602))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8601),U_8602))
| ~ class_Orderings_Olinorder(U_8601) ),
inference(variable_rename,[status(thm)],[f_2465_1]) ).
cnf(f_2465_3,plain,
( c_Big__Operators_Olattice_OInf__fin(U_8601,c_Orderings_Oord__class_Omin(U_8601),U_8602) = U_8603
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8601,tc_HOL_Obool)),U_8602),hAPP(hAPP(c_Set_Oinsert(U_8601),U_8603),c_Orderings_Obot__class_Obot(tc_fun(U_8601,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8601,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_8601),U_8603),U_8602))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8601),U_8602))
| ~ class_Orderings_Olinorder(U_8601) ),
inference(clausify,[status(thm)],[f_2465_2]) ).
cnf(f_2465_4,plain,
( c_Big__Operators_Olattice_OInf__fin(U_8601,c_Orderings_Oord__class_Omin(U_8601),U_8602) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8601),U_8603),c_Big__Operators_Olattice_OInf__fin(U_8601,c_Orderings_Oord__class_Omin(U_8601),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8601,tc_HOL_Obool)),U_8602),hAPP(hAPP(c_Set_Oinsert(U_8601),U_8603),c_Orderings_Obot__class_Obot(tc_fun(U_8601,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8601,tc_HOL_Obool)),U_8602),hAPP(hAPP(c_Set_Oinsert(U_8601),U_8603),c_Orderings_Obot__class_Obot(tc_fun(U_8601,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8601,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_8601),U_8603),U_8602))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8601),U_8602))
| ~ class_Orderings_Olinorder(U_8601) ),
inference(clausify,[status(thm)],[f_2465_2]) ).
fof(f_2466_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_2466_2,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_2466_1]) ).
fof(f_2467_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_2467_2,plain,
! [U_8605,U_8604] :
( c_Big__Operators_Olinorder__class_OMin(U_8604,hAPP(hAPP(c_Set_Oinsert(U_8604),U_8605),c_Orderings_Obot__class_Obot(tc_fun(U_8604,tc_HOL_Obool)))) = U_8605
| ~ class_Orderings_Olinorder(U_8604) ),
inference(variable_rename,[status(thm)],[f_2467_1]) ).
cnf(f_2467_3,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8604,hAPP(hAPP(c_Set_Oinsert(U_8604),U_8605),c_Orderings_Obot__class_Obot(tc_fun(U_8604,tc_HOL_Obool)))) = U_8605
| ~ class_Orderings_Olinorder(U_8604) ),
inference(clausify,[status(thm)],[f_2467_2]) ).
fof(f_2468_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_2468_2,plain,
! [U_8608,U_8607,U_8606] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8606),U_8608),c_Big__Operators_Olattice_OInf__fin(U_8606,c_Orderings_Oord__class_Omin(U_8606),U_8607)) = c_Big__Operators_Olattice_OInf__fin(U_8606,c_Orderings_Oord__class_Omin(U_8606),U_8607)
| ~ hBOOL(hAPP(hAPP(c_member(U_8606),U_8608),U_8607))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8606),U_8607))
| ~ class_Orderings_Olinorder(U_8606) ),
inference(variable_rename,[status(thm)],[f_2468_1]) ).
cnf(f_2468_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8606),U_8608),c_Big__Operators_Olattice_OInf__fin(U_8606,c_Orderings_Oord__class_Omin(U_8606),U_8607)) = c_Big__Operators_Olattice_OInf__fin(U_8606,c_Orderings_Oord__class_Omin(U_8606),U_8607)
| ~ hBOOL(hAPP(hAPP(c_member(U_8606),U_8608),U_8607))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8606),U_8607))
| ~ class_Orderings_Olinorder(U_8606) ),
inference(clausify,[status(thm)],[f_2468_2]) ).
fof(f_2469_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_2469_2,plain,
! [U_8611,U_8610,U_8609] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8609),c_Big__Operators_Olinorder__class_OMin(U_8609,U_8610)),U_8611))
| ~ hBOOL(hAPP(hAPP(c_member(U_8609),U_8611),U_8610))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8609),U_8610))
| ~ class_Orderings_Olinorder(U_8609) ),
inference(variable_rename,[status(thm)],[f_2469_1]) ).
cnf(f_2469_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8609),c_Big__Operators_Olinorder__class_OMin(U_8609,U_8610)),U_8611))
| ~ hBOOL(hAPP(hAPP(c_member(U_8609),U_8611),U_8610))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8609),U_8610))
| ~ class_Orderings_Olinorder(U_8609) ),
inference(clausify,[status(thm)],[f_2469_2]) ).
fof(f_2470_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_2470_2,plain,
! [U_8613,U_8612] :
( c_Big__Operators_Olattice_OInf__fin(U_8612,c_Orderings_Oord__class_Omin(U_8612),hAPP(hAPP(c_Set_Oinsert(U_8612),U_8613),c_Orderings_Obot__class_Obot(tc_fun(U_8612,tc_HOL_Obool)))) = U_8613
| ~ class_Orderings_Olinorder(U_8612) ),
inference(variable_rename,[status(thm)],[f_2470_1]) ).
cnf(f_2470_3,plain,
( c_Big__Operators_Olattice_OInf__fin(U_8612,c_Orderings_Oord__class_Omin(U_8612),hAPP(hAPP(c_Set_Oinsert(U_8612),U_8613),c_Orderings_Obot__class_Obot(tc_fun(U_8612,tc_HOL_Obool)))) = U_8613
| ~ class_Orderings_Olinorder(U_8612) ),
inference(clausify,[status(thm)],[f_2470_2]) ).
fof(f_2471_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_2471_2,plain,
! [U_8615,U_8614] :
( hBOOL(hAPP(hAPP(c_member(U_8614),c_Big__Operators_Olinorder__class_OMin(U_8614,U_8615)),U_8615))
| U_8615 = c_Orderings_Obot__class_Obot(tc_fun(U_8614,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8614),U_8615))
| ~ class_Orderings_Olinorder(U_8614) ),
inference(variable_rename,[status(thm)],[f_2471_1]) ).
cnf(f_2471_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8614),c_Big__Operators_Olinorder__class_OMin(U_8614,U_8615)),U_8615))
| U_8615 = c_Orderings_Obot__class_Obot(tc_fun(U_8614,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8614),U_8615))
| ~ class_Orderings_Olinorder(U_8614) ),
inference(clausify,[status(thm)],[f_2471_2]) ).
fof(f_2472_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_2472_2,plain,
! [U_8618,U_8617,U_8616] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8616),U_8618),c_Big__Operators_Olinorder__class_OMin(U_8616,U_8617)) = c_Big__Operators_Olinorder__class_OMin(U_8616,U_8617)
| ~ hBOOL(hAPP(hAPP(c_member(U_8616),U_8618),U_8617))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8616),U_8617))
| ~ class_Orderings_Olinorder(U_8616) ),
inference(variable_rename,[status(thm)],[f_2472_1]) ).
cnf(f_2472_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8616),U_8618),c_Big__Operators_Olinorder__class_OMin(U_8616,U_8617)) = c_Big__Operators_Olinorder__class_OMin(U_8616,U_8617)
| ~ hBOOL(hAPP(hAPP(c_member(U_8616),U_8618),U_8617))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8616),U_8617))
| ~ class_Orderings_Olinorder(U_8616) ),
inference(clausify,[status(thm)],[f_2472_2]) ).
fof(f_2473_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_2473_2,plain,
! [U_8620,U_8619] :
( c_Big__Operators_Olattice_OInf__fin(U_8619,c_Orderings_Oord__class_Omin(U_8619),U_8620) = hAPP(c_Finite__Set_Ofold1(U_8619,c_Orderings_Oord__class_Omin(U_8619)),U_8620)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8619),U_8620))
| ~ class_Orderings_Olinorder(U_8619) ),
inference(variable_rename,[status(thm)],[f_2473_1]) ).
cnf(f_2473_3,plain,
( c_Big__Operators_Olattice_OInf__fin(U_8619,c_Orderings_Oord__class_Omin(U_8619),U_8620) = hAPP(c_Finite__Set_Ofold1(U_8619,c_Orderings_Oord__class_Omin(U_8619)),U_8620)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8619),U_8620))
| ~ class_Orderings_Olinorder(U_8619) ),
inference(clausify,[status(thm)],[f_2473_2]) ).
fof(f_2474_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_2474_2,plain,
! [U_8622,U_8621] :
( c_Big__Operators_Olinorder__class_OMin(U_8621,U_8622) = hAPP(c_Finite__Set_Ofold1(U_8621,c_Orderings_Oord__class_Omin(U_8621)),U_8622)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8621),U_8622))
| ~ class_Orderings_Olinorder(U_8621) ),
inference(variable_rename,[status(thm)],[f_2474_1]) ).
cnf(f_2474_3,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8621,U_8622) = hAPP(c_Finite__Set_Ofold1(U_8621,c_Orderings_Oord__class_Omin(U_8621)),U_8622)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8621),U_8622))
| ~ class_Orderings_Olinorder(U_8621) ),
inference(clausify,[status(thm)],[f_2474_2]) ).
fof(f_2475_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_2475_2,plain,
! [U_8625,U_8624,U_8623] :
( c_Big__Operators_Olattice_OInf__fin(U_8623,c_Orderings_Oord__class_Omin(U_8623),hAPP(hAPP(c_Set_Oinsert(U_8623),U_8625),U_8624)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8623),U_8625),c_Big__Operators_Olattice_OInf__fin(U_8623,c_Orderings_Oord__class_Omin(U_8623),U_8624))
| U_8624 = c_Orderings_Obot__class_Obot(tc_fun(U_8623,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8623),U_8624))
| ~ class_Orderings_Olinorder(U_8623) ),
inference(variable_rename,[status(thm)],[f_2475_1]) ).
cnf(f_2475_3,plain,
( c_Big__Operators_Olattice_OInf__fin(U_8623,c_Orderings_Oord__class_Omin(U_8623),hAPP(hAPP(c_Set_Oinsert(U_8623),U_8625),U_8624)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8623),U_8625),c_Big__Operators_Olattice_OInf__fin(U_8623,c_Orderings_Oord__class_Omin(U_8623),U_8624))
| U_8624 = c_Orderings_Obot__class_Obot(tc_fun(U_8623,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8623),U_8624))
| ~ class_Orderings_Olinorder(U_8623) ),
inference(clausify,[status(thm)],[f_2475_2]) ).
fof(f_2476_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_2476_2,plain,
! [U_8628,U_8627,U_8626] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8626),c_Big__Operators_Olattice_OInf__fin(U_8626,c_Orderings_Oord__class_Omin(U_8626),U_8628)),c_Big__Operators_Olattice_OInf__fin(U_8626,c_Orderings_Oord__class_Omin(U_8626),U_8627)) = c_Big__Operators_Olattice_OInf__fin(U_8626,c_Orderings_Oord__class_Omin(U_8626),U_8627)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8626,tc_HOL_Obool)),U_8628),U_8627))
| U_8628 = c_Orderings_Obot__class_Obot(tc_fun(U_8626,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8626),U_8627))
| ~ class_Orderings_Olinorder(U_8626) ),
inference(variable_rename,[status(thm)],[f_2476_1]) ).
cnf(f_2476_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8626),c_Big__Operators_Olattice_OInf__fin(U_8626,c_Orderings_Oord__class_Omin(U_8626),U_8628)),c_Big__Operators_Olattice_OInf__fin(U_8626,c_Orderings_Oord__class_Omin(U_8626),U_8627)) = c_Big__Operators_Olattice_OInf__fin(U_8626,c_Orderings_Oord__class_Omin(U_8626),U_8627)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8626,tc_HOL_Obool)),U_8628),U_8627))
| U_8628 = c_Orderings_Obot__class_Obot(tc_fun(U_8626,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8626),U_8627))
| ~ class_Orderings_Olinorder(U_8626) ),
inference(clausify,[status(thm)],[f_2476_2]) ).
fof(f_2477_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_2477_2,plain,
! [U_8631,U_8630,U_8629] :
( c_Big__Operators_Olattice_OInf__fin(U_8629,c_Orderings_Oord__class_Omin(U_8629),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8629,tc_HOL_Obool)),U_8630),U_8631)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8629),c_Big__Operators_Olattice_OInf__fin(U_8629,c_Orderings_Oord__class_Omin(U_8629),U_8630)),c_Big__Operators_Olattice_OInf__fin(U_8629,c_Orderings_Oord__class_Omin(U_8629),U_8631))
| U_8631 = c_Orderings_Obot__class_Obot(tc_fun(U_8629,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8629),U_8631))
| U_8630 = c_Orderings_Obot__class_Obot(tc_fun(U_8629,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8629),U_8630))
| ~ class_Orderings_Olinorder(U_8629) ),
inference(variable_rename,[status(thm)],[f_2477_1]) ).
cnf(f_2477_3,plain,
( c_Big__Operators_Olattice_OInf__fin(U_8629,c_Orderings_Oord__class_Omin(U_8629),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8629,tc_HOL_Obool)),U_8630),U_8631)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8629),c_Big__Operators_Olattice_OInf__fin(U_8629,c_Orderings_Oord__class_Omin(U_8629),U_8630)),c_Big__Operators_Olattice_OInf__fin(U_8629,c_Orderings_Oord__class_Omin(U_8629),U_8631))
| U_8631 = c_Orderings_Obot__class_Obot(tc_fun(U_8629,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8629),U_8631))
| U_8630 = c_Orderings_Obot__class_Obot(tc_fun(U_8629,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8629),U_8630))
| ~ class_Orderings_Olinorder(U_8629) ),
inference(clausify,[status(thm)],[f_2477_2]) ).
fof(f_2478_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_2478_2,plain,
! [U_8634,U_8633,U_8632] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8632),c_Big__Operators_Olinorder__class_OMin(U_8632,U_8634)),c_Big__Operators_Olinorder__class_OMin(U_8632,U_8633)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8632),U_8634))
| U_8633 = c_Orderings_Obot__class_Obot(tc_fun(U_8632,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8632,tc_HOL_Obool)),U_8633),U_8634))
| ~ class_Orderings_Olinorder(U_8632) ),
inference(variable_rename,[status(thm)],[f_2478_1]) ).
cnf(f_2478_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8632),c_Big__Operators_Olinorder__class_OMin(U_8632,U_8634)),c_Big__Operators_Olinorder__class_OMin(U_8632,U_8633)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8632),U_8634))
| U_8633 = c_Orderings_Obot__class_Obot(tc_fun(U_8632,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8632,tc_HOL_Obool)),U_8633),U_8634))
| ~ class_Orderings_Olinorder(U_8632) ),
inference(clausify,[status(thm)],[f_2478_2]) ).
fof(f_2479_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_2479_2,plain,
! [U_8637,U_8636,U_8635] :
( c_Big__Operators_Olattice_OInf__fin(U_8635,c_Orderings_Oord__class_Omin(U_8635),hAPP(hAPP(c_Set_Oinsert(U_8635),U_8637),U_8636)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8635,U_8635,c_Orderings_Oord__class_Omin(U_8635)),U_8637),U_8636)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8635),U_8636))
| ~ class_Orderings_Olinorder(U_8635) ),
inference(variable_rename,[status(thm)],[f_2479_1]) ).
cnf(f_2479_3,plain,
( c_Big__Operators_Olattice_OInf__fin(U_8635,c_Orderings_Oord__class_Omin(U_8635),hAPP(hAPP(c_Set_Oinsert(U_8635),U_8637),U_8636)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8635,U_8635,c_Orderings_Oord__class_Omin(U_8635)),U_8637),U_8636)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8635),U_8636))
| ~ class_Orderings_Olinorder(U_8635) ),
inference(clausify,[status(thm)],[f_2479_2]) ).
fof(f_2480_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_2480_2,plain,
! [U_8640,U_8639,U_8638] :
( c_Big__Operators_Olinorder__class_OMin(U_8638,hAPP(hAPP(c_Set_Oinsert(U_8638),U_8640),U_8639)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8638),U_8640),c_Big__Operators_Olinorder__class_OMin(U_8638,U_8639))
| U_8639 = c_Orderings_Obot__class_Obot(tc_fun(U_8638,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8638),U_8639))
| ~ class_Orderings_Olinorder(U_8638) ),
inference(variable_rename,[status(thm)],[f_2480_1]) ).
cnf(f_2480_3,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8638,hAPP(hAPP(c_Set_Oinsert(U_8638),U_8640),U_8639)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8638),U_8640),c_Big__Operators_Olinorder__class_OMin(U_8638,U_8639))
| U_8639 = c_Orderings_Obot__class_Obot(tc_fun(U_8638,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8638),U_8639))
| ~ class_Orderings_Olinorder(U_8638) ),
inference(clausify,[status(thm)],[f_2480_2]) ).
fof(f_2481_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_2481_2,plain,
! [U_8643,U_8642,U_8641] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8641),c_Big__Operators_Olinorder__class_OMin(U_8641,U_8643)),c_Big__Operators_Olinorder__class_OMin(U_8641,U_8642)) = c_Big__Operators_Olinorder__class_OMin(U_8641,U_8642)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8641,tc_HOL_Obool)),U_8643),U_8642))
| U_8643 = c_Orderings_Obot__class_Obot(tc_fun(U_8641,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8641),U_8642))
| ~ class_Orderings_Olinorder(U_8641) ),
inference(variable_rename,[status(thm)],[f_2481_1]) ).
cnf(f_2481_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8641),c_Big__Operators_Olinorder__class_OMin(U_8641,U_8643)),c_Big__Operators_Olinorder__class_OMin(U_8641,U_8642)) = c_Big__Operators_Olinorder__class_OMin(U_8641,U_8642)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8641,tc_HOL_Obool)),U_8643),U_8642))
| U_8643 = c_Orderings_Obot__class_Obot(tc_fun(U_8641,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8641),U_8642))
| ~ class_Orderings_Olinorder(U_8641) ),
inference(clausify,[status(thm)],[f_2481_2]) ).
fof(f_2482_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_2482_2,plain,
! [U_8646,U_8645,U_8644] :
( c_Big__Operators_Olinorder__class_OMin(U_8644,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8644,tc_HOL_Obool)),U_8645),U_8646)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8644),c_Big__Operators_Olinorder__class_OMin(U_8644,U_8645)),c_Big__Operators_Olinorder__class_OMin(U_8644,U_8646))
| U_8646 = c_Orderings_Obot__class_Obot(tc_fun(U_8644,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8644),U_8646))
| U_8645 = c_Orderings_Obot__class_Obot(tc_fun(U_8644,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8644),U_8645))
| ~ class_Orderings_Olinorder(U_8644) ),
inference(variable_rename,[status(thm)],[f_2482_1]) ).
cnf(f_2482_3,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8644,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8644,tc_HOL_Obool)),U_8645),U_8646)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8644),c_Big__Operators_Olinorder__class_OMin(U_8644,U_8645)),c_Big__Operators_Olinorder__class_OMin(U_8644,U_8646))
| U_8646 = c_Orderings_Obot__class_Obot(tc_fun(U_8644,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8644),U_8646))
| U_8645 = c_Orderings_Obot__class_Obot(tc_fun(U_8644,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8644),U_8645))
| ~ class_Orderings_Olinorder(U_8644) ),
inference(clausify,[status(thm)],[f_2482_2]) ).
fof(f_2483_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_2483_2,plain,
! [U_8649,U_8648,U_8647] :
( c_Big__Operators_Olinorder__class_OMin(U_8647,hAPP(hAPP(c_Set_Oinsert(U_8647),U_8649),U_8648)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8647,U_8647,c_Orderings_Oord__class_Omin(U_8647)),U_8649),U_8648)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8647),U_8648))
| ~ class_Orderings_Olinorder(U_8647) ),
inference(variable_rename,[status(thm)],[f_2483_1]) ).
cnf(f_2483_3,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8647,hAPP(hAPP(c_Set_Oinsert(U_8647),U_8649),U_8648)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8647,U_8647,c_Orderings_Oord__class_Omin(U_8647)),U_8649),U_8648)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8647),U_8648))
| ~ class_Orderings_Olinorder(U_8647) ),
inference(clausify,[status(thm)],[f_2483_2]) ).
fof(f_2484_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_2484_2,plain,
! [U_8652,U_8651,U_8650] :
( c_Big__Operators_Olattice_OInf__fin(U_8650,c_Orderings_Oord__class_Omin(U_8650),hAPP(hAPP(c_Set_Oinsert(U_8650),U_8652),U_8651)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8650),U_8652),c_Big__Operators_Olattice_OInf__fin(U_8650,c_Orderings_Oord__class_Omin(U_8650),U_8651))
| U_8651 = c_Orderings_Obot__class_Obot(tc_fun(U_8650,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_8650),U_8652),U_8651))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8650),U_8651))
| ~ class_Orderings_Olinorder(U_8650) ),
inference(variable_rename,[status(thm)],[f_2484_1]) ).
cnf(f_2484_3,plain,
( c_Big__Operators_Olattice_OInf__fin(U_8650,c_Orderings_Oord__class_Omin(U_8650),hAPP(hAPP(c_Set_Oinsert(U_8650),U_8652),U_8651)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8650),U_8652),c_Big__Operators_Olattice_OInf__fin(U_8650,c_Orderings_Oord__class_Omin(U_8650),U_8651))
| U_8651 = c_Orderings_Obot__class_Obot(tc_fun(U_8650,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_8650),U_8652),U_8651))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8650),U_8651))
| ~ class_Orderings_Olinorder(U_8650) ),
inference(clausify,[status(thm)],[f_2484_2]) ).
fof(f_2485_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_2485_2,plain,
! [U_8655,U_8654,U_8653] :
( ( ( c_Big__Operators_Olattice_OInf__fin(U_8653,c_Orderings_Oord__class_Omin(U_8653),hAPP(hAPP(c_Set_Oinsert(U_8653),U_8655),U_8654)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8653),U_8655),c_Big__Operators_Olattice_OInf__fin(U_8653,c_Orderings_Oord__class_Omin(U_8653),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8653,tc_HOL_Obool)),U_8654),hAPP(hAPP(c_Set_Oinsert(U_8653),U_8655),c_Orderings_Obot__class_Obot(tc_fun(U_8653,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8653,tc_HOL_Obool)),U_8654),hAPP(hAPP(c_Set_Oinsert(U_8653),U_8655),c_Orderings_Obot__class_Obot(tc_fun(U_8653,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8653,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice_OInf__fin(U_8653,c_Orderings_Oord__class_Omin(U_8653),hAPP(hAPP(c_Set_Oinsert(U_8653),U_8655),U_8654)) = U_8655
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8653,tc_HOL_Obool)),U_8654),hAPP(hAPP(c_Set_Oinsert(U_8653),U_8655),c_Orderings_Obot__class_Obot(tc_fun(U_8653,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8653,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8653),U_8654))
| ~ class_Orderings_Olinorder(U_8653) ),
inference(variable_rename,[status(thm)],[f_2485_1]) ).
cnf(f_2485_3,plain,
( c_Big__Operators_Olattice_OInf__fin(U_8653,c_Orderings_Oord__class_Omin(U_8653),hAPP(hAPP(c_Set_Oinsert(U_8653),U_8655),U_8654)) = U_8655
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8653,tc_HOL_Obool)),U_8654),hAPP(hAPP(c_Set_Oinsert(U_8653),U_8655),c_Orderings_Obot__class_Obot(tc_fun(U_8653,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8653,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8653),U_8654))
| ~ class_Orderings_Olinorder(U_8653) ),
inference(clausify,[status(thm)],[f_2485_2]) ).
cnf(f_2485_4,plain,
( c_Big__Operators_Olattice_OInf__fin(U_8653,c_Orderings_Oord__class_Omin(U_8653),hAPP(hAPP(c_Set_Oinsert(U_8653),U_8655),U_8654)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8653),U_8655),c_Big__Operators_Olattice_OInf__fin(U_8653,c_Orderings_Oord__class_Omin(U_8653),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8653,tc_HOL_Obool)),U_8654),hAPP(hAPP(c_Set_Oinsert(U_8653),U_8655),c_Orderings_Obot__class_Obot(tc_fun(U_8653,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8653,tc_HOL_Obool)),U_8654),hAPP(hAPP(c_Set_Oinsert(U_8653),U_8655),c_Orderings_Obot__class_Obot(tc_fun(U_8653,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8653,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8653),U_8654))
| ~ class_Orderings_Olinorder(U_8653) ),
inference(clausify,[status(thm)],[f_2485_2]) ).
fof(f_2486_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_2486_2,plain,
! [U_8658,U_8657,U_8656] :
( c_Big__Operators_Olattice_OInf__fin(U_8656,c_Orderings_Oord__class_Omin(U_8656),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8656,tc_HOL_Obool)),U_8657),U_8658)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8656),c_Big__Operators_Olattice_OInf__fin(U_8656,c_Orderings_Oord__class_Omin(U_8656),U_8657)),c_Big__Operators_Olattice_OInf__fin(U_8656,c_Orderings_Oord__class_Omin(U_8656),U_8658))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8656,tc_HOL_Obool)),U_8657),U_8658) != c_Orderings_Obot__class_Obot(tc_fun(U_8656,tc_HOL_Obool))
| U_8658 = c_Orderings_Obot__class_Obot(tc_fun(U_8656,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8656),U_8658))
| U_8657 = c_Orderings_Obot__class_Obot(tc_fun(U_8656,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8656),U_8657))
| ~ class_Orderings_Olinorder(U_8656) ),
inference(variable_rename,[status(thm)],[f_2486_1]) ).
cnf(f_2486_3,plain,
( c_Big__Operators_Olattice_OInf__fin(U_8656,c_Orderings_Oord__class_Omin(U_8656),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8656,tc_HOL_Obool)),U_8657),U_8658)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8656),c_Big__Operators_Olattice_OInf__fin(U_8656,c_Orderings_Oord__class_Omin(U_8656),U_8657)),c_Big__Operators_Olattice_OInf__fin(U_8656,c_Orderings_Oord__class_Omin(U_8656),U_8658))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8656,tc_HOL_Obool)),U_8657),U_8658) != c_Orderings_Obot__class_Obot(tc_fun(U_8656,tc_HOL_Obool))
| U_8658 = c_Orderings_Obot__class_Obot(tc_fun(U_8656,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8656),U_8658))
| U_8657 = c_Orderings_Obot__class_Obot(tc_fun(U_8656,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8656),U_8657))
| ~ class_Orderings_Olinorder(U_8656) ),
inference(clausify,[status(thm)],[f_2486_2]) ).
fof(f_2487_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_2487_2,plain,
! [U_8661,U_8660,U_8659] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8659),c_Big__Operators_Olattice_OInf__fin(U_8659,c_Orderings_Oord__class_Omin(U_8659),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8659,tc_HOL_Obool)),U_8660),U_8661))),c_Big__Operators_Olattice_OInf__fin(U_8659,c_Orderings_Oord__class_Omin(U_8659),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8659,tc_HOL_Obool)),U_8660),U_8661))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8659),c_Big__Operators_Olattice_OInf__fin(U_8659,c_Orderings_Oord__class_Omin(U_8659),U_8660)),c_Big__Operators_Olattice_OInf__fin(U_8659,c_Orderings_Oord__class_Omin(U_8659),U_8661))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8659,tc_HOL_Obool)),U_8660),U_8661) = c_Orderings_Obot__class_Obot(tc_fun(U_8659,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8659),U_8661))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8659),U_8660))
| ~ class_Orderings_Olinorder(U_8659) ),
inference(variable_rename,[status(thm)],[f_2487_1]) ).
cnf(f_2487_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8659),c_Big__Operators_Olattice_OInf__fin(U_8659,c_Orderings_Oord__class_Omin(U_8659),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8659,tc_HOL_Obool)),U_8660),U_8661))),c_Big__Operators_Olattice_OInf__fin(U_8659,c_Orderings_Oord__class_Omin(U_8659),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8659,tc_HOL_Obool)),U_8660),U_8661))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8659),c_Big__Operators_Olattice_OInf__fin(U_8659,c_Orderings_Oord__class_Omin(U_8659),U_8660)),c_Big__Operators_Olattice_OInf__fin(U_8659,c_Orderings_Oord__class_Omin(U_8659),U_8661))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8659,tc_HOL_Obool)),U_8660),U_8661) = c_Orderings_Obot__class_Obot(tc_fun(U_8659,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8659),U_8661))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8659),U_8660))
| ~ class_Orderings_Olinorder(U_8659) ),
inference(clausify,[status(thm)],[f_2487_2]) ).
fof(f_2488_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_2488_2,plain,
! [U_8664,U_8663,U_8662] :
( c_Big__Operators_Olattice_OInf__fin(U_8662,c_Orderings_Oord__class_Omin(U_8662),hAPP(hAPP(c_Set_Oinsert(U_8662),U_8664),U_8663)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8662,U_8662,c_Orderings_Oord__class_Omin(U_8662)),U_8664),U_8663)
| hBOOL(hAPP(hAPP(c_member(U_8662),U_8664),U_8663))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8662),U_8663))
| ~ class_Orderings_Olinorder(U_8662) ),
inference(variable_rename,[status(thm)],[f_2488_1]) ).
cnf(f_2488_3,plain,
( c_Big__Operators_Olattice_OInf__fin(U_8662,c_Orderings_Oord__class_Omin(U_8662),hAPP(hAPP(c_Set_Oinsert(U_8662),U_8664),U_8663)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8662,U_8662,c_Orderings_Oord__class_Omin(U_8662)),U_8664),U_8663)
| hBOOL(hAPP(hAPP(c_member(U_8662),U_8664),U_8663))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8662),U_8663))
| ~ class_Orderings_Olinorder(U_8662) ),
inference(clausify,[status(thm)],[f_2488_2]) ).
fof(f_2489_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_2489_2,plain,
! [U_8667,U_8666,U_8665] :
( c_Big__Operators_Olinorder__class_OMin(U_8665,hAPP(hAPP(c_Set_Oinsert(U_8665),U_8667),U_8666)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8665),U_8667),c_Big__Operators_Olinorder__class_OMin(U_8665,U_8666))
| U_8666 = c_Orderings_Obot__class_Obot(tc_fun(U_8665,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_8665),U_8667),U_8666))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8665),U_8666))
| ~ class_Orderings_Olinorder(U_8665) ),
inference(variable_rename,[status(thm)],[f_2489_1]) ).
cnf(f_2489_3,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8665,hAPP(hAPP(c_Set_Oinsert(U_8665),U_8667),U_8666)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8665),U_8667),c_Big__Operators_Olinorder__class_OMin(U_8665,U_8666))
| U_8666 = c_Orderings_Obot__class_Obot(tc_fun(U_8665,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_8665),U_8667),U_8666))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8665),U_8666))
| ~ class_Orderings_Olinorder(U_8665) ),
inference(clausify,[status(thm)],[f_2489_2]) ).
fof(f_2490_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_2490_2,plain,
! [U_8670,U_8669,U_8668] :
( ( ( c_Big__Operators_Olinorder__class_OMin(U_8668,hAPP(hAPP(c_Set_Oinsert(U_8668),U_8670),U_8669)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8668),U_8670),c_Big__Operators_Olinorder__class_OMin(U_8668,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8668,tc_HOL_Obool)),U_8669),hAPP(hAPP(c_Set_Oinsert(U_8668),U_8670),c_Orderings_Obot__class_Obot(tc_fun(U_8668,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8668,tc_HOL_Obool)),U_8669),hAPP(hAPP(c_Set_Oinsert(U_8668),U_8670),c_Orderings_Obot__class_Obot(tc_fun(U_8668,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8668,tc_HOL_Obool)) )
& ( c_Big__Operators_Olinorder__class_OMin(U_8668,hAPP(hAPP(c_Set_Oinsert(U_8668),U_8670),U_8669)) = U_8670
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8668,tc_HOL_Obool)),U_8669),hAPP(hAPP(c_Set_Oinsert(U_8668),U_8670),c_Orderings_Obot__class_Obot(tc_fun(U_8668,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8668,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8668),U_8669))
| ~ class_Orderings_Olinorder(U_8668) ),
inference(variable_rename,[status(thm)],[f_2490_1]) ).
cnf(f_2490_3,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8668,hAPP(hAPP(c_Set_Oinsert(U_8668),U_8670),U_8669)) = U_8670
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8668,tc_HOL_Obool)),U_8669),hAPP(hAPP(c_Set_Oinsert(U_8668),U_8670),c_Orderings_Obot__class_Obot(tc_fun(U_8668,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8668,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8668),U_8669))
| ~ class_Orderings_Olinorder(U_8668) ),
inference(clausify,[status(thm)],[f_2490_2]) ).
cnf(f_2490_4,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8668,hAPP(hAPP(c_Set_Oinsert(U_8668),U_8670),U_8669)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8668),U_8670),c_Big__Operators_Olinorder__class_OMin(U_8668,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8668,tc_HOL_Obool)),U_8669),hAPP(hAPP(c_Set_Oinsert(U_8668),U_8670),c_Orderings_Obot__class_Obot(tc_fun(U_8668,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8668,tc_HOL_Obool)),U_8669),hAPP(hAPP(c_Set_Oinsert(U_8668),U_8670),c_Orderings_Obot__class_Obot(tc_fun(U_8668,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8668,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8668),U_8669))
| ~ class_Orderings_Olinorder(U_8668) ),
inference(clausify,[status(thm)],[f_2490_2]) ).
fof(f_2491_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_2491_2,plain,
! [U_8673,U_8672,U_8671] :
( c_Big__Operators_Olinorder__class_OMin(U_8671,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8671,tc_HOL_Obool)),U_8672),U_8673)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8671),c_Big__Operators_Olinorder__class_OMin(U_8671,U_8672)),c_Big__Operators_Olinorder__class_OMin(U_8671,U_8673))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8671,tc_HOL_Obool)),U_8672),U_8673) != c_Orderings_Obot__class_Obot(tc_fun(U_8671,tc_HOL_Obool))
| U_8673 = c_Orderings_Obot__class_Obot(tc_fun(U_8671,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8671),U_8673))
| U_8672 = c_Orderings_Obot__class_Obot(tc_fun(U_8671,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8671),U_8672))
| ~ class_Orderings_Olinorder(U_8671) ),
inference(variable_rename,[status(thm)],[f_2491_1]) ).
cnf(f_2491_3,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8671,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8671,tc_HOL_Obool)),U_8672),U_8673)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8671),c_Big__Operators_Olinorder__class_OMin(U_8671,U_8672)),c_Big__Operators_Olinorder__class_OMin(U_8671,U_8673))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8671,tc_HOL_Obool)),U_8672),U_8673) != c_Orderings_Obot__class_Obot(tc_fun(U_8671,tc_HOL_Obool))
| U_8673 = c_Orderings_Obot__class_Obot(tc_fun(U_8671,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8671),U_8673))
| U_8672 = c_Orderings_Obot__class_Obot(tc_fun(U_8671,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8671),U_8672))
| ~ class_Orderings_Olinorder(U_8671) ),
inference(clausify,[status(thm)],[f_2491_2]) ).
fof(f_2492_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_2492_2,plain,
! [U_8676,U_8675,U_8674] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8674),c_Big__Operators_Olinorder__class_OMin(U_8674,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8674,tc_HOL_Obool)),U_8675),U_8676))),c_Big__Operators_Olinorder__class_OMin(U_8674,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8674,tc_HOL_Obool)),U_8675),U_8676))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8674),c_Big__Operators_Olinorder__class_OMin(U_8674,U_8675)),c_Big__Operators_Olinorder__class_OMin(U_8674,U_8676))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8674,tc_HOL_Obool)),U_8675),U_8676) = c_Orderings_Obot__class_Obot(tc_fun(U_8674,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8674),U_8676))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8674),U_8675))
| ~ class_Orderings_Olinorder(U_8674) ),
inference(variable_rename,[status(thm)],[f_2492_1]) ).
cnf(f_2492_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8674),c_Big__Operators_Olinorder__class_OMin(U_8674,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8674,tc_HOL_Obool)),U_8675),U_8676))),c_Big__Operators_Olinorder__class_OMin(U_8674,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8674,tc_HOL_Obool)),U_8675),U_8676))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8674),c_Big__Operators_Olinorder__class_OMin(U_8674,U_8675)),c_Big__Operators_Olinorder__class_OMin(U_8674,U_8676))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8674,tc_HOL_Obool)),U_8675),U_8676) = c_Orderings_Obot__class_Obot(tc_fun(U_8674,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8674),U_8676))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8674),U_8675))
| ~ class_Orderings_Olinorder(U_8674) ),
inference(clausify,[status(thm)],[f_2492_2]) ).
fof(f_2493_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_2493_2,plain,
! [U_8679,U_8678,U_8677] :
( c_Big__Operators_Olinorder__class_OMin(U_8677,hAPP(hAPP(c_Set_Oinsert(U_8677),U_8679),U_8678)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8677,U_8677,c_Orderings_Oord__class_Omin(U_8677)),U_8679),U_8678)
| hBOOL(hAPP(hAPP(c_member(U_8677),U_8679),U_8678))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8677),U_8678))
| ~ class_Orderings_Olinorder(U_8677) ),
inference(variable_rename,[status(thm)],[f_2493_1]) ).
cnf(f_2493_3,plain,
( c_Big__Operators_Olinorder__class_OMin(U_8677,hAPP(hAPP(c_Set_Oinsert(U_8677),U_8679),U_8678)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8677,U_8677,c_Orderings_Oord__class_Omin(U_8677)),U_8679),U_8678)
| hBOOL(hAPP(hAPP(c_member(U_8677),U_8679),U_8678))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8677),U_8678))
| ~ class_Orderings_Olinorder(U_8677) ),
inference(clausify,[status(thm)],[f_2493_2]) ).
fof(f_2494_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_2494_2,plain,
! [U_8683,U_8682] :
( hBOOL(hAPP(hAPP(c_member(U_8682),c_Big__Operators_Olattice_OInf__fin(U_8682,c_Orderings_Oord__class_Omin(U_8682),U_8683)),U_8683))
| ? [U_8681,U_8680] : ~ hBOOL(hAPP(hAPP(c_member(U_8682),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8682),U_8681),U_8680)),hAPP(hAPP(c_Set_Oinsert(U_8682),U_8681),hAPP(hAPP(c_Set_Oinsert(U_8682),U_8680),c_Orderings_Obot__class_Obot(tc_fun(U_8682,tc_HOL_Obool))))))
| U_8683 = c_Orderings_Obot__class_Obot(tc_fun(U_8682,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8682),U_8683))
| ~ class_Orderings_Olinorder(U_8682) ),
inference(variable_rename,[status(thm)],[f_2494_1]) ).
fof(f_2494_3,plain,
! [U_8683,U_8682] :
( hBOOL(hAPP(hAPP(c_member(U_8682),c_Big__Operators_Olattice_OInf__fin(U_8682,c_Orderings_Oord__class_Omin(U_8682),U_8683)),U_8683))
| ? [U_8680] : ~ hBOOL(hAPP(hAPP(c_member(U_8682),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8682),sK215(U_8683,U_8682)),U_8680)),hAPP(hAPP(c_Set_Oinsert(U_8682),sK215(U_8683,U_8682)),hAPP(hAPP(c_Set_Oinsert(U_8682),U_8680),c_Orderings_Obot__class_Obot(tc_fun(U_8682,tc_HOL_Obool))))))
| U_8683 = c_Orderings_Obot__class_Obot(tc_fun(U_8682,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8682),U_8683))
| ~ class_Orderings_Olinorder(U_8682) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK215]),skolemize(U_8681,sK215(U_8683,U_8682))],[f_2494_2]) ).
fof(f_2494_4,plain,
! [U_8683,U_8682] :
( hBOOL(hAPP(hAPP(c_member(U_8682),c_Big__Operators_Olattice_OInf__fin(U_8682,c_Orderings_Oord__class_Omin(U_8682),U_8683)),U_8683))
| ~ hBOOL(hAPP(hAPP(c_member(U_8682),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8682),sK215(U_8683,U_8682)),sK216(U_8683,U_8682))),hAPP(hAPP(c_Set_Oinsert(U_8682),sK215(U_8683,U_8682)),hAPP(hAPP(c_Set_Oinsert(U_8682),sK216(U_8683,U_8682)),c_Orderings_Obot__class_Obot(tc_fun(U_8682,tc_HOL_Obool))))))
| U_8683 = c_Orderings_Obot__class_Obot(tc_fun(U_8682,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8682),U_8683))
| ~ class_Orderings_Olinorder(U_8682) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK216]),skolemize(U_8680,sK216(U_8683,U_8682))],[f_2494_3]) ).
cnf(f_2494_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_8682),c_Big__Operators_Olattice_OInf__fin(U_8682,c_Orderings_Oord__class_Omin(U_8682),U_8683)),U_8683))
| ~ hBOOL(hAPP(hAPP(c_member(U_8682),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8682),sK215(U_8683,U_8682)),sK216(U_8683,U_8682))),hAPP(hAPP(c_Set_Oinsert(U_8682),sK215(U_8683,U_8682)),hAPP(hAPP(c_Set_Oinsert(U_8682),sK216(U_8683,U_8682)),c_Orderings_Obot__class_Obot(tc_fun(U_8682,tc_HOL_Obool))))))
| U_8683 = c_Orderings_Obot__class_Obot(tc_fun(U_8682,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8682),U_8683))
| ~ class_Orderings_Olinorder(U_8682) ),
inference(clausify,[status(thm)],[f_2494_4]) ).
fof(f_2495_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_2495_2,plain,
! [U_8687,U_8686] :
( hBOOL(hAPP(hAPP(c_member(U_8686),c_Big__Operators_Olinorder__class_OMin(U_8686,U_8687)),U_8687))
| ? [U_8685,U_8684] : ~ hBOOL(hAPP(hAPP(c_member(U_8686),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8686),U_8685),U_8684)),hAPP(hAPP(c_Set_Oinsert(U_8686),U_8685),hAPP(hAPP(c_Set_Oinsert(U_8686),U_8684),c_Orderings_Obot__class_Obot(tc_fun(U_8686,tc_HOL_Obool))))))
| U_8687 = c_Orderings_Obot__class_Obot(tc_fun(U_8686,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8686),U_8687))
| ~ class_Orderings_Olinorder(U_8686) ),
inference(variable_rename,[status(thm)],[f_2495_1]) ).
fof(f_2495_3,plain,
! [U_8687,U_8686] :
( hBOOL(hAPP(hAPP(c_member(U_8686),c_Big__Operators_Olinorder__class_OMin(U_8686,U_8687)),U_8687))
| ? [U_8684] : ~ hBOOL(hAPP(hAPP(c_member(U_8686),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8686),sK217(U_8687,U_8686)),U_8684)),hAPP(hAPP(c_Set_Oinsert(U_8686),sK217(U_8687,U_8686)),hAPP(hAPP(c_Set_Oinsert(U_8686),U_8684),c_Orderings_Obot__class_Obot(tc_fun(U_8686,tc_HOL_Obool))))))
| U_8687 = c_Orderings_Obot__class_Obot(tc_fun(U_8686,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8686),U_8687))
| ~ class_Orderings_Olinorder(U_8686) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK217]),skolemize(U_8685,sK217(U_8687,U_8686))],[f_2495_2]) ).
fof(f_2495_4,plain,
! [U_8687,U_8686] :
( hBOOL(hAPP(hAPP(c_member(U_8686),c_Big__Operators_Olinorder__class_OMin(U_8686,U_8687)),U_8687))
| ~ hBOOL(hAPP(hAPP(c_member(U_8686),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8686),sK217(U_8687,U_8686)),sK218(U_8687,U_8686))),hAPP(hAPP(c_Set_Oinsert(U_8686),sK217(U_8687,U_8686)),hAPP(hAPP(c_Set_Oinsert(U_8686),sK218(U_8687,U_8686)),c_Orderings_Obot__class_Obot(tc_fun(U_8686,tc_HOL_Obool))))))
| U_8687 = c_Orderings_Obot__class_Obot(tc_fun(U_8686,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8686),U_8687))
| ~ class_Orderings_Olinorder(U_8686) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK218]),skolemize(U_8684,sK218(U_8687,U_8686))],[f_2495_3]) ).
cnf(f_2495_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_8686),c_Big__Operators_Olinorder__class_OMin(U_8686,U_8687)),U_8687))
| ~ hBOOL(hAPP(hAPP(c_member(U_8686),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8686),sK217(U_8687,U_8686)),sK218(U_8687,U_8686))),hAPP(hAPP(c_Set_Oinsert(U_8686),sK217(U_8687,U_8686)),hAPP(hAPP(c_Set_Oinsert(U_8686),sK218(U_8687,U_8686)),c_Orderings_Obot__class_Obot(tc_fun(U_8686,tc_HOL_Obool))))))
| U_8687 = c_Orderings_Obot__class_Obot(tc_fun(U_8686,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8686),U_8687))
| ~ class_Orderings_Olinorder(U_8686) ),
inference(clausify,[status(thm)],[f_2495_4]) ).
fof(f_2496_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_2496_2,plain,
! [U_8689,U_8688] : c_Nitpick_Oint__lcm(U_8688,U_8689) = 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_8688)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8689)))),
inference(variable_rename,[status(thm)],[f_2496_1]) ).
cnf(f_2496_3,plain,
c_Nitpick_Oint__lcm(U_8688,U_8689) = 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_8688)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8689)))),
inference(clausify,[status(thm)],[f_2496_2]) ).
fof(f_2497_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_2497_2,plain,
! [U_8694,U_8693,U_8692] :
( hAPP(U_8693,c_Big__Operators_Olattice_OInf__fin(U_8692,c_Orderings_Oord__class_Omin(U_8692),U_8694)) = c_Big__Operators_Olattice_OInf__fin(U_8692,c_Orderings_Oord__class_Omin(U_8692),hAPP(c_Set_Oimage(U_8692,U_8692,U_8693),U_8694))
| U_8694 = c_Orderings_Obot__class_Obot(tc_fun(U_8692,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8692),U_8694))
| ? [U_8691,U_8690] : hAPP(U_8693,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8692),U_8691),U_8690)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8692),hAPP(U_8693,U_8691)),hAPP(U_8693,U_8690))
| ~ class_Orderings_Olinorder(U_8692) ),
inference(variable_rename,[status(thm)],[f_2497_1]) ).
fof(f_2497_3,plain,
! [U_8694,U_8693,U_8692] :
( hAPP(U_8693,c_Big__Operators_Olattice_OInf__fin(U_8692,c_Orderings_Oord__class_Omin(U_8692),U_8694)) = c_Big__Operators_Olattice_OInf__fin(U_8692,c_Orderings_Oord__class_Omin(U_8692),hAPP(c_Set_Oimage(U_8692,U_8692,U_8693),U_8694))
| U_8694 = c_Orderings_Obot__class_Obot(tc_fun(U_8692,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8692),U_8694))
| ? [U_8690] : hAPP(U_8693,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8692),sK219(U_8694,U_8693,U_8692)),U_8690)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8692),hAPP(U_8693,sK219(U_8694,U_8693,U_8692))),hAPP(U_8693,U_8690))
| ~ class_Orderings_Olinorder(U_8692) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK219]),skolemize(U_8691,sK219(U_8694,U_8693,U_8692))],[f_2497_2]) ).
fof(f_2497_4,plain,
! [U_8694,U_8693,U_8692] :
( hAPP(U_8693,c_Big__Operators_Olattice_OInf__fin(U_8692,c_Orderings_Oord__class_Omin(U_8692),U_8694)) = c_Big__Operators_Olattice_OInf__fin(U_8692,c_Orderings_Oord__class_Omin(U_8692),hAPP(c_Set_Oimage(U_8692,U_8692,U_8693),U_8694))
| U_8694 = c_Orderings_Obot__class_Obot(tc_fun(U_8692,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8692),U_8694))
| hAPP(U_8693,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8692),sK219(U_8694,U_8693,U_8692)),sK220(U_8694,U_8693,U_8692))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8692),hAPP(U_8693,sK219(U_8694,U_8693,U_8692))),hAPP(U_8693,sK220(U_8694,U_8693,U_8692)))
| ~ class_Orderings_Olinorder(U_8692) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK220]),skolemize(U_8690,sK220(U_8694,U_8693,U_8692))],[f_2497_3]) ).
cnf(f_2497_5,plain,
( hAPP(U_8693,c_Big__Operators_Olattice_OInf__fin(U_8692,c_Orderings_Oord__class_Omin(U_8692),U_8694)) = c_Big__Operators_Olattice_OInf__fin(U_8692,c_Orderings_Oord__class_Omin(U_8692),hAPP(c_Set_Oimage(U_8692,U_8692,U_8693),U_8694))
| U_8694 = c_Orderings_Obot__class_Obot(tc_fun(U_8692,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8692),U_8694))
| hAPP(U_8693,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8692),sK219(U_8694,U_8693,U_8692)),sK220(U_8694,U_8693,U_8692))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8692),hAPP(U_8693,sK219(U_8694,U_8693,U_8692))),hAPP(U_8693,sK220(U_8694,U_8693,U_8692)))
| ~ class_Orderings_Olinorder(U_8692) ),
inference(clausify,[status(thm)],[f_2497_4]) ).
fof(f_2498_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_2498_2,plain,
! [U_8696,U_8695] : c_Nitpick_Onat__lcm(U_8695,U_8696) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8695),U_8696)),c_Nitpick_Onat__gcd(U_8695,U_8696)),
inference(variable_rename,[status(thm)],[f_2498_1]) ).
cnf(f_2498_3,plain,
c_Nitpick_Onat__lcm(U_8695,U_8696) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8695),U_8696)),c_Nitpick_Onat__gcd(U_8695,U_8696)),
inference(clausify,[status(thm)],[f_2498_2]) ).
fof(f_2499_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_2499_2,plain,
! [U_8701,U_8700,U_8699] :
( hAPP(U_8700,c_Big__Operators_Olinorder__class_OMin(U_8699,U_8701)) = c_Big__Operators_Olinorder__class_OMin(U_8699,hAPP(c_Set_Oimage(U_8699,U_8699,U_8700),U_8701))
| U_8701 = c_Orderings_Obot__class_Obot(tc_fun(U_8699,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8699),U_8701))
| ? [U_8698,U_8697] : hAPP(U_8700,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8699),U_8698),U_8697)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8699),hAPP(U_8700,U_8698)),hAPP(U_8700,U_8697))
| ~ class_Orderings_Olinorder(U_8699) ),
inference(variable_rename,[status(thm)],[f_2499_1]) ).
fof(f_2499_3,plain,
! [U_8701,U_8700,U_8699] :
( hAPP(U_8700,c_Big__Operators_Olinorder__class_OMin(U_8699,U_8701)) = c_Big__Operators_Olinorder__class_OMin(U_8699,hAPP(c_Set_Oimage(U_8699,U_8699,U_8700),U_8701))
| U_8701 = c_Orderings_Obot__class_Obot(tc_fun(U_8699,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8699),U_8701))
| ? [U_8697] : hAPP(U_8700,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8699),sK221(U_8701,U_8700,U_8699)),U_8697)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8699),hAPP(U_8700,sK221(U_8701,U_8700,U_8699))),hAPP(U_8700,U_8697))
| ~ class_Orderings_Olinorder(U_8699) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK221]),skolemize(U_8698,sK221(U_8701,U_8700,U_8699))],[f_2499_2]) ).
fof(f_2499_4,plain,
! [U_8701,U_8700,U_8699] :
( hAPP(U_8700,c_Big__Operators_Olinorder__class_OMin(U_8699,U_8701)) = c_Big__Operators_Olinorder__class_OMin(U_8699,hAPP(c_Set_Oimage(U_8699,U_8699,U_8700),U_8701))
| U_8701 = c_Orderings_Obot__class_Obot(tc_fun(U_8699,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8699),U_8701))
| hAPP(U_8700,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8699),sK221(U_8701,U_8700,U_8699)),sK222(U_8701,U_8700,U_8699))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8699),hAPP(U_8700,sK221(U_8701,U_8700,U_8699))),hAPP(U_8700,sK222(U_8701,U_8700,U_8699)))
| ~ class_Orderings_Olinorder(U_8699) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK222]),skolemize(U_8697,sK222(U_8701,U_8700,U_8699))],[f_2499_3]) ).
cnf(f_2499_5,plain,
( hAPP(U_8700,c_Big__Operators_Olinorder__class_OMin(U_8699,U_8701)) = c_Big__Operators_Olinorder__class_OMin(U_8699,hAPP(c_Set_Oimage(U_8699,U_8699,U_8700),U_8701))
| U_8701 = c_Orderings_Obot__class_Obot(tc_fun(U_8699,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8699),U_8701))
| hAPP(U_8700,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8699),sK221(U_8701,U_8700,U_8699)),sK222(U_8701,U_8700,U_8699))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8699),hAPP(U_8700,sK221(U_8701,U_8700,U_8699))),hAPP(U_8700,sK222(U_8701,U_8700,U_8699)))
| ~ class_Orderings_Olinorder(U_8699) ),
inference(clausify,[status(thm)],[f_2499_4]) ).
fof(f_2500_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_2500_2,plain,
! [U_8703,U_8702] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_8702),c_Big__Operators_Olinorder__class_OMin(U_8702,U_8703)) = c_Big__Operators_Olinorder__class_OMax(U_8702,hAPP(c_Set_Oimage(U_8702,U_8702,c_Groups_Ouminus__class_Ouminus(U_8702)),U_8703))
| U_8703 = c_Orderings_Obot__class_Obot(tc_fun(U_8702,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8702),U_8703))
| ~ class_Groups_Olinordered__ab__group__add(U_8702) ),
inference(variable_rename,[status(thm)],[f_2500_1]) ).
cnf(f_2500_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_8702),c_Big__Operators_Olinorder__class_OMin(U_8702,U_8703)) = c_Big__Operators_Olinorder__class_OMax(U_8702,hAPP(c_Set_Oimage(U_8702,U_8702,c_Groups_Ouminus__class_Ouminus(U_8702)),U_8703))
| U_8703 = c_Orderings_Obot__class_Obot(tc_fun(U_8702,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8702),U_8703))
| ~ class_Groups_Olinordered__ab__group__add(U_8702) ),
inference(clausify,[status(thm)],[f_2500_2]) ).
fof(f_2501_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_2501_2,plain,
! [U_8705,U_8704] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_8704),c_Big__Operators_Olinorder__class_OMax(U_8704,U_8705)) = c_Big__Operators_Olinorder__class_OMin(U_8704,hAPP(c_Set_Oimage(U_8704,U_8704,c_Groups_Ouminus__class_Ouminus(U_8704)),U_8705))
| U_8705 = c_Orderings_Obot__class_Obot(tc_fun(U_8704,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8704),U_8705))
| ~ class_Groups_Olinordered__ab__group__add(U_8704) ),
inference(variable_rename,[status(thm)],[f_2501_1]) ).
cnf(f_2501_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_8704),c_Big__Operators_Olinorder__class_OMax(U_8704,U_8705)) = c_Big__Operators_Olinorder__class_OMin(U_8704,hAPP(c_Set_Oimage(U_8704,U_8704,c_Groups_Ouminus__class_Ouminus(U_8704)),U_8705))
| U_8705 = c_Orderings_Obot__class_Obot(tc_fun(U_8704,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8704),U_8705))
| ~ class_Groups_Olinordered__ab__group__add(U_8704) ),
inference(clausify,[status(thm)],[f_2501_2]) ).
fof(f_2502_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_2502_2,plain,
! [U_8707,U_8706] :
( c_Big__Operators_Olinorder__class_OMax(U_8706,hAPP(hAPP(c_Set_Oinsert(U_8706),U_8707),c_Orderings_Obot__class_Obot(tc_fun(U_8706,tc_HOL_Obool)))) = U_8707
| ~ class_Orderings_Olinorder(U_8706) ),
inference(variable_rename,[status(thm)],[f_2502_1]) ).
cnf(f_2502_3,plain,
( c_Big__Operators_Olinorder__class_OMax(U_8706,hAPP(hAPP(c_Set_Oinsert(U_8706),U_8707),c_Orderings_Obot__class_Obot(tc_fun(U_8706,tc_HOL_Obool)))) = U_8707
| ~ class_Orderings_Olinorder(U_8706) ),
inference(clausify,[status(thm)],[f_2502_2]) ).
fof(f_2503_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_2503_2,plain,
! [U_8710,U_8709,U_8708] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8708),U_8710),c_Big__Operators_Olinorder__class_OMax(U_8708,U_8709)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8708),U_8710),U_8709))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8708),U_8709))
| ~ class_Orderings_Olinorder(U_8708) ),
inference(variable_rename,[status(thm)],[f_2503_1]) ).
cnf(f_2503_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8708),U_8710),c_Big__Operators_Olinorder__class_OMax(U_8708,U_8709)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8708),U_8710),U_8709))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8708),U_8709))
| ~ class_Orderings_Olinorder(U_8708) ),
inference(clausify,[status(thm)],[f_2503_2]) ).
fof(f_2504_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_2504_2,plain,
! [U_8712,U_8711] :
( hBOOL(hAPP(hAPP(c_member(U_8711),c_Big__Operators_Olinorder__class_OMax(U_8711,U_8712)),U_8712))
| U_8712 = c_Orderings_Obot__class_Obot(tc_fun(U_8711,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8711),U_8712))
| ~ class_Orderings_Olinorder(U_8711) ),
inference(variable_rename,[status(thm)],[f_2504_1]) ).
cnf(f_2504_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8711),c_Big__Operators_Olinorder__class_OMax(U_8711,U_8712)),U_8712))
| U_8712 = c_Orderings_Obot__class_Obot(tc_fun(U_8711,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8711),U_8712))
| ~ class_Orderings_Olinorder(U_8711) ),
inference(clausify,[status(thm)],[f_2504_2]) ).
fof(f_2505_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_2505_2,plain,
! [U_8715,U_8714,U_8713] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8713),c_Big__Operators_Olinorder__class_OMax(U_8713,U_8714)),c_Big__Operators_Olinorder__class_OMax(U_8713,U_8715)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8713),U_8715))
| U_8714 = c_Orderings_Obot__class_Obot(tc_fun(U_8713,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8713,tc_HOL_Obool)),U_8714),U_8715))
| ~ class_Orderings_Olinorder(U_8713) ),
inference(variable_rename,[status(thm)],[f_2505_1]) ).
cnf(f_2505_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8713),c_Big__Operators_Olinorder__class_OMax(U_8713,U_8714)),c_Big__Operators_Olinorder__class_OMax(U_8713,U_8715)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8713),U_8715))
| U_8714 = c_Orderings_Obot__class_Obot(tc_fun(U_8713,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8713,tc_HOL_Obool)),U_8714),U_8715))
| ~ class_Orderings_Olinorder(U_8713) ),
inference(clausify,[status(thm)],[f_2505_2]) ).
fof(f_2506_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_2506_2,plain,
! [U_8717,U_8716] :
( ( c_Nitpick_Onat__gcd(U_8717,U_8716) = c_Nitpick_Onat__gcd(U_8716,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8717,U_8716))
| U_8716 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Nitpick_Onat__gcd(U_8717,U_8716) = U_8717
| U_8716 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_2506_1]) ).
fof(f_2506_3,plain,
( ! [U_8721,U_8719] :
( c_Nitpick_Onat__gcd(U_8721,U_8719) = c_Nitpick_Onat__gcd(U_8719,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8721,U_8719))
| U_8719 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_8720,U_8718] :
( c_Nitpick_Onat__gcd(U_8720,U_8718) = U_8720
| U_8718 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_2506_2]) ).
cnf(f_2506_4,plain,
( c_Nitpick_Onat__gcd(U_8720,U_8718) = U_8720
| U_8718 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_2506_3]) ).
cnf(f_2506_5,plain,
( c_Nitpick_Onat__gcd(U_8721,U_8719) = c_Nitpick_Onat__gcd(U_8719,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8721,U_8719))
| U_8719 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_2506_3]) ).
fof(f_2507_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_2507_2,plain,
! [U_8723,U_8722] : hAPP(hAPP(c_Nitpick_Oint__gcd,U_8722),U_8723) = 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_8722)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8723)))),
inference(variable_rename,[status(thm)],[f_2507_1]) ).
cnf(f_2507_3,plain,
hAPP(hAPP(c_Nitpick_Oint__gcd,U_8722),U_8723) = 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_8722)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8723)))),
inference(clausify,[status(thm)],[f_2507_2]) ).
fof(f_2508_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_2508_2,plain,
! [U_8726,U_8725,U_8724] :
( ( ( c_Big__Operators_Olinorder__class_OMax(U_8724,U_8725) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8724),U_8726),c_Big__Operators_Olinorder__class_OMax(U_8724,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8724,tc_HOL_Obool)),U_8725),hAPP(hAPP(c_Set_Oinsert(U_8724),U_8726),c_Orderings_Obot__class_Obot(tc_fun(U_8724,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8724,tc_HOL_Obool)),U_8725),hAPP(hAPP(c_Set_Oinsert(U_8724),U_8726),c_Orderings_Obot__class_Obot(tc_fun(U_8724,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8724,tc_HOL_Obool)) )
& ( c_Big__Operators_Olinorder__class_OMax(U_8724,U_8725) = U_8726
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8724,tc_HOL_Obool)),U_8725),hAPP(hAPP(c_Set_Oinsert(U_8724),U_8726),c_Orderings_Obot__class_Obot(tc_fun(U_8724,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8724,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_8724),U_8726),U_8725))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8724),U_8725))
| ~ class_Orderings_Olinorder(U_8724) ),
inference(variable_rename,[status(thm)],[f_2508_1]) ).
cnf(f_2508_3,plain,
( c_Big__Operators_Olinorder__class_OMax(U_8724,U_8725) = U_8726
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8724,tc_HOL_Obool)),U_8725),hAPP(hAPP(c_Set_Oinsert(U_8724),U_8726),c_Orderings_Obot__class_Obot(tc_fun(U_8724,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8724,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_8724),U_8726),U_8725))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8724),U_8725))
| ~ class_Orderings_Olinorder(U_8724) ),
inference(clausify,[status(thm)],[f_2508_2]) ).
cnf(f_2508_4,plain,
( c_Big__Operators_Olinorder__class_OMax(U_8724,U_8725) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8724),U_8726),c_Big__Operators_Olinorder__class_OMax(U_8724,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8724,tc_HOL_Obool)),U_8725),hAPP(hAPP(c_Set_Oinsert(U_8724),U_8726),c_Orderings_Obot__class_Obot(tc_fun(U_8724,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8724,tc_HOL_Obool)),U_8725),hAPP(hAPP(c_Set_Oinsert(U_8724),U_8726),c_Orderings_Obot__class_Obot(tc_fun(U_8724,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8724,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_8724),U_8726),U_8725))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8724),U_8725))
| ~ class_Orderings_Olinorder(U_8724) ),
inference(clausify,[status(thm)],[f_2508_2]) ).
fof(f_2509_1,plain,
! [V_c_2,V_b_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_c_2),V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le__fold__inf]) ).
fof(f_2509_2,plain,
! [U_8731,U_8730,U_8729,U_8728] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8728),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8728),U_8730),U_8731)),hAPP(hAPP(c_Finite__Set_Ofold(U_8728,U_8728,c_Orderings_Oord__class_Omin(U_8728)),U_8731),U_8729)))
| ? [U_8727] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8728),U_8730),U_8727))
& hBOOL(hAPP(hAPP(c_member(U_8728),U_8727),U_8729)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8728),U_8729))
| ~ class_Orderings_Olinorder(U_8728) ),
inference(variable_rename,[status(thm)],[f_2509_1]) ).
fof(f_2509_3,plain,
! [U_8731,U_8730,U_8729,U_8728] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8728),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8728),U_8730),U_8731)),hAPP(hAPP(c_Finite__Set_Ofold(U_8728,U_8728,c_Orderings_Oord__class_Omin(U_8728)),U_8731),U_8729)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8728),U_8730),sK223(U_8731,U_8730,U_8729,U_8728)))
& hBOOL(hAPP(hAPP(c_member(U_8728),sK223(U_8731,U_8730,U_8729,U_8728)),U_8729)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8728),U_8729))
| ~ class_Orderings_Olinorder(U_8728) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK223]),skolemize(U_8727,sK223(U_8731,U_8730,U_8729,U_8728))],[f_2509_2]) ).
cnf(f_2509_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8728),sK223(U_8731,U_8730,U_8729,U_8728)),U_8729))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8728),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8728),U_8730),U_8731)),hAPP(hAPP(c_Finite__Set_Ofold(U_8728,U_8728,c_Orderings_Oord__class_Omin(U_8728)),U_8731),U_8729)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8728),U_8729))
| ~ class_Orderings_Olinorder(U_8728) ),
inference(clausify,[status(thm)],[f_2509_3]) ).
cnf(f_2509_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8728),U_8730),sK223(U_8731,U_8730,U_8729,U_8728)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8728),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8728),U_8730),U_8731)),hAPP(hAPP(c_Finite__Set_Ofold(U_8728,U_8728,c_Orderings_Oord__class_Omin(U_8728)),U_8731),U_8729)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8728),U_8729))
| ~ class_Orderings_Olinorder(U_8728) ),
inference(clausify,[status(thm)],[f_2509_3]) ).
fof(f_2510_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_2510_2,plain,
! [U_8735,U_8734,U_8733] :
( c_Big__Operators_Olinorder__class_OMax(U_8733,U_8734) = U_8735
| ~ hBOOL(hAPP(hAPP(c_member(U_8733),U_8735),U_8734))
| ? [U_8732] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8733),U_8732),U_8735))
& hBOOL(hAPP(hAPP(c_member(U_8733),U_8732),U_8734)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8733),U_8734))
| ~ class_Orderings_Olinorder(U_8733) ),
inference(variable_rename,[status(thm)],[f_2510_1]) ).
fof(f_2510_3,plain,
! [U_8735,U_8734,U_8733] :
( c_Big__Operators_Olinorder__class_OMax(U_8733,U_8734) = U_8735
| ~ hBOOL(hAPP(hAPP(c_member(U_8733),U_8735),U_8734))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8733),sK224(U_8735,U_8734,U_8733)),U_8735))
& hBOOL(hAPP(hAPP(c_member(U_8733),sK224(U_8735,U_8734,U_8733)),U_8734)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8733),U_8734))
| ~ class_Orderings_Olinorder(U_8733) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK224]),skolemize(U_8732,sK224(U_8735,U_8734,U_8733))],[f_2510_2]) ).
cnf(f_2510_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8733),sK224(U_8735,U_8734,U_8733)),U_8734))
| c_Big__Operators_Olinorder__class_OMax(U_8733,U_8734) = U_8735
| ~ hBOOL(hAPP(hAPP(c_member(U_8733),U_8735),U_8734))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8733),U_8734))
| ~ class_Orderings_Olinorder(U_8733) ),
inference(clausify,[status(thm)],[f_2510_3]) ).
cnf(f_2510_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8733),sK224(U_8735,U_8734,U_8733)),U_8735))
| c_Big__Operators_Olinorder__class_OMax(U_8733,U_8734) = U_8735
| ~ hBOOL(hAPP(hAPP(c_member(U_8733),U_8735),U_8734))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8733),U_8734))
| ~ class_Orderings_Olinorder(U_8733) ),
inference(clausify,[status(thm)],[f_2510_3]) ).
fof(f_2511_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_2511_2,plain,
! [U_8738,U_8737,U_8736] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8736),U_8737),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8736),U_8737),U_8738)) = U_8737
| ~ class_Orderings_Olinorder(U_8736) ),
inference(variable_rename,[status(thm)],[f_2511_1]) ).
cnf(f_2511_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8736),U_8737),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8736),U_8737),U_8738)) = U_8737
| ~ class_Orderings_Olinorder(U_8736) ),
inference(clausify,[status(thm)],[f_2511_2]) ).
fof(f_2512_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_2512_2,plain,
! [U_8741,U_8740,U_8739] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8739),U_8740),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8739),U_8740),U_8741)) = U_8740
| ~ class_Orderings_Olinorder(U_8739) ),
inference(variable_rename,[status(thm)],[f_2512_1]) ).
cnf(f_2512_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8739),U_8740),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8739),U_8740),U_8741)) = U_8740
| ~ class_Orderings_Olinorder(U_8739) ),
inference(clausify,[status(thm)],[f_2512_2]) ).
fof(f_2513_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_2513_2,plain,
! [U_8745,U_8744,U_8743,U_8742] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8742),U_8743),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8742),U_8744),U_8745)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8742),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8742),U_8743),U_8744)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8742),U_8743),U_8745))
| ~ class_Orderings_Olinorder(U_8742) ),
inference(variable_rename,[status(thm)],[f_2513_1]) ).
cnf(f_2513_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8742),U_8743),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8742),U_8744),U_8745)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8742),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8742),U_8743),U_8744)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8742),U_8743),U_8745))
| ~ class_Orderings_Olinorder(U_8742) ),
inference(clausify,[status(thm)],[f_2513_2]) ).
fof(f_2514_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_2514_2,plain,
! [U_8749,U_8748,U_8747,U_8746] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8746),U_8747),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8746),U_8748),U_8749)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8746),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8746),U_8747),U_8748)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8746),U_8747),U_8749))
| ~ class_Orderings_Olinorder(U_8746) ),
inference(variable_rename,[status(thm)],[f_2514_1]) ).
cnf(f_2514_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8746),U_8747),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8746),U_8748),U_8749)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8746),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8746),U_8747),U_8748)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8746),U_8747),U_8749))
| ~ class_Orderings_Olinorder(U_8746) ),
inference(clausify,[status(thm)],[f_2514_2]) ).
fof(f_2515_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_2515_2,plain,
! [U_8753,U_8752,U_8751,U_8750] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8750),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8750),U_8751),U_8752)),U_8753) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8750),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8750),U_8751),U_8753)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8750),U_8752),U_8753))
| ~ class_Orderings_Olinorder(U_8750) ),
inference(variable_rename,[status(thm)],[f_2515_1]) ).
cnf(f_2515_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8750),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8750),U_8751),U_8752)),U_8753) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8750),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8750),U_8751),U_8753)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8750),U_8752),U_8753))
| ~ class_Orderings_Olinorder(U_8750) ),
inference(clausify,[status(thm)],[f_2515_2]) ).
fof(f_2516_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_2516_2,plain,
! [U_8757,U_8756,U_8755,U_8754] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8754),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8754),U_8755),U_8756)),U_8757) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8754),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8754),U_8755),U_8757)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8754),U_8756),U_8757))
| ~ class_Orderings_Olinorder(U_8754) ),
inference(variable_rename,[status(thm)],[f_2516_1]) ).
cnf(f_2516_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8754),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8754),U_8755),U_8756)),U_8757) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8754),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8754),U_8755),U_8757)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8754),U_8756),U_8757))
| ~ class_Orderings_Olinorder(U_8754) ),
inference(clausify,[status(thm)],[f_2516_2]) ).
fof(f_2517_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_2517_2,plain,
! [U_8758] :
( c_Finite__Set_Ofun__left__comm__idem(U_8758,U_8758,c_Orderings_Oord__class_Omax(U_8758))
| ~ class_Orderings_Olinorder(U_8758) ),
inference(variable_rename,[status(thm)],[f_2517_1]) ).
cnf(f_2517_3,plain,
( c_Finite__Set_Ofun__left__comm__idem(U_8758,U_8758,c_Orderings_Oord__class_Omax(U_8758))
| ~ class_Orderings_Olinorder(U_8758) ),
inference(clausify,[status(thm)],[f_2517_2]) ).
fof(f_2518_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_2518_2,plain,
! [U_8759] :
( c_Lattices_Osemilattice__sup__class_Osup(U_8759) = c_Orderings_Oord__class_Omax(U_8759)
| ~ class_Orderings_Olinorder(U_8759)
| ~ class_Lattices_Osemilattice__sup(U_8759) ),
inference(variable_rename,[status(thm)],[f_2518_1]) ).
cnf(f_2518_3,plain,
( c_Lattices_Osemilattice__sup__class_Osup(U_8759) = c_Orderings_Oord__class_Omax(U_8759)
| ~ class_Orderings_Olinorder(U_8759)
| ~ class_Lattices_Osemilattice__sup(U_8759) ),
inference(clausify,[status(thm)],[f_2518_2]) ).
fof(f_2519_1,plain,
! [V_n_2,V_m_2,V_f_2,T_b,T_c] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,V_n_2)) = hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_m_2),V_n_2))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_max__of__mono]) ).
fof(f_2519_2,plain,
! [U_8764,U_8763,U_8762,U_8761,U_8760] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8760),hAPP(U_8762,U_8763)),hAPP(U_8762,U_8764)) = hAPP(U_8762,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8761),U_8763),U_8764))
| ~ c_Orderings_Oorder__class_Omono(U_8761,U_8760,U_8762)
| ~ class_Orderings_Olinorder(U_8761)
| ~ class_Orderings_Olinorder(U_8760) ),
inference(variable_rename,[status(thm)],[f_2519_1]) ).
cnf(f_2519_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8760),hAPP(U_8762,U_8763)),hAPP(U_8762,U_8764)) = hAPP(U_8762,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8761),U_8763),U_8764))
| ~ c_Orderings_Oorder__class_Omono(U_8761,U_8760,U_8762)
| ~ class_Orderings_Olinorder(U_8761)
| ~ class_Orderings_Olinorder(U_8760) ),
inference(clausify,[status(thm)],[f_2519_2]) ).
fof(f_2520_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_2520_2,plain,
! [U_8765] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8765),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_8765,
inference(variable_rename,[status(thm)],[f_2520_1]) ).
cnf(f_2520_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8765),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_8765,
inference(clausify,[status(thm)],[f_2520_2]) ).
fof(f_2521_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_2521_2,plain,
! [U_8766] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8766) = U_8766,
inference(variable_rename,[status(thm)],[f_2521_1]) ).
cnf(f_2521_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8766) = U_8766,
inference(clausify,[status(thm)],[f_2521_2]) ).
fof(f_2522_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_2522_2,plain,
! [U_8768,U_8767] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8767),U_8768),U_8768) = U_8768
| ~ class_Orderings_Olinorder(U_8767) ),
inference(variable_rename,[status(thm)],[f_2522_1]) ).
cnf(f_2522_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8767),U_8768),U_8768) = U_8768
| ~ class_Orderings_Olinorder(U_8767) ),
inference(clausify,[status(thm)],[f_2522_2]) ).
fof(f_2523_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_2523_2,plain,
! [U_8771,U_8770,U_8769] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8769),U_8770),U_8771) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8769),U_8771),U_8770)
| ~ class_Orderings_Olinorder(U_8769) ),
inference(variable_rename,[status(thm)],[f_2523_1]) ).
cnf(f_2523_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8769),U_8770),U_8771) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8769),U_8771),U_8770)
| ~ class_Orderings_Olinorder(U_8769) ),
inference(clausify,[status(thm)],[f_2523_2]) ).
fof(f_2524_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_2524_2,plain,
! [U_8774,U_8773,U_8772] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8772),U_8773),U_8774) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8772),U_8774),U_8773)
| ~ class_Orderings_Olinorder(U_8772) ),
inference(variable_rename,[status(thm)],[f_2524_1]) ).
cnf(f_2524_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8772),U_8773),U_8774) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8772),U_8774),U_8773)
| ~ class_Orderings_Olinorder(U_8772) ),
inference(clausify,[status(thm)],[f_2524_2]) ).
fof(f_2525_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_2525_2,plain,
! [U_8777,U_8776,U_8775] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8775),U_8776),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8775),U_8776),U_8777)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8775),U_8776),U_8777)
| ~ class_Orderings_Olinorder(U_8775) ),
inference(variable_rename,[status(thm)],[f_2525_1]) ).
cnf(f_2525_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8775),U_8776),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8775),U_8776),U_8777)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8775),U_8776),U_8777)
| ~ class_Orderings_Olinorder(U_8775) ),
inference(clausify,[status(thm)],[f_2525_2]) ).
fof(f_2526_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_2526_2,plain,
! [U_8780,U_8779,U_8778] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8778),U_8779),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8778),U_8779),U_8780)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8778),U_8779),U_8780)
| ~ class_Orderings_Olinorder(U_8778) ),
inference(variable_rename,[status(thm)],[f_2526_1]) ).
cnf(f_2526_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8778),U_8779),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8778),U_8779),U_8780)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8778),U_8779),U_8780)
| ~ class_Orderings_Olinorder(U_8778) ),
inference(clausify,[status(thm)],[f_2526_2]) ).
fof(f_2527_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_2527_2,plain,
! [U_8784,U_8783,U_8782,U_8781] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8781),U_8782),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8781),U_8783),U_8784)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8781),U_8783),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8781),U_8782),U_8784))
| ~ class_Orderings_Olinorder(U_8781) ),
inference(variable_rename,[status(thm)],[f_2527_1]) ).
cnf(f_2527_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8781),U_8782),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8781),U_8783),U_8784)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8781),U_8783),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8781),U_8782),U_8784))
| ~ class_Orderings_Olinorder(U_8781) ),
inference(clausify,[status(thm)],[f_2527_2]) ).
fof(f_2528_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_2528_2,plain,
! [U_8788,U_8787,U_8786,U_8785] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8785),U_8786),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8785),U_8787),U_8788)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8785),U_8787),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8785),U_8786),U_8788))
| ~ class_Orderings_Olinorder(U_8785) ),
inference(variable_rename,[status(thm)],[f_2528_1]) ).
cnf(f_2528_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8785),U_8786),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8785),U_8787),U_8788)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8785),U_8787),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8785),U_8786),U_8788))
| ~ class_Orderings_Olinorder(U_8785) ),
inference(clausify,[status(thm)],[f_2528_2]) ).
fof(f_2529_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_2529_2,plain,
! [U_8792,U_8791,U_8790,U_8789] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8789),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8789),U_8790),U_8791)),U_8792) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8789),U_8790),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8789),U_8791),U_8792))
| ~ class_Orderings_Olinorder(U_8789) ),
inference(variable_rename,[status(thm)],[f_2529_1]) ).
cnf(f_2529_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8789),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8789),U_8790),U_8791)),U_8792) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8789),U_8790),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8789),U_8791),U_8792))
| ~ class_Orderings_Olinorder(U_8789) ),
inference(clausify,[status(thm)],[f_2529_2]) ).
fof(f_2530_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_2530_2,plain,
! [U_8796,U_8795,U_8794,U_8793] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8793),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8793),U_8794),U_8795)),U_8796) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8793),U_8794),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8793),U_8795),U_8796))
| ~ class_Orderings_Olinorder(U_8793) ),
inference(variable_rename,[status(thm)],[f_2530_1]) ).
cnf(f_2530_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8793),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8793),U_8794),U_8795)),U_8796) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8793),U_8794),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8793),U_8795),U_8796))
| ~ class_Orderings_Olinorder(U_8793) ),
inference(clausify,[status(thm)],[f_2530_2]) ).
fof(f_2531_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_2531_2,plain,
! [U_8798,U_8797] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8797),U_8798),U_8798) = U_8798
| ~ class_Orderings_Olinorder(U_8797) ),
inference(variable_rename,[status(thm)],[f_2531_1]) ).
cnf(f_2531_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8797),U_8798),U_8798) = U_8798
| ~ class_Orderings_Olinorder(U_8797) ),
inference(clausify,[status(thm)],[f_2531_2]) ).
fof(f_2532_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_2532_2,plain,
! [U_8802,U_8801,U_8800,U_8799] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8799),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8799),U_8800),U_8801)),U_8802) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8799),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8799),U_8800),U_8802)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8799),U_8801),U_8802))
| ~ class_Groups_Oordered__ab__group__add(U_8799) ),
inference(variable_rename,[status(thm)],[f_2532_1]) ).
cnf(f_2532_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8799),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8799),U_8800),U_8801)),U_8802) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8799),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8799),U_8800),U_8802)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8799),U_8801),U_8802))
| ~ class_Groups_Oordered__ab__group__add(U_8799) ),
inference(clausify,[status(thm)],[f_2532_2]) ).
fof(f_2533_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_2533_2,plain,
! [U_8804,U_8803] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8803)),hAPP(c_Nat_OSuc,U_8804)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8803),U_8804)),
inference(variable_rename,[status(thm)],[f_2533_1]) ).
cnf(f_2533_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8803)),hAPP(c_Nat_OSuc,U_8804)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8803),U_8804)),
inference(clausify,[status(thm)],[f_2533_2]) ).
fof(f_2534_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_2534_2,plain,
! [U_8808,U_8807,U_8806,U_8805] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8805),U_8806),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8805),U_8807),U_8808)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8805),U_8806),U_8808))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8805),U_8806),U_8807)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8805),U_8806),U_8808))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8805),U_8806),U_8807))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8805),U_8806),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8805),U_8807),U_8808))) ) )
| ~ class_Orderings_Olinorder(U_8805) ),
inference(variable_rename,[status(thm)],[f_2534_1]) ).
cnf(f_2534_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8805),U_8806),U_8808))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8805),U_8806),U_8807))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8805),U_8806),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8805),U_8807),U_8808)))
| ~ class_Orderings_Olinorder(U_8805) ),
inference(clausify,[status(thm)],[f_2534_2]) ).
cnf(f_2534_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8805),U_8806),U_8807))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8805),U_8806),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8805),U_8807),U_8808)))
| ~ class_Orderings_Olinorder(U_8805) ),
inference(clausify,[status(thm)],[f_2534_2]) ).
cnf(f_2534_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8805),U_8806),U_8808))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8805),U_8806),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8805),U_8807),U_8808)))
| ~ class_Orderings_Olinorder(U_8805) ),
inference(clausify,[status(thm)],[f_2534_2]) ).
fof(f_2535_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_2535_2,plain,
! [U_8811,U_8810,U_8809] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8809),U_8810),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8809),U_8810),U_8811)))
| ~ class_Orderings_Olinorder(U_8809) ),
inference(variable_rename,[status(thm)],[f_2535_1]) ).
cnf(f_2535_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8809),U_8810),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8809),U_8810),U_8811)))
| ~ class_Orderings_Olinorder(U_8809) ),
inference(clausify,[status(thm)],[f_2535_2]) ).
fof(f_2536_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_2536_2,plain,
! [U_8814,U_8813,U_8812] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8812),U_8813),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8812),U_8814),U_8813)))
| ~ class_Orderings_Olinorder(U_8812) ),
inference(variable_rename,[status(thm)],[f_2536_1]) ).
cnf(f_2536_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8812),U_8813),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8812),U_8814),U_8813)))
| ~ class_Orderings_Olinorder(U_8812) ),
inference(clausify,[status(thm)],[f_2536_2]) ).
fof(f_2537_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_2537_2,plain,
! [U_8817,U_8816,U_8815] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8815),U_8816),U_8817))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8815),U_8816),U_8817) != U_8817 )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8815),U_8816),U_8817) = U_8817
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8815),U_8816),U_8817)) ) )
| ~ class_Orderings_Olinorder(U_8815) ),
inference(variable_rename,[status(thm)],[f_2537_1]) ).
cnf(f_2537_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8815),U_8816),U_8817) = U_8817
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8815),U_8816),U_8817))
| ~ class_Orderings_Olinorder(U_8815) ),
inference(clausify,[status(thm)],[f_2537_2]) ).
cnf(f_2537_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8815),U_8816),U_8817))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8815),U_8816),U_8817) != U_8817
| ~ class_Orderings_Olinorder(U_8815) ),
inference(clausify,[status(thm)],[f_2537_2]) ).
fof(f_2538_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_2538_2,plain,
! [U_8821,U_8820,U_8819,U_8818] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8818),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8818),U_8819),U_8820)),U_8821))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8818),U_8820),U_8821))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8818),U_8819),U_8821)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8818),U_8820),U_8821))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8818),U_8819),U_8821)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8818),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8818),U_8819),U_8820)),U_8821)) ) )
| ~ class_Orderings_Olinorder(U_8818) ),
inference(variable_rename,[status(thm)],[f_2538_1]) ).
cnf(f_2538_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8818),U_8819),U_8821))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8818),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8818),U_8819),U_8820)),U_8821))
| ~ class_Orderings_Olinorder(U_8818) ),
inference(clausify,[status(thm)],[f_2538_2]) ).
cnf(f_2538_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8818),U_8820),U_8821))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8818),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8818),U_8819),U_8820)),U_8821))
| ~ class_Orderings_Olinorder(U_8818) ),
inference(clausify,[status(thm)],[f_2538_2]) ).
cnf(f_2538_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8818),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8818),U_8819),U_8820)),U_8821))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8818),U_8820),U_8821))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8818),U_8819),U_8821))
| ~ class_Orderings_Olinorder(U_8818) ),
inference(clausify,[status(thm)],[f_2538_2]) ).
fof(f_2539_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_2539_2,plain,
! [U_8825,U_8824,U_8823,U_8822] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8822),U_8823),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8822),U_8824),U_8825)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8822),U_8823),U_8824))
| ~ class_Orderings_Olinorder(U_8822) ),
inference(variable_rename,[status(thm)],[f_2539_1]) ).
cnf(f_2539_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8822),U_8823),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8822),U_8824),U_8825)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8822),U_8823),U_8824))
| ~ class_Orderings_Olinorder(U_8822) ),
inference(clausify,[status(thm)],[f_2539_2]) ).
fof(f_2540_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_2540_2,plain,
! [U_8829,U_8828,U_8827,U_8826] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8826),U_8827),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8826),U_8829),U_8828)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8826),U_8827),U_8828))
| ~ class_Orderings_Olinorder(U_8826) ),
inference(variable_rename,[status(thm)],[f_2540_1]) ).
cnf(f_2540_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8826),U_8827),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8826),U_8829),U_8828)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8826),U_8827),U_8828))
| ~ class_Orderings_Olinorder(U_8826) ),
inference(clausify,[status(thm)],[f_2540_2]) ).
fof(f_2541_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_2541_2,plain,
! [U_8832,U_8831,U_8830] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8830),U_8831),U_8832) = U_8832
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8830),U_8831),U_8832))
| ~ class_Orderings_Olinorder(U_8830) ),
inference(variable_rename,[status(thm)],[f_2541_1]) ).
cnf(f_2541_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8830),U_8831),U_8832) = U_8832
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8830),U_8831),U_8832))
| ~ class_Orderings_Olinorder(U_8830) ),
inference(clausify,[status(thm)],[f_2541_2]) ).
fof(f_2542_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_2542_2,plain,
! [U_8835,U_8834,U_8833] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8833),U_8835),U_8834) = U_8835
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8833),U_8834),U_8835))
| ~ class_Orderings_Olinorder(U_8833) ),
inference(variable_rename,[status(thm)],[f_2542_1]) ).
cnf(f_2542_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8833),U_8835),U_8834) = U_8835
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8833),U_8834),U_8835))
| ~ class_Orderings_Olinorder(U_8833) ),
inference(clausify,[status(thm)],[f_2542_2]) ).
fof(f_2543_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_2543_2,plain,
! [U_8839,U_8838,U_8837,U_8836] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8836),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8836),U_8837),U_8839)),U_8838))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8836),U_8839),U_8838))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8836),U_8837),U_8838))
| ~ class_Orderings_Olinorder(U_8836) ),
inference(variable_rename,[status(thm)],[f_2543_1]) ).
cnf(f_2543_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8836),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8836),U_8837),U_8839)),U_8838))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8836),U_8839),U_8838))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8836),U_8837),U_8838))
| ~ class_Orderings_Olinorder(U_8836) ),
inference(clausify,[status(thm)],[f_2543_2]) ).
fof(f_2544_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_2544_2,plain,
! [U_8843,U_8842,U_8841,U_8840] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8840),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8840),U_8841),U_8843)),U_8842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8840),U_8843),U_8842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8840),U_8841),U_8842))
| ~ class_Orderings_Olinorder(U_8840) ),
inference(variable_rename,[status(thm)],[f_2544_1]) ).
cnf(f_2544_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8840),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8840),U_8841),U_8843)),U_8842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8840),U_8843),U_8842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8840),U_8841),U_8842))
| ~ class_Orderings_Olinorder(U_8840) ),
inference(clausify,[status(thm)],[f_2544_2]) ).
fof(f_2545_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_2545_2,plain,
! [U_8848,U_8847,U_8846,U_8845,U_8844] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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_8848)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8844),U_8847),U_8848))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8844),U_8845),U_8846))
| ~ class_Orderings_Olinorder(U_8844) ),
inference(variable_rename,[status(thm)],[f_2545_1]) ).
cnf(f_2545_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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_8848)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8844),U_8847),U_8848))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8844),U_8845),U_8846))
| ~ class_Orderings_Olinorder(U_8844) ),
inference(clausify,[status(thm)],[f_2545_2]) ).
fof(f_2546_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_2546_2,plain,
! [U_8852,U_8851,U_8850,U_8849] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8849),U_8851),U_8852))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8849),U_8850),U_8852)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8849),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8849),U_8850),U_8851)),U_8852))
| ~ class_Orderings_Olinorder(U_8849) ),
inference(variable_rename,[status(thm)],[f_2546_1]) ).
cnf(f_2546_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8849),U_8850),U_8852))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8849),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8849),U_8850),U_8851)),U_8852))
| ~ class_Orderings_Olinorder(U_8849) ),
inference(clausify,[status(thm)],[f_2546_2]) ).
cnf(f_2546_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8849),U_8851),U_8852))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8849),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8849),U_8850),U_8851)),U_8852))
| ~ class_Orderings_Olinorder(U_8849) ),
inference(clausify,[status(thm)],[f_2546_2]) ).
fof(f_2547_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_2547_2,plain,
! [U_8856,U_8855,U_8854,U_8853] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8853),U_8854),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8853),U_8855),U_8856)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8853),U_8854),U_8855))
| ~ class_Orderings_Olinorder(U_8853) ),
inference(variable_rename,[status(thm)],[f_2547_1]) ).
cnf(f_2547_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8853),U_8854),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8853),U_8855),U_8856)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8853),U_8854),U_8855))
| ~ class_Orderings_Olinorder(U_8853) ),
inference(clausify,[status(thm)],[f_2547_2]) ).
fof(f_2548_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_2548_2,plain,
! [U_8860,U_8859,U_8858,U_8857] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8857),U_8858),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8857),U_8860),U_8859)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8857),U_8858),U_8859))
| ~ class_Orderings_Olinorder(U_8857) ),
inference(variable_rename,[status(thm)],[f_2548_1]) ).
cnf(f_2548_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8857),U_8858),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8857),U_8860),U_8859)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8857),U_8858),U_8859))
| ~ class_Orderings_Olinorder(U_8857) ),
inference(clausify,[status(thm)],[f_2548_2]) ).
fof(f_2549_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_2549_2,plain,
! [U_8864,U_8863,U_8862,U_8861] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8861),U_8862),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8861),U_8863),U_8864)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8861),U_8862),U_8864))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8861),U_8862),U_8863)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8861),U_8862),U_8864))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8861),U_8862),U_8863))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8861),U_8862),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8861),U_8863),U_8864))) ) )
| ~ class_Orderings_Olinorder(U_8861) ),
inference(variable_rename,[status(thm)],[f_2549_1]) ).
cnf(f_2549_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8861),U_8862),U_8864))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8861),U_8862),U_8863))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8861),U_8862),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8861),U_8863),U_8864)))
| ~ class_Orderings_Olinorder(U_8861) ),
inference(clausify,[status(thm)],[f_2549_2]) ).
cnf(f_2549_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8861),U_8862),U_8863))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8861),U_8862),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8861),U_8863),U_8864)))
| ~ class_Orderings_Olinorder(U_8861) ),
inference(clausify,[status(thm)],[f_2549_2]) ).
cnf(f_2549_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8861),U_8862),U_8864))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8861),U_8862),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8861),U_8863),U_8864)))
| ~ class_Orderings_Olinorder(U_8861) ),
inference(clausify,[status(thm)],[f_2549_2]) ).
fof(f_2550_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_2550_2,plain,
! [U_8868,U_8867,U_8866,U_8865] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8865),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8865),U_8866),U_8867)),U_8868))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8865),U_8867),U_8868))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8865),U_8866),U_8868)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8865),U_8867),U_8868))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8865),U_8866),U_8868)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8865),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8865),U_8866),U_8867)),U_8868)) ) )
| ~ class_Orderings_Olinorder(U_8865) ),
inference(variable_rename,[status(thm)],[f_2550_1]) ).
cnf(f_2550_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8865),U_8866),U_8868))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8865),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8865),U_8866),U_8867)),U_8868))
| ~ class_Orderings_Olinorder(U_8865) ),
inference(clausify,[status(thm)],[f_2550_2]) ).
cnf(f_2550_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8865),U_8867),U_8868))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8865),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8865),U_8866),U_8867)),U_8868))
| ~ class_Orderings_Olinorder(U_8865) ),
inference(clausify,[status(thm)],[f_2550_2]) ).
cnf(f_2550_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8865),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8865),U_8866),U_8867)),U_8868))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8865),U_8867),U_8868))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8865),U_8866),U_8868))
| ~ class_Orderings_Olinorder(U_8865) ),
inference(clausify,[status(thm)],[f_2550_2]) ).
fof(f_2551_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_2551_2,plain,
! [U_8872,U_8871,U_8870,U_8869] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8869),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8869),U_8870),U_8871)),U_8872) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8869),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8869),U_8870),U_8872)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8869),U_8871),U_8872))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_8869) ),
inference(variable_rename,[status(thm)],[f_2551_1]) ).
cnf(f_2551_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8869),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8869),U_8870),U_8871)),U_8872) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8869),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8869),U_8870),U_8872)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8869),U_8871),U_8872))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_8869) ),
inference(clausify,[status(thm)],[f_2551_2]) ).
fof(f_2552_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_2552_2,plain,
! [U_8875,U_8874,U_8873] :
( ( ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8873),hAPP(c_Int_Onumber__class_Onumber__of(U_8873),U_8874)),hAPP(c_Int_Onumber__class_Onumber__of(U_8873),U_8875)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8873),U_8874)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8873),hAPP(c_Int_Onumber__class_Onumber__of(U_8873),U_8874)),hAPP(c_Int_Onumber__class_Onumber__of(U_8873),U_8875))) )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8873),hAPP(c_Int_Onumber__class_Onumber__of(U_8873),U_8874)),hAPP(c_Int_Onumber__class_Onumber__of(U_8873),U_8875)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8873),U_8875)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8873),hAPP(c_Int_Onumber__class_Onumber__of(U_8873),U_8874)),hAPP(c_Int_Onumber__class_Onumber__of(U_8873),U_8875))) ) )
| ~ class_Orderings_Oord(U_8873)
| ~ class_Int_Onumber(U_8873) ),
inference(variable_rename,[status(thm)],[f_2552_1]) ).
cnf(f_2552_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8873),hAPP(c_Int_Onumber__class_Onumber__of(U_8873),U_8874)),hAPP(c_Int_Onumber__class_Onumber__of(U_8873),U_8875)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8873),U_8875)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8873),hAPP(c_Int_Onumber__class_Onumber__of(U_8873),U_8874)),hAPP(c_Int_Onumber__class_Onumber__of(U_8873),U_8875)))
| ~ class_Orderings_Oord(U_8873)
| ~ class_Int_Onumber(U_8873) ),
inference(clausify,[status(thm)],[f_2552_2]) ).
cnf(f_2552_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8873),hAPP(c_Int_Onumber__class_Onumber__of(U_8873),U_8874)),hAPP(c_Int_Onumber__class_Onumber__of(U_8873),U_8875)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8873),U_8874)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8873),hAPP(c_Int_Onumber__class_Onumber__of(U_8873),U_8874)),hAPP(c_Int_Onumber__class_Onumber__of(U_8873),U_8875)))
| ~ class_Orderings_Oord(U_8873)
| ~ class_Int_Onumber(U_8873) ),
inference(clausify,[status(thm)],[f_2552_2]) ).
fof(f_2553_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_2553_2,plain,
! [U_8879,U_8878,U_8877,U_8876] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8876),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8876),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8876),U_8877),U_8878)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8876),U_8877),U_8879))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8876),U_8877),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8876),U_8878),U_8879))))
| ~ class_Orderings_Olinorder(U_8876) ),
inference(variable_rename,[status(thm)],[f_2553_1]) ).
cnf(f_2553_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8876),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8876),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8876),U_8877),U_8878)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8876),U_8877),U_8879))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8876),U_8877),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8876),U_8878),U_8879))))
| ~ class_Orderings_Olinorder(U_8876) ),
inference(clausify,[status(thm)],[f_2553_2]) ).
fof(f_2554_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_2554_2,plain,
! [U_8883,U_8882,U_8881,U_8880] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8880),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8880),U_8881),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8880),U_8882),U_8883))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8880),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8880),U_8881),U_8882)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8880),U_8881),U_8883))))
| ~ class_Orderings_Olinorder(U_8880) ),
inference(variable_rename,[status(thm)],[f_2554_1]) ).
cnf(f_2554_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8880),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8880),U_8881),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8880),U_8882),U_8883))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8880),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8880),U_8881),U_8882)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8880),U_8881),U_8883))))
| ~ class_Orderings_Olinorder(U_8880) ),
inference(clausify,[status(thm)],[f_2554_2]) ).
fof(f_2555_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_2555_2,plain,
! [U_8886,U_8885,U_8884] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_8884),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8884),U_8885),U_8886)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8884),hAPP(c_Groups_Ouminus__class_Ouminus(U_8884),U_8885)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8884),U_8886))
| ~ class_Groups_Olinordered__ab__group__add(U_8884) ),
inference(variable_rename,[status(thm)],[f_2555_1]) ).
cnf(f_2555_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_8884),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8884),U_8885),U_8886)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8884),hAPP(c_Groups_Ouminus__class_Ouminus(U_8884),U_8885)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8884),U_8886))
| ~ class_Groups_Olinordered__ab__group__add(U_8884) ),
inference(clausify,[status(thm)],[f_2555_2]) ).
fof(f_2556_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_2556_2,plain,
! [U_8889,U_8888,U_8887] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_8887),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8887),U_8888),U_8889)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8887),hAPP(c_Groups_Ouminus__class_Ouminus(U_8887),U_8888)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8887),U_8889))
| ~ class_Groups_Olinordered__ab__group__add(U_8887) ),
inference(variable_rename,[status(thm)],[f_2556_1]) ).
cnf(f_2556_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_8887),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8887),U_8888),U_8889)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8887),hAPP(c_Groups_Ouminus__class_Ouminus(U_8887),U_8888)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8887),U_8889))
| ~ class_Groups_Olinordered__ab__group__add(U_8887) ),
inference(clausify,[status(thm)],[f_2556_2]) ).
fof(f_2557_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_2557_2,plain,
! [U_8891,U_8890] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8890),U_8891)),U_8891) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8890),U_8891),
inference(variable_rename,[status(thm)],[f_2557_1]) ).
cnf(f_2557_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8890),U_8891)),U_8891) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8890),U_8891),
inference(clausify,[status(thm)],[f_2557_2]) ).
fof(f_2558_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_2558_2,plain,
! [U_8895,U_8894,U_8893,U_8892] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_8892,U_8892,c_Orderings_Oord__class_Omax(U_8892)),U_8894),hAPP(hAPP(c_Set_Oinsert(U_8892),U_8895),U_8893)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8892),U_8895),hAPP(hAPP(c_Finite__Set_Ofold(U_8892,U_8892,c_Orderings_Oord__class_Omax(U_8892)),U_8894),U_8893))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8892),U_8893))
| ~ class_Orderings_Olinorder(U_8892) ),
inference(variable_rename,[status(thm)],[f_2558_1]) ).
cnf(f_2558_3,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_8892,U_8892,c_Orderings_Oord__class_Omax(U_8892)),U_8894),hAPP(hAPP(c_Set_Oinsert(U_8892),U_8895),U_8893)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8892),U_8895),hAPP(hAPP(c_Finite__Set_Ofold(U_8892,U_8892,c_Orderings_Oord__class_Omax(U_8892)),U_8894),U_8893))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8892),U_8893))
| ~ class_Orderings_Olinorder(U_8892) ),
inference(clausify,[status(thm)],[f_2558_2]) ).
fof(f_2559_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_2559_2,plain,
! [U_8898,U_8897,U_8896] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8896),U_8898),c_Big__Operators_Olinorder__class_OMax(U_8896,U_8897)) = c_Big__Operators_Olinorder__class_OMax(U_8896,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_2559_1]) ).
cnf(f_2559_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8896),U_8898),c_Big__Operators_Olinorder__class_OMax(U_8896,U_8897)) = c_Big__Operators_Olinorder__class_OMax(U_8896,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_2559_2]) ).
fof(f_2560_1,plain,
! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_A_2),V_B_2))))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Lattices_Osemilattice__sup(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Omono__sup]) ).
fof(f_2560_2,plain,
! [U_8903,U_8902,U_8901,U_8900,U_8899] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8899),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8899),hAPP(U_8901,U_8902)),hAPP(U_8901,U_8903))),hAPP(U_8901,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8900),U_8902),U_8903))))
| ~ c_Orderings_Oorder__class_Omono(U_8900,U_8899,U_8901)
| ~ class_Orderings_Olinorder(U_8900)
| ~ class_Lattices_Osemilattice__sup(U_8899) ),
inference(variable_rename,[status(thm)],[f_2560_1]) ).
cnf(f_2560_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8899),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8899),hAPP(U_8901,U_8902)),hAPP(U_8901,U_8903))),hAPP(U_8901,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8900),U_8902),U_8903))))
| ~ c_Orderings_Oorder__class_Omono(U_8900,U_8899,U_8901)
| ~ class_Orderings_Olinorder(U_8900)
| ~ class_Lattices_Osemilattice__sup(U_8899) ),
inference(clausify,[status(thm)],[f_2560_2]) ).
fof(f_2561_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMost]) ).
fof(f_2561_2,plain,
! [U_8908,U_8907,U_8906,U_8905,U_8904] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8904,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8904,U_8905,U_8906)),c_SetInterval_Oord__class_OatLeastAtMost(U_8904,U_8907,U_8908)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8904,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8904),U_8905),U_8907),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8904),U_8906),U_8908))
| ~ class_Orderings_Olinorder(U_8904) ),
inference(variable_rename,[status(thm)],[f_2561_1]) ).
cnf(f_2561_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8904,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8904,U_8905,U_8906)),c_SetInterval_Oord__class_OatLeastAtMost(U_8904,U_8907,U_8908)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8904,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8904),U_8905),U_8907),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8904),U_8906),U_8908))
| ~ class_Orderings_Olinorder(U_8904) ),
inference(clausify,[status(thm)],[f_2561_2]) ).
fof(f_2562_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Int__atLeastLessThan]) ).
fof(f_2562_2,plain,
! [U_8913,U_8912,U_8911,U_8910,U_8909] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8909,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8909,U_8910),U_8911)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8909,U_8912),U_8913)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8909,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8909),U_8910),U_8912)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8909),U_8911),U_8913))
| ~ class_Orderings_Olinorder(U_8909) ),
inference(variable_rename,[status(thm)],[f_2562_1]) ).
cnf(f_2562_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8909,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8909,U_8910),U_8911)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8909,U_8912),U_8913)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8909,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8909),U_8910),U_8912)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8909),U_8911),U_8913))
| ~ class_Orderings_Olinorder(U_8909) ),
inference(clausify,[status(thm)],[f_2562_2]) ).
fof(f_2563_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Int__greaterThanAtMost]) ).
fof(f_2563_2,plain,
! [U_8918,U_8917,U_8916,U_8915,U_8914] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8914,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8914,U_8915,U_8916)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8914,U_8917,U_8918)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_8914,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8914),U_8915),U_8917),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8914),U_8916),U_8918))
| ~ class_Orderings_Olinorder(U_8914) ),
inference(variable_rename,[status(thm)],[f_2563_1]) ).
cnf(f_2563_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8914,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8914,U_8915,U_8916)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8914,U_8917,U_8918)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_8914,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8914),U_8915),U_8917),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8914),U_8916),U_8918))
| ~ class_Orderings_Olinorder(U_8914) ),
inference(clausify,[status(thm)],[f_2563_2]) ).
fof(f_2564_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Int__greaterThanLessThan]) ).
fof(f_2564_2,plain,
! [U_8923,U_8922,U_8921,U_8920,U_8919] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8919,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8919,U_8920,U_8921)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8919,U_8922,U_8923)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_8919,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8919),U_8920),U_8922),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8919),U_8921),U_8923))
| ~ class_Orderings_Olinorder(U_8919) ),
inference(variable_rename,[status(thm)],[f_2564_1]) ).
cnf(f_2564_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8919,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8919,U_8920,U_8921)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8919,U_8922,U_8923)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_8919,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8919),U_8920),U_8922),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8919),U_8921),U_8923))
| ~ class_Orderings_Olinorder(U_8919) ),
inference(clausify,[status(thm)],[f_2564_2]) ).
fof(f_2565_1,plain,
! [V_c_2,V_b_2,V_a_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_b_2)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL2]) ).
fof(f_2565_2,plain,
! [U_8927,U_8926,U_8925,U_8924] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8924,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8924,U_8925,U_8926)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8924),U_8927)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8924,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8924),U_8925),U_8927),U_8926)
| ~ class_Orderings_Olinorder(U_8924) ),
inference(variable_rename,[status(thm)],[f_2565_1]) ).
cnf(f_2565_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8924,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8924,U_8925,U_8926)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8924),U_8927)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8924,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8924),U_8925),U_8927),U_8926)
| ~ class_Orderings_Olinorder(U_8924) ),
inference(clausify,[status(thm)],[f_2565_2]) ).
fof(f_2566_1,plain,
! [V_d_2,V_c_2,V_a_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_d_2)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR2]) ).
fof(f_2566_2,plain,
! [U_8931,U_8930,U_8929,U_8928] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8928,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8928),U_8929)),c_SetInterval_Oord__class_OatLeastAtMost(U_8928,U_8930,U_8931)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8928,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8928),U_8929),U_8930),U_8931)
| ~ class_Orderings_Olinorder(U_8928) ),
inference(variable_rename,[status(thm)],[f_2566_1]) ).
cnf(f_2566_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8928,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8928),U_8929)),c_SetInterval_Oord__class_OatLeastAtMost(U_8928,U_8930,U_8931)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8928,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8928),U_8929),U_8930),U_8931)
| ~ class_Orderings_Olinorder(U_8928) ),
inference(clausify,[status(thm)],[f_2566_2]) ).
fof(f_2567_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_2567_2,plain,
! [U_8933,U_8932] :
( c_Big__Operators_Olinorder__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_2567_1]) ).
cnf(f_2567_3,plain,
( c_Big__Operators_Olinorder__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_2567_2]) ).
fof(f_2568_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_2568_2,plain,
! [U_8937,U_8936,U_8935,U_8934] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8934),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8934),U_8936),U_8937)),hAPP(hAPP(c_Finite__Set_Ofold(U_8934,U_8934,c_Orderings_Oord__class_Omax(U_8934)),U_8937),U_8935)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8934),U_8936),U_8935))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8934),U_8935))
| ~ class_Orderings_Olinorder(U_8934) ),
inference(variable_rename,[status(thm)],[f_2568_1]) ).
cnf(f_2568_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8934),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8934),U_8936),U_8937)),hAPP(hAPP(c_Finite__Set_Ofold(U_8934,U_8934,c_Orderings_Oord__class_Omax(U_8934)),U_8937),U_8935)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8934),U_8936),U_8935))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8934),U_8935))
| ~ class_Orderings_Olinorder(U_8934) ),
inference(clausify,[status(thm)],[f_2568_2]) ).
fof(f_2569_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_2569_2,plain,
! [U_8940,U_8939,U_8938] :
( c_Big__Operators_Olinorder__class_OMax(U_8938,hAPP(hAPP(c_Set_Oinsert(U_8938),U_8940),U_8939)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8938),U_8940),c_Big__Operators_Olinorder__class_OMax(U_8938,U_8939))
| U_8939 = c_Orderings_Obot__class_Obot(tc_fun(U_8938,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8938),U_8939))
| ~ class_Orderings_Olinorder(U_8938) ),
inference(variable_rename,[status(thm)],[f_2569_1]) ).
cnf(f_2569_3,plain,
( c_Big__Operators_Olinorder__class_OMax(U_8938,hAPP(hAPP(c_Set_Oinsert(U_8938),U_8940),U_8939)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8938),U_8940),c_Big__Operators_Olinorder__class_OMax(U_8938,U_8939))
| U_8939 = c_Orderings_Obot__class_Obot(tc_fun(U_8938,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8938),U_8939))
| ~ class_Orderings_Olinorder(U_8938) ),
inference(clausify,[status(thm)],[f_2569_2]) ).
fof(f_2570_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_2570_2,plain,
! [U_8943,U_8942,U_8941] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8941),c_Big__Operators_Olinorder__class_OMax(U_8941,U_8943)),c_Big__Operators_Olinorder__class_OMax(U_8941,U_8942)) = c_Big__Operators_Olinorder__class_OMax(U_8941,U_8942)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8941,tc_HOL_Obool)),U_8943),U_8942))
| U_8943 = c_Orderings_Obot__class_Obot(tc_fun(U_8941,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8941),U_8942))
| ~ class_Orderings_Olinorder(U_8941) ),
inference(variable_rename,[status(thm)],[f_2570_1]) ).
cnf(f_2570_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8941),c_Big__Operators_Olinorder__class_OMax(U_8941,U_8943)),c_Big__Operators_Olinorder__class_OMax(U_8941,U_8942)) = c_Big__Operators_Olinorder__class_OMax(U_8941,U_8942)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8941,tc_HOL_Obool)),U_8943),U_8942))
| U_8943 = c_Orderings_Obot__class_Obot(tc_fun(U_8941,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8941),U_8942))
| ~ class_Orderings_Olinorder(U_8941) ),
inference(clausify,[status(thm)],[f_2570_2]) ).
fof(f_2571_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_2571_2,plain,
! [U_8946,U_8945,U_8944] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8944),U_8946),c_Big__Operators_Olattice_OInf__fin(U_8944,c_Orderings_Oord__class_Omin(U_8944),U_8945)) = U_8946
| ~ hBOOL(hAPP(hAPP(c_member(U_8944),U_8946),U_8945))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8944),U_8945))
| ~ class_Orderings_Olinorder(U_8944) ),
inference(variable_rename,[status(thm)],[f_2571_1]) ).
cnf(f_2571_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8944),U_8946),c_Big__Operators_Olattice_OInf__fin(U_8944,c_Orderings_Oord__class_Omin(U_8944),U_8945)) = U_8946
| ~ hBOOL(hAPP(hAPP(c_member(U_8944),U_8946),U_8945))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8944),U_8945))
| ~ class_Orderings_Olinorder(U_8944) ),
inference(clausify,[status(thm)],[f_2571_2]) ).
fof(f_2572_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_2572_2,plain,
! [U_8949,U_8948,U_8947] :
( c_Big__Operators_Olinorder__class_OMax(U_8947,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8947,tc_HOL_Obool)),U_8948),U_8949)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8947),c_Big__Operators_Olinorder__class_OMax(U_8947,U_8948)),c_Big__Operators_Olinorder__class_OMax(U_8947,U_8949))
| U_8949 = c_Orderings_Obot__class_Obot(tc_fun(U_8947,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8947),U_8949))
| U_8948 = c_Orderings_Obot__class_Obot(tc_fun(U_8947,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8947),U_8948))
| ~ class_Orderings_Olinorder(U_8947) ),
inference(variable_rename,[status(thm)],[f_2572_1]) ).
cnf(f_2572_3,plain,
( c_Big__Operators_Olinorder__class_OMax(U_8947,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8947,tc_HOL_Obool)),U_8948),U_8949)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8947),c_Big__Operators_Olinorder__class_OMax(U_8947,U_8948)),c_Big__Operators_Olinorder__class_OMax(U_8947,U_8949))
| U_8949 = c_Orderings_Obot__class_Obot(tc_fun(U_8947,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8947),U_8949))
| U_8948 = c_Orderings_Obot__class_Obot(tc_fun(U_8947,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8947),U_8948))
| ~ class_Orderings_Olinorder(U_8947) ),
inference(clausify,[status(thm)],[f_2572_2]) ).
fof(f_2573_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_2573_2,plain,
! [U_8952,U_8951,U_8950] :
( c_Big__Operators_Olinorder__class_OMax(U_8950,hAPP(hAPP(c_Set_Oinsert(U_8950),U_8952),U_8951)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8950,U_8950,c_Orderings_Oord__class_Omax(U_8950)),U_8952),U_8951)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8950),U_8951))
| ~ class_Orderings_Olinorder(U_8950) ),
inference(variable_rename,[status(thm)],[f_2573_1]) ).
cnf(f_2573_3,plain,
( c_Big__Operators_Olinorder__class_OMax(U_8950,hAPP(hAPP(c_Set_Oinsert(U_8950),U_8952),U_8951)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8950,U_8950,c_Orderings_Oord__class_Omax(U_8950)),U_8952),U_8951)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8950),U_8951))
| ~ class_Orderings_Olinorder(U_8950) ),
inference(clausify,[status(thm)],[f_2573_2]) ).
fof(f_2574_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_2574_2,plain,
! [U_8955,U_8954,U_8953] :
( c_Big__Operators_Olinorder__class_OMax(U_8953,hAPP(hAPP(c_Set_Oinsert(U_8953),U_8955),U_8954)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8953),U_8955),c_Big__Operators_Olinorder__class_OMax(U_8953,U_8954))
| U_8954 = c_Orderings_Obot__class_Obot(tc_fun(U_8953,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_8953),U_8955),U_8954))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8953),U_8954))
| ~ class_Orderings_Olinorder(U_8953) ),
inference(variable_rename,[status(thm)],[f_2574_1]) ).
cnf(f_2574_3,plain,
( c_Big__Operators_Olinorder__class_OMax(U_8953,hAPP(hAPP(c_Set_Oinsert(U_8953),U_8955),U_8954)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8953),U_8955),c_Big__Operators_Olinorder__class_OMax(U_8953,U_8954))
| U_8954 = c_Orderings_Obot__class_Obot(tc_fun(U_8953,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_8953),U_8955),U_8954))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8953),U_8954))
| ~ class_Orderings_Olinorder(U_8953) ),
inference(clausify,[status(thm)],[f_2574_2]) ).
fof(f_2575_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_2575_2,plain,
! [U_8958,U_8957,U_8956] :
( ( ( c_Big__Operators_Olinorder__class_OMax(U_8956,hAPP(hAPP(c_Set_Oinsert(U_8956),U_8958),U_8957)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8956),U_8958),c_Big__Operators_Olinorder__class_OMax(U_8956,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8956,tc_HOL_Obool)),U_8957),hAPP(hAPP(c_Set_Oinsert(U_8956),U_8958),c_Orderings_Obot__class_Obot(tc_fun(U_8956,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8956,tc_HOL_Obool)),U_8957),hAPP(hAPP(c_Set_Oinsert(U_8956),U_8958),c_Orderings_Obot__class_Obot(tc_fun(U_8956,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8956,tc_HOL_Obool)) )
& ( c_Big__Operators_Olinorder__class_OMax(U_8956,hAPP(hAPP(c_Set_Oinsert(U_8956),U_8958),U_8957)) = U_8958
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8956,tc_HOL_Obool)),U_8957),hAPP(hAPP(c_Set_Oinsert(U_8956),U_8958),c_Orderings_Obot__class_Obot(tc_fun(U_8956,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8956,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8956),U_8957))
| ~ class_Orderings_Olinorder(U_8956) ),
inference(variable_rename,[status(thm)],[f_2575_1]) ).
cnf(f_2575_3,plain,
( c_Big__Operators_Olinorder__class_OMax(U_8956,hAPP(hAPP(c_Set_Oinsert(U_8956),U_8958),U_8957)) = U_8958
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8956,tc_HOL_Obool)),U_8957),hAPP(hAPP(c_Set_Oinsert(U_8956),U_8958),c_Orderings_Obot__class_Obot(tc_fun(U_8956,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8956,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8956),U_8957))
| ~ class_Orderings_Olinorder(U_8956) ),
inference(clausify,[status(thm)],[f_2575_2]) ).
cnf(f_2575_4,plain,
( c_Big__Operators_Olinorder__class_OMax(U_8956,hAPP(hAPP(c_Set_Oinsert(U_8956),U_8958),U_8957)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8956),U_8958),c_Big__Operators_Olinorder__class_OMax(U_8956,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8956,tc_HOL_Obool)),U_8957),hAPP(hAPP(c_Set_Oinsert(U_8956),U_8958),c_Orderings_Obot__class_Obot(tc_fun(U_8956,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8956,tc_HOL_Obool)),U_8957),hAPP(hAPP(c_Set_Oinsert(U_8956),U_8958),c_Orderings_Obot__class_Obot(tc_fun(U_8956,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8956,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8956),U_8957))
| ~ class_Orderings_Olinorder(U_8956) ),
inference(clausify,[status(thm)],[f_2575_2]) ).
fof(f_2576_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_2576_2,plain,
! [U_8961,U_8960,U_8959] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8959),c_Big__Operators_Olinorder__class_OMax(U_8959,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8959,tc_HOL_Obool)),U_8960),U_8961))),c_Big__Operators_Olinorder__class_OMax(U_8959,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8959,tc_HOL_Obool)),U_8960),U_8961))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8959),c_Big__Operators_Olinorder__class_OMax(U_8959,U_8960)),c_Big__Operators_Olinorder__class_OMax(U_8959,U_8961))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8959,tc_HOL_Obool)),U_8960),U_8961) = c_Orderings_Obot__class_Obot(tc_fun(U_8959,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8959),U_8961))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8959),U_8960))
| ~ class_Orderings_Olinorder(U_8959) ),
inference(variable_rename,[status(thm)],[f_2576_1]) ).
cnf(f_2576_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8959),c_Big__Operators_Olinorder__class_OMax(U_8959,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8959,tc_HOL_Obool)),U_8960),U_8961))),c_Big__Operators_Olinorder__class_OMax(U_8959,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8959,tc_HOL_Obool)),U_8960),U_8961))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8959),c_Big__Operators_Olinorder__class_OMax(U_8959,U_8960)),c_Big__Operators_Olinorder__class_OMax(U_8959,U_8961))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8959,tc_HOL_Obool)),U_8960),U_8961) = c_Orderings_Obot__class_Obot(tc_fun(U_8959,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8959),U_8961))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8959),U_8960))
| ~ class_Orderings_Olinorder(U_8959) ),
inference(clausify,[status(thm)],[f_2576_2]) ).
fof(f_2577_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_2577_2,plain,
! [U_8964,U_8963,U_8962] :
( c_Big__Operators_Olinorder__class_OMax(U_8962,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8962,tc_HOL_Obool)),U_8963),U_8964)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8962),c_Big__Operators_Olinorder__class_OMax(U_8962,U_8963)),c_Big__Operators_Olinorder__class_OMax(U_8962,U_8964))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8962,tc_HOL_Obool)),U_8963),U_8964) != c_Orderings_Obot__class_Obot(tc_fun(U_8962,tc_HOL_Obool))
| U_8964 = c_Orderings_Obot__class_Obot(tc_fun(U_8962,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8962),U_8964))
| U_8963 = c_Orderings_Obot__class_Obot(tc_fun(U_8962,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8962),U_8963))
| ~ class_Orderings_Olinorder(U_8962) ),
inference(variable_rename,[status(thm)],[f_2577_1]) ).
cnf(f_2577_3,plain,
( c_Big__Operators_Olinorder__class_OMax(U_8962,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8962,tc_HOL_Obool)),U_8963),U_8964)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8962),c_Big__Operators_Olinorder__class_OMax(U_8962,U_8963)),c_Big__Operators_Olinorder__class_OMax(U_8962,U_8964))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8962,tc_HOL_Obool)),U_8963),U_8964) != c_Orderings_Obot__class_Obot(tc_fun(U_8962,tc_HOL_Obool))
| U_8964 = c_Orderings_Obot__class_Obot(tc_fun(U_8962,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8962),U_8964))
| U_8963 = c_Orderings_Obot__class_Obot(tc_fun(U_8962,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8962),U_8963))
| ~ class_Orderings_Olinorder(U_8962) ),
inference(clausify,[status(thm)],[f_2577_2]) ).
fof(f_2578_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_2578_2,plain,
! [U_8967,U_8966,U_8965] :
( c_Big__Operators_Olinorder__class_OMax(U_8965,hAPP(hAPP(c_Set_Oinsert(U_8965),U_8967),U_8966)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8965,U_8965,c_Orderings_Oord__class_Omax(U_8965)),U_8967),U_8966)
| hBOOL(hAPP(hAPP(c_member(U_8965),U_8967),U_8966))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8965),U_8966))
| ~ class_Orderings_Olinorder(U_8965) ),
inference(variable_rename,[status(thm)],[f_2578_1]) ).
cnf(f_2578_3,plain,
( c_Big__Operators_Olinorder__class_OMax(U_8965,hAPP(hAPP(c_Set_Oinsert(U_8965),U_8967),U_8966)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8965,U_8965,c_Orderings_Oord__class_Omax(U_8965)),U_8967),U_8966)
| hBOOL(hAPP(hAPP(c_member(U_8965),U_8967),U_8966))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8965),U_8966))
| ~ class_Orderings_Olinorder(U_8965) ),
inference(clausify,[status(thm)],[f_2578_2]) ).
fof(f_2579_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_2579_2,plain,
! [U_8968] :
( c_Orderings_Oord__class_Omax(U_8968) = c_Orderings_Oord_Omax(U_8968,c_Orderings_Oord__class_Oless__eq(U_8968))
| ~ class_Orderings_Oord(U_8968) ),
inference(variable_rename,[status(thm)],[f_2579_1]) ).
cnf(f_2579_3,plain,
( c_Orderings_Oord__class_Omax(U_8968) = c_Orderings_Oord_Omax(U_8968,c_Orderings_Oord__class_Oless__eq(U_8968))
| ~ class_Orderings_Oord(U_8968) ),
inference(clausify,[status(thm)],[f_2579_2]) ).
fof(f_2580_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_2580_2,plain,
! [U_8972,U_8971] :
( hBOOL(hAPP(hAPP(c_member(U_8971),c_Big__Operators_Olinorder__class_OMax(U_8971,U_8972)),U_8972))
| ? [U_8970,U_8969] : ~ hBOOL(hAPP(hAPP(c_member(U_8971),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8971),U_8970),U_8969)),hAPP(hAPP(c_Set_Oinsert(U_8971),U_8970),hAPP(hAPP(c_Set_Oinsert(U_8971),U_8969),c_Orderings_Obot__class_Obot(tc_fun(U_8971,tc_HOL_Obool))))))
| U_8972 = c_Orderings_Obot__class_Obot(tc_fun(U_8971,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8971),U_8972))
| ~ class_Orderings_Olinorder(U_8971) ),
inference(variable_rename,[status(thm)],[f_2580_1]) ).
fof(f_2580_3,plain,
! [U_8972,U_8971] :
( hBOOL(hAPP(hAPP(c_member(U_8971),c_Big__Operators_Olinorder__class_OMax(U_8971,U_8972)),U_8972))
| ? [U_8969] : ~ hBOOL(hAPP(hAPP(c_member(U_8971),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8971),sK225(U_8972,U_8971)),U_8969)),hAPP(hAPP(c_Set_Oinsert(U_8971),sK225(U_8972,U_8971)),hAPP(hAPP(c_Set_Oinsert(U_8971),U_8969),c_Orderings_Obot__class_Obot(tc_fun(U_8971,tc_HOL_Obool))))))
| U_8972 = c_Orderings_Obot__class_Obot(tc_fun(U_8971,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8971),U_8972))
| ~ class_Orderings_Olinorder(U_8971) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK225]),skolemize(U_8970,sK225(U_8972,U_8971))],[f_2580_2]) ).
fof(f_2580_4,plain,
! [U_8972,U_8971] :
( hBOOL(hAPP(hAPP(c_member(U_8971),c_Big__Operators_Olinorder__class_OMax(U_8971,U_8972)),U_8972))
| ~ hBOOL(hAPP(hAPP(c_member(U_8971),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8971),sK225(U_8972,U_8971)),sK226(U_8972,U_8971))),hAPP(hAPP(c_Set_Oinsert(U_8971),sK225(U_8972,U_8971)),hAPP(hAPP(c_Set_Oinsert(U_8971),sK226(U_8972,U_8971)),c_Orderings_Obot__class_Obot(tc_fun(U_8971,tc_HOL_Obool))))))
| U_8972 = c_Orderings_Obot__class_Obot(tc_fun(U_8971,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8971),U_8972))
| ~ class_Orderings_Olinorder(U_8971) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK226]),skolemize(U_8969,sK226(U_8972,U_8971))],[f_2580_3]) ).
cnf(f_2580_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_8971),c_Big__Operators_Olinorder__class_OMax(U_8971,U_8972)),U_8972))
| ~ hBOOL(hAPP(hAPP(c_member(U_8971),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8971),sK225(U_8972,U_8971)),sK226(U_8972,U_8971))),hAPP(hAPP(c_Set_Oinsert(U_8971),sK225(U_8972,U_8971)),hAPP(hAPP(c_Set_Oinsert(U_8971),sK226(U_8972,U_8971)),c_Orderings_Obot__class_Obot(tc_fun(U_8971,tc_HOL_Obool))))))
| U_8972 = c_Orderings_Obot__class_Obot(tc_fun(U_8971,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8971),U_8972))
| ~ class_Orderings_Olinorder(U_8971) ),
inference(clausify,[status(thm)],[f_2580_4]) ).
fof(f_2581_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_2581_2,plain,
! [U_8974,U_8973] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8973),c_Big__Operators_Olattice_OInf__fin(U_8973,c_Orderings_Oord__class_Omin(U_8973),U_8974)),c_Big__Operators_Olattice_OSup__fin(U_8973,c_Orderings_Oord__class_Omax(U_8973),U_8974)))
| U_8974 = c_Orderings_Obot__class_Obot(tc_fun(U_8973,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8973),U_8974))
| ~ class_Orderings_Olinorder(U_8973) ),
inference(variable_rename,[status(thm)],[f_2581_1]) ).
cnf(f_2581_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8973),c_Big__Operators_Olattice_OInf__fin(U_8973,c_Orderings_Oord__class_Omin(U_8973),U_8974)),c_Big__Operators_Olattice_OSup__fin(U_8973,c_Orderings_Oord__class_Omax(U_8973),U_8974)))
| U_8974 = c_Orderings_Obot__class_Obot(tc_fun(U_8973,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8973),U_8974))
| ~ class_Orderings_Olinorder(U_8973) ),
inference(clausify,[status(thm)],[f_2581_2]) ).
fof(f_2582_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_2582_2,plain,
! [U_8977,U_8976,U_8975] :
( ( ( c_Big__Operators_Olattice_OSup__fin(U_8975,c_Orderings_Oord__class_Omax(U_8975),U_8976) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8975),U_8977),c_Big__Operators_Olattice_OSup__fin(U_8975,c_Orderings_Oord__class_Omax(U_8975),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8975,tc_HOL_Obool)),U_8976),hAPP(hAPP(c_Set_Oinsert(U_8975),U_8977),c_Orderings_Obot__class_Obot(tc_fun(U_8975,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8975,tc_HOL_Obool)),U_8976),hAPP(hAPP(c_Set_Oinsert(U_8975),U_8977),c_Orderings_Obot__class_Obot(tc_fun(U_8975,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8975,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice_OSup__fin(U_8975,c_Orderings_Oord__class_Omax(U_8975),U_8976) = U_8977
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8975,tc_HOL_Obool)),U_8976),hAPP(hAPP(c_Set_Oinsert(U_8975),U_8977),c_Orderings_Obot__class_Obot(tc_fun(U_8975,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8975,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_8975),U_8977),U_8976))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8975),U_8976))
| ~ class_Orderings_Olinorder(U_8975) ),
inference(variable_rename,[status(thm)],[f_2582_1]) ).
cnf(f_2582_3,plain,
( c_Big__Operators_Olattice_OSup__fin(U_8975,c_Orderings_Oord__class_Omax(U_8975),U_8976) = U_8977
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8975,tc_HOL_Obool)),U_8976),hAPP(hAPP(c_Set_Oinsert(U_8975),U_8977),c_Orderings_Obot__class_Obot(tc_fun(U_8975,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8975,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_8975),U_8977),U_8976))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8975),U_8976))
| ~ class_Orderings_Olinorder(U_8975) ),
inference(clausify,[status(thm)],[f_2582_2]) ).
cnf(f_2582_4,plain,
( c_Big__Operators_Olattice_OSup__fin(U_8975,c_Orderings_Oord__class_Omax(U_8975),U_8976) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8975),U_8977),c_Big__Operators_Olattice_OSup__fin(U_8975,c_Orderings_Oord__class_Omax(U_8975),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8975,tc_HOL_Obool)),U_8976),hAPP(hAPP(c_Set_Oinsert(U_8975),U_8977),c_Orderings_Obot__class_Obot(tc_fun(U_8975,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8975,tc_HOL_Obool)),U_8976),hAPP(hAPP(c_Set_Oinsert(U_8975),U_8977),c_Orderings_Obot__class_Obot(tc_fun(U_8975,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8975,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_8975),U_8977),U_8976))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8975),U_8976))
| ~ class_Orderings_Olinorder(U_8975) ),
inference(clausify,[status(thm)],[f_2582_2]) ).
fof(f_2583_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_2583_2,plain,
c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_2583_1]) ).
fof(f_2584_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_2584_2,plain,
! [U_8980,U_8979,U_8978] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8978),U_8980),c_Big__Operators_Olattice_OSup__fin(U_8978,c_Orderings_Oord__class_Omax(U_8978),U_8979)) = c_Big__Operators_Olattice_OSup__fin(U_8978,c_Orderings_Oord__class_Omax(U_8978),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_2584_1]) ).
cnf(f_2584_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8978),U_8980),c_Big__Operators_Olattice_OSup__fin(U_8978,c_Orderings_Oord__class_Omax(U_8978),U_8979)) = c_Big__Operators_Olattice_OSup__fin(U_8978,c_Orderings_Oord__class_Omax(U_8978),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_2584_2]) ).
fof(f_2585_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_2585_2,plain,
! [U_8982,U_8981] :
( c_Big__Operators_Olattice_OSup__fin(U_8981,c_Orderings_Oord__class_Omax(U_8981),hAPP(hAPP(c_Set_Oinsert(U_8981),U_8982),c_Orderings_Obot__class_Obot(tc_fun(U_8981,tc_HOL_Obool)))) = U_8982
| ~ class_Orderings_Olinorder(U_8981) ),
inference(variable_rename,[status(thm)],[f_2585_1]) ).
cnf(f_2585_3,plain,
( c_Big__Operators_Olattice_OSup__fin(U_8981,c_Orderings_Oord__class_Omax(U_8981),hAPP(hAPP(c_Set_Oinsert(U_8981),U_8982),c_Orderings_Obot__class_Obot(tc_fun(U_8981,tc_HOL_Obool)))) = U_8982
| ~ class_Orderings_Olinorder(U_8981) ),
inference(clausify,[status(thm)],[f_2585_2]) ).
fof(f_2586_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_2586_2,plain,
! [U_8984,U_8983] :
( c_Big__Operators_Olattice_OSup__fin(U_8983,c_Orderings_Oord__class_Omax(U_8983),U_8984) = hAPP(c_Finite__Set_Ofold1(U_8983,c_Orderings_Oord__class_Omax(U_8983)),U_8984)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8983),U_8984))
| ~ class_Orderings_Olinorder(U_8983) ),
inference(variable_rename,[status(thm)],[f_2586_1]) ).
cnf(f_2586_3,plain,
( c_Big__Operators_Olattice_OSup__fin(U_8983,c_Orderings_Oord__class_Omax(U_8983),U_8984) = hAPP(c_Finite__Set_Ofold1(U_8983,c_Orderings_Oord__class_Omax(U_8983)),U_8984)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8983),U_8984))
| ~ class_Orderings_Olinorder(U_8983) ),
inference(clausify,[status(thm)],[f_2586_2]) ).
fof(f_2587_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_2587_2,plain,
! [U_8987,U_8986,U_8985] :
( c_Big__Operators_Olattice_OSup__fin(U_8985,c_Orderings_Oord__class_Omax(U_8985),hAPP(hAPP(c_Set_Oinsert(U_8985),U_8987),U_8986)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8985),U_8987),c_Big__Operators_Olattice_OSup__fin(U_8985,c_Orderings_Oord__class_Omax(U_8985),U_8986))
| U_8986 = c_Orderings_Obot__class_Obot(tc_fun(U_8985,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8985),U_8986))
| ~ class_Orderings_Olinorder(U_8985) ),
inference(variable_rename,[status(thm)],[f_2587_1]) ).
cnf(f_2587_3,plain,
( c_Big__Operators_Olattice_OSup__fin(U_8985,c_Orderings_Oord__class_Omax(U_8985),hAPP(hAPP(c_Set_Oinsert(U_8985),U_8987),U_8986)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8985),U_8987),c_Big__Operators_Olattice_OSup__fin(U_8985,c_Orderings_Oord__class_Omax(U_8985),U_8986))
| U_8986 = c_Orderings_Obot__class_Obot(tc_fun(U_8985,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8985),U_8986))
| ~ class_Orderings_Olinorder(U_8985) ),
inference(clausify,[status(thm)],[f_2587_2]) ).
fof(f_2588_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_2588_2,plain,
! [U_8990,U_8989,U_8988] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8988),c_Big__Operators_Olattice_OSup__fin(U_8988,c_Orderings_Oord__class_Omax(U_8988),U_8990)),c_Big__Operators_Olattice_OSup__fin(U_8988,c_Orderings_Oord__class_Omax(U_8988),U_8989)) = c_Big__Operators_Olattice_OSup__fin(U_8988,c_Orderings_Oord__class_Omax(U_8988),U_8989)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8988,tc_HOL_Obool)),U_8990),U_8989))
| U_8990 = c_Orderings_Obot__class_Obot(tc_fun(U_8988,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8988),U_8989))
| ~ class_Orderings_Olinorder(U_8988) ),
inference(variable_rename,[status(thm)],[f_2588_1]) ).
cnf(f_2588_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8988),c_Big__Operators_Olattice_OSup__fin(U_8988,c_Orderings_Oord__class_Omax(U_8988),U_8990)),c_Big__Operators_Olattice_OSup__fin(U_8988,c_Orderings_Oord__class_Omax(U_8988),U_8989)) = c_Big__Operators_Olattice_OSup__fin(U_8988,c_Orderings_Oord__class_Omax(U_8988),U_8989)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8988,tc_HOL_Obool)),U_8990),U_8989))
| U_8990 = c_Orderings_Obot__class_Obot(tc_fun(U_8988,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8988),U_8989))
| ~ class_Orderings_Olinorder(U_8988) ),
inference(clausify,[status(thm)],[f_2588_2]) ).
fof(f_2589_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_2589_2,plain,
! [U_8993,U_8992,U_8991] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8991),U_8993),c_Big__Operators_Olattice_OSup__fin(U_8991,c_Orderings_Oord__class_Omax(U_8991),U_8992)) = U_8993
| ~ hBOOL(hAPP(hAPP(c_member(U_8991),U_8993),U_8992))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8991),U_8992))
| ~ class_Orderings_Olinorder(U_8991) ),
inference(variable_rename,[status(thm)],[f_2589_1]) ).
cnf(f_2589_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8991),U_8993),c_Big__Operators_Olattice_OSup__fin(U_8991,c_Orderings_Oord__class_Omax(U_8991),U_8992)) = U_8993
| ~ hBOOL(hAPP(hAPP(c_member(U_8991),U_8993),U_8992))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8991),U_8992))
| ~ class_Orderings_Olinorder(U_8991) ),
inference(clausify,[status(thm)],[f_2589_2]) ).
fof(f_2590_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_2590_2,plain,
! [U_8996,U_8995,U_8994] :
( c_Big__Operators_Olattice_OSup__fin(U_8994,c_Orderings_Oord__class_Omax(U_8994),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8994,tc_HOL_Obool)),U_8995),U_8996)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8994),c_Big__Operators_Olattice_OSup__fin(U_8994,c_Orderings_Oord__class_Omax(U_8994),U_8995)),c_Big__Operators_Olattice_OSup__fin(U_8994,c_Orderings_Oord__class_Omax(U_8994),U_8996))
| U_8996 = c_Orderings_Obot__class_Obot(tc_fun(U_8994,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8994),U_8996))
| U_8995 = c_Orderings_Obot__class_Obot(tc_fun(U_8994,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8994),U_8995))
| ~ class_Orderings_Olinorder(U_8994) ),
inference(variable_rename,[status(thm)],[f_2590_1]) ).
cnf(f_2590_3,plain,
( c_Big__Operators_Olattice_OSup__fin(U_8994,c_Orderings_Oord__class_Omax(U_8994),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8994,tc_HOL_Obool)),U_8995),U_8996)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8994),c_Big__Operators_Olattice_OSup__fin(U_8994,c_Orderings_Oord__class_Omax(U_8994),U_8995)),c_Big__Operators_Olattice_OSup__fin(U_8994,c_Orderings_Oord__class_Omax(U_8994),U_8996))
| U_8996 = c_Orderings_Obot__class_Obot(tc_fun(U_8994,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8994),U_8996))
| U_8995 = c_Orderings_Obot__class_Obot(tc_fun(U_8994,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8994),U_8995))
| ~ class_Orderings_Olinorder(U_8994) ),
inference(clausify,[status(thm)],[f_2590_2]) ).
fof(f_2591_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_2591_2,plain,
! [U_8999,U_8998,U_8997] :
( c_Big__Operators_Olattice_OSup__fin(U_8997,c_Orderings_Oord__class_Omax(U_8997),hAPP(hAPP(c_Set_Oinsert(U_8997),U_8999),U_8998)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8997,U_8997,c_Orderings_Oord__class_Omax(U_8997)),U_8999),U_8998)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8997),U_8998))
| ~ class_Orderings_Olinorder(U_8997) ),
inference(variable_rename,[status(thm)],[f_2591_1]) ).
cnf(f_2591_3,plain,
( c_Big__Operators_Olattice_OSup__fin(U_8997,c_Orderings_Oord__class_Omax(U_8997),hAPP(hAPP(c_Set_Oinsert(U_8997),U_8999),U_8998)) = hAPP(hAPP(c_Finite__Set_Ofold(U_8997,U_8997,c_Orderings_Oord__class_Omax(U_8997)),U_8999),U_8998)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8997),U_8998))
| ~ class_Orderings_Olinorder(U_8997) ),
inference(clausify,[status(thm)],[f_2591_2]) ).
fof(f_2592_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_2592_2,plain,
! [U_9002,U_9001,U_9000] :
( c_Big__Operators_Olattice_OSup__fin(U_9000,c_Orderings_Oord__class_Omax(U_9000),hAPP(hAPP(c_Set_Oinsert(U_9000),U_9002),U_9001)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9000),U_9002),c_Big__Operators_Olattice_OSup__fin(U_9000,c_Orderings_Oord__class_Omax(U_9000),U_9001))
| U_9001 = c_Orderings_Obot__class_Obot(tc_fun(U_9000,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_9000),U_9002),U_9001))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9000),U_9001))
| ~ class_Orderings_Olinorder(U_9000) ),
inference(variable_rename,[status(thm)],[f_2592_1]) ).
cnf(f_2592_3,plain,
( c_Big__Operators_Olattice_OSup__fin(U_9000,c_Orderings_Oord__class_Omax(U_9000),hAPP(hAPP(c_Set_Oinsert(U_9000),U_9002),U_9001)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9000),U_9002),c_Big__Operators_Olattice_OSup__fin(U_9000,c_Orderings_Oord__class_Omax(U_9000),U_9001))
| U_9001 = c_Orderings_Obot__class_Obot(tc_fun(U_9000,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_9000),U_9002),U_9001))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9000),U_9001))
| ~ class_Orderings_Olinorder(U_9000) ),
inference(clausify,[status(thm)],[f_2592_2]) ).
fof(f_2593_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_2593_2,plain,
! [U_9005,U_9004,U_9003] :
( ( ( c_Big__Operators_Olattice_OSup__fin(U_9003,c_Orderings_Oord__class_Omax(U_9003),hAPP(hAPP(c_Set_Oinsert(U_9003),U_9005),U_9004)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9003),U_9005),c_Big__Operators_Olattice_OSup__fin(U_9003,c_Orderings_Oord__class_Omax(U_9003),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9003,tc_HOL_Obool)),U_9004),hAPP(hAPP(c_Set_Oinsert(U_9003),U_9005),c_Orderings_Obot__class_Obot(tc_fun(U_9003,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9003,tc_HOL_Obool)),U_9004),hAPP(hAPP(c_Set_Oinsert(U_9003),U_9005),c_Orderings_Obot__class_Obot(tc_fun(U_9003,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9003,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice_OSup__fin(U_9003,c_Orderings_Oord__class_Omax(U_9003),hAPP(hAPP(c_Set_Oinsert(U_9003),U_9005),U_9004)) = U_9005
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9003,tc_HOL_Obool)),U_9004),hAPP(hAPP(c_Set_Oinsert(U_9003),U_9005),c_Orderings_Obot__class_Obot(tc_fun(U_9003,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9003,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9003),U_9004))
| ~ class_Orderings_Olinorder(U_9003) ),
inference(variable_rename,[status(thm)],[f_2593_1]) ).
cnf(f_2593_3,plain,
( c_Big__Operators_Olattice_OSup__fin(U_9003,c_Orderings_Oord__class_Omax(U_9003),hAPP(hAPP(c_Set_Oinsert(U_9003),U_9005),U_9004)) = U_9005
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9003,tc_HOL_Obool)),U_9004),hAPP(hAPP(c_Set_Oinsert(U_9003),U_9005),c_Orderings_Obot__class_Obot(tc_fun(U_9003,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9003,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9003),U_9004))
| ~ class_Orderings_Olinorder(U_9003) ),
inference(clausify,[status(thm)],[f_2593_2]) ).
cnf(f_2593_4,plain,
( c_Big__Operators_Olattice_OSup__fin(U_9003,c_Orderings_Oord__class_Omax(U_9003),hAPP(hAPP(c_Set_Oinsert(U_9003),U_9005),U_9004)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9003),U_9005),c_Big__Operators_Olattice_OSup__fin(U_9003,c_Orderings_Oord__class_Omax(U_9003),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9003,tc_HOL_Obool)),U_9004),hAPP(hAPP(c_Set_Oinsert(U_9003),U_9005),c_Orderings_Obot__class_Obot(tc_fun(U_9003,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9003,tc_HOL_Obool)),U_9004),hAPP(hAPP(c_Set_Oinsert(U_9003),U_9005),c_Orderings_Obot__class_Obot(tc_fun(U_9003,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9003,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9003),U_9004))
| ~ class_Orderings_Olinorder(U_9003) ),
inference(clausify,[status(thm)],[f_2593_2]) ).
fof(f_2594_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_2594_2,plain,
! [U_9008,U_9007,U_9006] :
( c_Big__Operators_Olattice_OSup__fin(U_9006,c_Orderings_Oord__class_Omax(U_9006),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9006,tc_HOL_Obool)),U_9007),U_9008)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9006),c_Big__Operators_Olattice_OSup__fin(U_9006,c_Orderings_Oord__class_Omax(U_9006),U_9007)),c_Big__Operators_Olattice_OSup__fin(U_9006,c_Orderings_Oord__class_Omax(U_9006),U_9008))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9006,tc_HOL_Obool)),U_9007),U_9008) != c_Orderings_Obot__class_Obot(tc_fun(U_9006,tc_HOL_Obool))
| U_9008 = c_Orderings_Obot__class_Obot(tc_fun(U_9006,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9006),U_9008))
| U_9007 = c_Orderings_Obot__class_Obot(tc_fun(U_9006,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9006),U_9007))
| ~ class_Orderings_Olinorder(U_9006) ),
inference(variable_rename,[status(thm)],[f_2594_1]) ).
cnf(f_2594_3,plain,
( c_Big__Operators_Olattice_OSup__fin(U_9006,c_Orderings_Oord__class_Omax(U_9006),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9006,tc_HOL_Obool)),U_9007),U_9008)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9006),c_Big__Operators_Olattice_OSup__fin(U_9006,c_Orderings_Oord__class_Omax(U_9006),U_9007)),c_Big__Operators_Olattice_OSup__fin(U_9006,c_Orderings_Oord__class_Omax(U_9006),U_9008))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9006,tc_HOL_Obool)),U_9007),U_9008) != c_Orderings_Obot__class_Obot(tc_fun(U_9006,tc_HOL_Obool))
| U_9008 = c_Orderings_Obot__class_Obot(tc_fun(U_9006,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9006),U_9008))
| U_9007 = c_Orderings_Obot__class_Obot(tc_fun(U_9006,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9006),U_9007))
| ~ class_Orderings_Olinorder(U_9006) ),
inference(clausify,[status(thm)],[f_2594_2]) ).
fof(f_2595_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_2595_2,plain,
! [U_9011,U_9010,U_9009] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9009),c_Big__Operators_Olattice_OSup__fin(U_9009,c_Orderings_Oord__class_Omax(U_9009),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9009,tc_HOL_Obool)),U_9010),U_9011))),c_Big__Operators_Olattice_OSup__fin(U_9009,c_Orderings_Oord__class_Omax(U_9009),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9009,tc_HOL_Obool)),U_9010),U_9011))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9009),c_Big__Operators_Olattice_OSup__fin(U_9009,c_Orderings_Oord__class_Omax(U_9009),U_9010)),c_Big__Operators_Olattice_OSup__fin(U_9009,c_Orderings_Oord__class_Omax(U_9009),U_9011))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9009,tc_HOL_Obool)),U_9010),U_9011) = c_Orderings_Obot__class_Obot(tc_fun(U_9009,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9009),U_9011))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9009),U_9010))
| ~ class_Orderings_Olinorder(U_9009) ),
inference(variable_rename,[status(thm)],[f_2595_1]) ).
cnf(f_2595_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9009),c_Big__Operators_Olattice_OSup__fin(U_9009,c_Orderings_Oord__class_Omax(U_9009),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9009,tc_HOL_Obool)),U_9010),U_9011))),c_Big__Operators_Olattice_OSup__fin(U_9009,c_Orderings_Oord__class_Omax(U_9009),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9009,tc_HOL_Obool)),U_9010),U_9011))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9009),c_Big__Operators_Olattice_OSup__fin(U_9009,c_Orderings_Oord__class_Omax(U_9009),U_9010)),c_Big__Operators_Olattice_OSup__fin(U_9009,c_Orderings_Oord__class_Omax(U_9009),U_9011))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9009,tc_HOL_Obool)),U_9010),U_9011) = c_Orderings_Obot__class_Obot(tc_fun(U_9009,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9009),U_9011))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9009),U_9010))
| ~ class_Orderings_Olinorder(U_9009) ),
inference(clausify,[status(thm)],[f_2595_2]) ).
fof(f_2596_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_2596_2,plain,
! [U_9014,U_9013,U_9012] :
( c_Big__Operators_Olattice_OSup__fin(U_9012,c_Orderings_Oord__class_Omax(U_9012),hAPP(hAPP(c_Set_Oinsert(U_9012),U_9014),U_9013)) = hAPP(hAPP(c_Finite__Set_Ofold(U_9012,U_9012,c_Orderings_Oord__class_Omax(U_9012)),U_9014),U_9013)
| hBOOL(hAPP(hAPP(c_member(U_9012),U_9014),U_9013))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9012),U_9013))
| ~ class_Orderings_Olinorder(U_9012) ),
inference(variable_rename,[status(thm)],[f_2596_1]) ).
cnf(f_2596_3,plain,
( c_Big__Operators_Olattice_OSup__fin(U_9012,c_Orderings_Oord__class_Omax(U_9012),hAPP(hAPP(c_Set_Oinsert(U_9012),U_9014),U_9013)) = hAPP(hAPP(c_Finite__Set_Ofold(U_9012,U_9012,c_Orderings_Oord__class_Omax(U_9012)),U_9014),U_9013)
| hBOOL(hAPP(hAPP(c_member(U_9012),U_9014),U_9013))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9012),U_9013))
| ~ class_Orderings_Olinorder(U_9012) ),
inference(clausify,[status(thm)],[f_2596_2]) ).
fof(f_2597_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_2597_2,plain,
! [U_9018,U_9017] :
( hBOOL(hAPP(hAPP(c_member(U_9017),c_Big__Operators_Olattice_OSup__fin(U_9017,c_Orderings_Oord__class_Omax(U_9017),U_9018)),U_9018))
| ? [U_9016,U_9015] : ~ hBOOL(hAPP(hAPP(c_member(U_9017),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9017),U_9016),U_9015)),hAPP(hAPP(c_Set_Oinsert(U_9017),U_9016),hAPP(hAPP(c_Set_Oinsert(U_9017),U_9015),c_Orderings_Obot__class_Obot(tc_fun(U_9017,tc_HOL_Obool))))))
| U_9018 = c_Orderings_Obot__class_Obot(tc_fun(U_9017,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9017),U_9018))
| ~ class_Orderings_Olinorder(U_9017) ),
inference(variable_rename,[status(thm)],[f_2597_1]) ).
fof(f_2597_3,plain,
! [U_9018,U_9017] :
( hBOOL(hAPP(hAPP(c_member(U_9017),c_Big__Operators_Olattice_OSup__fin(U_9017,c_Orderings_Oord__class_Omax(U_9017),U_9018)),U_9018))
| ? [U_9015] : ~ hBOOL(hAPP(hAPP(c_member(U_9017),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9017),sK227(U_9018,U_9017)),U_9015)),hAPP(hAPP(c_Set_Oinsert(U_9017),sK227(U_9018,U_9017)),hAPP(hAPP(c_Set_Oinsert(U_9017),U_9015),c_Orderings_Obot__class_Obot(tc_fun(U_9017,tc_HOL_Obool))))))
| U_9018 = c_Orderings_Obot__class_Obot(tc_fun(U_9017,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9017),U_9018))
| ~ class_Orderings_Olinorder(U_9017) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK227]),skolemize(U_9016,sK227(U_9018,U_9017))],[f_2597_2]) ).
fof(f_2597_4,plain,
! [U_9018,U_9017] :
( hBOOL(hAPP(hAPP(c_member(U_9017),c_Big__Operators_Olattice_OSup__fin(U_9017,c_Orderings_Oord__class_Omax(U_9017),U_9018)),U_9018))
| ~ hBOOL(hAPP(hAPP(c_member(U_9017),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9017),sK227(U_9018,U_9017)),sK228(U_9018,U_9017))),hAPP(hAPP(c_Set_Oinsert(U_9017),sK227(U_9018,U_9017)),hAPP(hAPP(c_Set_Oinsert(U_9017),sK228(U_9018,U_9017)),c_Orderings_Obot__class_Obot(tc_fun(U_9017,tc_HOL_Obool))))))
| U_9018 = c_Orderings_Obot__class_Obot(tc_fun(U_9017,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9017),U_9018))
| ~ class_Orderings_Olinorder(U_9017) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK228]),skolemize(U_9015,sK228(U_9018,U_9017))],[f_2597_3]) ).
cnf(f_2597_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_9017),c_Big__Operators_Olattice_OSup__fin(U_9017,c_Orderings_Oord__class_Omax(U_9017),U_9018)),U_9018))
| ~ hBOOL(hAPP(hAPP(c_member(U_9017),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9017),sK227(U_9018,U_9017)),sK228(U_9018,U_9017))),hAPP(hAPP(c_Set_Oinsert(U_9017),sK227(U_9018,U_9017)),hAPP(hAPP(c_Set_Oinsert(U_9017),sK228(U_9018,U_9017)),c_Orderings_Obot__class_Obot(tc_fun(U_9017,tc_HOL_Obool))))))
| U_9018 = c_Orderings_Obot__class_Obot(tc_fun(U_9017,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9017),U_9018))
| ~ class_Orderings_Olinorder(U_9017) ),
inference(clausify,[status(thm)],[f_2597_4]) ).
fof(f_2598_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_2598_2,plain,
! [U_9023,U_9022,U_9021] :
( hAPP(U_9022,c_Big__Operators_Olattice_OSup__fin(U_9021,c_Orderings_Oord__class_Omax(U_9021),U_9023)) = c_Big__Operators_Olattice_OSup__fin(U_9021,c_Orderings_Oord__class_Omax(U_9021),hAPP(c_Set_Oimage(U_9021,U_9021,U_9022),U_9023))
| U_9023 = c_Orderings_Obot__class_Obot(tc_fun(U_9021,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9021),U_9023))
| ? [U_9020,U_9019] : hAPP(U_9022,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9021),U_9020),U_9019)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9021),hAPP(U_9022,U_9020)),hAPP(U_9022,U_9019))
| ~ class_Orderings_Olinorder(U_9021) ),
inference(variable_rename,[status(thm)],[f_2598_1]) ).
fof(f_2598_3,plain,
! [U_9023,U_9022,U_9021] :
( hAPP(U_9022,c_Big__Operators_Olattice_OSup__fin(U_9021,c_Orderings_Oord__class_Omax(U_9021),U_9023)) = c_Big__Operators_Olattice_OSup__fin(U_9021,c_Orderings_Oord__class_Omax(U_9021),hAPP(c_Set_Oimage(U_9021,U_9021,U_9022),U_9023))
| U_9023 = c_Orderings_Obot__class_Obot(tc_fun(U_9021,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9021),U_9023))
| ? [U_9019] : hAPP(U_9022,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9021),sK229(U_9023,U_9022,U_9021)),U_9019)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9021),hAPP(U_9022,sK229(U_9023,U_9022,U_9021))),hAPP(U_9022,U_9019))
| ~ class_Orderings_Olinorder(U_9021) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK229]),skolemize(U_9020,sK229(U_9023,U_9022,U_9021))],[f_2598_2]) ).
fof(f_2598_4,plain,
! [U_9023,U_9022,U_9021] :
( hAPP(U_9022,c_Big__Operators_Olattice_OSup__fin(U_9021,c_Orderings_Oord__class_Omax(U_9021),U_9023)) = c_Big__Operators_Olattice_OSup__fin(U_9021,c_Orderings_Oord__class_Omax(U_9021),hAPP(c_Set_Oimage(U_9021,U_9021,U_9022),U_9023))
| U_9023 = c_Orderings_Obot__class_Obot(tc_fun(U_9021,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9021),U_9023))
| hAPP(U_9022,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9021),sK229(U_9023,U_9022,U_9021)),sK230(U_9023,U_9022,U_9021))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9021),hAPP(U_9022,sK229(U_9023,U_9022,U_9021))),hAPP(U_9022,sK230(U_9023,U_9022,U_9021)))
| ~ class_Orderings_Olinorder(U_9021) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK230]),skolemize(U_9019,sK230(U_9023,U_9022,U_9021))],[f_2598_3]) ).
cnf(f_2598_5,plain,
( hAPP(U_9022,c_Big__Operators_Olattice_OSup__fin(U_9021,c_Orderings_Oord__class_Omax(U_9021),U_9023)) = c_Big__Operators_Olattice_OSup__fin(U_9021,c_Orderings_Oord__class_Omax(U_9021),hAPP(c_Set_Oimage(U_9021,U_9021,U_9022),U_9023))
| U_9023 = c_Orderings_Obot__class_Obot(tc_fun(U_9021,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9021),U_9023))
| hAPP(U_9022,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9021),sK229(U_9023,U_9022,U_9021)),sK230(U_9023,U_9022,U_9021))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9021),hAPP(U_9022,sK229(U_9023,U_9022,U_9021))),hAPP(U_9022,sK230(U_9023,U_9022,U_9021)))
| ~ class_Orderings_Olinorder(U_9021) ),
inference(clausify,[status(thm)],[f_2598_4]) ).
fof(f_2599_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_2599_2,plain,
! [U_9028,U_9027,U_9026] :
( hAPP(U_9027,c_Big__Operators_Olinorder__class_OMax(U_9026,U_9028)) = c_Big__Operators_Olinorder__class_OMax(U_9026,hAPP(c_Set_Oimage(U_9026,U_9026,U_9027),U_9028))
| U_9028 = c_Orderings_Obot__class_Obot(tc_fun(U_9026,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9026),U_9028))
| ? [U_9025,U_9024] : hAPP(U_9027,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9026),U_9025),U_9024)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9026),hAPP(U_9027,U_9025)),hAPP(U_9027,U_9024))
| ~ class_Orderings_Olinorder(U_9026) ),
inference(variable_rename,[status(thm)],[f_2599_1]) ).
fof(f_2599_3,plain,
! [U_9028,U_9027,U_9026] :
( hAPP(U_9027,c_Big__Operators_Olinorder__class_OMax(U_9026,U_9028)) = c_Big__Operators_Olinorder__class_OMax(U_9026,hAPP(c_Set_Oimage(U_9026,U_9026,U_9027),U_9028))
| U_9028 = c_Orderings_Obot__class_Obot(tc_fun(U_9026,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9026),U_9028))
| ? [U_9024] : hAPP(U_9027,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9026),sK231(U_9028,U_9027,U_9026)),U_9024)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9026),hAPP(U_9027,sK231(U_9028,U_9027,U_9026))),hAPP(U_9027,U_9024))
| ~ class_Orderings_Olinorder(U_9026) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK231]),skolemize(U_9025,sK231(U_9028,U_9027,U_9026))],[f_2599_2]) ).
fof(f_2599_4,plain,
! [U_9028,U_9027,U_9026] :
( hAPP(U_9027,c_Big__Operators_Olinorder__class_OMax(U_9026,U_9028)) = c_Big__Operators_Olinorder__class_OMax(U_9026,hAPP(c_Set_Oimage(U_9026,U_9026,U_9027),U_9028))
| U_9028 = c_Orderings_Obot__class_Obot(tc_fun(U_9026,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9026),U_9028))
| hAPP(U_9027,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9026),sK231(U_9028,U_9027,U_9026)),sK232(U_9028,U_9027,U_9026))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9026),hAPP(U_9027,sK231(U_9028,U_9027,U_9026))),hAPP(U_9027,sK232(U_9028,U_9027,U_9026)))
| ~ class_Orderings_Olinorder(U_9026) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK232]),skolemize(U_9024,sK232(U_9028,U_9027,U_9026))],[f_2599_3]) ).
cnf(f_2599_5,plain,
( hAPP(U_9027,c_Big__Operators_Olinorder__class_OMax(U_9026,U_9028)) = c_Big__Operators_Olinorder__class_OMax(U_9026,hAPP(c_Set_Oimage(U_9026,U_9026,U_9027),U_9028))
| U_9028 = c_Orderings_Obot__class_Obot(tc_fun(U_9026,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9026),U_9028))
| hAPP(U_9027,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9026),sK231(U_9028,U_9027,U_9026)),sK232(U_9028,U_9027,U_9026))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9026),hAPP(U_9027,sK231(U_9028,U_9027,U_9026))),hAPP(U_9027,sK232(U_9028,U_9027,U_9026)))
| ~ class_Orderings_Olinorder(U_9026) ),
inference(clausify,[status(thm)],[f_2599_4]) ).
fof(f_2600_1,plain,
! [V_c_2,V_b_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_c_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__sup__le__sup]) ).
fof(f_2600_2,plain,
! [U_9033,U_9032,U_9031,U_9030] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9030),hAPP(hAPP(c_Finite__Set_Ofold(U_9030,U_9030,c_Orderings_Oord__class_Omax(U_9030)),U_9033),U_9031)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9030),U_9032),U_9033)))
| ? [U_9029] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9030),U_9029),U_9032))
& hBOOL(hAPP(hAPP(c_member(U_9030),U_9029),U_9031)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9030),U_9031))
| ~ class_Orderings_Olinorder(U_9030) ),
inference(variable_rename,[status(thm)],[f_2600_1]) ).
fof(f_2600_3,plain,
! [U_9033,U_9032,U_9031,U_9030] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9030),hAPP(hAPP(c_Finite__Set_Ofold(U_9030,U_9030,c_Orderings_Oord__class_Omax(U_9030)),U_9033),U_9031)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9030),U_9032),U_9033)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9030),sK233(U_9033,U_9032,U_9031,U_9030)),U_9032))
& hBOOL(hAPP(hAPP(c_member(U_9030),sK233(U_9033,U_9032,U_9031,U_9030)),U_9031)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9030),U_9031))
| ~ class_Orderings_Olinorder(U_9030) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK233]),skolemize(U_9029,sK233(U_9033,U_9032,U_9031,U_9030))],[f_2600_2]) ).
cnf(f_2600_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_9030),sK233(U_9033,U_9032,U_9031,U_9030)),U_9031))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9030),hAPP(hAPP(c_Finite__Set_Ofold(U_9030,U_9030,c_Orderings_Oord__class_Omax(U_9030)),U_9033),U_9031)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9030),U_9032),U_9033)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9030),U_9031))
| ~ class_Orderings_Olinorder(U_9030) ),
inference(clausify,[status(thm)],[f_2600_3]) ).
cnf(f_2600_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9030),sK233(U_9033,U_9032,U_9031,U_9030)),U_9032))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9030),hAPP(hAPP(c_Finite__Set_Ofold(U_9030,U_9030,c_Orderings_Oord__class_Omax(U_9030)),U_9033),U_9031)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9030),U_9032),U_9033)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9030),U_9031))
| ~ class_Orderings_Olinorder(U_9030) ),
inference(clausify,[status(thm)],[f_2600_3]) ).
fof(f_2601_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_2601_2,plain,
! [U_9037,U_9036,U_9035] :
( c_Big__Operators_Olinorder__class_OMin(U_9035,U_9036) = U_9037
| ~ hBOOL(hAPP(hAPP(c_member(U_9035),U_9037),U_9036))
| ? [U_9034] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9035),U_9037),U_9034))
& hBOOL(hAPP(hAPP(c_member(U_9035),U_9034),U_9036)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9035),U_9036))
| ~ class_Orderings_Olinorder(U_9035) ),
inference(variable_rename,[status(thm)],[f_2601_1]) ).
fof(f_2601_3,plain,
! [U_9037,U_9036,U_9035] :
( c_Big__Operators_Olinorder__class_OMin(U_9035,U_9036) = U_9037
| ~ hBOOL(hAPP(hAPP(c_member(U_9035),U_9037),U_9036))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9035),U_9037),sK234(U_9037,U_9036,U_9035)))
& hBOOL(hAPP(hAPP(c_member(U_9035),sK234(U_9037,U_9036,U_9035)),U_9036)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9035),U_9036))
| ~ class_Orderings_Olinorder(U_9035) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK234]),skolemize(U_9034,sK234(U_9037,U_9036,U_9035))],[f_2601_2]) ).
cnf(f_2601_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_9035),sK234(U_9037,U_9036,U_9035)),U_9036))
| c_Big__Operators_Olinorder__class_OMin(U_9035,U_9036) = U_9037
| ~ hBOOL(hAPP(hAPP(c_member(U_9035),U_9037),U_9036))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9035),U_9036))
| ~ class_Orderings_Olinorder(U_9035) ),
inference(clausify,[status(thm)],[f_2601_3]) ).
cnf(f_2601_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9035),U_9037),sK234(U_9037,U_9036,U_9035)))
| c_Big__Operators_Olinorder__class_OMin(U_9035,U_9036) = U_9037
| ~ hBOOL(hAPP(hAPP(c_member(U_9035),U_9037),U_9036))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9035),U_9036))
| ~ class_Orderings_Olinorder(U_9035) ),
inference(clausify,[status(thm)],[f_2601_3]) ).
fof(f_2602_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_2602_2,plain,
! [U_9041,U_9040,U_9039] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9039),U_9040),U_9041))
| ? [U_9038] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9039),U_9040),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9039),U_9041),U_9038)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9039),c_Groups_Ozero__class_Ozero(U_9039)),U_9038)) )
| ~ class_Fields_Olinordered__field(U_9039) ),
inference(variable_rename,[status(thm)],[f_2602_1]) ).
fof(f_2602_3,plain,
! [U_9041,U_9040,U_9039] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9039),U_9040),U_9041))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9039),U_9040),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9039),U_9041),sK235(U_9041,U_9040,U_9039))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9039),c_Groups_Ozero__class_Ozero(U_9039)),sK235(U_9041,U_9040,U_9039))) )
| ~ class_Fields_Olinordered__field(U_9039) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK235]),skolemize(U_9038,sK235(U_9041,U_9040,U_9039))],[f_2602_2]) ).
cnf(f_2602_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9039),c_Groups_Ozero__class_Ozero(U_9039)),sK235(U_9041,U_9040,U_9039)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9039),U_9040),U_9041))
| ~ class_Fields_Olinordered__field(U_9039) ),
inference(clausify,[status(thm)],[f_2602_3]) ).
cnf(f_2602_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9039),U_9040),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9039),U_9041),sK235(U_9041,U_9040,U_9039))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9039),U_9040),U_9041))
| ~ class_Fields_Olinordered__field(U_9039) ),
inference(clausify,[status(thm)],[f_2602_3]) ).
fof(f_2603_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_2603_2,plain,
! [U_9043,U_9042] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_9042),U_9043) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,U_9042),U_9043),
inference(variable_rename,[status(thm)],[f_2603_1]) ).
cnf(f_2603_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_9042),U_9043) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,U_9042),U_9043),
inference(clausify,[status(thm)],[f_2603_2]) ).
fof(f_2604_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_2604_2,plain,
c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_2604_1]) ).
fof(f_2605_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_2605_2,plain,
! [U_9049,U_9048,U_9047,U_9046,U_9045,U_9044] : c_Nitpick_Opair__box_Opair__box__size(U_9044,U_9045,U_9046,U_9047,c_Nitpick_Opair__box_OPairBox(U_9044,U_9045,U_9048,U_9049)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_9046,U_9048)),hAPP(U_9047,U_9049))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_2605_1]) ).
cnf(f_2605_3,plain,
c_Nitpick_Opair__box_Opair__box__size(U_9044,U_9045,U_9046,U_9047,c_Nitpick_Opair__box_OPairBox(U_9044,U_9045,U_9048,U_9049)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_9046,U_9048)),hAPP(U_9047,U_9049))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_2605_2]) ).
fof(f_2606_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_2606_2,plain,
! [U_9052,U_9051,U_9050] : hAPP(hAPP(c_Groups_Otimes__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_9050)),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_9051))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_9052))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9052)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9050),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9050),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_9052),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_9051)))),
inference(variable_rename,[status(thm)],[f_2606_1]) ).
cnf(f_2606_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_9050)),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_9051))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_9052))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9052)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9050),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9050),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_9052),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_9051)))),
inference(clausify,[status(thm)],[f_2606_2]) ).
fof(f_2607_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_2607_2,plain,
! [U_9053] :
( ( ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_9053)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_9053)),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_9053))))
| 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_9053)))) )
& ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_9053)) = 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_9053)))
| ~ 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_9053)))) ) )
| ~ 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_9053))) ),
inference(variable_rename,[status(thm)],[f_2607_1]) ).
cnf(f_2607_3,plain,
( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_9053)) = 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_9053)))
| ~ 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_9053))))
| ~ 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_9053))) ),
inference(clausify,[status(thm)],[f_2607_2]) ).
cnf(f_2607_4,plain,
( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_9053)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_9053)),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_9053))))
| 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_9053))))
| ~ 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_9053))) ),
inference(clausify,[status(thm)],[f_2607_2]) ).
fof(f_2608_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_2608_2,plain,
! [U_9060,U_9059,U_9058,U_9057,U_9056,U_9055,U_9054] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_9054,U_9057,c_Groups_Otimes__class_Otimes(U_9054)),U_9059),U_9060),hAPP(c_Set_Oimage(U_9055,U_9057,U_9058),U_9056)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_9054,U_9055,c_Groups_Otimes__class_Otimes(U_9054)),hAPP(c_Fun_Ocomp(U_9057,U_9054,U_9055,U_9059),U_9058)),U_9060),U_9056)
| ~ c_Fun_Oinj__on(U_9055,U_9057,U_9058,U_9056)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9055),U_9056))
| ~ class_Groups_Oab__semigroup__mult(U_9054) ),
inference(variable_rename,[status(thm)],[f_2608_1]) ).
cnf(f_2608_3,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_9054,U_9057,c_Groups_Otimes__class_Otimes(U_9054)),U_9059),U_9060),hAPP(c_Set_Oimage(U_9055,U_9057,U_9058),U_9056)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_9054,U_9055,c_Groups_Otimes__class_Otimes(U_9054)),hAPP(c_Fun_Ocomp(U_9057,U_9054,U_9055,U_9059),U_9058)),U_9060),U_9056)
| ~ c_Fun_Oinj__on(U_9055,U_9057,U_9058,U_9056)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9055),U_9056))
| ~ class_Groups_Oab__semigroup__mult(U_9054) ),
inference(clausify,[status(thm)],[f_2608_2]) ).
fof(f_2609_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_2609_2,plain,
! [U_9066,U_9065,U_9064,U_9063,U_9062,U_9061] :
( hBOOL(hAPP(hAPP(U_9064,U_9066),U_9065))
| ~ hBOOL(hAPP(hAPP(c_member(U_9061),U_9066),U_9063))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9061,tc_fun(U_9062,tc_HOL_Obool)),U_9063),U_9064),U_9065)) ),
inference(variable_rename,[status(thm)],[f_2609_1]) ).
cnf(f_2609_3,plain,
( hBOOL(hAPP(hAPP(U_9064,U_9066),U_9065))
| ~ hBOOL(hAPP(hAPP(c_member(U_9061),U_9066),U_9063))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9061,tc_fun(U_9062,tc_HOL_Obool)),U_9063),U_9064),U_9065)) ),
inference(clausify,[status(thm)],[f_2609_2]) ).
fof(f_2610_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_2610_2,plain,
! [U_9072,U_9071,U_9070,U_9069,U_9068,U_9067] :
( ~ hBOOL(hAPP(hAPP(c_member(U_9067),U_9072),U_9069))
| hBOOL(hAPP(hAPP(U_9070,U_9072),U_9071))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9067,tc_fun(U_9068,tc_HOL_Obool)),U_9069),U_9070),U_9071)) ),
inference(variable_rename,[status(thm)],[f_2610_1]) ).
cnf(f_2610_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_9067),U_9072),U_9069))
| hBOOL(hAPP(hAPP(U_9070,U_9072),U_9071))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9067,tc_fun(U_9068,tc_HOL_Obool)),U_9069),U_9070),U_9071)) ),
inference(clausify,[status(thm)],[f_2610_2]) ).
fof(f_2611_1,plain,
! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ),
inference(fof_nnf,[status(thm)],[fact_INF2__D]) ).
fof(f_2611_2,plain,
! [U_9080,U_9079,U_9078,U_9077,U_9076,U_9075,U_9074,U_9073] :
( hBOOL(hAPP(hAPP(hAPP(U_9077,U_9080),U_9078),U_9079))
| ~ hBOOL(hAPP(hAPP(c_member(U_9073),U_9080),U_9076))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9073,tc_fun(U_9074,tc_fun(U_9075,tc_HOL_Obool))),U_9076),U_9077),U_9078),U_9079)) ),
inference(variable_rename,[status(thm)],[f_2611_1]) ).
cnf(f_2611_3,plain,
( hBOOL(hAPP(hAPP(hAPP(U_9077,U_9080),U_9078),U_9079))
| ~ hBOOL(hAPP(hAPP(c_member(U_9073),U_9080),U_9076))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9073,tc_fun(U_9074,tc_fun(U_9075,tc_HOL_Obool))),U_9076),U_9077),U_9078),U_9079)) ),
inference(clausify,[status(thm)],[f_2611_2]) ).
fof(f_2612_1,plain,
! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ),
inference(fof_nnf,[status(thm)],[fact_INF2__E]) ).
fof(f_2612_2,plain,
! [U_9088,U_9087,U_9086,U_9085,U_9084,U_9083,U_9082,U_9081] :
( ~ hBOOL(hAPP(hAPP(c_member(U_9081),U_9088),U_9084))
| hBOOL(hAPP(hAPP(hAPP(U_9085,U_9088),U_9086),U_9087))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9081,tc_fun(U_9082,tc_fun(U_9083,tc_HOL_Obool))),U_9084),U_9085),U_9086),U_9087)) ),
inference(variable_rename,[status(thm)],[f_2612_1]) ).
cnf(f_2612_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_9081),U_9088),U_9084))
| hBOOL(hAPP(hAPP(hAPP(U_9085,U_9088),U_9086),U_9087))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9081,tc_fun(U_9082,tc_fun(U_9083,tc_HOL_Obool))),U_9084),U_9085),U_9086),U_9087)) ),
inference(clausify,[status(thm)],[f_2612_2]) ).
fof(f_2613_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_2613_2,plain,
! [U_9094,U_9093,U_9092,U_9091,U_9090,U_9089] :
( hBOOL(hAPP(hAPP(c_member(U_9089),U_9090),hAPP(U_9093,U_9094)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9091),U_9094),U_9092))
| ~ hBOOL(hAPP(hAPP(c_member(U_9089),U_9090),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9091,tc_fun(U_9089,tc_HOL_Obool)),U_9092),U_9093))) ),
inference(variable_rename,[status(thm)],[f_2613_1]) ).
cnf(f_2613_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_9089),U_9090),hAPP(U_9093,U_9094)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9091),U_9094),U_9092))
| ~ hBOOL(hAPP(hAPP(c_member(U_9089),U_9090),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9091,tc_fun(U_9089,tc_HOL_Obool)),U_9092),U_9093))) ),
inference(clausify,[status(thm)],[f_2613_2]) ).
fof(f_2614_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_2614_2,plain,
! [U_9100,U_9099,U_9098,U_9097,U_9096,U_9095] :
( ~ hBOOL(hAPP(hAPP(c_member(U_9097),U_9100),U_9098))
| hBOOL(hAPP(hAPP(c_member(U_9095),U_9096),hAPP(U_9099,U_9100)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9095),U_9096),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9097,tc_fun(U_9095,tc_HOL_Obool)),U_9098),U_9099))) ),
inference(variable_rename,[status(thm)],[f_2614_1]) ).
cnf(f_2614_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_9097),U_9100),U_9098))
| hBOOL(hAPP(hAPP(c_member(U_9095),U_9096),hAPP(U_9099,U_9100)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9095),U_9096),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9097,tc_fun(U_9095,tc_HOL_Obool)),U_9098),U_9099))) ),
inference(clausify,[status(thm)],[f_2614_2]) ).
fof(f_2615_1,plain,
! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_SUP2__I]) ).
fof(f_2615_2,plain,
! [U_9108,U_9107,U_9106,U_9105,U_9104,U_9103,U_9102,U_9101] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9101,tc_fun(U_9107,tc_fun(U_9108,tc_HOL_Obool))),U_9103),U_9104),U_9105),U_9106))
| ~ hBOOL(hAPP(hAPP(hAPP(U_9104,U_9102),U_9105),U_9106))
| ~ hBOOL(hAPP(hAPP(c_member(U_9101),U_9102),U_9103)) ),
inference(variable_rename,[status(thm)],[f_2615_1]) ).
cnf(f_2615_3,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9101,tc_fun(U_9107,tc_fun(U_9108,tc_HOL_Obool))),U_9103),U_9104),U_9105),U_9106))
| ~ hBOOL(hAPP(hAPP(hAPP(U_9104,U_9102),U_9105),U_9106))
| ~ hBOOL(hAPP(hAPP(c_member(U_9101),U_9102),U_9103)) ),
inference(clausify,[status(thm)],[f_2615_2]) ).
fof(f_2616_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_2616_2,plain,
! [U_9113,U_9112,U_9111,U_9110] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9112),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9110,tc_fun(U_9112,tc_HOL_Obool)),U_9111),U_9113)))
| ! [U_9109] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9112),hAPP(U_9113,U_9109)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9110),U_9109),U_9111)) ) ),
inference(variable_rename,[status(thm)],[f_2616_1]) ).
cnf(f_2616_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9112),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9110,tc_fun(U_9112,tc_HOL_Obool)),U_9111),U_9113)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9112),hAPP(U_9113,U_9109)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9110),U_9109),U_9111)) ),
inference(clausify,[status(thm)],[f_2616_2]) ).
fof(f_2617_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_2617_2,plain,
! [U_9119,U_9118,U_9117,U_9116,U_9115,U_9114] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9114,tc_fun(U_9119,tc_HOL_Obool)),U_9116),U_9117),U_9118))
| ~ hBOOL(hAPP(hAPP(U_9117,U_9115),U_9118))
| ~ hBOOL(hAPP(hAPP(c_member(U_9114),U_9115),U_9116)) ),
inference(variable_rename,[status(thm)],[f_2617_1]) ).
cnf(f_2617_3,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9114,tc_fun(U_9119,tc_HOL_Obool)),U_9116),U_9117),U_9118))
| ~ hBOOL(hAPP(hAPP(U_9117,U_9115),U_9118))
| ~ hBOOL(hAPP(hAPP(c_member(U_9114),U_9115),U_9116)) ),
inference(clausify,[status(thm)],[f_2617_2]) ).
fof(f_2618_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_2618_2,plain,
! [U_9125,U_9124,U_9123,U_9122,U_9121,U_9120] :
( hBOOL(hAPP(hAPP(c_member(U_9123),U_9124),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9120,tc_fun(U_9123,tc_HOL_Obool)),U_9122),U_9125)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9123),U_9124),hAPP(U_9125,U_9121)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9120),U_9121),U_9122)) ),
inference(variable_rename,[status(thm)],[f_2618_1]) ).
cnf(f_2618_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_9123),U_9124),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9120,tc_fun(U_9123,tc_HOL_Obool)),U_9122),U_9125)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9123),U_9124),hAPP(U_9125,U_9121)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9120),U_9121),U_9122)) ),
inference(clausify,[status(thm)],[f_2618_2]) ).
fof(f_2619_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_2619_2,plain,
! [U_9129,U_9128,U_9127,U_9126] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9126),hAPP(c_Groups_Oabs__class_Oabs(U_9126),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9127,U_9126),U_9128),U_9129))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9127,U_9126),hAPP(hAPP(c_COMBB(U_9126,U_9126,U_9127),c_Groups_Oabs__class_Oabs(U_9126)),U_9128)),U_9129)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9126) ),
inference(variable_rename,[status(thm)],[f_2619_1]) ).
cnf(f_2619_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9126),hAPP(c_Groups_Oabs__class_Oabs(U_9126),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9127,U_9126),U_9128),U_9129))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9127,U_9126),hAPP(hAPP(c_COMBB(U_9126,U_9126,U_9127),c_Groups_Oabs__class_Oabs(U_9126)),U_9128)),U_9129)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9126) ),
inference(clausify,[status(thm)],[f_2619_2]) ).
fof(f_2620_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_2620_2,plain,
! [U_9133,U_9132,U_9131,U_9130] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9130),c_Groups_Ozero__class_Ozero(U_9130)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9131,U_9130),hAPP(hAPP(c_COMBB(U_9130,U_9130,U_9131),c_Groups_Oabs__class_Oabs(U_9130)),U_9132)),U_9133)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9130) ),
inference(variable_rename,[status(thm)],[f_2620_1]) ).
cnf(f_2620_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9130),c_Groups_Ozero__class_Ozero(U_9130)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9131,U_9130),hAPP(hAPP(c_COMBB(U_9130,U_9130,U_9131),c_Groups_Oabs__class_Oabs(U_9130)),U_9132)),U_9133)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9130) ),
inference(clausify,[status(thm)],[f_2620_2]) ).
fof(f_2621_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_2621_2,plain,
! [U_9135,U_9134] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_9134),hAPP(c_Nat_OSuc,U_9135)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9135),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_9135)),U_9134),
inference(variable_rename,[status(thm)],[f_2621_1]) ).
cnf(f_2621_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_9134),hAPP(c_Nat_OSuc,U_9135)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9135),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_9135)),U_9134),
inference(clausify,[status(thm)],[f_2621_2]) ).
fof(f_2622_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_2622_2,plain,
! [U_9137,U_9136] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9136)),U_9137) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9136),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_9136)),U_9137),
inference(variable_rename,[status(thm)],[f_2622_1]) ).
cnf(f_2622_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9136)),U_9137) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9136),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_9136)),U_9137),
inference(clausify,[status(thm)],[f_2622_2]) ).
fof(f_2623_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_2623_2,plain,
! [U_9141,U_9140,U_9139,U_9138] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9138,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9139,tc_fun(U_9138,tc_HOL_Obool),U_9140),U_9141)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9139,tc_fun(U_9138,tc_HOL_Obool)),U_9141),U_9140),
inference(variable_rename,[status(thm)],[f_2623_1]) ).
cnf(f_2623_3,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9138,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9139,tc_fun(U_9138,tc_HOL_Obool),U_9140),U_9141)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9139,tc_fun(U_9138,tc_HOL_Obool)),U_9141),U_9140),
inference(clausify,[status(thm)],[f_2623_2]) ).
fof(f_2624_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_2624_2,plain,
! [U_9145,U_9144,U_9143,U_9142] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9142,tc_fun(U_9143,tc_HOL_Obool)),U_9144),U_9145) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9143,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9142,tc_fun(U_9143,tc_HOL_Obool),U_9145),U_9144)),
inference(variable_rename,[status(thm)],[f_2624_1]) ).
cnf(f_2624_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9142,tc_fun(U_9143,tc_HOL_Obool)),U_9144),U_9145) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9143,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9142,tc_fun(U_9143,tc_HOL_Obool),U_9145),U_9144)),
inference(clausify,[status(thm)],[f_2624_2]) ).
fof(f_2625_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_2625_2,plain,
! [U_9150,U_9149,U_9148,U_9147,U_9146] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9146,tc_fun(U_9147,tc_HOL_Obool)),U_9148),hAPP(hAPP(c_COMBS(U_9146,tc_fun(U_9147,tc_HOL_Obool),tc_fun(U_9147,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9147,tc_HOL_Obool),tc_fun(tc_fun(U_9147,tc_HOL_Obool),tc_fun(U_9147,tc_HOL_Obool)),U_9146),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9147,tc_HOL_Obool))),U_9149)),U_9150)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9147,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9147,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9146,tc_fun(U_9147,tc_HOL_Obool),U_9149),U_9148))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9147,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9146,tc_fun(U_9147,tc_HOL_Obool),U_9150),U_9148))),
inference(variable_rename,[status(thm)],[f_2625_1]) ).
cnf(f_2625_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9146,tc_fun(U_9147,tc_HOL_Obool)),U_9148),hAPP(hAPP(c_COMBS(U_9146,tc_fun(U_9147,tc_HOL_Obool),tc_fun(U_9147,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9147,tc_HOL_Obool),tc_fun(tc_fun(U_9147,tc_HOL_Obool),tc_fun(U_9147,tc_HOL_Obool)),U_9146),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9147,tc_HOL_Obool))),U_9149)),U_9150)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9147,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9147,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9146,tc_fun(U_9147,tc_HOL_Obool),U_9149),U_9148))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9147,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9146,tc_fun(U_9147,tc_HOL_Obool),U_9150),U_9148))),
inference(clausify,[status(thm)],[f_2625_2]) ).
fof(f_2626_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_2626_2,plain,
! [U_9152,U_9151] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9151)),U_9152) = 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_9151)),U_9152),
inference(variable_rename,[status(thm)],[f_2626_1]) ).
cnf(f_2626_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9151)),U_9152) = 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_9151)),U_9152),
inference(clausify,[status(thm)],[f_2626_2]) ).
fof(f_2627_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_2627_2,plain,
! [U_9154,U_9153] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_9153),hAPP(c_Nat_OSuc,U_9154)) = 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_9154)),U_9153),
inference(variable_rename,[status(thm)],[f_2627_1]) ).
cnf(f_2627_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_9153),hAPP(c_Nat_OSuc,U_9154)) = 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_9154)),U_9153),
inference(clausify,[status(thm)],[f_2627_2]) ).
fof(f_2628_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_2628_2,plain,
! [U_9158,U_9157,U_9156,U_9155] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9155),U_9156),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9157)),hAPP(c_Nat_OSuc,U_9158))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9155),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9155,tc_Nat_Onat),U_9156),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_9157),U_9158))
| ~ class_Groups_Ocomm__monoid__add(U_9155) ),
inference(variable_rename,[status(thm)],[f_2628_1]) ).
cnf(f_2628_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9155),U_9156),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9157)),hAPP(c_Nat_OSuc,U_9158))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9155),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9155,tc_Nat_Onat),U_9156),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_9157),U_9158))
| ~ class_Groups_Ocomm__monoid__add(U_9155) ),
inference(clausify,[status(thm)],[f_2628_2]) ).
fof(f_2629_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_2629_2,plain,
! [U_9161,U_9160,U_9159] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9159,tc_Nat_Onat),U_9160),U_9161) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9159,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_9159),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9160)),U_9161)),
inference(variable_rename,[status(thm)],[f_2629_1]) ).
cnf(f_2629_3,plain,
hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9159,tc_Nat_Onat),U_9160),U_9161) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9159,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_9159),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9160)),U_9161)),
inference(clausify,[status(thm)],[f_2629_2]) ).
fof(f_2630_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_2630_2,plain,
! [U_9166,U_9165,U_9164,U_9163,U_9162] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9162),U_9163),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9164),U_9165)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9166),U_9165))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9162),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9162,tc_Nat_Onat),U_9163),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_9165))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_9164),U_9166))
| ~ class_Groups_Ocomm__monoid__add(U_9162) ),
inference(variable_rename,[status(thm)],[f_2630_1]) ).
cnf(f_2630_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9162),U_9163),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9164),U_9165)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9166),U_9165))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9162),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9162,tc_Nat_Onat),U_9163),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_9165))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_9164),U_9166))
| ~ class_Groups_Ocomm__monoid__add(U_9162) ),
inference(clausify,[status(thm)],[f_2630_2]) ).
fof(f_2631_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_2631_2,plain,
! [U_9168,U_9167] : hAPP(c_Finite__Set_Ocard(U_9167),U_9168) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9167,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_9167),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_9168),
inference(variable_rename,[status(thm)],[f_2631_1]) ).
cnf(f_2631_3,plain,
hAPP(c_Finite__Set_Ocard(U_9167),U_9168) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9167,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_9167),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_9168),
inference(clausify,[status(thm)],[f_2631_2]) ).
fof(f_2632_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_2632_2,plain,
! [U_9170,U_9169] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_9169,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_9169,tc_HOL_Obool)),tc_fun(U_9169,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_9169,tc_HOL_Obool)),tc_fun(U_9169,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_9169,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_9170)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_9169,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_9170),
inference(variable_rename,[status(thm)],[f_2632_1]) ).
cnf(f_2632_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_9169,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_9169,tc_HOL_Obool)),tc_fun(U_9169,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_9169,tc_HOL_Obool)),tc_fun(U_9169,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_9169,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_9170)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_9169,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_9170),
inference(clausify,[status(thm)],[f_2632_2]) ).
fof(f_2633_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_2633_2,plain,
! [U_9174,U_9173,U_9172,U_9171] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9171),U_9172),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9173),hAPP(c_Nat_OSuc,U_9174))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9171),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9171,tc_Nat_Onat),U_9172),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9173,U_9174))
| ~ class_Groups_Ocomm__monoid__add(U_9171) ),
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,U_9171),U_9172),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9173),hAPP(c_Nat_OSuc,U_9174))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9171),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9171,tc_Nat_Onat),U_9172),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9173,U_9174))
| ~ class_Groups_Ocomm__monoid__add(U_9171) ),
inference(clausify,[status(thm)],[f_2633_2]) ).
fof(f_2634_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_2634_2,plain,
! [U_9177,U_9176,U_9175] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_9175),U_9176),U_9177) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_9175),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9175,tc_Int_Oint),U_9176),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9177))
| ~ class_Groups_Ocomm__monoid__mult(U_9175)
| ~ class_Groups_Ocomm__monoid__add(U_9175) ),
inference(variable_rename,[status(thm)],[f_2634_1]) ).
cnf(f_2634_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_9175),U_9176),U_9177) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_9175),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9175,tc_Int_Oint),U_9176),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9177))
| ~ class_Groups_Ocomm__monoid__mult(U_9175)
| ~ class_Groups_Ocomm__monoid__add(U_9175) ),
inference(clausify,[status(thm)],[f_2634_2]) ).
fof(f_2635_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_2635_2,plain,
! [U_9182,U_9181,U_9180,U_9179,U_9178] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9178),U_9179),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9180),U_9181),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9182),U_9181))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9178),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9178,tc_Nat_Onat),U_9179),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_9181))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9180,U_9182))
| ~ class_Groups_Ocomm__monoid__add(U_9178) ),
inference(variable_rename,[status(thm)],[f_2635_1]) ).
cnf(f_2635_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9178),U_9179),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9180),U_9181),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9182),U_9181))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9178),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9178,tc_Nat_Onat),U_9179),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_9181))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9180,U_9182))
| ~ class_Groups_Ocomm__monoid__add(U_9178) ),
inference(clausify,[status(thm)],[f_2635_2]) ).
fof(f_2636_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_2636_2,plain,
! [U_9187,U_9186,U_9185,U_9184,U_9183] :
( c_Finite__Set_Ofun__left__comm__idem(U_9186,U_9184,hAPP(hAPP(c_COMBB(U_9183,tc_fun(U_9184,U_9184),U_9186),U_9185),U_9187))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_9183,U_9184,U_9185) ),
inference(variable_rename,[status(thm)],[f_2636_1]) ).
cnf(f_2636_3,plain,
( c_Finite__Set_Ofun__left__comm__idem(U_9186,U_9184,hAPP(hAPP(c_COMBB(U_9183,tc_fun(U_9184,U_9184),U_9186),U_9185),U_9187))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_9183,U_9184,U_9185) ),
inference(clausify,[status(thm)],[f_2636_2]) ).
fof(f_2637_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_2637_2,plain,
! [U_9191,U_9190,U_9189,U_9188] :
( hAPP(c_Fun_Ocomp(U_9189,U_9189,U_9189,hAPP(U_9190,U_9191)),hAPP(U_9190,U_9191)) = hAPP(U_9190,U_9191)
| ~ c_Finite__Set_Ofun__left__comm__idem(U_9188,U_9189,U_9190) ),
inference(variable_rename,[status(thm)],[f_2637_1]) ).
fof(f_2637_3,plain,
! [U_9191,U_9190,U_9189] :
( ! [U_9188] : ~ c_Finite__Set_Ofun__left__comm__idem(U_9188,U_9189,U_9190)
| hAPP(c_Fun_Ocomp(U_9189,U_9189,U_9189,hAPP(U_9190,U_9191)),hAPP(U_9190,U_9191)) = hAPP(U_9190,U_9191) ),
inference(miniscope,[status(thm)],[f_2637_2]) ).
cnf(f_2637_4,plain,
( ~ c_Finite__Set_Ofun__left__comm__idem(U_9188,U_9189,U_9190)
| hAPP(c_Fun_Ocomp(U_9189,U_9189,U_9189,hAPP(U_9190,U_9191)),hAPP(U_9190,U_9191)) = hAPP(U_9190,U_9191) ),
inference(clausify,[status(thm)],[f_2637_3]) ).
fof(f_2638_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_2638_2,plain,
! [U_9195,U_9194,U_9193,U_9192] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9192),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9193,tc_Nat_Onat),U_9194),U_9195)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9193,U_9192),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9192,U_9193),c_Nat_Osemiring__1__class_Oof__nat(U_9192)),U_9194)),U_9195)
| ~ class_Rings_Osemiring__1(U_9192) ),
inference(variable_rename,[status(thm)],[f_2638_1]) ).
cnf(f_2638_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9192),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9193,tc_Nat_Onat),U_9194),U_9195)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9193,U_9192),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9192,U_9193),c_Nat_Osemiring__1__class_Oof__nat(U_9192)),U_9194)),U_9195)
| ~ class_Rings_Osemiring__1(U_9192) ),
inference(clausify,[status(thm)],[f_2638_2]) ).
fof(f_2639_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_2639_2,plain,
! [U_9199,U_9198,U_9197,U_9196] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9196),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9197,U_9196),U_9198),U_9199)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9197,U_9196),hAPP(hAPP(c_COMBB(U_9196,U_9196,U_9197),c_Groups_Oabs__class_Oabs(U_9196)),U_9198)),U_9199)
| ~ class_Fields_Olinordered__field(U_9196) ),
inference(variable_rename,[status(thm)],[f_2639_1]) ).
cnf(f_2639_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9196),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9197,U_9196),U_9198),U_9199)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9197,U_9196),hAPP(hAPP(c_COMBB(U_9196,U_9196,U_9197),c_Groups_Oabs__class_Oabs(U_9196)),U_9198)),U_9199)
| ~ class_Fields_Olinordered__field(U_9196) ),
inference(clausify,[status(thm)],[f_2639_2]) ).
fof(f_2640_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_2640_2,plain,
! [U_9202,U_9201,U_9200] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9201,U_9200),hAPP(c_COMBK(U_9200,U_9201),c_Groups_Oone__class_Oone(U_9200))),U_9202) = c_Groups_Oone__class_Oone(U_9200)
| ~ class_Groups_Ocomm__monoid__mult(U_9200) ),
inference(variable_rename,[status(thm)],[f_2640_1]) ).
cnf(f_2640_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9201,U_9200),hAPP(c_COMBK(U_9200,U_9201),c_Groups_Oone__class_Oone(U_9200))),U_9202) = c_Groups_Oone__class_Oone(U_9200)
| ~ class_Groups_Ocomm__monoid__mult(U_9200) ),
inference(clausify,[status(thm)],[f_2640_2]) ).
fof(f_2641_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_2641_2,plain,
! [U_9205,U_9204,U_9203] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9203,tc_Nat_Onat),U_9204),U_9205)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9203,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_9203),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9204)),U_9205),
inference(variable_rename,[status(thm)],[f_2641_1]) ).
cnf(f_2641_3,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9203,tc_Nat_Onat),U_9204),U_9205)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9203,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_9203),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9204)),U_9205),
inference(clausify,[status(thm)],[f_2641_2]) ).
fof(f_2642_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_2642_2,plain,
! [U_9210,U_9209,U_9208,U_9207,U_9206] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9207,U_9206),hAPP(hAPP(c_COMBS(U_9207,U_9206,U_9206),hAPP(hAPP(c_COMBB(U_9206,tc_fun(U_9206,U_9206),U_9207),c_Groups_Otimes__class_Otimes(U_9206)),U_9208)),U_9209)),U_9210) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9206),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9207,U_9206),U_9208),U_9210)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9207,U_9206),U_9209),U_9210))
| ~ class_Groups_Ocomm__monoid__mult(U_9206) ),
inference(variable_rename,[status(thm)],[f_2642_1]) ).
cnf(f_2642_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9207,U_9206),hAPP(hAPP(c_COMBS(U_9207,U_9206,U_9206),hAPP(hAPP(c_COMBB(U_9206,tc_fun(U_9206,U_9206),U_9207),c_Groups_Otimes__class_Otimes(U_9206)),U_9208)),U_9209)),U_9210) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9206),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9207,U_9206),U_9208),U_9210)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9207,U_9206),U_9209),U_9210))
| ~ class_Groups_Ocomm__monoid__mult(U_9206) ),
inference(clausify,[status(thm)],[f_2642_2]) ).
fof(f_2643_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_2643_2,plain,
! [U_9215,U_9214,U_9213,U_9212,U_9211] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9212,U_9211),hAPP(hAPP(c_COMBS(U_9212,U_9211,U_9211),hAPP(hAPP(c_COMBB(U_9211,tc_fun(U_9211,U_9211),U_9212),c_Groups_Otimes__class_Otimes(U_9211)),U_9214)),U_9215)),U_9213) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9211),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9212,U_9211),U_9214),U_9213)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9212,U_9211),U_9215),U_9213))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9212),U_9213))
| ~ class_Groups_Ocomm__monoid__mult(U_9211) ),
inference(variable_rename,[status(thm)],[f_2643_1]) ).
cnf(f_2643_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9212,U_9211),hAPP(hAPP(c_COMBS(U_9212,U_9211,U_9211),hAPP(hAPP(c_COMBB(U_9211,tc_fun(U_9211,U_9211),U_9212),c_Groups_Otimes__class_Otimes(U_9211)),U_9214)),U_9215)),U_9213) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9211),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9212,U_9211),U_9214),U_9213)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9212,U_9211),U_9215),U_9213))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9212),U_9213))
| ~ class_Groups_Ocomm__monoid__mult(U_9211) ),
inference(clausify,[status(thm)],[f_2643_2]) ).
fof(f_2644_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_2644_2,plain,
! [U_9219,U_9218,U_9217,U_9216] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_9216),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9217,tc_Int_Oint),U_9218),U_9219)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9217,U_9216),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_9216,U_9217),c_Int_Oring__1__class_Oof__int(U_9216)),U_9218)),U_9219)
| ~ class_Rings_Oring__1(U_9216)
| ~ class_Groups_Ocomm__monoid__mult(U_9216) ),
inference(variable_rename,[status(thm)],[f_2644_1]) ).
cnf(f_2644_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_9216),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9217,tc_Int_Oint),U_9218),U_9219)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9217,U_9216),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_9216,U_9217),c_Int_Oring__1__class_Oof__int(U_9216)),U_9218)),U_9219)
| ~ class_Rings_Oring__1(U_9216)
| ~ class_Groups_Ocomm__monoid__mult(U_9216) ),
inference(clausify,[status(thm)],[f_2644_2]) ).
fof(f_2645_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_2645_2,plain,
! [U_9224,U_9223,U_9222,U_9221,U_9220] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9221,U_9220),hAPP(hAPP(c_COMBS(U_9221,U_9220,U_9220),hAPP(hAPP(c_COMBB(U_9220,tc_fun(U_9220,U_9220),U_9221),c_Rings_Oinverse__class_Odivide(U_9220)),U_9223)),U_9224)),U_9222) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9220),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9221,U_9220),U_9223),U_9222)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9221,U_9220),U_9224),U_9222))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9221),U_9222))
| ~ class_Fields_Ofield__inverse__zero(U_9220) ),
inference(variable_rename,[status(thm)],[f_2645_1]) ).
cnf(f_2645_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9221,U_9220),hAPP(hAPP(c_COMBS(U_9221,U_9220,U_9220),hAPP(hAPP(c_COMBB(U_9220,tc_fun(U_9220,U_9220),U_9221),c_Rings_Oinverse__class_Odivide(U_9220)),U_9223)),U_9224)),U_9222) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9220),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9221,U_9220),U_9223),U_9222)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9221,U_9220),U_9224),U_9222))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9221),U_9222))
| ~ class_Fields_Ofield__inverse__zero(U_9220) ),
inference(clausify,[status(thm)],[f_2645_2]) ).
fof(f_2646_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_2646_2,plain,
! [U_9228,U_9227,U_9226,U_9225] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9225),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9226,U_9225),hAPP(hAPP(c_COMBB(U_9225,U_9225,U_9226),c_Groups_Oabs__class_Oabs(U_9225)),U_9227)),U_9228)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9226,U_9225),hAPP(hAPP(c_COMBB(U_9225,U_9225,U_9226),c_Groups_Oabs__class_Oabs(U_9225)),U_9227)),U_9228)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9225) ),
inference(variable_rename,[status(thm)],[f_2646_1]) ).
cnf(f_2646_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9225),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9226,U_9225),hAPP(hAPP(c_COMBB(U_9225,U_9225,U_9226),c_Groups_Oabs__class_Oabs(U_9225)),U_9227)),U_9228)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9226,U_9225),hAPP(hAPP(c_COMBB(U_9225,U_9225,U_9226),c_Groups_Oabs__class_Oabs(U_9225)),U_9227)),U_9228)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9225) ),
inference(clausify,[status(thm)],[f_2646_2]) ).
fof(f_2647_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_2647_2,plain,
! [U_9229] : c_Fun_Oinj__on(U_9229,tc_fun(U_9229,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_9229,tc_fun(U_9229,tc_HOL_Obool),tc_fun(U_9229,tc_HOL_Obool)),c_Set_Oinsert(U_9229)),c_Orderings_Obot__class_Obot(tc_fun(U_9229,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9229,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_2647_1]) ).
cnf(f_2647_3,plain,
c_Fun_Oinj__on(U_9229,tc_fun(U_9229,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_9229,tc_fun(U_9229,tc_HOL_Obool),tc_fun(U_9229,tc_HOL_Obool)),c_Set_Oinsert(U_9229)),c_Orderings_Obot__class_Obot(tc_fun(U_9229,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9229,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_2647_2]) ).
fof(f_2648_1,plain,
! [V_c_2,T_c,T_b,V_A_2] :
( ( hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_image__constant__conv]) ).
fof(f_2648_2,plain,
! [U_9233,U_9232,U_9231,U_9230] :
( ( hAPP(c_Set_Oimage(U_9231,U_9232,hAPP(c_COMBK(U_9232,U_9231),U_9233)),U_9230) = hAPP(hAPP(c_Set_Oinsert(U_9232),U_9233),c_Orderings_Obot__class_Obot(tc_fun(U_9232,tc_HOL_Obool)))
| U_9230 = c_Orderings_Obot__class_Obot(tc_fun(U_9231,tc_HOL_Obool)) )
& ( hAPP(c_Set_Oimage(U_9231,U_9232,hAPP(c_COMBK(U_9232,U_9231),U_9233)),U_9230) = c_Orderings_Obot__class_Obot(tc_fun(U_9232,tc_HOL_Obool))
| U_9230 != c_Orderings_Obot__class_Obot(tc_fun(U_9231,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2648_1]) ).
fof(f_2648_3,plain,
( ! [U_9241,U_9239,U_9237,U_9235] :
( hAPP(c_Set_Oimage(U_9237,U_9239,hAPP(c_COMBK(U_9239,U_9237),U_9241)),U_9235) = hAPP(hAPP(c_Set_Oinsert(U_9239),U_9241),c_Orderings_Obot__class_Obot(tc_fun(U_9239,tc_HOL_Obool)))
| U_9235 = c_Orderings_Obot__class_Obot(tc_fun(U_9237,tc_HOL_Obool)) )
& ! [U_9240,U_9238,U_9236,U_9234] :
( hAPP(c_Set_Oimage(U_9236,U_9238,hAPP(c_COMBK(U_9238,U_9236),U_9240)),U_9234) = c_Orderings_Obot__class_Obot(tc_fun(U_9238,tc_HOL_Obool))
| U_9234 != c_Orderings_Obot__class_Obot(tc_fun(U_9236,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2648_2]) ).
cnf(f_2648_4,plain,
( hAPP(c_Set_Oimage(U_9236,U_9238,hAPP(c_COMBK(U_9238,U_9236),U_9240)),U_9234) = c_Orderings_Obot__class_Obot(tc_fun(U_9238,tc_HOL_Obool))
| U_9234 != c_Orderings_Obot__class_Obot(tc_fun(U_9236,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2648_3]) ).
cnf(f_2648_5,plain,
( hAPP(c_Set_Oimage(U_9237,U_9239,hAPP(c_COMBK(U_9239,U_9237),U_9241)),U_9235) = hAPP(hAPP(c_Set_Oinsert(U_9239),U_9241),c_Orderings_Obot__class_Obot(tc_fun(U_9239,tc_HOL_Obool)))
| U_9235 = c_Orderings_Obot__class_Obot(tc_fun(U_9237,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2648_3]) ).
fof(f_2649_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_2649_2,plain,
! [U_9247,U_9246,U_9245,U_9244,U_9243,U_9242] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9242,tc_fun(U_9245,tc_HOL_Obool)),U_9244),hAPP(hAPP(c_COMBB(tc_fun(U_9245,tc_HOL_Obool),tc_fun(U_9245,tc_HOL_Obool),U_9242),hAPP(c_Set_Oinsert(U_9245),U_9246)),U_9247)) = hAPP(hAPP(c_Set_Oinsert(U_9245),U_9246),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9242,tc_fun(U_9245,tc_HOL_Obool)),U_9244),U_9247))
| ~ hBOOL(hAPP(hAPP(c_member(U_9242),U_9243),U_9244)) ),
inference(variable_rename,[status(thm)],[f_2649_1]) ).
cnf(f_2649_3,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9242,tc_fun(U_9245,tc_HOL_Obool)),U_9244),hAPP(hAPP(c_COMBB(tc_fun(U_9245,tc_HOL_Obool),tc_fun(U_9245,tc_HOL_Obool),U_9242),hAPP(c_Set_Oinsert(U_9245),U_9246)),U_9247)) = hAPP(hAPP(c_Set_Oinsert(U_9245),U_9246),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9242,tc_fun(U_9245,tc_HOL_Obool)),U_9244),U_9247))
| ~ hBOOL(hAPP(hAPP(c_member(U_9242),U_9243),U_9244)) ),
inference(clausify,[status(thm)],[f_2649_2]) ).
fof(f_2650_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_2650_2,plain,
! [U_9251,U_9250,U_9249,U_9248] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9248,tc_fun(U_9249,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9248,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9249,tc_HOL_Obool),tc_fun(U_9249,tc_HOL_Obool),U_9248),hAPP(c_COMBC(U_9249,tc_fun(U_9249,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9249))),U_9250)),U_9251))
| ~ hBOOL(hAPP(hAPP(c_member(U_9249),U_9251),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9248,tc_fun(U_9249,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9248,tc_HOL_Obool))),U_9250))) )
& ( hBOOL(hAPP(hAPP(c_member(U_9249),U_9251),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9248,tc_fun(U_9249,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9248,tc_HOL_Obool))),U_9250)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9248,tc_fun(U_9249,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9248,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9249,tc_HOL_Obool),tc_fun(U_9249,tc_HOL_Obool),U_9248),hAPP(c_COMBC(U_9249,tc_fun(U_9249,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9249))),U_9250)),U_9251)) ) ),
inference(variable_rename,[status(thm)],[f_2650_1]) ).
fof(f_2650_3,plain,
( ! [U_9259,U_9257,U_9255,U_9253] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9253,tc_fun(U_9255,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9253,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9255,tc_HOL_Obool),tc_fun(U_9255,tc_HOL_Obool),U_9253),hAPP(c_COMBC(U_9255,tc_fun(U_9255,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9255))),U_9257)),U_9259))
| ~ hBOOL(hAPP(hAPP(c_member(U_9255),U_9259),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9253,tc_fun(U_9255,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9253,tc_HOL_Obool))),U_9257))) )
& ! [U_9258,U_9256,U_9254,U_9252] :
( hBOOL(hAPP(hAPP(c_member(U_9254),U_9258),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9252,tc_fun(U_9254,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9252,tc_HOL_Obool))),U_9256)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9252,tc_fun(U_9254,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9252,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9254,tc_HOL_Obool),tc_fun(U_9254,tc_HOL_Obool),U_9252),hAPP(c_COMBC(U_9254,tc_fun(U_9254,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9254))),U_9256)),U_9258)) ) ),
inference(miniscope,[status(thm)],[f_2650_2]) ).
cnf(f_2650_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_9254),U_9258),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9252,tc_fun(U_9254,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9252,tc_HOL_Obool))),U_9256)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9252,tc_fun(U_9254,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9252,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9254,tc_HOL_Obool),tc_fun(U_9254,tc_HOL_Obool),U_9252),hAPP(c_COMBC(U_9254,tc_fun(U_9254,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9254))),U_9256)),U_9258)) ),
inference(clausify,[status(thm)],[f_2650_3]) ).
cnf(f_2650_5,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9253,tc_fun(U_9255,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9253,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9255,tc_HOL_Obool),tc_fun(U_9255,tc_HOL_Obool),U_9253),hAPP(c_COMBC(U_9255,tc_fun(U_9255,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9255))),U_9257)),U_9259))
| ~ hBOOL(hAPP(hAPP(c_member(U_9255),U_9259),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9253,tc_fun(U_9255,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9253,tc_HOL_Obool))),U_9257))) ),
inference(clausify,[status(thm)],[f_2650_3]) ).
fof(f_2651_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_2651_2,plain,
! [U_9264,U_9263,U_9262,U_9261,U_9260] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9263),hAPP(c_Set_Oimage(U_9261,U_9263,hAPP(hAPP(c_COMBB(U_9260,U_9263,U_9261),U_9264),U_9262)),c_Orderings_Otop__class_Otop(tc_fun(U_9261,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9260),hAPP(c_Set_Oimage(U_9261,U_9260,U_9262),c_Orderings_Otop__class_Otop(tc_fun(U_9261,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[f_2651_1]) ).
cnf(f_2651_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9263),hAPP(c_Set_Oimage(U_9261,U_9263,hAPP(hAPP(c_COMBB(U_9260,U_9263,U_9261),U_9264),U_9262)),c_Orderings_Otop__class_Otop(tc_fun(U_9261,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9260),hAPP(c_Set_Oimage(U_9261,U_9260,U_9262),c_Orderings_Otop__class_Otop(tc_fun(U_9261,tc_HOL_Obool))))) ),
inference(clausify,[status(thm)],[f_2651_2]) ).
fof(f_2652_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_2652_2,plain,
! [U_9269,U_9268,U_9267,U_9266,U_9265] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9266,tc_fun(U_9267,tc_HOL_Obool)),U_9265),hAPP(hAPP(c_COMBB(tc_fun(U_9267,tc_HOL_Obool),tc_fun(U_9267,tc_HOL_Obool),U_9266),hAPP(c_Set_Oinsert(U_9267),U_9268)),U_9269)) = hAPP(hAPP(c_Set_Oinsert(U_9267),U_9268),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9266,tc_fun(U_9267,tc_HOL_Obool)),U_9265),U_9269))
| U_9265 = c_Orderings_Obot__class_Obot(tc_fun(U_9266,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9266,tc_fun(U_9267,tc_HOL_Obool)),U_9265),hAPP(hAPP(c_COMBB(tc_fun(U_9267,tc_HOL_Obool),tc_fun(U_9267,tc_HOL_Obool),U_9266),hAPP(c_Set_Oinsert(U_9267),U_9268)),U_9269)) = c_Orderings_Obot__class_Obot(tc_fun(U_9267,tc_HOL_Obool))
| U_9265 != c_Orderings_Obot__class_Obot(tc_fun(U_9266,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2652_1]) ).
fof(f_2652_3,plain,
( ! [U_9279,U_9277,U_9275,U_9273,U_9271] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9273,tc_fun(U_9275,tc_HOL_Obool)),U_9271),hAPP(hAPP(c_COMBB(tc_fun(U_9275,tc_HOL_Obool),tc_fun(U_9275,tc_HOL_Obool),U_9273),hAPP(c_Set_Oinsert(U_9275),U_9277)),U_9279)) = hAPP(hAPP(c_Set_Oinsert(U_9275),U_9277),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9273,tc_fun(U_9275,tc_HOL_Obool)),U_9271),U_9279))
| U_9271 = c_Orderings_Obot__class_Obot(tc_fun(U_9273,tc_HOL_Obool)) )
& ! [U_9278,U_9276,U_9274,U_9272,U_9270] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9272,tc_fun(U_9274,tc_HOL_Obool)),U_9270),hAPP(hAPP(c_COMBB(tc_fun(U_9274,tc_HOL_Obool),tc_fun(U_9274,tc_HOL_Obool),U_9272),hAPP(c_Set_Oinsert(U_9274),U_9276)),U_9278)) = c_Orderings_Obot__class_Obot(tc_fun(U_9274,tc_HOL_Obool))
| U_9270 != c_Orderings_Obot__class_Obot(tc_fun(U_9272,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2652_2]) ).
cnf(f_2652_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9272,tc_fun(U_9274,tc_HOL_Obool)),U_9270),hAPP(hAPP(c_COMBB(tc_fun(U_9274,tc_HOL_Obool),tc_fun(U_9274,tc_HOL_Obool),U_9272),hAPP(c_Set_Oinsert(U_9274),U_9276)),U_9278)) = c_Orderings_Obot__class_Obot(tc_fun(U_9274,tc_HOL_Obool))
| U_9270 != c_Orderings_Obot__class_Obot(tc_fun(U_9272,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2652_3]) ).
cnf(f_2652_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9273,tc_fun(U_9275,tc_HOL_Obool)),U_9271),hAPP(hAPP(c_COMBB(tc_fun(U_9275,tc_HOL_Obool),tc_fun(U_9275,tc_HOL_Obool),U_9273),hAPP(c_Set_Oinsert(U_9275),U_9277)),U_9279)) = hAPP(hAPP(c_Set_Oinsert(U_9275),U_9277),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9273,tc_fun(U_9275,tc_HOL_Obool)),U_9271),U_9279))
| U_9271 = c_Orderings_Obot__class_Obot(tc_fun(U_9273,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2652_3]) ).
fof(f_2653_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_2653_2,plain,
! [U_9281,U_9280] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9280,tc_fun(U_9280,tc_HOL_Obool)),U_9281),hAPP(hAPP(c_COMBC(U_9280,tc_fun(U_9280,tc_HOL_Obool),tc_fun(U_9280,tc_HOL_Obool)),c_Set_Oinsert(U_9280)),c_Orderings_Obot__class_Obot(tc_fun(U_9280,tc_HOL_Obool)))) = U_9281,
inference(variable_rename,[status(thm)],[f_2653_1]) ).
cnf(f_2653_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9280,tc_fun(U_9280,tc_HOL_Obool)),U_9281),hAPP(hAPP(c_COMBC(U_9280,tc_fun(U_9280,tc_HOL_Obool),tc_fun(U_9280,tc_HOL_Obool)),c_Set_Oinsert(U_9280)),c_Orderings_Obot__class_Obot(tc_fun(U_9280,tc_HOL_Obool)))) = U_9281,
inference(clausify,[status(thm)],[f_2653_2]) ).
fof(f_2654_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_2654_2,plain,
! [U_9286,U_9285,U_9284,U_9283,U_9282] :
( ( hAPP(hAPP(c_Set_Oinsert(U_9284),U_9285),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9283,tc_fun(U_9284,tc_HOL_Obool)),U_9282),U_9286)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9283,tc_fun(U_9284,tc_HOL_Obool)),U_9282),hAPP(hAPP(c_COMBB(tc_fun(U_9284,tc_HOL_Obool),tc_fun(U_9284,tc_HOL_Obool),U_9283),hAPP(c_Set_Oinsert(U_9284),U_9285)),U_9286))
| U_9282 = c_Orderings_Obot__class_Obot(tc_fun(U_9283,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Set_Oinsert(U_9284),U_9285),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9283,tc_fun(U_9284,tc_HOL_Obool)),U_9282),U_9286)) = hAPP(hAPP(c_Set_Oinsert(U_9284),U_9285),c_Orderings_Obot__class_Obot(tc_fun(U_9284,tc_HOL_Obool)))
| U_9282 != c_Orderings_Obot__class_Obot(tc_fun(U_9283,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2654_1]) ).
fof(f_2654_3,plain,
( ! [U_9296,U_9294,U_9292,U_9290,U_9288] :
( hAPP(hAPP(c_Set_Oinsert(U_9292),U_9294),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9290,tc_fun(U_9292,tc_HOL_Obool)),U_9288),U_9296)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9290,tc_fun(U_9292,tc_HOL_Obool)),U_9288),hAPP(hAPP(c_COMBB(tc_fun(U_9292,tc_HOL_Obool),tc_fun(U_9292,tc_HOL_Obool),U_9290),hAPP(c_Set_Oinsert(U_9292),U_9294)),U_9296))
| U_9288 = c_Orderings_Obot__class_Obot(tc_fun(U_9290,tc_HOL_Obool)) )
& ! [U_9295,U_9293,U_9291,U_9289,U_9287] :
( hAPP(hAPP(c_Set_Oinsert(U_9291),U_9293),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9289,tc_fun(U_9291,tc_HOL_Obool)),U_9287),U_9295)) = hAPP(hAPP(c_Set_Oinsert(U_9291),U_9293),c_Orderings_Obot__class_Obot(tc_fun(U_9291,tc_HOL_Obool)))
| U_9287 != c_Orderings_Obot__class_Obot(tc_fun(U_9289,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2654_2]) ).
cnf(f_2654_4,plain,
( hAPP(hAPP(c_Set_Oinsert(U_9291),U_9293),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9289,tc_fun(U_9291,tc_HOL_Obool)),U_9287),U_9295)) = hAPP(hAPP(c_Set_Oinsert(U_9291),U_9293),c_Orderings_Obot__class_Obot(tc_fun(U_9291,tc_HOL_Obool)))
| U_9287 != c_Orderings_Obot__class_Obot(tc_fun(U_9289,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2654_3]) ).
cnf(f_2654_5,plain,
( hAPP(hAPP(c_Set_Oinsert(U_9292),U_9294),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9290,tc_fun(U_9292,tc_HOL_Obool)),U_9288),U_9296)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9290,tc_fun(U_9292,tc_HOL_Obool)),U_9288),hAPP(hAPP(c_COMBB(tc_fun(U_9292,tc_HOL_Obool),tc_fun(U_9292,tc_HOL_Obool),U_9290),hAPP(c_Set_Oinsert(U_9292),U_9294)),U_9296))
| U_9288 = c_Orderings_Obot__class_Obot(tc_fun(U_9290,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2654_3]) ).
fof(f_2655_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_2655_2,plain,
! [U_9301,U_9300,U_9299,U_9298,U_9297] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9298,tc_fun(U_9299,tc_HOL_Obool)),U_9297),hAPP(hAPP(c_COMBC(U_9298,tc_fun(U_9299,tc_HOL_Obool),tc_fun(U_9299,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9299,tc_HOL_Obool),tc_fun(tc_fun(U_9299,tc_HOL_Obool),tc_fun(U_9299,tc_HOL_Obool)),U_9298),c_Groups_Ominus__class_Ominus(tc_fun(U_9299,tc_HOL_Obool))),U_9300)),U_9301)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9299,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9298,tc_fun(U_9299,tc_HOL_Obool)),U_9297),U_9300)),U_9301)
| U_9297 = c_Orderings_Obot__class_Obot(tc_fun(U_9298,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9298,tc_fun(U_9299,tc_HOL_Obool)),U_9297),hAPP(hAPP(c_COMBC(U_9298,tc_fun(U_9299,tc_HOL_Obool),tc_fun(U_9299,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9299,tc_HOL_Obool),tc_fun(tc_fun(U_9299,tc_HOL_Obool),tc_fun(U_9299,tc_HOL_Obool)),U_9298),c_Groups_Ominus__class_Ominus(tc_fun(U_9299,tc_HOL_Obool))),U_9300)),U_9301)) = c_Orderings_Otop__class_Otop(tc_fun(U_9299,tc_HOL_Obool))
| U_9297 != c_Orderings_Obot__class_Obot(tc_fun(U_9298,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2655_1]) ).
fof(f_2655_3,plain,
( ! [U_9311,U_9309,U_9307,U_9305,U_9303] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9305,tc_fun(U_9307,tc_HOL_Obool)),U_9303),hAPP(hAPP(c_COMBC(U_9305,tc_fun(U_9307,tc_HOL_Obool),tc_fun(U_9307,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9307,tc_HOL_Obool),tc_fun(tc_fun(U_9307,tc_HOL_Obool),tc_fun(U_9307,tc_HOL_Obool)),U_9305),c_Groups_Ominus__class_Ominus(tc_fun(U_9307,tc_HOL_Obool))),U_9309)),U_9311)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9307,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9305,tc_fun(U_9307,tc_HOL_Obool)),U_9303),U_9309)),U_9311)
| U_9303 = c_Orderings_Obot__class_Obot(tc_fun(U_9305,tc_HOL_Obool)) )
& ! [U_9310,U_9308,U_9306,U_9304,U_9302] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9304,tc_fun(U_9306,tc_HOL_Obool)),U_9302),hAPP(hAPP(c_COMBC(U_9304,tc_fun(U_9306,tc_HOL_Obool),tc_fun(U_9306,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9306,tc_HOL_Obool),tc_fun(tc_fun(U_9306,tc_HOL_Obool),tc_fun(U_9306,tc_HOL_Obool)),U_9304),c_Groups_Ominus__class_Ominus(tc_fun(U_9306,tc_HOL_Obool))),U_9308)),U_9310)) = c_Orderings_Otop__class_Otop(tc_fun(U_9306,tc_HOL_Obool))
| U_9302 != c_Orderings_Obot__class_Obot(tc_fun(U_9304,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2655_2]) ).
cnf(f_2655_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9304,tc_fun(U_9306,tc_HOL_Obool)),U_9302),hAPP(hAPP(c_COMBC(U_9304,tc_fun(U_9306,tc_HOL_Obool),tc_fun(U_9306,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9306,tc_HOL_Obool),tc_fun(tc_fun(U_9306,tc_HOL_Obool),tc_fun(U_9306,tc_HOL_Obool)),U_9304),c_Groups_Ominus__class_Ominus(tc_fun(U_9306,tc_HOL_Obool))),U_9308)),U_9310)) = c_Orderings_Otop__class_Otop(tc_fun(U_9306,tc_HOL_Obool))
| U_9302 != c_Orderings_Obot__class_Obot(tc_fun(U_9304,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2655_3]) ).
cnf(f_2655_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9305,tc_fun(U_9307,tc_HOL_Obool)),U_9303),hAPP(hAPP(c_COMBC(U_9305,tc_fun(U_9307,tc_HOL_Obool),tc_fun(U_9307,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9307,tc_HOL_Obool),tc_fun(tc_fun(U_9307,tc_HOL_Obool),tc_fun(U_9307,tc_HOL_Obool)),U_9305),c_Groups_Ominus__class_Ominus(tc_fun(U_9307,tc_HOL_Obool))),U_9309)),U_9311)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9307,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9305,tc_fun(U_9307,tc_HOL_Obool)),U_9303),U_9309)),U_9311)
| U_9303 = c_Orderings_Obot__class_Obot(tc_fun(U_9305,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2655_3]) ).
fof(f_2656_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_2656_2,plain,
! [U_9316,U_9315,U_9314,U_9313,U_9312] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9314,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9313,tc_fun(U_9314,tc_HOL_Obool)),U_9312),U_9315)),U_9316) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9313,tc_fun(U_9314,tc_HOL_Obool)),U_9312),hAPP(hAPP(c_COMBC(U_9313,tc_fun(U_9314,tc_HOL_Obool),tc_fun(U_9314,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9314,tc_HOL_Obool),tc_fun(tc_fun(U_9314,tc_HOL_Obool),tc_fun(U_9314,tc_HOL_Obool)),U_9313),c_Groups_Ominus__class_Ominus(tc_fun(U_9314,tc_HOL_Obool))),U_9315)),U_9316))
| U_9312 = c_Orderings_Obot__class_Obot(tc_fun(U_9313,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9314,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9313,tc_fun(U_9314,tc_HOL_Obool)),U_9312),U_9315)),U_9316) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9314,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9314,tc_HOL_Obool))),U_9316)
| U_9312 != c_Orderings_Obot__class_Obot(tc_fun(U_9313,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2656_1]) ).
fof(f_2656_3,plain,
( ! [U_9326,U_9324,U_9322,U_9320,U_9318] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9322,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9320,tc_fun(U_9322,tc_HOL_Obool)),U_9318),U_9324)),U_9326) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9320,tc_fun(U_9322,tc_HOL_Obool)),U_9318),hAPP(hAPP(c_COMBC(U_9320,tc_fun(U_9322,tc_HOL_Obool),tc_fun(U_9322,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9322,tc_HOL_Obool),tc_fun(tc_fun(U_9322,tc_HOL_Obool),tc_fun(U_9322,tc_HOL_Obool)),U_9320),c_Groups_Ominus__class_Ominus(tc_fun(U_9322,tc_HOL_Obool))),U_9324)),U_9326))
| U_9318 = c_Orderings_Obot__class_Obot(tc_fun(U_9320,tc_HOL_Obool)) )
& ! [U_9325,U_9323,U_9321,U_9319,U_9317] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9321,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9319,tc_fun(U_9321,tc_HOL_Obool)),U_9317),U_9323)),U_9325) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9321,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9321,tc_HOL_Obool))),U_9325)
| U_9317 != c_Orderings_Obot__class_Obot(tc_fun(U_9319,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2656_2]) ).
cnf(f_2656_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9321,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9319,tc_fun(U_9321,tc_HOL_Obool)),U_9317),U_9323)),U_9325) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9321,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9321,tc_HOL_Obool))),U_9325)
| U_9317 != c_Orderings_Obot__class_Obot(tc_fun(U_9319,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2656_3]) ).
cnf(f_2656_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9322,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9320,tc_fun(U_9322,tc_HOL_Obool)),U_9318),U_9324)),U_9326) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9320,tc_fun(U_9322,tc_HOL_Obool)),U_9318),hAPP(hAPP(c_COMBC(U_9320,tc_fun(U_9322,tc_HOL_Obool),tc_fun(U_9322,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9322,tc_HOL_Obool),tc_fun(tc_fun(U_9322,tc_HOL_Obool),tc_fun(U_9322,tc_HOL_Obool)),U_9320),c_Groups_Ominus__class_Ominus(tc_fun(U_9322,tc_HOL_Obool))),U_9324)),U_9326))
| U_9318 = c_Orderings_Obot__class_Obot(tc_fun(U_9320,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2656_3]) ).
fof(f_2657_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_2657_2,plain,
! [U_9328,U_9327] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9327),hAPP(c_Nat_OSuc,U_9328)) = 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_9327),U_9328)),
inference(variable_rename,[status(thm)],[f_2657_1]) ).
cnf(f_2657_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9327),hAPP(c_Nat_OSuc,U_9328)) = 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_9327),U_9328)),
inference(clausify,[status(thm)],[f_2657_2]) ).
fof(f_2658_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_2658_2,plain,
! [U_9333,U_9332,U_9331,U_9330,U_9329] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9331,tc_HOL_Obool)),U_9332),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9330,tc_fun(U_9331,tc_HOL_Obool)),U_9329),U_9333)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9330,tc_fun(U_9331,tc_HOL_Obool)),U_9329),hAPP(hAPP(c_COMBB(tc_fun(U_9331,tc_HOL_Obool),tc_fun(U_9331,tc_HOL_Obool),U_9330),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9331,tc_HOL_Obool)),U_9332)),U_9333))
| U_9329 = c_Orderings_Obot__class_Obot(tc_fun(U_9330,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9331,tc_HOL_Obool)),U_9332),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9330,tc_fun(U_9331,tc_HOL_Obool)),U_9329),U_9333)) = U_9332
| U_9329 != c_Orderings_Obot__class_Obot(tc_fun(U_9330,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2658_1]) ).
fof(f_2658_3,plain,
( ! [U_9343,U_9341,U_9339,U_9337,U_9335] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9339,tc_HOL_Obool)),U_9341),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9337,tc_fun(U_9339,tc_HOL_Obool)),U_9335),U_9343)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9337,tc_fun(U_9339,tc_HOL_Obool)),U_9335),hAPP(hAPP(c_COMBB(tc_fun(U_9339,tc_HOL_Obool),tc_fun(U_9339,tc_HOL_Obool),U_9337),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9339,tc_HOL_Obool)),U_9341)),U_9343))
| U_9335 = c_Orderings_Obot__class_Obot(tc_fun(U_9337,tc_HOL_Obool)) )
& ! [U_9342,U_9340,U_9338,U_9336,U_9334] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9338,tc_HOL_Obool)),U_9340),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9336,tc_fun(U_9338,tc_HOL_Obool)),U_9334),U_9342)) = U_9340
| U_9334 != c_Orderings_Obot__class_Obot(tc_fun(U_9336,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2658_2]) ).
cnf(f_2658_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9338,tc_HOL_Obool)),U_9340),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9336,tc_fun(U_9338,tc_HOL_Obool)),U_9334),U_9342)) = U_9340
| U_9334 != c_Orderings_Obot__class_Obot(tc_fun(U_9336,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2658_3]) ).
cnf(f_2658_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9339,tc_HOL_Obool)),U_9341),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9337,tc_fun(U_9339,tc_HOL_Obool)),U_9335),U_9343)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9337,tc_fun(U_9339,tc_HOL_Obool)),U_9335),hAPP(hAPP(c_COMBB(tc_fun(U_9339,tc_HOL_Obool),tc_fun(U_9339,tc_HOL_Obool),U_9337),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9339,tc_HOL_Obool)),U_9341)),U_9343))
| U_9335 = c_Orderings_Obot__class_Obot(tc_fun(U_9337,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2658_3]) ).
fof(f_2659_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_2659_2,plain,
! [U_9349,U_9348,U_9347,U_9346,U_9345,U_9344] : hAPP(c_Set_Oimage(U_9344,U_9345,hAPP(c_Fun_Ocomp(U_9346,U_9345,U_9344,U_9347),U_9348)),U_9349) = hAPP(c_Set_Oimage(U_9346,U_9345,U_9347),hAPP(c_Set_Oimage(U_9344,U_9346,U_9348),U_9349)),
inference(variable_rename,[status(thm)],[f_2659_1]) ).
cnf(f_2659_3,plain,
hAPP(c_Set_Oimage(U_9344,U_9345,hAPP(c_Fun_Ocomp(U_9346,U_9345,U_9344,U_9347),U_9348)),U_9349) = hAPP(c_Set_Oimage(U_9346,U_9345,U_9347),hAPP(c_Set_Oimage(U_9344,U_9346,U_9348),U_9349)),
inference(clausify,[status(thm)],[f_2659_2]) ).
fof(f_2660_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_2660_2,plain,
! [U_9351,U_9350] : hAPP(c_Set_Oimage(U_9350,U_9350,c_COMBI(U_9350)),U_9351) = U_9351,
inference(variable_rename,[status(thm)],[f_2660_1]) ).
cnf(f_2660_3,plain,
hAPP(c_Set_Oimage(U_9350,U_9350,c_COMBI(U_9350)),U_9351) = U_9351,
inference(clausify,[status(thm)],[f_2660_2]) ).
fof(f_2661_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_2661_2,plain,
! [U_9357,U_9356,U_9355,U_9354,U_9353,U_9352] : hAPP(c_Set_Oimage(U_9352,U_9353,U_9354),hAPP(c_Set_Oimage(U_9355,U_9352,U_9356),U_9357)) = hAPP(c_Set_Oimage(U_9355,U_9353,hAPP(hAPP(c_COMBB(U_9352,U_9353,U_9355),U_9354),U_9356)),U_9357),
inference(variable_rename,[status(thm)],[f_2661_1]) ).
cnf(f_2661_3,plain,
hAPP(c_Set_Oimage(U_9352,U_9353,U_9354),hAPP(c_Set_Oimage(U_9355,U_9352,U_9356),U_9357)) = hAPP(c_Set_Oimage(U_9355,U_9353,hAPP(hAPP(c_COMBB(U_9352,U_9353,U_9355),U_9354),U_9356)),U_9357),
inference(clausify,[status(thm)],[f_2661_2]) ).
fof(f_2662_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_2662_2,plain,
! [U_9363,U_9362,U_9361,U_9360,U_9359,U_9358] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9358,tc_fun(U_9359,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9360,U_9358,U_9361),U_9362)),U_9363) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9360,tc_fun(U_9359,tc_HOL_Obool)),U_9362),hAPP(hAPP(c_COMBB(U_9358,tc_fun(U_9359,tc_HOL_Obool),U_9360),U_9363),U_9361)),
inference(variable_rename,[status(thm)],[f_2662_1]) ).
cnf(f_2662_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9358,tc_fun(U_9359,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9360,U_9358,U_9361),U_9362)),U_9363) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9360,tc_fun(U_9359,tc_HOL_Obool)),U_9362),hAPP(hAPP(c_COMBB(U_9358,tc_fun(U_9359,tc_HOL_Obool),U_9360),U_9363),U_9361)),
inference(clausify,[status(thm)],[f_2662_2]) ).
fof(f_2663_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_2663_2,plain,
! [U_9369,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)),U_9366),hAPP(hAPP(c_COMBB(U_9367,tc_fun(U_9365,tc_HOL_Obool),U_9364),U_9368),U_9369)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9367,tc_fun(U_9365,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9364,U_9367,U_9369),U_9366)),U_9368),
inference(variable_rename,[status(thm)],[f_2663_1]) ).
cnf(f_2663_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9364,tc_fun(U_9365,tc_HOL_Obool)),U_9366),hAPP(hAPP(c_COMBB(U_9367,tc_fun(U_9365,tc_HOL_Obool),U_9364),U_9368),U_9369)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9367,tc_fun(U_9365,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9364,U_9367,U_9369),U_9366)),U_9368),
inference(clausify,[status(thm)],[f_2663_2]) ).
fof(f_2664_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_2664_2,plain,
! [U_9375,U_9374,U_9373,U_9372,U_9371,U_9370] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9370,tc_fun(U_9371,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9372,U_9370,U_9373),U_9374)),U_9375) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9372,tc_fun(U_9371,tc_HOL_Obool)),U_9374),hAPP(hAPP(c_COMBB(U_9370,tc_fun(U_9371,tc_HOL_Obool),U_9372),U_9375),U_9373)),
inference(variable_rename,[status(thm)],[f_2664_1]) ).
cnf(f_2664_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9370,tc_fun(U_9371,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9372,U_9370,U_9373),U_9374)),U_9375) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9372,tc_fun(U_9371,tc_HOL_Obool)),U_9374),hAPP(hAPP(c_COMBB(U_9370,tc_fun(U_9371,tc_HOL_Obool),U_9372),U_9375),U_9373)),
inference(clausify,[status(thm)],[f_2664_2]) ).
fof(f_2665_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_2665_2,plain,
! [U_9381,U_9380,U_9379,U_9378,U_9377,U_9376] : hAPP(c_Set_Oimage(U_9376,U_9377,U_9378),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9379,tc_fun(U_9376,tc_HOL_Obool)),U_9380),U_9381)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9379,tc_fun(U_9377,tc_HOL_Obool)),U_9380),hAPP(hAPP(c_COMBB(tc_fun(U_9376,tc_HOL_Obool),tc_fun(U_9377,tc_HOL_Obool),U_9379),c_Set_Oimage(U_9376,U_9377,U_9378)),U_9381)),
inference(variable_rename,[status(thm)],[f_2665_1]) ).
cnf(f_2665_3,plain,
hAPP(c_Set_Oimage(U_9376,U_9377,U_9378),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9379,tc_fun(U_9376,tc_HOL_Obool)),U_9380),U_9381)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9379,tc_fun(U_9377,tc_HOL_Obool)),U_9380),hAPP(hAPP(c_COMBB(tc_fun(U_9376,tc_HOL_Obool),tc_fun(U_9377,tc_HOL_Obool),U_9379),c_Set_Oimage(U_9376,U_9377,U_9378)),U_9381)),
inference(clausify,[status(thm)],[f_2665_2]) ).
fof(f_2666_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_2666_2,plain,
! [U_9387,U_9386,U_9385,U_9384,U_9383,U_9382] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9382,tc_fun(U_9383,tc_HOL_Obool)),U_9384),hAPP(hAPP(c_COMBB(U_9385,tc_fun(U_9383,tc_HOL_Obool),U_9382),U_9386),U_9387)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9385,tc_fun(U_9383,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9382,U_9385,U_9387),U_9384)),U_9386),
inference(variable_rename,[status(thm)],[f_2666_1]) ).
cnf(f_2666_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9382,tc_fun(U_9383,tc_HOL_Obool)),U_9384),hAPP(hAPP(c_COMBB(U_9385,tc_fun(U_9383,tc_HOL_Obool),U_9382),U_9386),U_9387)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9385,tc_fun(U_9383,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9382,U_9385,U_9387),U_9384)),U_9386),
inference(clausify,[status(thm)],[f_2666_2]) ).
fof(f_2667_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_2667_2,plain,
! [U_9391,U_9390,U_9389,U_9388] : hAPP(c_Set_Oimage(U_9388,U_9389,U_9390),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9388,tc_HOL_Obool),U_9391)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9388,tc_HOL_Obool),tc_fun(U_9389,tc_HOL_Obool)),U_9391),c_Set_Oimage(U_9388,U_9389,U_9390)),
inference(variable_rename,[status(thm)],[f_2667_1]) ).
cnf(f_2667_3,plain,
hAPP(c_Set_Oimage(U_9388,U_9389,U_9390),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9388,tc_HOL_Obool),U_9391)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9388,tc_HOL_Obool),tc_fun(U_9389,tc_HOL_Obool)),U_9391),c_Set_Oimage(U_9388,U_9389,U_9390)),
inference(clausify,[status(thm)],[f_2667_2]) ).
fof(f_2668_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_2668_2,plain,
! [U_9396,U_9395,U_9394,U_9393,U_9392] : hAPP(c_Set_Oimage(U_9392,U_9393,hAPP(hAPP(c_COMBB(U_9394,U_9393,U_9392),U_9395),U_9396)),c_Orderings_Otop__class_Otop(tc_fun(U_9392,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_9394,U_9393,U_9395),hAPP(c_Set_Oimage(U_9392,U_9394,U_9396),c_Orderings_Otop__class_Otop(tc_fun(U_9392,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_2668_1]) ).
cnf(f_2668_3,plain,
hAPP(c_Set_Oimage(U_9392,U_9393,hAPP(hAPP(c_COMBB(U_9394,U_9393,U_9392),U_9395),U_9396)),c_Orderings_Otop__class_Otop(tc_fun(U_9392,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_9394,U_9393,U_9395),hAPP(c_Set_Oimage(U_9392,U_9394,U_9396),c_Orderings_Otop__class_Otop(tc_fun(U_9392,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_2668_2]) ).
fof(f_2669_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_2669_2,plain,
! [U_9400,U_9399,U_9398,U_9397] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9397,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9398,tc_fun(U_9397,tc_HOL_Obool),U_9399),U_9400)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9398,tc_fun(U_9397,tc_HOL_Obool)),U_9400),U_9399),
inference(variable_rename,[status(thm)],[f_2669_1]) ).
cnf(f_2669_3,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9397,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9398,tc_fun(U_9397,tc_HOL_Obool),U_9399),U_9400)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9398,tc_fun(U_9397,tc_HOL_Obool)),U_9400),U_9399),
inference(clausify,[status(thm)],[f_2669_2]) ).
fof(f_2670_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_2670_2,plain,
! [U_9404,U_9403,U_9402,U_9401] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9401,tc_fun(U_9402,tc_HOL_Obool)),U_9403),U_9404) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9402,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9401,tc_fun(U_9402,tc_HOL_Obool),U_9404),U_9403)),
inference(variable_rename,[status(thm)],[f_2670_1]) ).
cnf(f_2670_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9401,tc_fun(U_9402,tc_HOL_Obool)),U_9403),U_9404) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9402,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9401,tc_fun(U_9402,tc_HOL_Obool),U_9404),U_9403)),
inference(clausify,[status(thm)],[f_2670_2]) ).
fof(f_2671_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_2671_2,plain,
! [U_9409,U_9408,U_9407] :
( ( hBOOL(hAPP(c_Predicate_OPowp(U_9407,U_9408),U_9409))
| ? [U_9406] :
( ~ hBOOL(hAPP(U_9408,U_9406))
& hBOOL(hAPP(hAPP(c_member(U_9407),U_9406),U_9409)) ) )
& ( ! [U_9405] :
( hBOOL(hAPP(U_9408,U_9405))
| ~ hBOOL(hAPP(hAPP(c_member(U_9407),U_9405),U_9409)) )
| ~ hBOOL(hAPP(c_Predicate_OPowp(U_9407,U_9408),U_9409)) ) ),
inference(variable_rename,[status(thm)],[f_2671_1]) ).
fof(f_2671_3,plain,
( ! [U_9415,U_9413,U_9411] :
( hBOOL(hAPP(c_Predicate_OPowp(U_9411,U_9413),U_9415))
| ? [U_9406] :
( ~ hBOOL(hAPP(U_9413,U_9406))
& hBOOL(hAPP(hAPP(c_member(U_9411),U_9406),U_9415)) ) )
& ! [U_9414,U_9412,U_9410] :
( ! [U_9405] :
( hBOOL(hAPP(U_9412,U_9405))
| ~ hBOOL(hAPP(hAPP(c_member(U_9410),U_9405),U_9414)) )
| ~ hBOOL(hAPP(c_Predicate_OPowp(U_9410,U_9412),U_9414)) ) ),
inference(miniscope,[status(thm)],[f_2671_2]) ).
fof(f_2671_4,plain,
( ! [U_9415,U_9413,U_9411] :
( hBOOL(hAPP(c_Predicate_OPowp(U_9411,U_9413),U_9415))
| ( ~ hBOOL(hAPP(U_9413,sK236(U_9415,U_9413,U_9411)))
& hBOOL(hAPP(hAPP(c_member(U_9411),sK236(U_9415,U_9413,U_9411)),U_9415)) ) )
& ! [U_9414,U_9412,U_9410] :
( ! [U_9405] :
( hBOOL(hAPP(U_9412,U_9405))
| ~ hBOOL(hAPP(hAPP(c_member(U_9410),U_9405),U_9414)) )
| ~ hBOOL(hAPP(c_Predicate_OPowp(U_9410,U_9412),U_9414)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK236]),skolemize(U_9406,sK236(U_9415,U_9413,U_9411))],[f_2671_3]) ).
cnf(f_2671_5,plain,
( hBOOL(hAPP(U_9412,U_9405))
| ~ hBOOL(hAPP(hAPP(c_member(U_9410),U_9405),U_9414))
| ~ hBOOL(hAPP(c_Predicate_OPowp(U_9410,U_9412),U_9414)) ),
inference(clausify,[status(thm)],[f_2671_4]) ).
cnf(f_2671_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_9411),sK236(U_9415,U_9413,U_9411)),U_9415))
| hBOOL(hAPP(c_Predicate_OPowp(U_9411,U_9413),U_9415)) ),
inference(clausify,[status(thm)],[f_2671_4]) ).
cnf(f_2671_7,plain,
( ~ hBOOL(hAPP(U_9413,sK236(U_9415,U_9413,U_9411)))
| hBOOL(hAPP(c_Predicate_OPowp(U_9411,U_9413),U_9415)) ),
inference(clausify,[status(thm)],[f_2671_4]) ).
fof(f_2672_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_2672_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_2672_1]) ).
fof(f_2673_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_2673_2,plain,
! [U_9421,U_9420,U_9419,U_9418,U_9417,U_9416] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9416,tc_fun(U_9417,tc_fun(U_9418,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9416,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9417,U_9418),tc_HOL_Obool),tc_fun(U_9417,tc_fun(U_9418,tc_HOL_Obool)),U_9416),hAPP(c_COMBC(U_9417,tc_fun(tc_prod(U_9417,U_9418),tc_HOL_Obool),tc_fun(U_9418,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9418,tc_fun(tc_fun(tc_prod(U_9417,U_9418),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9417,U_9418),tc_HOL_Obool),tc_fun(U_9418,tc_HOL_Obool)),U_9417),c_COMBC(U_9418,tc_fun(tc_prod(U_9417,U_9418),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9418,tc_prod(U_9417,U_9418)),tc_fun(U_9418,tc_fun(tc_fun(tc_prod(U_9417,U_9418),tc_HOL_Obool),tc_HOL_Obool)),U_9417),hAPP(c_COMBB(tc_prod(U_9417,U_9418),tc_fun(tc_fun(tc_prod(U_9417,U_9418),tc_HOL_Obool),tc_HOL_Obool),U_9418),c_member(tc_prod(U_9417,U_9418)))),c_Product__Type_OPair(U_9417,U_9418))))),U_9419)),U_9420),U_9421))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9417,U_9418)),hAPP(hAPP(c_Product__Type_OPair(U_9417,U_9418),U_9420),U_9421)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9416,tc_fun(tc_prod(U_9417,U_9418),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9416,tc_HOL_Obool))),U_9419))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9417,U_9418)),hAPP(hAPP(c_Product__Type_OPair(U_9417,U_9418),U_9420),U_9421)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9416,tc_fun(tc_prod(U_9417,U_9418),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9416,tc_HOL_Obool))),U_9419)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9416,tc_fun(U_9417,tc_fun(U_9418,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9416,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9417,U_9418),tc_HOL_Obool),tc_fun(U_9417,tc_fun(U_9418,tc_HOL_Obool)),U_9416),hAPP(c_COMBC(U_9417,tc_fun(tc_prod(U_9417,U_9418),tc_HOL_Obool),tc_fun(U_9418,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9418,tc_fun(tc_fun(tc_prod(U_9417,U_9418),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9417,U_9418),tc_HOL_Obool),tc_fun(U_9418,tc_HOL_Obool)),U_9417),c_COMBC(U_9418,tc_fun(tc_prod(U_9417,U_9418),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9418,tc_prod(U_9417,U_9418)),tc_fun(U_9418,tc_fun(tc_fun(tc_prod(U_9417,U_9418),tc_HOL_Obool),tc_HOL_Obool)),U_9417),hAPP(c_COMBB(tc_prod(U_9417,U_9418),tc_fun(tc_fun(tc_prod(U_9417,U_9418),tc_HOL_Obool),tc_HOL_Obool),U_9418),c_member(tc_prod(U_9417,U_9418)))),c_Product__Type_OPair(U_9417,U_9418))))),U_9419)),U_9420),U_9421)) ) ),
inference(variable_rename,[status(thm)],[f_2673_1]) ).
fof(f_2673_3,plain,
( ! [U_9433,U_9431,U_9429,U_9427,U_9425,U_9423] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9423,tc_fun(U_9425,tc_fun(U_9427,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9423,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9425,U_9427),tc_HOL_Obool),tc_fun(U_9425,tc_fun(U_9427,tc_HOL_Obool)),U_9423),hAPP(c_COMBC(U_9425,tc_fun(tc_prod(U_9425,U_9427),tc_HOL_Obool),tc_fun(U_9427,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9427,tc_fun(tc_fun(tc_prod(U_9425,U_9427),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9425,U_9427),tc_HOL_Obool),tc_fun(U_9427,tc_HOL_Obool)),U_9425),c_COMBC(U_9427,tc_fun(tc_prod(U_9425,U_9427),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9427,tc_prod(U_9425,U_9427)),tc_fun(U_9427,tc_fun(tc_fun(tc_prod(U_9425,U_9427),tc_HOL_Obool),tc_HOL_Obool)),U_9425),hAPP(c_COMBB(tc_prod(U_9425,U_9427),tc_fun(tc_fun(tc_prod(U_9425,U_9427),tc_HOL_Obool),tc_HOL_Obool),U_9427),c_member(tc_prod(U_9425,U_9427)))),c_Product__Type_OPair(U_9425,U_9427))))),U_9429)),U_9431),U_9433))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9425,U_9427)),hAPP(hAPP(c_Product__Type_OPair(U_9425,U_9427),U_9431),U_9433)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9423,tc_fun(tc_prod(U_9425,U_9427),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9423,tc_HOL_Obool))),U_9429))) )
& ! [U_9432,U_9430,U_9428,U_9426,U_9424,U_9422] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9424,U_9426)),hAPP(hAPP(c_Product__Type_OPair(U_9424,U_9426),U_9430),U_9432)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9422,tc_fun(tc_prod(U_9424,U_9426),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9422,tc_HOL_Obool))),U_9428)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9422,tc_fun(U_9424,tc_fun(U_9426,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9422,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9424,U_9426),tc_HOL_Obool),tc_fun(U_9424,tc_fun(U_9426,tc_HOL_Obool)),U_9422),hAPP(c_COMBC(U_9424,tc_fun(tc_prod(U_9424,U_9426),tc_HOL_Obool),tc_fun(U_9426,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9426,tc_fun(tc_fun(tc_prod(U_9424,U_9426),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9424,U_9426),tc_HOL_Obool),tc_fun(U_9426,tc_HOL_Obool)),U_9424),c_COMBC(U_9426,tc_fun(tc_prod(U_9424,U_9426),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9426,tc_prod(U_9424,U_9426)),tc_fun(U_9426,tc_fun(tc_fun(tc_prod(U_9424,U_9426),tc_HOL_Obool),tc_HOL_Obool)),U_9424),hAPP(c_COMBB(tc_prod(U_9424,U_9426),tc_fun(tc_fun(tc_prod(U_9424,U_9426),tc_HOL_Obool),tc_HOL_Obool),U_9426),c_member(tc_prod(U_9424,U_9426)))),c_Product__Type_OPair(U_9424,U_9426))))),U_9428)),U_9430),U_9432)) ) ),
inference(miniscope,[status(thm)],[f_2673_2]) ).
cnf(f_2673_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9424,U_9426)),hAPP(hAPP(c_Product__Type_OPair(U_9424,U_9426),U_9430),U_9432)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9422,tc_fun(tc_prod(U_9424,U_9426),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9422,tc_HOL_Obool))),U_9428)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9422,tc_fun(U_9424,tc_fun(U_9426,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9422,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9424,U_9426),tc_HOL_Obool),tc_fun(U_9424,tc_fun(U_9426,tc_HOL_Obool)),U_9422),hAPP(c_COMBC(U_9424,tc_fun(tc_prod(U_9424,U_9426),tc_HOL_Obool),tc_fun(U_9426,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9426,tc_fun(tc_fun(tc_prod(U_9424,U_9426),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9424,U_9426),tc_HOL_Obool),tc_fun(U_9426,tc_HOL_Obool)),U_9424),c_COMBC(U_9426,tc_fun(tc_prod(U_9424,U_9426),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9426,tc_prod(U_9424,U_9426)),tc_fun(U_9426,tc_fun(tc_fun(tc_prod(U_9424,U_9426),tc_HOL_Obool),tc_HOL_Obool)),U_9424),hAPP(c_COMBB(tc_prod(U_9424,U_9426),tc_fun(tc_fun(tc_prod(U_9424,U_9426),tc_HOL_Obool),tc_HOL_Obool),U_9426),c_member(tc_prod(U_9424,U_9426)))),c_Product__Type_OPair(U_9424,U_9426))))),U_9428)),U_9430),U_9432)) ),
inference(clausify,[status(thm)],[f_2673_3]) ).
cnf(f_2673_5,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9423,tc_fun(U_9425,tc_fun(U_9427,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9423,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9425,U_9427),tc_HOL_Obool),tc_fun(U_9425,tc_fun(U_9427,tc_HOL_Obool)),U_9423),hAPP(c_COMBC(U_9425,tc_fun(tc_prod(U_9425,U_9427),tc_HOL_Obool),tc_fun(U_9427,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9427,tc_fun(tc_fun(tc_prod(U_9425,U_9427),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9425,U_9427),tc_HOL_Obool),tc_fun(U_9427,tc_HOL_Obool)),U_9425),c_COMBC(U_9427,tc_fun(tc_prod(U_9425,U_9427),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9427,tc_prod(U_9425,U_9427)),tc_fun(U_9427,tc_fun(tc_fun(tc_prod(U_9425,U_9427),tc_HOL_Obool),tc_HOL_Obool)),U_9425),hAPP(c_COMBB(tc_prod(U_9425,U_9427),tc_fun(tc_fun(tc_prod(U_9425,U_9427),tc_HOL_Obool),tc_HOL_Obool),U_9427),c_member(tc_prod(U_9425,U_9427)))),c_Product__Type_OPair(U_9425,U_9427))))),U_9429)),U_9431),U_9433))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9425,U_9427)),hAPP(hAPP(c_Product__Type_OPair(U_9425,U_9427),U_9431),U_9433)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9423,tc_fun(tc_prod(U_9425,U_9427),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9423,tc_HOL_Obool))),U_9429))) ),
inference(clausify,[status(thm)],[f_2673_3]) ).
fof(f_2674_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_2674_2,plain,
! [U_9439,U_9438,U_9437,U_9436,U_9435,U_9434] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9434,tc_fun(U_9435,tc_fun(U_9436,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9434,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9435,U_9436),tc_HOL_Obool),tc_fun(U_9435,tc_fun(U_9436,tc_HOL_Obool)),U_9434),hAPP(c_COMBC(U_9435,tc_fun(tc_prod(U_9435,U_9436),tc_HOL_Obool),tc_fun(U_9436,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9436,tc_fun(tc_fun(tc_prod(U_9435,U_9436),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9435,U_9436),tc_HOL_Obool),tc_fun(U_9436,tc_HOL_Obool)),U_9435),c_COMBC(U_9436,tc_fun(tc_prod(U_9435,U_9436),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9436,tc_prod(U_9435,U_9436)),tc_fun(U_9436,tc_fun(tc_fun(tc_prod(U_9435,U_9436),tc_HOL_Obool),tc_HOL_Obool)),U_9435),hAPP(c_COMBB(tc_prod(U_9435,U_9436),tc_fun(tc_fun(tc_prod(U_9435,U_9436),tc_HOL_Obool),tc_HOL_Obool),U_9436),c_member(tc_prod(U_9435,U_9436)))),c_Product__Type_OPair(U_9435,U_9436))))),U_9437)),U_9438),U_9439))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9435,U_9436)),hAPP(hAPP(c_Product__Type_OPair(U_9435,U_9436),U_9438),U_9439)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9434,tc_fun(tc_prod(U_9435,U_9436),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9434,tc_HOL_Obool))),U_9437))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9435,U_9436)),hAPP(hAPP(c_Product__Type_OPair(U_9435,U_9436),U_9438),U_9439)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9434,tc_fun(tc_prod(U_9435,U_9436),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9434,tc_HOL_Obool))),U_9437)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9434,tc_fun(U_9435,tc_fun(U_9436,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9434,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9435,U_9436),tc_HOL_Obool),tc_fun(U_9435,tc_fun(U_9436,tc_HOL_Obool)),U_9434),hAPP(c_COMBC(U_9435,tc_fun(tc_prod(U_9435,U_9436),tc_HOL_Obool),tc_fun(U_9436,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9436,tc_fun(tc_fun(tc_prod(U_9435,U_9436),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9435,U_9436),tc_HOL_Obool),tc_fun(U_9436,tc_HOL_Obool)),U_9435),c_COMBC(U_9436,tc_fun(tc_prod(U_9435,U_9436),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9436,tc_prod(U_9435,U_9436)),tc_fun(U_9436,tc_fun(tc_fun(tc_prod(U_9435,U_9436),tc_HOL_Obool),tc_HOL_Obool)),U_9435),hAPP(c_COMBB(tc_prod(U_9435,U_9436),tc_fun(tc_fun(tc_prod(U_9435,U_9436),tc_HOL_Obool),tc_HOL_Obool),U_9436),c_member(tc_prod(U_9435,U_9436)))),c_Product__Type_OPair(U_9435,U_9436))))),U_9437)),U_9438),U_9439)) ) ),
inference(variable_rename,[status(thm)],[f_2674_1]) ).
fof(f_2674_3,plain,
( ! [U_9451,U_9449,U_9447,U_9445,U_9443,U_9441] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9441,tc_fun(U_9443,tc_fun(U_9445,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9441,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9443,U_9445),tc_HOL_Obool),tc_fun(U_9443,tc_fun(U_9445,tc_HOL_Obool)),U_9441),hAPP(c_COMBC(U_9443,tc_fun(tc_prod(U_9443,U_9445),tc_HOL_Obool),tc_fun(U_9445,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9445,tc_fun(tc_fun(tc_prod(U_9443,U_9445),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9443,U_9445),tc_HOL_Obool),tc_fun(U_9445,tc_HOL_Obool)),U_9443),c_COMBC(U_9445,tc_fun(tc_prod(U_9443,U_9445),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9445,tc_prod(U_9443,U_9445)),tc_fun(U_9445,tc_fun(tc_fun(tc_prod(U_9443,U_9445),tc_HOL_Obool),tc_HOL_Obool)),U_9443),hAPP(c_COMBB(tc_prod(U_9443,U_9445),tc_fun(tc_fun(tc_prod(U_9443,U_9445),tc_HOL_Obool),tc_HOL_Obool),U_9445),c_member(tc_prod(U_9443,U_9445)))),c_Product__Type_OPair(U_9443,U_9445))))),U_9447)),U_9449),U_9451))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9443,U_9445)),hAPP(hAPP(c_Product__Type_OPair(U_9443,U_9445),U_9449),U_9451)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9441,tc_fun(tc_prod(U_9443,U_9445),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9441,tc_HOL_Obool))),U_9447))) )
& ! [U_9450,U_9448,U_9446,U_9444,U_9442,U_9440] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9442,U_9444)),hAPP(hAPP(c_Product__Type_OPair(U_9442,U_9444),U_9448),U_9450)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9440,tc_fun(tc_prod(U_9442,U_9444),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9440,tc_HOL_Obool))),U_9446)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9440,tc_fun(U_9442,tc_fun(U_9444,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9440,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9442,U_9444),tc_HOL_Obool),tc_fun(U_9442,tc_fun(U_9444,tc_HOL_Obool)),U_9440),hAPP(c_COMBC(U_9442,tc_fun(tc_prod(U_9442,U_9444),tc_HOL_Obool),tc_fun(U_9444,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9444,tc_fun(tc_fun(tc_prod(U_9442,U_9444),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9442,U_9444),tc_HOL_Obool),tc_fun(U_9444,tc_HOL_Obool)),U_9442),c_COMBC(U_9444,tc_fun(tc_prod(U_9442,U_9444),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9444,tc_prod(U_9442,U_9444)),tc_fun(U_9444,tc_fun(tc_fun(tc_prod(U_9442,U_9444),tc_HOL_Obool),tc_HOL_Obool)),U_9442),hAPP(c_COMBB(tc_prod(U_9442,U_9444),tc_fun(tc_fun(tc_prod(U_9442,U_9444),tc_HOL_Obool),tc_HOL_Obool),U_9444),c_member(tc_prod(U_9442,U_9444)))),c_Product__Type_OPair(U_9442,U_9444))))),U_9446)),U_9448),U_9450)) ) ),
inference(miniscope,[status(thm)],[f_2674_2]) ).
cnf(f_2674_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9442,U_9444)),hAPP(hAPP(c_Product__Type_OPair(U_9442,U_9444),U_9448),U_9450)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9440,tc_fun(tc_prod(U_9442,U_9444),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9440,tc_HOL_Obool))),U_9446)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9440,tc_fun(U_9442,tc_fun(U_9444,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9440,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9442,U_9444),tc_HOL_Obool),tc_fun(U_9442,tc_fun(U_9444,tc_HOL_Obool)),U_9440),hAPP(c_COMBC(U_9442,tc_fun(tc_prod(U_9442,U_9444),tc_HOL_Obool),tc_fun(U_9444,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9444,tc_fun(tc_fun(tc_prod(U_9442,U_9444),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9442,U_9444),tc_HOL_Obool),tc_fun(U_9444,tc_HOL_Obool)),U_9442),c_COMBC(U_9444,tc_fun(tc_prod(U_9442,U_9444),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9444,tc_prod(U_9442,U_9444)),tc_fun(U_9444,tc_fun(tc_fun(tc_prod(U_9442,U_9444),tc_HOL_Obool),tc_HOL_Obool)),U_9442),hAPP(c_COMBB(tc_prod(U_9442,U_9444),tc_fun(tc_fun(tc_prod(U_9442,U_9444),tc_HOL_Obool),tc_HOL_Obool),U_9444),c_member(tc_prod(U_9442,U_9444)))),c_Product__Type_OPair(U_9442,U_9444))))),U_9446)),U_9448),U_9450)) ),
inference(clausify,[status(thm)],[f_2674_3]) ).
cnf(f_2674_5,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9441,tc_fun(U_9443,tc_fun(U_9445,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9441,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9443,U_9445),tc_HOL_Obool),tc_fun(U_9443,tc_fun(U_9445,tc_HOL_Obool)),U_9441),hAPP(c_COMBC(U_9443,tc_fun(tc_prod(U_9443,U_9445),tc_HOL_Obool),tc_fun(U_9445,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9445,tc_fun(tc_fun(tc_prod(U_9443,U_9445),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9443,U_9445),tc_HOL_Obool),tc_fun(U_9445,tc_HOL_Obool)),U_9443),c_COMBC(U_9445,tc_fun(tc_prod(U_9443,U_9445),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9445,tc_prod(U_9443,U_9445)),tc_fun(U_9445,tc_fun(tc_fun(tc_prod(U_9443,U_9445),tc_HOL_Obool),tc_HOL_Obool)),U_9443),hAPP(c_COMBB(tc_prod(U_9443,U_9445),tc_fun(tc_fun(tc_prod(U_9443,U_9445),tc_HOL_Obool),tc_HOL_Obool),U_9445),c_member(tc_prod(U_9443,U_9445)))),c_Product__Type_OPair(U_9443,U_9445))))),U_9447)),U_9449),U_9451))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9443,U_9445)),hAPP(hAPP(c_Product__Type_OPair(U_9443,U_9445),U_9449),U_9451)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9441,tc_fun(tc_prod(U_9443,U_9445),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9441,tc_HOL_Obool))),U_9447))) ),
inference(clausify,[status(thm)],[f_2674_3]) ).
fof(f_2675_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_2675_2,plain,
! [U_9455,U_9454,U_9453,U_9452] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9452,tc_fun(U_9453,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9452,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9453,tc_HOL_Obool),tc_fun(U_9453,tc_HOL_Obool),U_9452),hAPP(c_COMBC(U_9453,tc_fun(U_9453,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9453))),U_9454)),U_9455))
| ~ hBOOL(hAPP(hAPP(c_member(U_9453),U_9455),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9452,tc_fun(U_9453,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9452,tc_HOL_Obool))),U_9454))) )
& ( hBOOL(hAPP(hAPP(c_member(U_9453),U_9455),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9452,tc_fun(U_9453,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9452,tc_HOL_Obool))),U_9454)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9452,tc_fun(U_9453,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9452,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9453,tc_HOL_Obool),tc_fun(U_9453,tc_HOL_Obool),U_9452),hAPP(c_COMBC(U_9453,tc_fun(U_9453,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9453))),U_9454)),U_9455)) ) ),
inference(variable_rename,[status(thm)],[f_2675_1]) ).
fof(f_2675_3,plain,
( ! [U_9463,U_9461,U_9459,U_9457] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9457,tc_fun(U_9459,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9457,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9459,tc_HOL_Obool),tc_fun(U_9459,tc_HOL_Obool),U_9457),hAPP(c_COMBC(U_9459,tc_fun(U_9459,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9459))),U_9461)),U_9463))
| ~ hBOOL(hAPP(hAPP(c_member(U_9459),U_9463),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9457,tc_fun(U_9459,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9457,tc_HOL_Obool))),U_9461))) )
& ! [U_9462,U_9460,U_9458,U_9456] :
( hBOOL(hAPP(hAPP(c_member(U_9458),U_9462),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9456,tc_fun(U_9458,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9456,tc_HOL_Obool))),U_9460)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9456,tc_fun(U_9458,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9456,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9458,tc_HOL_Obool),tc_fun(U_9458,tc_HOL_Obool),U_9456),hAPP(c_COMBC(U_9458,tc_fun(U_9458,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9458))),U_9460)),U_9462)) ) ),
inference(miniscope,[status(thm)],[f_2675_2]) ).
cnf(f_2675_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_9458),U_9462),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9456,tc_fun(U_9458,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9456,tc_HOL_Obool))),U_9460)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9456,tc_fun(U_9458,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9456,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9458,tc_HOL_Obool),tc_fun(U_9458,tc_HOL_Obool),U_9456),hAPP(c_COMBC(U_9458,tc_fun(U_9458,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9458))),U_9460)),U_9462)) ),
inference(clausify,[status(thm)],[f_2675_3]) ).
cnf(f_2675_5,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9457,tc_fun(U_9459,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9457,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9459,tc_HOL_Obool),tc_fun(U_9459,tc_HOL_Obool),U_9457),hAPP(c_COMBC(U_9459,tc_fun(U_9459,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9459))),U_9461)),U_9463))
| ~ hBOOL(hAPP(hAPP(c_member(U_9459),U_9463),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9457,tc_fun(U_9459,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9457,tc_HOL_Obool))),U_9461))) ),
inference(clausify,[status(thm)],[f_2675_3]) ).
fof(f_2676_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_2676_2,plain,
! [U_9468,U_9467,U_9466,U_9465,U_9464] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9465,U_9464),hAPP(hAPP(c_COMBS(U_9465,U_9464,U_9464),hAPP(hAPP(c_COMBB(U_9464,tc_fun(U_9464,U_9464),U_9465),c_Groups_Ominus__class_Ominus(U_9464)),U_9466)),U_9467)),U_9468) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9464),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9465,U_9464),U_9466),U_9468)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9465,U_9464),U_9467),U_9468))
| ~ class_Groups_Oab__group__add(U_9464) ),
inference(variable_rename,[status(thm)],[f_2676_1]) ).
cnf(f_2676_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9465,U_9464),hAPP(hAPP(c_COMBS(U_9465,U_9464,U_9464),hAPP(hAPP(c_COMBB(U_9464,tc_fun(U_9464,U_9464),U_9465),c_Groups_Ominus__class_Ominus(U_9464)),U_9466)),U_9467)),U_9468) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9464),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9465,U_9464),U_9466),U_9468)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9465,U_9464),U_9467),U_9468))
| ~ class_Groups_Oab__group__add(U_9464) ),
inference(clausify,[status(thm)],[f_2676_2]) ).
fof(f_2677_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_2677_2,plain,
! [U_9473,U_9472,U_9471,U_9470,U_9469] :
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9470,U_9469)),U_9471),U_9472),U_9473) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9469),hAPP(U_9471,U_9473)),hAPP(U_9472,U_9473))
| ~ class_Groups_Ominus(U_9469) ),
inference(variable_rename,[status(thm)],[f_2677_1]) ).
cnf(f_2677_3,plain,
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9470,U_9469)),U_9471),U_9472),U_9473) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9469),hAPP(U_9471,U_9473)),hAPP(U_9472,U_9473))
| ~ class_Groups_Ominus(U_9469) ),
inference(clausify,[status(thm)],[f_2677_2]) ).
fof(f_2678_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_2678_2,plain,
! [U_9477,U_9476,U_9475,U_9474] :
( c_Fun_Oinj__on(U_9474,tc_fun(U_9477,U_9475),hAPP(hAPP(c_COMBB(U_9475,tc_fun(U_9477,U_9475),U_9474),c_COMBK(U_9475,U_9477)),U_9476),c_Orderings_Otop__class_Otop(tc_fun(U_9474,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(U_9474,U_9475,U_9476,c_Orderings_Otop__class_Otop(tc_fun(U_9474,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_2678_1]) ).
cnf(f_2678_3,plain,
( c_Fun_Oinj__on(U_9474,tc_fun(U_9477,U_9475),hAPP(hAPP(c_COMBB(U_9475,tc_fun(U_9477,U_9475),U_9474),c_COMBK(U_9475,U_9477)),U_9476),c_Orderings_Otop__class_Otop(tc_fun(U_9474,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(U_9474,U_9475,U_9476,c_Orderings_Otop__class_Otop(tc_fun(U_9474,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_2678_2]) ).
fof(f_2679_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_2679_2,plain,
! [U_9482,U_9481,U_9480,U_9479,U_9478] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9478,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9479,tc_fun(U_9478,tc_HOL_Obool)),U_9480),U_9481)),U_9482) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9479,tc_fun(U_9478,tc_HOL_Obool)),U_9480),hAPP(hAPP(c_COMBC(U_9479,tc_fun(U_9478,tc_HOL_Obool),tc_fun(U_9478,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9478,tc_HOL_Obool),tc_fun(tc_fun(U_9478,tc_HOL_Obool),tc_fun(U_9478,tc_HOL_Obool)),U_9479),c_Groups_Ominus__class_Ominus(tc_fun(U_9478,tc_HOL_Obool))),U_9481)),U_9482)),
inference(variable_rename,[status(thm)],[f_2679_1]) ).
cnf(f_2679_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9478,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9479,tc_fun(U_9478,tc_HOL_Obool)),U_9480),U_9481)),U_9482) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9479,tc_fun(U_9478,tc_HOL_Obool)),U_9480),hAPP(hAPP(c_COMBC(U_9479,tc_fun(U_9478,tc_HOL_Obool),tc_fun(U_9478,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9478,tc_HOL_Obool),tc_fun(tc_fun(U_9478,tc_HOL_Obool),tc_fun(U_9478,tc_HOL_Obool)),U_9479),c_Groups_Ominus__class_Ominus(tc_fun(U_9478,tc_HOL_Obool))),U_9481)),U_9482)),
inference(clausify,[status(thm)],[f_2679_2]) ).
fof(f_2680_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_2680_2,plain,
! [U_9487,U_9486,U_9485,U_9484,U_9483] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9483,tc_fun(U_9484,tc_HOL_Obool)),U_9485),hAPP(hAPP(c_COMBC(U_9483,tc_fun(U_9484,tc_HOL_Obool),tc_fun(U_9484,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9484,tc_HOL_Obool),tc_fun(tc_fun(U_9484,tc_HOL_Obool),tc_fun(U_9484,tc_HOL_Obool)),U_9483),c_Groups_Ominus__class_Ominus(tc_fun(U_9484,tc_HOL_Obool))),U_9486)),U_9487)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9484,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9483,tc_fun(U_9484,tc_HOL_Obool)),U_9485),U_9486)),U_9487),
inference(variable_rename,[status(thm)],[f_2680_1]) ).
cnf(f_2680_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9483,tc_fun(U_9484,tc_HOL_Obool)),U_9485),hAPP(hAPP(c_COMBC(U_9483,tc_fun(U_9484,tc_HOL_Obool),tc_fun(U_9484,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9484,tc_HOL_Obool),tc_fun(tc_fun(U_9484,tc_HOL_Obool),tc_fun(U_9484,tc_HOL_Obool)),U_9483),c_Groups_Ominus__class_Ominus(tc_fun(U_9484,tc_HOL_Obool))),U_9486)),U_9487)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9484,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9483,tc_fun(U_9484,tc_HOL_Obool)),U_9485),U_9486)),U_9487),
inference(clausify,[status(thm)],[f_2680_2]) ).
fof(f_2681_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_2681_2,plain,
! [U_9492,U_9491,U_9490,U_9489,U_9488] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9488,tc_HOL_Obool)),U_9489),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9490,tc_fun(U_9488,tc_HOL_Obool)),U_9491),U_9492)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9490,tc_fun(U_9488,tc_HOL_Obool)),U_9491),hAPP(hAPP(c_COMBB(tc_fun(U_9488,tc_HOL_Obool),tc_fun(U_9488,tc_HOL_Obool),U_9490),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9488,tc_HOL_Obool)),U_9489)),U_9492)),
inference(variable_rename,[status(thm)],[f_2681_1]) ).
cnf(f_2681_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9488,tc_HOL_Obool)),U_9489),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9490,tc_fun(U_9488,tc_HOL_Obool)),U_9491),U_9492)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9490,tc_fun(U_9488,tc_HOL_Obool)),U_9491),hAPP(hAPP(c_COMBB(tc_fun(U_9488,tc_HOL_Obool),tc_fun(U_9488,tc_HOL_Obool),U_9490),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9488,tc_HOL_Obool)),U_9489)),U_9492)),
inference(clausify,[status(thm)],[f_2681_2]) ).
fof(f_2682_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_2682_2,plain,
! [U_9497,U_9496,U_9495,U_9494,U_9493] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9493,tc_fun(U_9494,tc_HOL_Obool)),U_9495),hAPP(hAPP(c_COMBB(tc_fun(U_9494,tc_HOL_Obool),tc_fun(U_9494,tc_HOL_Obool),U_9493),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9494,tc_HOL_Obool)),U_9496)),U_9497)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9494,tc_HOL_Obool)),U_9496),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9493,tc_fun(U_9494,tc_HOL_Obool)),U_9495),U_9497)),
inference(variable_rename,[status(thm)],[f_2682_1]) ).
cnf(f_2682_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9493,tc_fun(U_9494,tc_HOL_Obool)),U_9495),hAPP(hAPP(c_COMBB(tc_fun(U_9494,tc_HOL_Obool),tc_fun(U_9494,tc_HOL_Obool),U_9493),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9494,tc_HOL_Obool)),U_9496)),U_9497)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9494,tc_HOL_Obool)),U_9496),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9493,tc_fun(U_9494,tc_HOL_Obool)),U_9495),U_9497)),
inference(clausify,[status(thm)],[f_2682_2]) ).
fof(f_2683_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_2683_2,plain,
! [U_9503,U_9502,U_9501,U_9500] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9500,tc_fun(U_9501,tc_HOL_Obool)),U_9502),U_9503) = c_Orderings_Otop__class_Otop(tc_fun(U_9501,tc_HOL_Obool))
| ? [U_9499] :
( hAPP(U_9503,U_9499) != c_Orderings_Otop__class_Otop(tc_fun(U_9501,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_9500),U_9499),U_9502)) ) )
& ( ! [U_9498] :
( hAPP(U_9503,U_9498) = c_Orderings_Otop__class_Otop(tc_fun(U_9501,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9500),U_9498),U_9502)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9500,tc_fun(U_9501,tc_HOL_Obool)),U_9502),U_9503) != c_Orderings_Otop__class_Otop(tc_fun(U_9501,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2683_1]) ).
fof(f_2683_3,plain,
( ! [U_9511,U_9509,U_9507,U_9505] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9505,tc_fun(U_9507,tc_HOL_Obool)),U_9509),U_9511) = c_Orderings_Otop__class_Otop(tc_fun(U_9507,tc_HOL_Obool))
| ? [U_9499] :
( hAPP(U_9511,U_9499) != c_Orderings_Otop__class_Otop(tc_fun(U_9507,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_9505),U_9499),U_9509)) ) )
& ! [U_9510,U_9508,U_9506,U_9504] :
( ! [U_9498] :
( hAPP(U_9510,U_9498) = c_Orderings_Otop__class_Otop(tc_fun(U_9506,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9504),U_9498),U_9508)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9504,tc_fun(U_9506,tc_HOL_Obool)),U_9508),U_9510) != c_Orderings_Otop__class_Otop(tc_fun(U_9506,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2683_2]) ).
fof(f_2683_4,plain,
( ! [U_9511,U_9509,U_9507,U_9505] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9505,tc_fun(U_9507,tc_HOL_Obool)),U_9509),U_9511) = c_Orderings_Otop__class_Otop(tc_fun(U_9507,tc_HOL_Obool))
| ( hAPP(U_9511,sK237(U_9511,U_9509,U_9507,U_9505)) != c_Orderings_Otop__class_Otop(tc_fun(U_9507,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_9505),sK237(U_9511,U_9509,U_9507,U_9505)),U_9509)) ) )
& ! [U_9510,U_9508,U_9506,U_9504] :
( ! [U_9498] :
( hAPP(U_9510,U_9498) = c_Orderings_Otop__class_Otop(tc_fun(U_9506,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9504),U_9498),U_9508)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9504,tc_fun(U_9506,tc_HOL_Obool)),U_9508),U_9510) != c_Orderings_Otop__class_Otop(tc_fun(U_9506,tc_HOL_Obool)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK237]),skolemize(U_9499,sK237(U_9511,U_9509,U_9507,U_9505))],[f_2683_3]) ).
cnf(f_2683_5,plain,
( hAPP(U_9510,U_9498) = c_Orderings_Otop__class_Otop(tc_fun(U_9506,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9504),U_9498),U_9508))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9504,tc_fun(U_9506,tc_HOL_Obool)),U_9508),U_9510) != c_Orderings_Otop__class_Otop(tc_fun(U_9506,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2683_4]) ).
cnf(f_2683_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_9505),sK237(U_9511,U_9509,U_9507,U_9505)),U_9509))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9505,tc_fun(U_9507,tc_HOL_Obool)),U_9509),U_9511) = c_Orderings_Otop__class_Otop(tc_fun(U_9507,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2683_4]) ).
cnf(f_2683_7,plain,
( hAPP(U_9511,sK237(U_9511,U_9509,U_9507,U_9505)) != c_Orderings_Otop__class_Otop(tc_fun(U_9507,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9505,tc_fun(U_9507,tc_HOL_Obool)),U_9509),U_9511) = c_Orderings_Otop__class_Otop(tc_fun(U_9507,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2683_4]) ).
fof(f_2684_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_2684_2,plain,
! [U_9517,U_9516,U_9515,U_9514] :
( ( c_Orderings_Otop__class_Otop(tc_fun(U_9514,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9515,tc_fun(U_9514,tc_HOL_Obool)),U_9516),U_9517)
| ? [U_9513] :
( hAPP(U_9517,U_9513) != c_Orderings_Otop__class_Otop(tc_fun(U_9514,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_9515),U_9513),U_9516)) ) )
& ( ! [U_9512] :
( hAPP(U_9517,U_9512) = c_Orderings_Otop__class_Otop(tc_fun(U_9514,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9515),U_9512),U_9516)) )
| c_Orderings_Otop__class_Otop(tc_fun(U_9514,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9515,tc_fun(U_9514,tc_HOL_Obool)),U_9516),U_9517) ) ),
inference(variable_rename,[status(thm)],[f_2684_1]) ).
fof(f_2684_3,plain,
( ! [U_9525,U_9523,U_9521,U_9519] :
( c_Orderings_Otop__class_Otop(tc_fun(U_9519,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9521,tc_fun(U_9519,tc_HOL_Obool)),U_9523),U_9525)
| ? [U_9513] :
( hAPP(U_9525,U_9513) != c_Orderings_Otop__class_Otop(tc_fun(U_9519,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_9521),U_9513),U_9523)) ) )
& ! [U_9524,U_9522,U_9520,U_9518] :
( ! [U_9512] :
( hAPP(U_9524,U_9512) = c_Orderings_Otop__class_Otop(tc_fun(U_9518,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9520),U_9512),U_9522)) )
| c_Orderings_Otop__class_Otop(tc_fun(U_9518,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9520,tc_fun(U_9518,tc_HOL_Obool)),U_9522),U_9524) ) ),
inference(miniscope,[status(thm)],[f_2684_2]) ).
fof(f_2684_4,plain,
( ! [U_9525,U_9523,U_9521,U_9519] :
( c_Orderings_Otop__class_Otop(tc_fun(U_9519,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9521,tc_fun(U_9519,tc_HOL_Obool)),U_9523),U_9525)
| ( hAPP(U_9525,sK238(U_9525,U_9523,U_9521,U_9519)) != c_Orderings_Otop__class_Otop(tc_fun(U_9519,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_9521),sK238(U_9525,U_9523,U_9521,U_9519)),U_9523)) ) )
& ! [U_9524,U_9522,U_9520,U_9518] :
( ! [U_9512] :
( hAPP(U_9524,U_9512) = c_Orderings_Otop__class_Otop(tc_fun(U_9518,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9520),U_9512),U_9522)) )
| c_Orderings_Otop__class_Otop(tc_fun(U_9518,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9520,tc_fun(U_9518,tc_HOL_Obool)),U_9522),U_9524) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK238]),skolemize(U_9513,sK238(U_9525,U_9523,U_9521,U_9519))],[f_2684_3]) ).
cnf(f_2684_5,plain,
( hAPP(U_9524,U_9512) = c_Orderings_Otop__class_Otop(tc_fun(U_9518,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9520),U_9512),U_9522))
| c_Orderings_Otop__class_Otop(tc_fun(U_9518,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9520,tc_fun(U_9518,tc_HOL_Obool)),U_9522),U_9524) ),
inference(clausify,[status(thm)],[f_2684_4]) ).
cnf(f_2684_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_9521),sK238(U_9525,U_9523,U_9521,U_9519)),U_9523))
| c_Orderings_Otop__class_Otop(tc_fun(U_9519,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9521,tc_fun(U_9519,tc_HOL_Obool)),U_9523),U_9525) ),
inference(clausify,[status(thm)],[f_2684_4]) ).
cnf(f_2684_7,plain,
( hAPP(U_9525,sK238(U_9525,U_9523,U_9521,U_9519)) != c_Orderings_Otop__class_Otop(tc_fun(U_9519,tc_HOL_Obool))
| c_Orderings_Otop__class_Otop(tc_fun(U_9519,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9521,tc_fun(U_9519,tc_HOL_Obool)),U_9523),U_9525) ),
inference(clausify,[status(thm)],[f_2684_4]) ).
fof(f_2685_1,plain,
! [V_c_2,T_c,T_b,V_A_2] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__constant]) ).
fof(f_2685_2,plain,
! [U_9529,U_9528,U_9527,U_9526] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9527,tc_fun(U_9528,tc_HOL_Obool)),U_9526),hAPP(c_COMBK(tc_fun(U_9528,tc_HOL_Obool),U_9527),U_9529)) = U_9529
| U_9526 = c_Orderings_Obot__class_Obot(tc_fun(U_9527,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9527,tc_fun(U_9528,tc_HOL_Obool)),U_9526),hAPP(c_COMBK(tc_fun(U_9528,tc_HOL_Obool),U_9527),U_9529)) = c_Orderings_Otop__class_Otop(tc_fun(U_9528,tc_HOL_Obool))
| U_9526 != c_Orderings_Obot__class_Obot(tc_fun(U_9527,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2685_1]) ).
fof(f_2685_3,plain,
( ! [U_9537,U_9535,U_9533,U_9531] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9533,tc_fun(U_9535,tc_HOL_Obool)),U_9531),hAPP(c_COMBK(tc_fun(U_9535,tc_HOL_Obool),U_9533),U_9537)) = U_9537
| U_9531 = c_Orderings_Obot__class_Obot(tc_fun(U_9533,tc_HOL_Obool)) )
& ! [U_9536,U_9534,U_9532,U_9530] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9532,tc_fun(U_9534,tc_HOL_Obool)),U_9530),hAPP(c_COMBK(tc_fun(U_9534,tc_HOL_Obool),U_9532),U_9536)) = c_Orderings_Otop__class_Otop(tc_fun(U_9534,tc_HOL_Obool))
| U_9530 != c_Orderings_Obot__class_Obot(tc_fun(U_9532,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2685_2]) ).
cnf(f_2685_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9532,tc_fun(U_9534,tc_HOL_Obool)),U_9530),hAPP(c_COMBK(tc_fun(U_9534,tc_HOL_Obool),U_9532),U_9536)) = c_Orderings_Otop__class_Otop(tc_fun(U_9534,tc_HOL_Obool))
| U_9530 != c_Orderings_Obot__class_Obot(tc_fun(U_9532,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2685_3]) ).
cnf(f_2685_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9533,tc_fun(U_9535,tc_HOL_Obool)),U_9531),hAPP(c_COMBK(tc_fun(U_9535,tc_HOL_Obool),U_9533),U_9537)) = U_9537
| U_9531 = c_Orderings_Obot__class_Obot(tc_fun(U_9533,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2685_3]) ).
fof(f_2686_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_2686_2,plain,
! [U_9540,U_9539,U_9538] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9538,tc_fun(U_9539,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_9538,tc_HOL_Obool))),U_9540) = c_Orderings_Otop__class_Otop(tc_fun(U_9539,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2686_1]) ).
cnf(f_2686_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9538,tc_fun(U_9539,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_9538,tc_HOL_Obool))),U_9540) = c_Orderings_Otop__class_Otop(tc_fun(U_9539,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2686_2]) ).
fof(f_2687_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_2687_2,plain,
! [U_9543,U_9542,U_9541] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9542,U_9541),hAPP(c_COMBK(U_9541,U_9542),c_Groups_Ozero__class_Ozero(U_9541))),U_9543) = c_Groups_Ozero__class_Ozero(U_9541)
| ~ class_Groups_Ocomm__monoid__add(U_9541) ),
inference(variable_rename,[status(thm)],[f_2687_1]) ).
cnf(f_2687_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9542,U_9541),hAPP(c_COMBK(U_9541,U_9542),c_Groups_Ozero__class_Ozero(U_9541))),U_9543) = c_Groups_Ozero__class_Ozero(U_9541)
| ~ class_Groups_Ocomm__monoid__add(U_9541) ),
inference(clausify,[status(thm)],[f_2687_2]) ).
fof(f_2688_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_2688_2,plain,
! [U_9547,U_9546,U_9545,U_9544] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9544,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9545,tc_fun(U_9544,tc_HOL_Obool)),U_9546),U_9547)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9545,tc_fun(U_9544,tc_HOL_Obool)),U_9546),hAPP(hAPP(c_COMBB(tc_fun(U_9544,tc_HOL_Obool),tc_fun(U_9544,tc_HOL_Obool),U_9545),c_Groups_Ouminus__class_Ouminus(tc_fun(U_9544,tc_HOL_Obool))),U_9547)),
inference(variable_rename,[status(thm)],[f_2688_1]) ).
cnf(f_2688_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9544,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9545,tc_fun(U_9544,tc_HOL_Obool)),U_9546),U_9547)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9545,tc_fun(U_9544,tc_HOL_Obool)),U_9546),hAPP(hAPP(c_COMBB(tc_fun(U_9544,tc_HOL_Obool),tc_fun(U_9544,tc_HOL_Obool),U_9545),c_Groups_Ouminus__class_Ouminus(tc_fun(U_9544,tc_HOL_Obool))),U_9547)),
inference(clausify,[status(thm)],[f_2688_2]) ).
fof(f_2689_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_2689_2,plain,
! [U_9551,U_9550,U_9549,U_9548] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9548,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9549,tc_fun(U_9548,tc_HOL_Obool)),U_9550),U_9551)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9549,tc_fun(U_9548,tc_HOL_Obool)),U_9550),hAPP(hAPP(c_COMBB(tc_fun(U_9548,tc_HOL_Obool),tc_fun(U_9548,tc_HOL_Obool),U_9549),c_Groups_Ouminus__class_Ouminus(tc_fun(U_9548,tc_HOL_Obool))),U_9551)),
inference(variable_rename,[status(thm)],[f_2689_1]) ).
cnf(f_2689_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9548,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9549,tc_fun(U_9548,tc_HOL_Obool)),U_9550),U_9551)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9549,tc_fun(U_9548,tc_HOL_Obool)),U_9550),hAPP(hAPP(c_COMBB(tc_fun(U_9548,tc_HOL_Obool),tc_fun(U_9548,tc_HOL_Obool),U_9549),c_Groups_Ouminus__class_Ouminus(tc_fun(U_9548,tc_HOL_Obool))),U_9551)),
inference(clausify,[status(thm)],[f_2689_2]) ).
fof(f_2690_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_2690_2,plain,
! [U_9557,U_9556,U_9555,U_9554,U_9553,U_9552] : hAPP(c_Set_Ovimage(U_9552,U_9553,U_9554),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9555,tc_fun(U_9553,tc_HOL_Obool)),U_9556),U_9557)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9555,tc_fun(U_9552,tc_HOL_Obool)),U_9556),hAPP(hAPP(c_COMBB(tc_fun(U_9553,tc_HOL_Obool),tc_fun(U_9552,tc_HOL_Obool),U_9555),c_Set_Ovimage(U_9552,U_9553,U_9554)),U_9557)),
inference(variable_rename,[status(thm)],[f_2690_1]) ).
cnf(f_2690_3,plain,
hAPP(c_Set_Ovimage(U_9552,U_9553,U_9554),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9555,tc_fun(U_9553,tc_HOL_Obool)),U_9556),U_9557)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9555,tc_fun(U_9552,tc_HOL_Obool)),U_9556),hAPP(hAPP(c_COMBB(tc_fun(U_9553,tc_HOL_Obool),tc_fun(U_9552,tc_HOL_Obool),U_9555),c_Set_Ovimage(U_9552,U_9553,U_9554)),U_9557)),
inference(clausify,[status(thm)],[f_2690_2]) ).
fof(f_2691_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_2691_2,plain,
! [U_9561,U_9560,U_9559,U_9558] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9558,tc_HOL_Obool),tc_fun(U_9559,tc_HOL_Obool)),U_9560),hAPP(hAPP(c_COMBC(tc_fun(U_9558,tc_HOL_Obool),tc_fun(U_9558,tc_fun(U_9559,tc_HOL_Obool)),tc_fun(U_9559,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9558,tc_fun(U_9559,tc_HOL_Obool))),U_9561)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9558,tc_fun(U_9559,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9558,tc_HOL_Obool),U_9560)),U_9561),
inference(variable_rename,[status(thm)],[f_2691_1]) ).
cnf(f_2691_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9558,tc_HOL_Obool),tc_fun(U_9559,tc_HOL_Obool)),U_9560),hAPP(hAPP(c_COMBC(tc_fun(U_9558,tc_HOL_Obool),tc_fun(U_9558,tc_fun(U_9559,tc_HOL_Obool)),tc_fun(U_9559,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9558,tc_fun(U_9559,tc_HOL_Obool))),U_9561)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9558,tc_fun(U_9559,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9558,tc_HOL_Obool),U_9560)),U_9561),
inference(clausify,[status(thm)],[f_2691_2]) ).
fof(f_2692_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_2692_2,plain,
! [U_9565,U_9564,U_9563,U_9562] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9562,tc_fun(U_9563,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9562,tc_HOL_Obool),U_9564)),U_9565) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9562,tc_HOL_Obool),tc_fun(U_9563,tc_HOL_Obool)),U_9564),hAPP(hAPP(c_COMBC(tc_fun(U_9562,tc_HOL_Obool),tc_fun(U_9562,tc_fun(U_9563,tc_HOL_Obool)),tc_fun(U_9563,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9562,tc_fun(U_9563,tc_HOL_Obool))),U_9565)),
inference(variable_rename,[status(thm)],[f_2692_1]) ).
cnf(f_2692_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9562,tc_fun(U_9563,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9562,tc_HOL_Obool),U_9564)),U_9565) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9562,tc_HOL_Obool),tc_fun(U_9563,tc_HOL_Obool)),U_9564),hAPP(hAPP(c_COMBC(tc_fun(U_9562,tc_HOL_Obool),tc_fun(U_9562,tc_fun(U_9563,tc_HOL_Obool)),tc_fun(U_9563,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9562,tc_fun(U_9563,tc_HOL_Obool))),U_9565)),
inference(clausify,[status(thm)],[f_2692_2]) ).
fof(f_2693_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_2693_2,plain,
! [U_9576,U_9575,U_9574,U_9573,U_9572,U_9571,U_9570,U_9569,U_9568,U_9567,U_9566] :
( hAPP(hAPP(c_Fun_Ocomp(U_9572,U_9573,U_9574,U_9566),U_9567),U_9568) = hAPP(hAPP(c_Fun_Ocomp(U_9575,U_9573,U_9576,U_9569),U_9570),U_9571)
| hAPP(U_9566,hAPP(U_9567,U_9568)) != hAPP(U_9569,hAPP(U_9570,U_9571)) ),
inference(variable_rename,[status(thm)],[f_2693_1]) ).
cnf(f_2693_3,plain,
( hAPP(hAPP(c_Fun_Ocomp(U_9572,U_9573,U_9574,U_9566),U_9567),U_9568) = hAPP(hAPP(c_Fun_Ocomp(U_9575,U_9573,U_9576,U_9569),U_9570),U_9571)
| hAPP(U_9566,hAPP(U_9567,U_9568)) != hAPP(U_9569,hAPP(U_9570,U_9571)) ),
inference(clausify,[status(thm)],[f_2693_2]) ).
fof(f_2694_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_2694_2,plain,
! [U_9580,U_9579,U_9578,U_9577] : hAPP(c_Set_OPow(U_9577),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9578,tc_fun(U_9577,tc_HOL_Obool)),U_9579),U_9580)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9578,tc_fun(tc_fun(U_9577,tc_HOL_Obool),tc_HOL_Obool)),U_9579),hAPP(hAPP(c_COMBB(tc_fun(U_9577,tc_HOL_Obool),tc_fun(tc_fun(U_9577,tc_HOL_Obool),tc_HOL_Obool),U_9578),c_Set_OPow(U_9577)),U_9580)),
inference(variable_rename,[status(thm)],[f_2694_1]) ).
cnf(f_2694_3,plain,
hAPP(c_Set_OPow(U_9577),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9578,tc_fun(U_9577,tc_HOL_Obool)),U_9579),U_9580)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9578,tc_fun(tc_fun(U_9577,tc_HOL_Obool),tc_HOL_Obool)),U_9579),hAPP(hAPP(c_COMBB(tc_fun(U_9577,tc_HOL_Obool),tc_fun(tc_fun(U_9577,tc_HOL_Obool),tc_HOL_Obool),U_9578),c_Set_OPow(U_9577)),U_9580)),
inference(clausify,[status(thm)],[f_2694_2]) ).
fof(f_2695_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_2695_2,plain,
! [U_9582,U_9581] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9581,tc_HOL_Obool),U_9582) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9581,tc_HOL_Obool),tc_fun(U_9581,tc_HOL_Obool)),U_9582),c_COMBI(tc_fun(U_9581,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_2695_1]) ).
cnf(f_2695_3,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9581,tc_HOL_Obool),U_9582) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9581,tc_HOL_Obool),tc_fun(U_9581,tc_HOL_Obool)),U_9582),c_COMBI(tc_fun(U_9581,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_2695_2]) ).
fof(f_2696_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_2696_2,plain,
! [U_9588,U_9587,U_9586,U_9585,U_9584,U_9583] : hAPP(hAPP(c_Fun_Ocomp(U_9583,U_9584,U_9585,U_9586),U_9587),U_9588) = hAPP(U_9586,hAPP(U_9587,U_9588)),
inference(variable_rename,[status(thm)],[f_2696_1]) ).
cnf(f_2696_3,plain,
hAPP(hAPP(c_Fun_Ocomp(U_9583,U_9584,U_9585,U_9586),U_9587),U_9588) = hAPP(U_9586,hAPP(U_9587,U_9588)),
inference(clausify,[status(thm)],[f_2696_2]) ).
fof(f_2697_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_2697_2,plain,
! [U_9595,U_9594,U_9593,U_9592,U_9591,U_9590,U_9589] : hAPP(c_Fun_Ocomp(U_9589,U_9590,U_9591,U_9592),hAPP(c_Fun_Ocomp(U_9593,U_9589,U_9591,U_9594),U_9595)) = hAPP(c_Fun_Ocomp(U_9593,U_9590,U_9591,hAPP(c_Fun_Ocomp(U_9589,U_9590,U_9593,U_9592),U_9594)),U_9595),
inference(variable_rename,[status(thm)],[f_2697_1]) ).
cnf(f_2697_3,plain,
hAPP(c_Fun_Ocomp(U_9589,U_9590,U_9591,U_9592),hAPP(c_Fun_Ocomp(U_9593,U_9589,U_9591,U_9594),U_9595)) = hAPP(c_Fun_Ocomp(U_9593,U_9590,U_9591,hAPP(c_Fun_Ocomp(U_9589,U_9590,U_9593,U_9592),U_9594)),U_9595),
inference(clausify,[status(thm)],[f_2697_2]) ).
fof(f_2698_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_2698_2,plain,
! [U_9601,U_9600,U_9599,U_9598,U_9597,U_9596] : hAPP(hAPP(c_Fun_Ocomp(U_9596,U_9597,U_9598,U_9599),U_9600),U_9601) = hAPP(U_9599,hAPP(U_9600,U_9601)),
inference(variable_rename,[status(thm)],[f_2698_1]) ).
cnf(f_2698_3,plain,
hAPP(hAPP(c_Fun_Ocomp(U_9596,U_9597,U_9598,U_9599),U_9600),U_9601) = hAPP(U_9599,hAPP(U_9600,U_9601)),
inference(clausify,[status(thm)],[f_2698_2]) ).
fof(f_2699_1,plain,
! [V_v_2,V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
( hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2))
| hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) != hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2) ),
inference(fof_nnf,[status(thm)],[fact_o__eq__dest]) ).
fof(f_2699_2,plain,
! [U_9610,U_9609,U_9608,U_9607,U_9606,U_9605,U_9604,U_9603,U_9602] :
( hAPP(U_9605,hAPP(U_9606,U_9610)) = hAPP(U_9608,hAPP(U_9609,U_9610))
| hAPP(c_Fun_Ocomp(U_9602,U_9603,U_9604,U_9605),U_9606) != hAPP(c_Fun_Ocomp(U_9607,U_9603,U_9604,U_9608),U_9609) ),
inference(variable_rename,[status(thm)],[f_2699_1]) ).
fof(f_2699_3,plain,
! [U_9610,U_9609,U_9608,U_9607,U_9606,U_9605] :
( ! [U_9604,U_9603,U_9602] : hAPP(c_Fun_Ocomp(U_9602,U_9603,U_9604,U_9605),U_9606) != hAPP(c_Fun_Ocomp(U_9607,U_9603,U_9604,U_9608),U_9609)
| hAPP(U_9605,hAPP(U_9606,U_9610)) = hAPP(U_9608,hAPP(U_9609,U_9610)) ),
inference(miniscope,[status(thm)],[f_2699_2]) ).
cnf(f_2699_4,plain,
( hAPP(c_Fun_Ocomp(U_9602,U_9603,U_9604,U_9605),U_9606) != hAPP(c_Fun_Ocomp(U_9607,U_9603,U_9604,U_9608),U_9609)
| hAPP(U_9605,hAPP(U_9606,U_9610)) = hAPP(U_9608,hAPP(U_9609,U_9610)) ),
inference(clausify,[status(thm)],[f_2699_3]) ).
fof(f_2700_1,plain,
! [V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
( ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v))
| hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) != hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2) ),
inference(fof_nnf,[status(thm)],[fact_o__eq__elim]) ).
fof(f_2700_2,plain,
! [U_9619,U_9618,U_9617,U_9616,U_9615,U_9614,U_9613,U_9612] :
( ! [U_9611] : hAPP(U_9615,hAPP(U_9616,U_9611)) = hAPP(U_9618,hAPP(U_9619,U_9611))
| hAPP(c_Fun_Ocomp(U_9612,U_9613,U_9614,U_9615),U_9616) != hAPP(c_Fun_Ocomp(U_9617,U_9613,U_9614,U_9618),U_9619) ),
inference(variable_rename,[status(thm)],[f_2700_1]) ).
fof(f_2700_3,plain,
! [U_9619,U_9618,U_9617,U_9616,U_9615] :
( ! [U_9614,U_9613,U_9612] : hAPP(c_Fun_Ocomp(U_9612,U_9613,U_9614,U_9615),U_9616) != hAPP(c_Fun_Ocomp(U_9617,U_9613,U_9614,U_9618),U_9619)
| ! [U_9611] : hAPP(U_9615,hAPP(U_9616,U_9611)) = hAPP(U_9618,hAPP(U_9619,U_9611)) ),
inference(miniscope,[status(thm)],[f_2700_2]) ).
cnf(f_2700_4,plain,
( hAPP(c_Fun_Ocomp(U_9612,U_9613,U_9614,U_9615),U_9616) != hAPP(c_Fun_Ocomp(U_9617,U_9613,U_9614,U_9618),U_9619)
| hAPP(U_9615,hAPP(U_9616,U_9611)) = hAPP(U_9618,hAPP(U_9619,U_9611)) ),
inference(clausify,[status(thm)],[f_2700_3]) ).
fof(f_2701_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_2701_2,plain,
! [U_9625,U_9624,U_9623,U_9622,U_9621,U_9620] :
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9621,tc_fun(U_9622,U_9620)),U_9623),U_9624),U_9625) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9621,U_9620),U_9623),hAPP(hAPP(c_COMBC(U_9621,U_9622,U_9620),U_9624),U_9625))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9620) ),
inference(variable_rename,[status(thm)],[f_2701_1]) ).
cnf(f_2701_3,plain,
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9621,tc_fun(U_9622,U_9620)),U_9623),U_9624),U_9625) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9621,U_9620),U_9623),hAPP(hAPP(c_COMBC(U_9621,U_9622,U_9620),U_9624),U_9625))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9620) ),
inference(clausify,[status(thm)],[f_2701_2]) ).
fof(f_2702_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_2702_2,plain,
! [U_9631,U_9630,U_9629,U_9628,U_9627,U_9626] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9627,U_9626),U_9628),hAPP(hAPP(c_COMBB(tc_fun(U_9629,U_9626),U_9626,U_9627),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9629,U_9626),U_9630)),U_9631)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9629,U_9626),U_9630),hAPP(hAPP(c_COMBB(tc_fun(U_9627,U_9626),U_9626,U_9629),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9627,U_9626),U_9628)),hAPP(c_COMBC(U_9627,U_9629,U_9626),U_9631)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9626) ),
inference(variable_rename,[status(thm)],[f_2702_1]) ).
cnf(f_2702_3,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9627,U_9626),U_9628),hAPP(hAPP(c_COMBB(tc_fun(U_9629,U_9626),U_9626,U_9627),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9629,U_9626),U_9630)),U_9631)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9629,U_9626),U_9630),hAPP(hAPP(c_COMBB(tc_fun(U_9627,U_9626),U_9626,U_9629),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9627,U_9626),U_9628)),hAPP(c_COMBC(U_9627,U_9629,U_9626),U_9631)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9626) ),
inference(clausify,[status(thm)],[f_2702_2]) ).
fof(f_2703_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_2703_2,plain,
! [U_9635,U_9634,U_9633,U_9632] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9632,tc_fun(U_9633,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9632,tc_HOL_Obool),U_9634)),U_9635) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9632,tc_HOL_Obool),tc_fun(U_9633,tc_HOL_Obool)),U_9634),hAPP(hAPP(c_COMBC(tc_fun(U_9632,tc_HOL_Obool),tc_fun(U_9632,tc_fun(U_9633,tc_HOL_Obool)),tc_fun(U_9633,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9632,tc_fun(U_9633,tc_HOL_Obool))),U_9635)),
inference(variable_rename,[status(thm)],[f_2703_1]) ).
cnf(f_2703_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9632,tc_fun(U_9633,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9632,tc_HOL_Obool),U_9634)),U_9635) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9632,tc_HOL_Obool),tc_fun(U_9633,tc_HOL_Obool)),U_9634),hAPP(hAPP(c_COMBC(tc_fun(U_9632,tc_HOL_Obool),tc_fun(U_9632,tc_fun(U_9633,tc_HOL_Obool)),tc_fun(U_9633,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9632,tc_fun(U_9633,tc_HOL_Obool))),U_9635)),
inference(clausify,[status(thm)],[f_2703_2]) ).
fof(f_2704_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_2704_2,plain,
! [U_9639,U_9638,U_9637,U_9636] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9636,tc_HOL_Obool),tc_fun(U_9637,tc_HOL_Obool)),U_9638),hAPP(hAPP(c_COMBC(tc_fun(U_9636,tc_HOL_Obool),tc_fun(U_9636,tc_fun(U_9637,tc_HOL_Obool)),tc_fun(U_9637,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9636,tc_fun(U_9637,tc_HOL_Obool))),U_9639)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9636,tc_fun(U_9637,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9636,tc_HOL_Obool),U_9638)),U_9639),
inference(variable_rename,[status(thm)],[f_2704_1]) ).
cnf(f_2704_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9636,tc_HOL_Obool),tc_fun(U_9637,tc_HOL_Obool)),U_9638),hAPP(hAPP(c_COMBC(tc_fun(U_9636,tc_HOL_Obool),tc_fun(U_9636,tc_fun(U_9637,tc_HOL_Obool)),tc_fun(U_9637,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9636,tc_fun(U_9637,tc_HOL_Obool))),U_9639)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9636,tc_fun(U_9637,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9636,tc_HOL_Obool),U_9638)),U_9639),
inference(clausify,[status(thm)],[f_2704_2]) ).
fof(f_2705_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_2705_2,plain,
! [U_9645,U_9644,U_9643,U_9642,U_9641,U_9640] : hAPP(c_Set_Ovimage(U_9640,U_9641,U_9642),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9643,tc_fun(U_9641,tc_HOL_Obool)),U_9644),U_9645)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9643,tc_fun(U_9640,tc_HOL_Obool)),U_9644),hAPP(hAPP(c_COMBB(tc_fun(U_9641,tc_HOL_Obool),tc_fun(U_9640,tc_HOL_Obool),U_9643),c_Set_Ovimage(U_9640,U_9641,U_9642)),U_9645)),
inference(variable_rename,[status(thm)],[f_2705_1]) ).
cnf(f_2705_3,plain,
hAPP(c_Set_Ovimage(U_9640,U_9641,U_9642),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9643,tc_fun(U_9641,tc_HOL_Obool)),U_9644),U_9645)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9643,tc_fun(U_9640,tc_HOL_Obool)),U_9644),hAPP(hAPP(c_COMBB(tc_fun(U_9641,tc_HOL_Obool),tc_fun(U_9640,tc_HOL_Obool),U_9643),c_Set_Ovimage(U_9640,U_9641,U_9642)),U_9645)),
inference(clausify,[status(thm)],[f_2705_2]) ).
fof(f_2706_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_2706_2,plain,
! [U_9647,U_9646] : hAPP(c_Set_Ovimage(U_9646,U_9646,c_COMBI(U_9646)),U_9647) = U_9647,
inference(variable_rename,[status(thm)],[f_2706_1]) ).
cnf(f_2706_3,plain,
hAPP(c_Set_Ovimage(U_9646,U_9646,c_COMBI(U_9646)),U_9647) = U_9647,
inference(clausify,[status(thm)],[f_2706_2]) ).
fof(f_2707_1,plain,
! [V_x_2,V_f_2,V_c_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_f_2),V_x_2) = V_c_2,
inference(fof_nnf,[status(thm)],[fact_K__record__comp]) ).
fof(f_2707_2,plain,
! [U_9653,U_9652,U_9651,U_9650,U_9649,U_9648] : hAPP(hAPP(c_Fun_Ocomp(U_9648,U_9649,U_9650,hAPP(c_COMBK(U_9649,U_9648),U_9651)),U_9652),U_9653) = U_9651,
inference(variable_rename,[status(thm)],[f_2707_1]) ).
cnf(f_2707_3,plain,
hAPP(hAPP(c_Fun_Ocomp(U_9648,U_9649,U_9650,hAPP(c_COMBK(U_9649,U_9648),U_9651)),U_9652),U_9653) = U_9651,
inference(clausify,[status(thm)],[f_2707_2]) ).
fof(f_2708_1,plain,
! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
( hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2)
| hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) != V_c_2 ),
inference(fof_nnf,[status(thm)],[fact_o__eq__dest__lhs]) ).
fof(f_2708_2,plain,
! [U_9660,U_9659,U_9658,U_9657,U_9656,U_9655,U_9654] :
( hAPP(U_9657,hAPP(U_9658,U_9660)) = hAPP(U_9659,U_9660)
| hAPP(c_Fun_Ocomp(U_9654,U_9655,U_9656,U_9657),U_9658) != U_9659 ),
inference(variable_rename,[status(thm)],[f_2708_1]) ).
fof(f_2708_3,plain,
! [U_9660,U_9659,U_9658,U_9657] :
( ! [U_9656,U_9655,U_9654] : hAPP(c_Fun_Ocomp(U_9654,U_9655,U_9656,U_9657),U_9658) != U_9659
| hAPP(U_9657,hAPP(U_9658,U_9660)) = hAPP(U_9659,U_9660) ),
inference(miniscope,[status(thm)],[f_2708_2]) ).
cnf(f_2708_4,plain,
( hAPP(c_Fun_Ocomp(U_9654,U_9655,U_9656,U_9657),U_9658) != U_9659
| hAPP(U_9657,hAPP(U_9658,U_9660)) = hAPP(U_9659,U_9660) ),
inference(clausify,[status(thm)],[f_2708_3]) ).
fof(f_2709_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_2709_2,plain,
! [U_9666,U_9665,U_9664,U_9663,U_9662,U_9661] :
( ( hAPP(c_Fun_Ofun__upd(U_9663,U_9664,U_9665,U_9662,U_9666),U_9661) = hAPP(U_9665,U_9661)
| U_9661 = U_9662 )
& ( hAPP(c_Fun_Ofun__upd(U_9663,U_9664,U_9665,U_9662,U_9666),U_9661) = U_9666
| U_9661 != U_9662 ) ),
inference(variable_rename,[status(thm)],[f_2709_1]) ).
fof(f_2709_3,plain,
( ! [U_9678,U_9676,U_9674,U_9672,U_9670,U_9668] :
( hAPP(c_Fun_Ofun__upd(U_9672,U_9674,U_9676,U_9670,U_9678),U_9668) = hAPP(U_9676,U_9668)
| U_9668 = U_9670 )
& ! [U_9677,U_9675,U_9673,U_9671,U_9669,U_9667] :
( hAPP(c_Fun_Ofun__upd(U_9671,U_9673,U_9675,U_9669,U_9677),U_9667) = U_9677
| U_9667 != U_9669 ) ),
inference(miniscope,[status(thm)],[f_2709_2]) ).
cnf(f_2709_4,plain,
( hAPP(c_Fun_Ofun__upd(U_9671,U_9673,U_9675,U_9669,U_9677),U_9667) = U_9677
| U_9667 != U_9669 ),
inference(clausify,[status(thm)],[f_2709_3]) ).
cnf(f_2709_5,plain,
( hAPP(c_Fun_Ofun__upd(U_9672,U_9674,U_9676,U_9670,U_9678),U_9668) = hAPP(U_9676,U_9668)
| U_9668 = U_9670 ),
inference(clausify,[status(thm)],[f_2709_3]) ).
fof(f_2710_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_2710_2,plain,
! [U_9684,U_9683,U_9682,U_9681,U_9680,U_9679] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9680,U_9679),hAPP(hAPP(c_COMBC(U_9680,tc_fun(U_9681,tc_HOL_Obool),U_9679),hAPP(hAPP(c_COMBB(tc_fun(U_9681,U_9679),tc_fun(tc_fun(U_9681,tc_HOL_Obool),U_9679),U_9680),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9681,U_9679)),U_9682)),U_9683)),U_9684) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9681,U_9679),hAPP(hAPP(c_COMBC(U_9681,tc_fun(U_9680,tc_HOL_Obool),U_9679),hAPP(hAPP(c_COMBB(tc_fun(U_9680,U_9679),tc_fun(tc_fun(U_9680,tc_HOL_Obool),U_9679),U_9681),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9680,U_9679)),hAPP(c_COMBC(U_9680,U_9681,U_9679),U_9682))),U_9684)),U_9683)
| ~ class_Groups_Ocomm__monoid__add(U_9679) ),
inference(variable_rename,[status(thm)],[f_2710_1]) ).
cnf(f_2710_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9680,U_9679),hAPP(hAPP(c_COMBC(U_9680,tc_fun(U_9681,tc_HOL_Obool),U_9679),hAPP(hAPP(c_COMBB(tc_fun(U_9681,U_9679),tc_fun(tc_fun(U_9681,tc_HOL_Obool),U_9679),U_9680),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9681,U_9679)),U_9682)),U_9683)),U_9684) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9681,U_9679),hAPP(hAPP(c_COMBC(U_9681,tc_fun(U_9680,tc_HOL_Obool),U_9679),hAPP(hAPP(c_COMBB(tc_fun(U_9680,U_9679),tc_fun(tc_fun(U_9680,tc_HOL_Obool),U_9679),U_9681),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9680,U_9679)),hAPP(c_COMBC(U_9680,U_9681,U_9679),U_9682))),U_9684)),U_9683)
| ~ class_Groups_Ocomm__monoid__add(U_9679) ),
inference(clausify,[status(thm)],[f_2710_2]) ).
fof(f_2711_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_2711_2,plain,
! [U_9686,U_9685] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9685,tc_HOL_Obool),U_9686) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9685,tc_HOL_Obool),tc_fun(U_9685,tc_HOL_Obool)),U_9686),c_COMBI(tc_fun(U_9685,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_2711_1]) ).
cnf(f_2711_3,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9685,tc_HOL_Obool),U_9686) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9685,tc_HOL_Obool),tc_fun(U_9685,tc_HOL_Obool)),U_9686),c_COMBI(tc_fun(U_9685,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_2711_2]) ).
fof(f_2712_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_2712_2,plain,
! [U_9693,U_9692,U_9691,U_9690,U_9689] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9689,tc_fun(U_9690,tc_HOL_Obool)),U_9691),U_9692),U_9693))
| ! [U_9688] :
( ~ hBOOL(hAPP(hAPP(U_9692,U_9688),U_9693))
| ~ hBOOL(hAPP(hAPP(c_member(U_9689),U_9688),U_9691)) ) )
& ( ? [U_9687] :
( hBOOL(hAPP(hAPP(U_9692,U_9687),U_9693))
& hBOOL(hAPP(hAPP(c_member(U_9689),U_9687),U_9691)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9689,tc_fun(U_9690,tc_HOL_Obool)),U_9691),U_9692),U_9693)) ) ),
inference(variable_rename,[status(thm)],[f_2712_1]) ).
fof(f_2712_3,plain,
( ! [U_9703,U_9701,U_9699,U_9697,U_9695] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9695,tc_fun(U_9697,tc_HOL_Obool)),U_9699),U_9701),U_9703))
| ! [U_9688] :
( ~ hBOOL(hAPP(hAPP(U_9701,U_9688),U_9703))
| ~ hBOOL(hAPP(hAPP(c_member(U_9695),U_9688),U_9699)) ) )
& ! [U_9702,U_9700,U_9698,U_9696,U_9694] :
( ? [U_9687] :
( hBOOL(hAPP(hAPP(U_9700,U_9687),U_9702))
& hBOOL(hAPP(hAPP(c_member(U_9694),U_9687),U_9698)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9694,tc_fun(U_9696,tc_HOL_Obool)),U_9698),U_9700),U_9702)) ) ),
inference(miniscope,[status(thm)],[f_2712_2]) ).
fof(f_2712_4,plain,
( ! [U_9703,U_9701,U_9699,U_9697,U_9695] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9695,tc_fun(U_9697,tc_HOL_Obool)),U_9699),U_9701),U_9703))
| ! [U_9688] :
( ~ hBOOL(hAPP(hAPP(U_9701,U_9688),U_9703))
| ~ hBOOL(hAPP(hAPP(c_member(U_9695),U_9688),U_9699)) ) )
& ! [U_9702,U_9700,U_9698,U_9696,U_9694] :
( ( hBOOL(hAPP(hAPP(U_9700,sK239(U_9702,U_9700,U_9698,U_9696,U_9694)),U_9702))
& hBOOL(hAPP(hAPP(c_member(U_9694),sK239(U_9702,U_9700,U_9698,U_9696,U_9694)),U_9698)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9694,tc_fun(U_9696,tc_HOL_Obool)),U_9698),U_9700),U_9702)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK239]),skolemize(U_9687,sK239(U_9702,U_9700,U_9698,U_9696,U_9694))],[f_2712_3]) ).
cnf(f_2712_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_9694),sK239(U_9702,U_9700,U_9698,U_9696,U_9694)),U_9698))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9694,tc_fun(U_9696,tc_HOL_Obool)),U_9698),U_9700),U_9702)) ),
inference(clausify,[status(thm)],[f_2712_4]) ).
cnf(f_2712_6,plain,
( hBOOL(hAPP(hAPP(U_9700,sK239(U_9702,U_9700,U_9698,U_9696,U_9694)),U_9702))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9694,tc_fun(U_9696,tc_HOL_Obool)),U_9698),U_9700),U_9702)) ),
inference(clausify,[status(thm)],[f_2712_4]) ).
cnf(f_2712_7,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9695,tc_fun(U_9697,tc_HOL_Obool)),U_9699),U_9701),U_9703))
| ~ hBOOL(hAPP(hAPP(U_9701,U_9688),U_9703))
| ~ hBOOL(hAPP(hAPP(c_member(U_9695),U_9688),U_9699)) ),
inference(clausify,[status(thm)],[f_2712_4]) ).
fof(f_2713_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_2713_2,plain,
! [U_9709,U_9708,U_9707,U_9706,U_9705,U_9704] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9704,tc_fun(U_9705,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9706,tc_fun(U_9704,tc_HOL_Obool)),U_9707),U_9708)),U_9709) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9706,tc_fun(U_9705,tc_HOL_Obool)),U_9707),hAPP(hAPP(c_COMBC(U_9706,tc_fun(U_9704,tc_fun(U_9705,tc_HOL_Obool)),tc_fun(U_9705,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9704,tc_HOL_Obool),tc_fun(tc_fun(U_9704,tc_fun(U_9705,tc_HOL_Obool)),tc_fun(U_9705,tc_HOL_Obool)),U_9706),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9704,tc_fun(U_9705,tc_HOL_Obool))),U_9708)),U_9709)),
inference(variable_rename,[status(thm)],[f_2713_1]) ).
cnf(f_2713_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9704,tc_fun(U_9705,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9706,tc_fun(U_9704,tc_HOL_Obool)),U_9707),U_9708)),U_9709) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9706,tc_fun(U_9705,tc_HOL_Obool)),U_9707),hAPP(hAPP(c_COMBC(U_9706,tc_fun(U_9704,tc_fun(U_9705,tc_HOL_Obool)),tc_fun(U_9705,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9704,tc_HOL_Obool),tc_fun(tc_fun(U_9704,tc_fun(U_9705,tc_HOL_Obool)),tc_fun(U_9705,tc_HOL_Obool)),U_9706),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9704,tc_fun(U_9705,tc_HOL_Obool))),U_9708)),U_9709)),
inference(clausify,[status(thm)],[f_2713_2]) ).
fof(f_2714_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_2714_2,plain,
! [U_9715,U_9714,U_9713,U_9712,U_9711,U_9710] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9710,tc_fun(U_9711,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9712,tc_fun(U_9710,tc_HOL_Obool)),U_9713),U_9714)),U_9715) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9712,tc_fun(U_9711,tc_HOL_Obool)),U_9713),hAPP(hAPP(c_COMBC(U_9712,tc_fun(U_9710,tc_fun(U_9711,tc_HOL_Obool)),tc_fun(U_9711,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9710,tc_HOL_Obool),tc_fun(tc_fun(U_9710,tc_fun(U_9711,tc_HOL_Obool)),tc_fun(U_9711,tc_HOL_Obool)),U_9712),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9710,tc_fun(U_9711,tc_HOL_Obool))),U_9714)),U_9715)),
inference(variable_rename,[status(thm)],[f_2714_1]) ).
cnf(f_2714_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9710,tc_fun(U_9711,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9712,tc_fun(U_9710,tc_HOL_Obool)),U_9713),U_9714)),U_9715) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9712,tc_fun(U_9711,tc_HOL_Obool)),U_9713),hAPP(hAPP(c_COMBC(U_9712,tc_fun(U_9710,tc_fun(U_9711,tc_HOL_Obool)),tc_fun(U_9711,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9710,tc_HOL_Obool),tc_fun(tc_fun(U_9710,tc_fun(U_9711,tc_HOL_Obool)),tc_fun(U_9711,tc_HOL_Obool)),U_9712),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9710,tc_fun(U_9711,tc_HOL_Obool))),U_9714)),U_9715)),
inference(clausify,[status(thm)],[f_2714_2]) ).
fof(f_2715_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_2715_2,plain,
! [U_9721,U_9720,U_9719,U_9718,U_9717,U_9716] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9716,tc_fun(U_9717,tc_HOL_Obool)),U_9718),hAPP(hAPP(c_COMBC(U_9716,tc_fun(U_9719,tc_fun(U_9717,tc_HOL_Obool)),tc_fun(U_9717,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9719,tc_HOL_Obool),tc_fun(tc_fun(U_9719,tc_fun(U_9717,tc_HOL_Obool)),tc_fun(U_9717,tc_HOL_Obool)),U_9716),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9719,tc_fun(U_9717,tc_HOL_Obool))),U_9720)),U_9721)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9719,tc_fun(U_9717,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9716,tc_fun(U_9719,tc_HOL_Obool)),U_9718),U_9720)),U_9721),
inference(variable_rename,[status(thm)],[f_2715_1]) ).
cnf(f_2715_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9716,tc_fun(U_9717,tc_HOL_Obool)),U_9718),hAPP(hAPP(c_COMBC(U_9716,tc_fun(U_9719,tc_fun(U_9717,tc_HOL_Obool)),tc_fun(U_9717,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9719,tc_HOL_Obool),tc_fun(tc_fun(U_9719,tc_fun(U_9717,tc_HOL_Obool)),tc_fun(U_9717,tc_HOL_Obool)),U_9716),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9719,tc_fun(U_9717,tc_HOL_Obool))),U_9720)),U_9721)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9719,tc_fun(U_9717,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9716,tc_fun(U_9719,tc_HOL_Obool)),U_9718),U_9720)),U_9721),
inference(clausify,[status(thm)],[f_2715_2]) ).
fof(f_2716_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_2716_2,plain,
! [U_9727,U_9726,U_9725,U_9724,U_9723,U_9722] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9722,tc_fun(U_9723,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9724,tc_fun(U_9722,tc_HOL_Obool)),U_9725),U_9726)),U_9727) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9724,tc_fun(U_9723,tc_HOL_Obool)),U_9725),hAPP(hAPP(c_COMBC(U_9724,tc_fun(U_9722,tc_fun(U_9723,tc_HOL_Obool)),tc_fun(U_9723,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9722,tc_HOL_Obool),tc_fun(tc_fun(U_9722,tc_fun(U_9723,tc_HOL_Obool)),tc_fun(U_9723,tc_HOL_Obool)),U_9724),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9722,tc_fun(U_9723,tc_HOL_Obool))),U_9726)),U_9727)),
inference(variable_rename,[status(thm)],[f_2716_1]) ).
cnf(f_2716_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9722,tc_fun(U_9723,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9724,tc_fun(U_9722,tc_HOL_Obool)),U_9725),U_9726)),U_9727) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9724,tc_fun(U_9723,tc_HOL_Obool)),U_9725),hAPP(hAPP(c_COMBC(U_9724,tc_fun(U_9722,tc_fun(U_9723,tc_HOL_Obool)),tc_fun(U_9723,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9722,tc_HOL_Obool),tc_fun(tc_fun(U_9722,tc_fun(U_9723,tc_HOL_Obool)),tc_fun(U_9723,tc_HOL_Obool)),U_9724),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9722,tc_fun(U_9723,tc_HOL_Obool))),U_9726)),U_9727)),
inference(clausify,[status(thm)],[f_2716_2]) ).
fof(f_2717_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_2717_2,plain,
! [U_9733,U_9732,U_9731,U_9730,U_9729,U_9728] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9728,tc_fun(U_9729,tc_HOL_Obool)),U_9730),hAPP(hAPP(c_COMBC(U_9728,tc_fun(U_9731,tc_fun(U_9729,tc_HOL_Obool)),tc_fun(U_9729,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9731,tc_HOL_Obool),tc_fun(tc_fun(U_9731,tc_fun(U_9729,tc_HOL_Obool)),tc_fun(U_9729,tc_HOL_Obool)),U_9728),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9731,tc_fun(U_9729,tc_HOL_Obool))),U_9732)),U_9733)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9731,tc_fun(U_9729,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9728,tc_fun(U_9731,tc_HOL_Obool)),U_9730),U_9732)),U_9733),
inference(variable_rename,[status(thm)],[f_2717_1]) ).
cnf(f_2717_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9728,tc_fun(U_9729,tc_HOL_Obool)),U_9730),hAPP(hAPP(c_COMBC(U_9728,tc_fun(U_9731,tc_fun(U_9729,tc_HOL_Obool)),tc_fun(U_9729,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9731,tc_HOL_Obool),tc_fun(tc_fun(U_9731,tc_fun(U_9729,tc_HOL_Obool)),tc_fun(U_9729,tc_HOL_Obool)),U_9728),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9731,tc_fun(U_9729,tc_HOL_Obool))),U_9732)),U_9733)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9731,tc_fun(U_9729,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9728,tc_fun(U_9731,tc_HOL_Obool)),U_9730),U_9732)),U_9733),
inference(clausify,[status(thm)],[f_2717_2]) ).
fof(f_2718_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_2718_2,plain,
! [U_9739,U_9738,U_9737,U_9736,U_9735,U_9734] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9735,U_9734),U_9736),hAPP(hAPP(c_COMBB(tc_fun(U_9737,U_9734),U_9734,U_9735),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9737,U_9734),U_9738)),U_9739)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9737,U_9734),U_9738),hAPP(hAPP(c_COMBB(tc_fun(U_9735,U_9734),U_9734,U_9737),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9735,U_9734),U_9736)),hAPP(c_COMBC(U_9735,U_9737,U_9734),U_9739)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9734) ),
inference(variable_rename,[status(thm)],[f_2718_1]) ).
cnf(f_2718_3,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9735,U_9734),U_9736),hAPP(hAPP(c_COMBB(tc_fun(U_9737,U_9734),U_9734,U_9735),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9737,U_9734),U_9738)),U_9739)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9737,U_9734),U_9738),hAPP(hAPP(c_COMBB(tc_fun(U_9735,U_9734),U_9734,U_9737),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9735,U_9734),U_9736)),hAPP(c_COMBC(U_9735,U_9737,U_9734),U_9739)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9734) ),
inference(clausify,[status(thm)],[f_2718_2]) ).
fof(f_2719_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_2719_2,plain,
! [U_9744,U_9743,U_9742,U_9741,U_9740] : hAPP(hAPP(c_Set_Oinsert(U_9740),U_9741),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9742,tc_fun(U_9740,tc_HOL_Obool)),U_9743),U_9744)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9742,tc_fun(U_9740,tc_HOL_Obool)),U_9743),hAPP(hAPP(c_COMBB(tc_fun(U_9740,tc_HOL_Obool),tc_fun(U_9740,tc_HOL_Obool),U_9742),hAPP(c_Set_Oinsert(U_9740),U_9741)),U_9744)),
inference(variable_rename,[status(thm)],[f_2719_1]) ).
cnf(f_2719_3,plain,
hAPP(hAPP(c_Set_Oinsert(U_9740),U_9741),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9742,tc_fun(U_9740,tc_HOL_Obool)),U_9743),U_9744)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9742,tc_fun(U_9740,tc_HOL_Obool)),U_9743),hAPP(hAPP(c_COMBB(tc_fun(U_9740,tc_HOL_Obool),tc_fun(U_9740,tc_HOL_Obool),U_9742),hAPP(c_Set_Oinsert(U_9740),U_9741)),U_9744)),
inference(clausify,[status(thm)],[f_2719_2]) ).
fof(f_2720_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_2720_2,plain,
! [U_9749,U_9748,U_9747,U_9746,U_9745] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9745,tc_fun(U_9746,tc_HOL_Obool)),U_9747),hAPP(hAPP(c_COMBB(tc_fun(U_9746,tc_HOL_Obool),tc_fun(U_9746,tc_HOL_Obool),U_9745),hAPP(c_Set_Oinsert(U_9746),U_9748)),U_9749)) = hAPP(hAPP(c_Set_Oinsert(U_9746),U_9748),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9745,tc_fun(U_9746,tc_HOL_Obool)),U_9747),U_9749)),
inference(variable_rename,[status(thm)],[f_2720_1]) ).
cnf(f_2720_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9745,tc_fun(U_9746,tc_HOL_Obool)),U_9747),hAPP(hAPP(c_COMBB(tc_fun(U_9746,tc_HOL_Obool),tc_fun(U_9746,tc_HOL_Obool),U_9745),hAPP(c_Set_Oinsert(U_9746),U_9748)),U_9749)) = hAPP(hAPP(c_Set_Oinsert(U_9746),U_9748),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9745,tc_fun(U_9746,tc_HOL_Obool)),U_9747),U_9749)),
inference(clausify,[status(thm)],[f_2720_2]) ).
fof(f_2721_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_2721_2,plain,
! [U_9754,U_9753,U_9752,U_9751,U_9750] :
( c_Finite__Set_Ofun__left__comm(U_9753,U_9751,hAPP(hAPP(c_COMBB(U_9750,tc_fun(U_9751,U_9751),U_9753),U_9752),U_9754))
| ~ c_Finite__Set_Ofun__left__comm(U_9750,U_9751,U_9752) ),
inference(variable_rename,[status(thm)],[f_2721_1]) ).
cnf(f_2721_3,plain,
( c_Finite__Set_Ofun__left__comm(U_9753,U_9751,hAPP(hAPP(c_COMBB(U_9750,tc_fun(U_9751,U_9751),U_9753),U_9752),U_9754))
| ~ c_Finite__Set_Ofun__left__comm(U_9750,U_9751,U_9752) ),
inference(clausify,[status(thm)],[f_2721_2]) ).
fof(f_2722_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_2722_2,plain,
! [U_9757,U_9756,U_9755] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9756,U_9755)),U_9757) = c_Orderings_Obot__class_Obot(U_9755)
| ~ class_Orderings_Obot(U_9755) ),
inference(variable_rename,[status(thm)],[f_2722_1]) ).
cnf(f_2722_3,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9756,U_9755)),U_9757) = c_Orderings_Obot__class_Obot(U_9755)
| ~ class_Orderings_Obot(U_9755) ),
inference(clausify,[status(thm)],[f_2722_2]) ).
fof(f_2723_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_2723_2,plain,
! [U_9761,U_9760,U_9759,U_9758] :
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9759,U_9758)),U_9760),U_9761) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9758),hAPP(U_9760,U_9761))
| ~ class_Groups_Ouminus(U_9758) ),
inference(variable_rename,[status(thm)],[f_2723_1]) ).
cnf(f_2723_3,plain,
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9759,U_9758)),U_9760),U_9761) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9758),hAPP(U_9760,U_9761))
| ~ class_Groups_Ouminus(U_9758) ),
inference(clausify,[status(thm)],[f_2723_2]) ).
fof(f_2724_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_2724_2,plain,
! [U_9767,U_9766,U_9765,U_9764,U_9763,U_9762] :
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9763,tc_fun(U_9764,U_9762)),U_9765),U_9766),U_9767) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9763,U_9762),U_9765),hAPP(hAPP(c_COMBC(U_9763,U_9764,U_9762),U_9766),U_9767))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9762) ),
inference(variable_rename,[status(thm)],[f_2724_1]) ).
cnf(f_2724_3,plain,
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9763,tc_fun(U_9764,U_9762)),U_9765),U_9766),U_9767) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9763,U_9762),U_9765),hAPP(hAPP(c_COMBC(U_9763,U_9764,U_9762),U_9766),U_9767))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9762) ),
inference(clausify,[status(thm)],[f_2724_2]) ).
fof(f_2725_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_2725_2,plain,
! [U_9771,U_9770,U_9769,U_9768] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9770,U_9768),U_9769),hAPP(c_COMBK(U_9768,U_9770),U_9771)) = U_9771
| U_9769 = c_Orderings_Obot__class_Obot(tc_fun(U_9770,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9768) ),
inference(variable_rename,[status(thm)],[f_2725_1]) ).
cnf(f_2725_3,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9770,U_9768),U_9769),hAPP(c_COMBK(U_9768,U_9770),U_9771)) = U_9771
| U_9769 = c_Orderings_Obot__class_Obot(tc_fun(U_9770,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9768) ),
inference(clausify,[status(thm)],[f_2725_2]) ).
fof(f_2726_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_2726_2,plain,
! [U_9775,U_9774,U_9773,U_9772] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9773,U_9772),hAPP(hAPP(c_COMBB(U_9772,U_9772,U_9773),c_Groups_Ouminus__class_Ouminus(U_9772)),U_9774)),U_9775) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9772),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9773,U_9772),U_9774),U_9775))
| ~ class_Groups_Oab__group__add(U_9772) ),
inference(variable_rename,[status(thm)],[f_2726_1]) ).
cnf(f_2726_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9773,U_9772),hAPP(hAPP(c_COMBB(U_9772,U_9772,U_9773),c_Groups_Ouminus__class_Ouminus(U_9772)),U_9774)),U_9775) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9772),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9773,U_9772),U_9774),U_9775))
| ~ class_Groups_Oab__group__add(U_9772) ),
inference(clausify,[status(thm)],[f_2726_2]) ).
fof(f_2727_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_2727_2,plain,
! [U_9781,U_9780,U_9779,U_9778] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9778,tc_fun(U_9779,tc_HOL_Obool)),U_9780),U_9781) = c_Orderings_Obot__class_Obot(tc_fun(U_9779,tc_HOL_Obool))
| ? [U_9777] :
( hAPP(U_9781,U_9777) != c_Orderings_Obot__class_Obot(tc_fun(U_9779,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_9778),U_9777),U_9780)) ) )
& ( ! [U_9776] :
( hAPP(U_9781,U_9776) = c_Orderings_Obot__class_Obot(tc_fun(U_9779,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9778),U_9776),U_9780)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9778,tc_fun(U_9779,tc_HOL_Obool)),U_9780),U_9781) != c_Orderings_Obot__class_Obot(tc_fun(U_9779,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2727_1]) ).
fof(f_2727_3,plain,
( ! [U_9789,U_9787,U_9785,U_9783] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9783,tc_fun(U_9785,tc_HOL_Obool)),U_9787),U_9789) = c_Orderings_Obot__class_Obot(tc_fun(U_9785,tc_HOL_Obool))
| ? [U_9777] :
( hAPP(U_9789,U_9777) != c_Orderings_Obot__class_Obot(tc_fun(U_9785,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_9783),U_9777),U_9787)) ) )
& ! [U_9788,U_9786,U_9784,U_9782] :
( ! [U_9776] :
( hAPP(U_9788,U_9776) = c_Orderings_Obot__class_Obot(tc_fun(U_9784,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9782),U_9776),U_9786)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9782,tc_fun(U_9784,tc_HOL_Obool)),U_9786),U_9788) != c_Orderings_Obot__class_Obot(tc_fun(U_9784,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2727_2]) ).
fof(f_2727_4,plain,
( ! [U_9789,U_9787,U_9785,U_9783] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9783,tc_fun(U_9785,tc_HOL_Obool)),U_9787),U_9789) = c_Orderings_Obot__class_Obot(tc_fun(U_9785,tc_HOL_Obool))
| ( hAPP(U_9789,sK240(U_9789,U_9787,U_9785,U_9783)) != c_Orderings_Obot__class_Obot(tc_fun(U_9785,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_9783),sK240(U_9789,U_9787,U_9785,U_9783)),U_9787)) ) )
& ! [U_9788,U_9786,U_9784,U_9782] :
( ! [U_9776] :
( hAPP(U_9788,U_9776) = c_Orderings_Obot__class_Obot(tc_fun(U_9784,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9782),U_9776),U_9786)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9782,tc_fun(U_9784,tc_HOL_Obool)),U_9786),U_9788) != c_Orderings_Obot__class_Obot(tc_fun(U_9784,tc_HOL_Obool)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK240]),skolemize(U_9777,sK240(U_9789,U_9787,U_9785,U_9783))],[f_2727_3]) ).
cnf(f_2727_5,plain,
( hAPP(U_9788,U_9776) = c_Orderings_Obot__class_Obot(tc_fun(U_9784,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9782),U_9776),U_9786))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9782,tc_fun(U_9784,tc_HOL_Obool)),U_9786),U_9788) != c_Orderings_Obot__class_Obot(tc_fun(U_9784,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2727_4]) ).
cnf(f_2727_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_9783),sK240(U_9789,U_9787,U_9785,U_9783)),U_9787))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9783,tc_fun(U_9785,tc_HOL_Obool)),U_9787),U_9789) = c_Orderings_Obot__class_Obot(tc_fun(U_9785,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2727_4]) ).
cnf(f_2727_7,plain,
( hAPP(U_9789,sK240(U_9789,U_9787,U_9785,U_9783)) != c_Orderings_Obot__class_Obot(tc_fun(U_9785,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9783,tc_fun(U_9785,tc_HOL_Obool)),U_9787),U_9789) = c_Orderings_Obot__class_Obot(tc_fun(U_9785,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2727_4]) ).
fof(f_2728_1,plain,
! [V_c_2,T_c,T_b,V_A_2] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__constant]) ).
fof(f_2728_2,plain,
! [U_9793,U_9792,U_9791,U_9790] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9791,tc_fun(U_9792,tc_HOL_Obool)),U_9790),hAPP(c_COMBK(tc_fun(U_9792,tc_HOL_Obool),U_9791),U_9793)) = U_9793
| U_9790 = c_Orderings_Obot__class_Obot(tc_fun(U_9791,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9791,tc_fun(U_9792,tc_HOL_Obool)),U_9790),hAPP(c_COMBK(tc_fun(U_9792,tc_HOL_Obool),U_9791),U_9793)) = c_Orderings_Obot__class_Obot(tc_fun(U_9792,tc_HOL_Obool))
| U_9790 != c_Orderings_Obot__class_Obot(tc_fun(U_9791,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2728_1]) ).
fof(f_2728_3,plain,
( ! [U_9801,U_9799,U_9797,U_9795] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9797,tc_fun(U_9799,tc_HOL_Obool)),U_9795),hAPP(c_COMBK(tc_fun(U_9799,tc_HOL_Obool),U_9797),U_9801)) = U_9801
| U_9795 = c_Orderings_Obot__class_Obot(tc_fun(U_9797,tc_HOL_Obool)) )
& ! [U_9800,U_9798,U_9796,U_9794] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9796,tc_fun(U_9798,tc_HOL_Obool)),U_9794),hAPP(c_COMBK(tc_fun(U_9798,tc_HOL_Obool),U_9796),U_9800)) = c_Orderings_Obot__class_Obot(tc_fun(U_9798,tc_HOL_Obool))
| U_9794 != c_Orderings_Obot__class_Obot(tc_fun(U_9796,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2728_2]) ).
cnf(f_2728_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9796,tc_fun(U_9798,tc_HOL_Obool)),U_9794),hAPP(c_COMBK(tc_fun(U_9798,tc_HOL_Obool),U_9796),U_9800)) = c_Orderings_Obot__class_Obot(tc_fun(U_9798,tc_HOL_Obool))
| U_9794 != c_Orderings_Obot__class_Obot(tc_fun(U_9796,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2728_3]) ).
cnf(f_2728_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9797,tc_fun(U_9799,tc_HOL_Obool)),U_9795),hAPP(c_COMBK(tc_fun(U_9799,tc_HOL_Obool),U_9797),U_9801)) = U_9801
| U_9795 = c_Orderings_Obot__class_Obot(tc_fun(U_9797,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2728_3]) ).
fof(f_2729_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_2729_2,plain,
! [U_9804,U_9803,U_9802] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9802,tc_fun(U_9803,tc_HOL_Obool)),U_9804),hAPP(c_COMBK(tc_fun(U_9803,tc_HOL_Obool),U_9802),c_Orderings_Obot__class_Obot(tc_fun(U_9803,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9803,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2729_1]) ).
cnf(f_2729_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9802,tc_fun(U_9803,tc_HOL_Obool)),U_9804),hAPP(c_COMBK(tc_fun(U_9803,tc_HOL_Obool),U_9802),c_Orderings_Obot__class_Obot(tc_fun(U_9803,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9803,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2729_2]) ).
fof(f_2730_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_2730_2,plain,
! [U_9810,U_9809,U_9808,U_9807] :
( ( c_Orderings_Obot__class_Obot(tc_fun(U_9807,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9808,tc_fun(U_9807,tc_HOL_Obool)),U_9809),U_9810)
| ? [U_9806] :
( hAPP(U_9810,U_9806) != c_Orderings_Obot__class_Obot(tc_fun(U_9807,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_9808),U_9806),U_9809)) ) )
& ( ! [U_9805] :
( hAPP(U_9810,U_9805) = c_Orderings_Obot__class_Obot(tc_fun(U_9807,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9808),U_9805),U_9809)) )
| c_Orderings_Obot__class_Obot(tc_fun(U_9807,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9808,tc_fun(U_9807,tc_HOL_Obool)),U_9809),U_9810) ) ),
inference(variable_rename,[status(thm)],[f_2730_1]) ).
fof(f_2730_3,plain,
( ! [U_9818,U_9816,U_9814,U_9812] :
( c_Orderings_Obot__class_Obot(tc_fun(U_9812,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9814,tc_fun(U_9812,tc_HOL_Obool)),U_9816),U_9818)
| ? [U_9806] :
( hAPP(U_9818,U_9806) != c_Orderings_Obot__class_Obot(tc_fun(U_9812,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_9814),U_9806),U_9816)) ) )
& ! [U_9817,U_9815,U_9813,U_9811] :
( ! [U_9805] :
( hAPP(U_9817,U_9805) = c_Orderings_Obot__class_Obot(tc_fun(U_9811,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9813),U_9805),U_9815)) )
| c_Orderings_Obot__class_Obot(tc_fun(U_9811,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9813,tc_fun(U_9811,tc_HOL_Obool)),U_9815),U_9817) ) ),
inference(miniscope,[status(thm)],[f_2730_2]) ).
fof(f_2730_4,plain,
( ! [U_9818,U_9816,U_9814,U_9812] :
( c_Orderings_Obot__class_Obot(tc_fun(U_9812,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9814,tc_fun(U_9812,tc_HOL_Obool)),U_9816),U_9818)
| ( hAPP(U_9818,sK241(U_9818,U_9816,U_9814,U_9812)) != c_Orderings_Obot__class_Obot(tc_fun(U_9812,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_9814),sK241(U_9818,U_9816,U_9814,U_9812)),U_9816)) ) )
& ! [U_9817,U_9815,U_9813,U_9811] :
( ! [U_9805] :
( hAPP(U_9817,U_9805) = c_Orderings_Obot__class_Obot(tc_fun(U_9811,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9813),U_9805),U_9815)) )
| c_Orderings_Obot__class_Obot(tc_fun(U_9811,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9813,tc_fun(U_9811,tc_HOL_Obool)),U_9815),U_9817) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK241]),skolemize(U_9806,sK241(U_9818,U_9816,U_9814,U_9812))],[f_2730_3]) ).
cnf(f_2730_5,plain,
( hAPP(U_9817,U_9805) = c_Orderings_Obot__class_Obot(tc_fun(U_9811,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9813),U_9805),U_9815))
| c_Orderings_Obot__class_Obot(tc_fun(U_9811,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9813,tc_fun(U_9811,tc_HOL_Obool)),U_9815),U_9817) ),
inference(clausify,[status(thm)],[f_2730_4]) ).
cnf(f_2730_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_9814),sK241(U_9818,U_9816,U_9814,U_9812)),U_9816))
| c_Orderings_Obot__class_Obot(tc_fun(U_9812,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9814,tc_fun(U_9812,tc_HOL_Obool)),U_9816),U_9818) ),
inference(clausify,[status(thm)],[f_2730_4]) ).
cnf(f_2730_7,plain,
( hAPP(U_9818,sK241(U_9818,U_9816,U_9814,U_9812)) != c_Orderings_Obot__class_Obot(tc_fun(U_9812,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(U_9812,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9814,tc_fun(U_9812,tc_HOL_Obool)),U_9816),U_9818) ),
inference(clausify,[status(thm)],[f_2730_4]) ).
fof(f_2731_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_2731_2,plain,
! [U_9822,U_9821,U_9820,U_9819] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9821,U_9819),U_9820),hAPP(c_COMBK(U_9819,U_9821),U_9822)) = U_9822
| U_9820 = c_Orderings_Obot__class_Obot(tc_fun(U_9821,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9819) ),
inference(variable_rename,[status(thm)],[f_2731_1]) ).
cnf(f_2731_3,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9821,U_9819),U_9820),hAPP(c_COMBK(U_9819,U_9821),U_9822)) = U_9822
| U_9820 = c_Orderings_Obot__class_Obot(tc_fun(U_9821,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9819) ),
inference(clausify,[status(thm)],[f_2731_2]) ).
fof(f_2732_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_2732_2,plain,
! [U_9824,U_9823] : c_Fun_Oinj__on(U_9823,U_9823,c_COMBI(U_9823),U_9824),
inference(variable_rename,[status(thm)],[f_2732_1]) ).
cnf(f_2732_3,plain,
c_Fun_Oinj__on(U_9823,U_9823,c_COMBI(U_9823),U_9824),
inference(clausify,[status(thm)],[f_2732_2]) ).
fof(f_2733_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_2733_2,plain,
! [U_9830,U_9829,U_9828,U_9827,U_9826,U_9825] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9825,tc_fun(U_9828,tc_HOL_Obool)),U_9827),hAPP(hAPP(c_COMBB(tc_fun(U_9828,tc_HOL_Obool),tc_fun(U_9828,tc_HOL_Obool),U_9825),hAPP(c_Set_Oinsert(U_9828),U_9829)),U_9830)) = hAPP(hAPP(c_Set_Oinsert(U_9828),U_9829),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9825,tc_fun(U_9828,tc_HOL_Obool)),U_9827),U_9830))
| ~ hBOOL(hAPP(hAPP(c_member(U_9825),U_9826),U_9827)) ),
inference(variable_rename,[status(thm)],[f_2733_1]) ).
cnf(f_2733_3,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9825,tc_fun(U_9828,tc_HOL_Obool)),U_9827),hAPP(hAPP(c_COMBB(tc_fun(U_9828,tc_HOL_Obool),tc_fun(U_9828,tc_HOL_Obool),U_9825),hAPP(c_Set_Oinsert(U_9828),U_9829)),U_9830)) = hAPP(hAPP(c_Set_Oinsert(U_9828),U_9829),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9825,tc_fun(U_9828,tc_HOL_Obool)),U_9827),U_9830))
| ~ hBOOL(hAPP(hAPP(c_member(U_9825),U_9826),U_9827)) ),
inference(clausify,[status(thm)],[f_2733_2]) ).
fof(f_2734_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_2734_2,plain,
! [U_9837,U_9836,U_9835,U_9834,U_9833] :
( ( hBOOL(hAPP(hAPP(c_member(U_9833),U_9834),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9835,tc_fun(U_9833,tc_HOL_Obool)),U_9836),U_9837)))
| ? [U_9832] :
( ~ hBOOL(hAPP(hAPP(c_member(U_9833),U_9834),hAPP(U_9837,U_9832)))
& hBOOL(hAPP(hAPP(c_member(U_9835),U_9832),U_9836)) ) )
& ( ! [U_9831] :
( hBOOL(hAPP(hAPP(c_member(U_9833),U_9834),hAPP(U_9837,U_9831)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9835),U_9831),U_9836)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9833),U_9834),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9835,tc_fun(U_9833,tc_HOL_Obool)),U_9836),U_9837))) ) ),
inference(variable_rename,[status(thm)],[f_2734_1]) ).
fof(f_2734_3,plain,
( ! [U_9847,U_9845,U_9843,U_9841,U_9839] :
( hBOOL(hAPP(hAPP(c_member(U_9839),U_9841),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9843,tc_fun(U_9839,tc_HOL_Obool)),U_9845),U_9847)))
| ? [U_9832] :
( ~ hBOOL(hAPP(hAPP(c_member(U_9839),U_9841),hAPP(U_9847,U_9832)))
& hBOOL(hAPP(hAPP(c_member(U_9843),U_9832),U_9845)) ) )
& ! [U_9846,U_9844,U_9842,U_9840,U_9838] :
( ! [U_9831] :
( hBOOL(hAPP(hAPP(c_member(U_9838),U_9840),hAPP(U_9846,U_9831)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9842),U_9831),U_9844)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9838),U_9840),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9842,tc_fun(U_9838,tc_HOL_Obool)),U_9844),U_9846))) ) ),
inference(miniscope,[status(thm)],[f_2734_2]) ).
fof(f_2734_4,plain,
( ! [U_9847,U_9845,U_9843,U_9841,U_9839] :
( hBOOL(hAPP(hAPP(c_member(U_9839),U_9841),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9843,tc_fun(U_9839,tc_HOL_Obool)),U_9845),U_9847)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_9839),U_9841),hAPP(U_9847,sK242(U_9847,U_9845,U_9843,U_9841,U_9839))))
& hBOOL(hAPP(hAPP(c_member(U_9843),sK242(U_9847,U_9845,U_9843,U_9841,U_9839)),U_9845)) ) )
& ! [U_9846,U_9844,U_9842,U_9840,U_9838] :
( ! [U_9831] :
( hBOOL(hAPP(hAPP(c_member(U_9838),U_9840),hAPP(U_9846,U_9831)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9842),U_9831),U_9844)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9838),U_9840),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9842,tc_fun(U_9838,tc_HOL_Obool)),U_9844),U_9846))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK242]),skolemize(U_9832,sK242(U_9847,U_9845,U_9843,U_9841,U_9839))],[f_2734_3]) ).
cnf(f_2734_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_9838),U_9840),hAPP(U_9846,U_9831)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9842),U_9831),U_9844))
| ~ hBOOL(hAPP(hAPP(c_member(U_9838),U_9840),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9842,tc_fun(U_9838,tc_HOL_Obool)),U_9844),U_9846))) ),
inference(clausify,[status(thm)],[f_2734_4]) ).
cnf(f_2734_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_9843),sK242(U_9847,U_9845,U_9843,U_9841,U_9839)),U_9845))
| hBOOL(hAPP(hAPP(c_member(U_9839),U_9841),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9843,tc_fun(U_9839,tc_HOL_Obool)),U_9845),U_9847))) ),
inference(clausify,[status(thm)],[f_2734_4]) ).
cnf(f_2734_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_9839),U_9841),hAPP(U_9847,sK242(U_9847,U_9845,U_9843,U_9841,U_9839))))
| hBOOL(hAPP(hAPP(c_member(U_9839),U_9841),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9843,tc_fun(U_9839,tc_HOL_Obool)),U_9845),U_9847))) ),
inference(clausify,[status(thm)],[f_2734_4]) ).
fof(f_2735_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_2735_2,plain,
! [U_9851,U_9850,U_9849,U_9848] :
( ( hAPP(hAPP(c_COMBC(U_9848,tc_fun(tc_prod(U_9848,U_9849),tc_HOL_Obool),tc_fun(U_9849,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9849,tc_fun(tc_fun(tc_prod(U_9848,U_9849),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9848,U_9849),tc_HOL_Obool),tc_fun(U_9849,tc_HOL_Obool)),U_9848),c_COMBC(U_9849,tc_fun(tc_prod(U_9848,U_9849),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9849,tc_prod(U_9848,U_9849)),tc_fun(U_9849,tc_fun(tc_fun(tc_prod(U_9848,U_9849),tc_HOL_Obool),tc_HOL_Obool)),U_9848),hAPP(c_COMBB(tc_prod(U_9848,U_9849),tc_fun(tc_fun(tc_prod(U_9848,U_9849),tc_HOL_Obool),tc_HOL_Obool),U_9849),c_member(tc_prod(U_9848,U_9849)))),c_Product__Type_OPair(U_9848,U_9849)))),U_9850) = hAPP(hAPP(c_COMBC(U_9848,tc_fun(tc_prod(U_9848,U_9849),tc_HOL_Obool),tc_fun(U_9849,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9849,tc_fun(tc_fun(tc_prod(U_9848,U_9849),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9848,U_9849),tc_HOL_Obool),tc_fun(U_9849,tc_HOL_Obool)),U_9848),c_COMBC(U_9849,tc_fun(tc_prod(U_9848,U_9849),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9849,tc_prod(U_9848,U_9849)),tc_fun(U_9849,tc_fun(tc_fun(tc_prod(U_9848,U_9849),tc_HOL_Obool),tc_HOL_Obool)),U_9848),hAPP(c_COMBB(tc_prod(U_9848,U_9849),tc_fun(tc_fun(tc_prod(U_9848,U_9849),tc_HOL_Obool),tc_HOL_Obool),U_9849),c_member(tc_prod(U_9848,U_9849)))),c_Product__Type_OPair(U_9848,U_9849)))),U_9851)
| U_9850 != U_9851 )
& ( U_9850 = U_9851
| hAPP(hAPP(c_COMBC(U_9848,tc_fun(tc_prod(U_9848,U_9849),tc_HOL_Obool),tc_fun(U_9849,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9849,tc_fun(tc_fun(tc_prod(U_9848,U_9849),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9848,U_9849),tc_HOL_Obool),tc_fun(U_9849,tc_HOL_Obool)),U_9848),c_COMBC(U_9849,tc_fun(tc_prod(U_9848,U_9849),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9849,tc_prod(U_9848,U_9849)),tc_fun(U_9849,tc_fun(tc_fun(tc_prod(U_9848,U_9849),tc_HOL_Obool),tc_HOL_Obool)),U_9848),hAPP(c_COMBB(tc_prod(U_9848,U_9849),tc_fun(tc_fun(tc_prod(U_9848,U_9849),tc_HOL_Obool),tc_HOL_Obool),U_9849),c_member(tc_prod(U_9848,U_9849)))),c_Product__Type_OPair(U_9848,U_9849)))),U_9850) != hAPP(hAPP(c_COMBC(U_9848,tc_fun(tc_prod(U_9848,U_9849),tc_HOL_Obool),tc_fun(U_9849,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9849,tc_fun(tc_fun(tc_prod(U_9848,U_9849),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9848,U_9849),tc_HOL_Obool),tc_fun(U_9849,tc_HOL_Obool)),U_9848),c_COMBC(U_9849,tc_fun(tc_prod(U_9848,U_9849),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9849,tc_prod(U_9848,U_9849)),tc_fun(U_9849,tc_fun(tc_fun(tc_prod(U_9848,U_9849),tc_HOL_Obool),tc_HOL_Obool)),U_9848),hAPP(c_COMBB(tc_prod(U_9848,U_9849),tc_fun(tc_fun(tc_prod(U_9848,U_9849),tc_HOL_Obool),tc_HOL_Obool),U_9849),c_member(tc_prod(U_9848,U_9849)))),c_Product__Type_OPair(U_9848,U_9849)))),U_9851) ) ),
inference(variable_rename,[status(thm)],[f_2735_1]) ).
fof(f_2735_3,plain,
( ! [U_9859,U_9857] :
( ! [U_9855,U_9853] : hAPP(hAPP(c_COMBC(U_9853,tc_fun(tc_prod(U_9853,U_9855),tc_HOL_Obool),tc_fun(U_9855,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9855,tc_fun(tc_fun(tc_prod(U_9853,U_9855),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9853,U_9855),tc_HOL_Obool),tc_fun(U_9855,tc_HOL_Obool)),U_9853),c_COMBC(U_9855,tc_fun(tc_prod(U_9853,U_9855),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9855,tc_prod(U_9853,U_9855)),tc_fun(U_9855,tc_fun(tc_fun(tc_prod(U_9853,U_9855),tc_HOL_Obool),tc_HOL_Obool)),U_9853),hAPP(c_COMBB(tc_prod(U_9853,U_9855),tc_fun(tc_fun(tc_prod(U_9853,U_9855),tc_HOL_Obool),tc_HOL_Obool),U_9855),c_member(tc_prod(U_9853,U_9855)))),c_Product__Type_OPair(U_9853,U_9855)))),U_9857) = hAPP(hAPP(c_COMBC(U_9853,tc_fun(tc_prod(U_9853,U_9855),tc_HOL_Obool),tc_fun(U_9855,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9855,tc_fun(tc_fun(tc_prod(U_9853,U_9855),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9853,U_9855),tc_HOL_Obool),tc_fun(U_9855,tc_HOL_Obool)),U_9853),c_COMBC(U_9855,tc_fun(tc_prod(U_9853,U_9855),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9855,tc_prod(U_9853,U_9855)),tc_fun(U_9855,tc_fun(tc_fun(tc_prod(U_9853,U_9855),tc_HOL_Obool),tc_HOL_Obool)),U_9853),hAPP(c_COMBB(tc_prod(U_9853,U_9855),tc_fun(tc_fun(tc_prod(U_9853,U_9855),tc_HOL_Obool),tc_HOL_Obool),U_9855),c_member(tc_prod(U_9853,U_9855)))),c_Product__Type_OPair(U_9853,U_9855)))),U_9859)
| U_9857 != U_9859 )
& ! [U_9858,U_9856] :
( ! [U_9854,U_9852] : hAPP(hAPP(c_COMBC(U_9852,tc_fun(tc_prod(U_9852,U_9854),tc_HOL_Obool),tc_fun(U_9854,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9854,tc_fun(tc_fun(tc_prod(U_9852,U_9854),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9852,U_9854),tc_HOL_Obool),tc_fun(U_9854,tc_HOL_Obool)),U_9852),c_COMBC(U_9854,tc_fun(tc_prod(U_9852,U_9854),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9854,tc_prod(U_9852,U_9854)),tc_fun(U_9854,tc_fun(tc_fun(tc_prod(U_9852,U_9854),tc_HOL_Obool),tc_HOL_Obool)),U_9852),hAPP(c_COMBB(tc_prod(U_9852,U_9854),tc_fun(tc_fun(tc_prod(U_9852,U_9854),tc_HOL_Obool),tc_HOL_Obool),U_9854),c_member(tc_prod(U_9852,U_9854)))),c_Product__Type_OPair(U_9852,U_9854)))),U_9856) != hAPP(hAPP(c_COMBC(U_9852,tc_fun(tc_prod(U_9852,U_9854),tc_HOL_Obool),tc_fun(U_9854,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9854,tc_fun(tc_fun(tc_prod(U_9852,U_9854),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9852,U_9854),tc_HOL_Obool),tc_fun(U_9854,tc_HOL_Obool)),U_9852),c_COMBC(U_9854,tc_fun(tc_prod(U_9852,U_9854),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9854,tc_prod(U_9852,U_9854)),tc_fun(U_9854,tc_fun(tc_fun(tc_prod(U_9852,U_9854),tc_HOL_Obool),tc_HOL_Obool)),U_9852),hAPP(c_COMBB(tc_prod(U_9852,U_9854),tc_fun(tc_fun(tc_prod(U_9852,U_9854),tc_HOL_Obool),tc_HOL_Obool),U_9854),c_member(tc_prod(U_9852,U_9854)))),c_Product__Type_OPair(U_9852,U_9854)))),U_9858)
| U_9856 = U_9858 ) ),
inference(miniscope,[status(thm)],[f_2735_2]) ).
cnf(f_2735_4,plain,
( hAPP(hAPP(c_COMBC(U_9852,tc_fun(tc_prod(U_9852,U_9854),tc_HOL_Obool),tc_fun(U_9854,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9854,tc_fun(tc_fun(tc_prod(U_9852,U_9854),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9852,U_9854),tc_HOL_Obool),tc_fun(U_9854,tc_HOL_Obool)),U_9852),c_COMBC(U_9854,tc_fun(tc_prod(U_9852,U_9854),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9854,tc_prod(U_9852,U_9854)),tc_fun(U_9854,tc_fun(tc_fun(tc_prod(U_9852,U_9854),tc_HOL_Obool),tc_HOL_Obool)),U_9852),hAPP(c_COMBB(tc_prod(U_9852,U_9854),tc_fun(tc_fun(tc_prod(U_9852,U_9854),tc_HOL_Obool),tc_HOL_Obool),U_9854),c_member(tc_prod(U_9852,U_9854)))),c_Product__Type_OPair(U_9852,U_9854)))),U_9856) != hAPP(hAPP(c_COMBC(U_9852,tc_fun(tc_prod(U_9852,U_9854),tc_HOL_Obool),tc_fun(U_9854,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9854,tc_fun(tc_fun(tc_prod(U_9852,U_9854),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9852,U_9854),tc_HOL_Obool),tc_fun(U_9854,tc_HOL_Obool)),U_9852),c_COMBC(U_9854,tc_fun(tc_prod(U_9852,U_9854),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9854,tc_prod(U_9852,U_9854)),tc_fun(U_9854,tc_fun(tc_fun(tc_prod(U_9852,U_9854),tc_HOL_Obool),tc_HOL_Obool)),U_9852),hAPP(c_COMBB(tc_prod(U_9852,U_9854),tc_fun(tc_fun(tc_prod(U_9852,U_9854),tc_HOL_Obool),tc_HOL_Obool),U_9854),c_member(tc_prod(U_9852,U_9854)))),c_Product__Type_OPair(U_9852,U_9854)))),U_9858)
| U_9856 = U_9858 ),
inference(clausify,[status(thm)],[f_2735_3]) ).
cnf(f_2735_5,plain,
( hAPP(hAPP(c_COMBC(U_9853,tc_fun(tc_prod(U_9853,U_9855),tc_HOL_Obool),tc_fun(U_9855,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9855,tc_fun(tc_fun(tc_prod(U_9853,U_9855),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9853,U_9855),tc_HOL_Obool),tc_fun(U_9855,tc_HOL_Obool)),U_9853),c_COMBC(U_9855,tc_fun(tc_prod(U_9853,U_9855),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9855,tc_prod(U_9853,U_9855)),tc_fun(U_9855,tc_fun(tc_fun(tc_prod(U_9853,U_9855),tc_HOL_Obool),tc_HOL_Obool)),U_9853),hAPP(c_COMBB(tc_prod(U_9853,U_9855),tc_fun(tc_fun(tc_prod(U_9853,U_9855),tc_HOL_Obool),tc_HOL_Obool),U_9855),c_member(tc_prod(U_9853,U_9855)))),c_Product__Type_OPair(U_9853,U_9855)))),U_9857) = hAPP(hAPP(c_COMBC(U_9853,tc_fun(tc_prod(U_9853,U_9855),tc_HOL_Obool),tc_fun(U_9855,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9855,tc_fun(tc_fun(tc_prod(U_9853,U_9855),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9853,U_9855),tc_HOL_Obool),tc_fun(U_9855,tc_HOL_Obool)),U_9853),c_COMBC(U_9855,tc_fun(tc_prod(U_9853,U_9855),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9855,tc_prod(U_9853,U_9855)),tc_fun(U_9855,tc_fun(tc_fun(tc_prod(U_9853,U_9855),tc_HOL_Obool),tc_HOL_Obool)),U_9853),hAPP(c_COMBB(tc_prod(U_9853,U_9855),tc_fun(tc_fun(tc_prod(U_9853,U_9855),tc_HOL_Obool),tc_HOL_Obool),U_9855),c_member(tc_prod(U_9853,U_9855)))),c_Product__Type_OPair(U_9853,U_9855)))),U_9859)
| U_9857 != U_9859 ),
inference(clausify,[status(thm)],[f_2735_3]) ).
fof(f_2736_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_2736_2,plain,
! [U_9862,U_9861,U_9860] :
( ( hAPP(hAPP(c_COMBC(U_9860,tc_fun(U_9860,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9860)),U_9861) = hAPP(hAPP(c_COMBC(U_9860,tc_fun(U_9860,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9860)),U_9862)
| U_9861 != U_9862 )
& ( U_9861 = U_9862
| hAPP(hAPP(c_COMBC(U_9860,tc_fun(U_9860,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9860)),U_9861) != hAPP(hAPP(c_COMBC(U_9860,tc_fun(U_9860,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9860)),U_9862) ) ),
inference(variable_rename,[status(thm)],[f_2736_1]) ).
fof(f_2736_3,plain,
( ! [U_9868,U_9866] :
( ! [U_9864] : hAPP(hAPP(c_COMBC(U_9864,tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9864)),U_9866) = hAPP(hAPP(c_COMBC(U_9864,tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9864)),U_9868)
| U_9866 != U_9868 )
& ! [U_9867,U_9865] :
( ! [U_9863] : hAPP(hAPP(c_COMBC(U_9863,tc_fun(U_9863,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9863)),U_9865) != hAPP(hAPP(c_COMBC(U_9863,tc_fun(U_9863,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9863)),U_9867)
| U_9865 = U_9867 ) ),
inference(miniscope,[status(thm)],[f_2736_2]) ).
cnf(f_2736_4,plain,
( hAPP(hAPP(c_COMBC(U_9863,tc_fun(U_9863,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9863)),U_9865) != hAPP(hAPP(c_COMBC(U_9863,tc_fun(U_9863,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9863)),U_9867)
| U_9865 = U_9867 ),
inference(clausify,[status(thm)],[f_2736_3]) ).
cnf(f_2736_5,plain,
( hAPP(hAPP(c_COMBC(U_9864,tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9864)),U_9866) = hAPP(hAPP(c_COMBC(U_9864,tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9864)),U_9868)
| U_9866 != U_9868 ),
inference(clausify,[status(thm)],[f_2736_3]) ).
fof(f_2737_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_2737_2,plain,
! [U_9870,U_9869] :
( ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9869,tc_HOL_Obool)),U_9870))
| ~ hBOOL(hAPP(hAPP(c_member(U_9869),U_9870),c_Orderings_Obot__class_Obot(tc_fun(U_9869,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(hAPP(c_member(U_9869),U_9870),c_Orderings_Obot__class_Obot(tc_fun(U_9869,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9869,tc_HOL_Obool)),U_9870)) ) ),
inference(variable_rename,[status(thm)],[f_2737_1]) ).
fof(f_2737_3,plain,
( ! [U_9874,U_9872] :
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9872,tc_HOL_Obool)),U_9874))
| ~ hBOOL(hAPP(hAPP(c_member(U_9872),U_9874),c_Orderings_Obot__class_Obot(tc_fun(U_9872,tc_HOL_Obool)))) )
& ! [U_9873,U_9871] :
( hBOOL(hAPP(hAPP(c_member(U_9871),U_9873),c_Orderings_Obot__class_Obot(tc_fun(U_9871,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9871,tc_HOL_Obool)),U_9873)) ) ),
inference(miniscope,[status(thm)],[f_2737_2]) ).
cnf(f_2737_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_9871),U_9873),c_Orderings_Obot__class_Obot(tc_fun(U_9871,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9871,tc_HOL_Obool)),U_9873)) ),
inference(clausify,[status(thm)],[f_2737_3]) ).
cnf(f_2737_5,plain,
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9872,tc_HOL_Obool)),U_9874))
| ~ hBOOL(hAPP(hAPP(c_member(U_9872),U_9874),c_Orderings_Obot__class_Obot(tc_fun(U_9872,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_2737_3]) ).
fof(f_2738_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_2738_2,plain,
! [U_9878,U_9877,U_9876,U_9875] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9875,tc_fun(U_9876,tc_HOL_Obool))),U_9877),U_9878))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9875,U_9876)),hAPP(hAPP(c_Product__Type_OPair(U_9875,U_9876),U_9877),U_9878)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9875,U_9876),tc_HOL_Obool)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9875,U_9876)),hAPP(hAPP(c_Product__Type_OPair(U_9875,U_9876),U_9877),U_9878)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9875,U_9876),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9875,tc_fun(U_9876,tc_HOL_Obool))),U_9877),U_9878)) ) ),
inference(variable_rename,[status(thm)],[f_2738_1]) ).
fof(f_2738_3,plain,
( ! [U_9886,U_9884,U_9882,U_9880] :
( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9880,tc_fun(U_9882,tc_HOL_Obool))),U_9884),U_9886))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9880,U_9882)),hAPP(hAPP(c_Product__Type_OPair(U_9880,U_9882),U_9884),U_9886)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9880,U_9882),tc_HOL_Obool)))) )
& ! [U_9885,U_9883,U_9881,U_9879] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9879,U_9881)),hAPP(hAPP(c_Product__Type_OPair(U_9879,U_9881),U_9883),U_9885)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9879,U_9881),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9879,tc_fun(U_9881,tc_HOL_Obool))),U_9883),U_9885)) ) ),
inference(miniscope,[status(thm)],[f_2738_2]) ).
cnf(f_2738_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9879,U_9881)),hAPP(hAPP(c_Product__Type_OPair(U_9879,U_9881),U_9883),U_9885)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9879,U_9881),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9879,tc_fun(U_9881,tc_HOL_Obool))),U_9883),U_9885)) ),
inference(clausify,[status(thm)],[f_2738_3]) ).
cnf(f_2738_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9880,tc_fun(U_9882,tc_HOL_Obool))),U_9884),U_9886))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9880,U_9882)),hAPP(hAPP(c_Product__Type_OPair(U_9880,U_9882),U_9884),U_9886)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9880,U_9882),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_2738_3]) ).
fof(f_2739_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_2739_2,plain,
! [U_9893,U_9892,U_9891,U_9890,U_9889] :
( ( hBOOL(hAPP(hAPP(c_member(U_9889),U_9890),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9891,tc_fun(U_9889,tc_HOL_Obool)),U_9892),U_9893)))
| ! [U_9888] :
( ~ hBOOL(hAPP(hAPP(c_member(U_9889),U_9890),hAPP(U_9893,U_9888)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9891),U_9888),U_9892)) ) )
& ( ? [U_9887] :
( hBOOL(hAPP(hAPP(c_member(U_9889),U_9890),hAPP(U_9893,U_9887)))
& hBOOL(hAPP(hAPP(c_member(U_9891),U_9887),U_9892)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9889),U_9890),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9891,tc_fun(U_9889,tc_HOL_Obool)),U_9892),U_9893))) ) ),
inference(variable_rename,[status(thm)],[f_2739_1]) ).
fof(f_2739_3,plain,
( ! [U_9903,U_9901,U_9899,U_9897,U_9895] :
( hBOOL(hAPP(hAPP(c_member(U_9895),U_9897),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9899,tc_fun(U_9895,tc_HOL_Obool)),U_9901),U_9903)))
| ! [U_9888] :
( ~ hBOOL(hAPP(hAPP(c_member(U_9895),U_9897),hAPP(U_9903,U_9888)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9899),U_9888),U_9901)) ) )
& ! [U_9902,U_9900,U_9898,U_9896,U_9894] :
( ? [U_9887] :
( hBOOL(hAPP(hAPP(c_member(U_9894),U_9896),hAPP(U_9902,U_9887)))
& hBOOL(hAPP(hAPP(c_member(U_9898),U_9887),U_9900)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9894),U_9896),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9898,tc_fun(U_9894,tc_HOL_Obool)),U_9900),U_9902))) ) ),
inference(miniscope,[status(thm)],[f_2739_2]) ).
fof(f_2739_4,plain,
( ! [U_9903,U_9901,U_9899,U_9897,U_9895] :
( hBOOL(hAPP(hAPP(c_member(U_9895),U_9897),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9899,tc_fun(U_9895,tc_HOL_Obool)),U_9901),U_9903)))
| ! [U_9888] :
( ~ hBOOL(hAPP(hAPP(c_member(U_9895),U_9897),hAPP(U_9903,U_9888)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9899),U_9888),U_9901)) ) )
& ! [U_9902,U_9900,U_9898,U_9896,U_9894] :
( ( hBOOL(hAPP(hAPP(c_member(U_9894),U_9896),hAPP(U_9902,sK243(U_9902,U_9900,U_9898,U_9896,U_9894))))
& hBOOL(hAPP(hAPP(c_member(U_9898),sK243(U_9902,U_9900,U_9898,U_9896,U_9894)),U_9900)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9894),U_9896),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9898,tc_fun(U_9894,tc_HOL_Obool)),U_9900),U_9902))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK243]),skolemize(U_9887,sK243(U_9902,U_9900,U_9898,U_9896,U_9894))],[f_2739_3]) ).
cnf(f_2739_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_9898),sK243(U_9902,U_9900,U_9898,U_9896,U_9894)),U_9900))
| ~ hBOOL(hAPP(hAPP(c_member(U_9894),U_9896),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9898,tc_fun(U_9894,tc_HOL_Obool)),U_9900),U_9902))) ),
inference(clausify,[status(thm)],[f_2739_4]) ).
cnf(f_2739_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_9894),U_9896),hAPP(U_9902,sK243(U_9902,U_9900,U_9898,U_9896,U_9894))))
| ~ hBOOL(hAPP(hAPP(c_member(U_9894),U_9896),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9898,tc_fun(U_9894,tc_HOL_Obool)),U_9900),U_9902))) ),
inference(clausify,[status(thm)],[f_2739_4]) ).
cnf(f_2739_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_9895),U_9897),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9899,tc_fun(U_9895,tc_HOL_Obool)),U_9901),U_9903)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9895),U_9897),hAPP(U_9903,U_9888)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9899),U_9888),U_9901)) ),
inference(clausify,[status(thm)],[f_2739_4]) ).
fof(f_2740_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_2740_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_2740_1]) ).
fof(f_2741_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_2741_2,plain,
! [U_9909,U_9908,U_9907,U_9906,U_9905,U_9904] :
( c_Fun_Oinj__on(U_9904,U_9906,U_9908,U_9909)
| ~ c_Fun_Oinj__on(U_9904,U_9905,hAPP(c_Fun_Ocomp(U_9906,U_9905,U_9904,U_9907),U_9908),U_9909) ),
inference(variable_rename,[status(thm)],[f_2741_1]) ).
cnf(f_2741_3,plain,
( c_Fun_Oinj__on(U_9904,U_9906,U_9908,U_9909)
| ~ c_Fun_Oinj__on(U_9904,U_9905,hAPP(c_Fun_Ocomp(U_9906,U_9905,U_9904,U_9907),U_9908),U_9909) ),
inference(clausify,[status(thm)],[f_2741_2]) ).
fof(f_2742_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_2742_2,plain,
! [U_9913,U_9912,U_9911,U_9910] : hAPP(c_Set_Ovimage(U_9910,U_9911,U_9912),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9911,tc_HOL_Obool),U_9913)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9911,tc_HOL_Obool),tc_fun(U_9910,tc_HOL_Obool)),U_9913),c_Set_Ovimage(U_9910,U_9911,U_9912)),
inference(variable_rename,[status(thm)],[f_2742_1]) ).
cnf(f_2742_3,plain,
hAPP(c_Set_Ovimage(U_9910,U_9911,U_9912),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9911,tc_HOL_Obool),U_9913)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9911,tc_HOL_Obool),tc_fun(U_9910,tc_HOL_Obool)),U_9913),c_Set_Ovimage(U_9910,U_9911,U_9912)),
inference(clausify,[status(thm)],[f_2742_2]) ).
fof(f_2743_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_2743_2,plain,
! [U_9916,U_9915,U_9914] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9914,tc_Nat_Onat),U_9915),U_9916)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9914,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_9914),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9915)),U_9916),
inference(variable_rename,[status(thm)],[f_2743_1]) ).
cnf(f_2743_3,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9914,tc_Nat_Onat),U_9915),U_9916)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9914,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_9914),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9915)),U_9916),
inference(clausify,[status(thm)],[f_2743_2]) ).
fof(f_2744_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_2744_2,plain,
! [U_9923,U_9922,U_9921,U_9920,U_9919,U_9918,U_9917] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9917),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9918,U_9917),U_9919),U_9920)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9921,U_9917),U_9922),U_9923)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9918,U_9917),hAPP(hAPP(c_COMBC(U_9918,tc_fun(U_9921,tc_HOL_Obool),U_9917),hAPP(hAPP(c_COMBB(tc_fun(U_9921,U_9917),tc_fun(tc_fun(U_9921,tc_HOL_Obool),U_9917),U_9918),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9921,U_9917)),hAPP(hAPP(c_COMBC(U_9918,tc_fun(U_9921,U_9917),tc_fun(U_9921,U_9917)),hAPP(hAPP(c_COMBB(tc_fun(U_9917,U_9917),tc_fun(tc_fun(U_9921,U_9917),tc_fun(U_9921,U_9917)),U_9918),c_COMBB(U_9917,U_9917,U_9921)),hAPP(hAPP(c_COMBB(U_9917,tc_fun(U_9917,U_9917),U_9918),c_Groups_Otimes__class_Otimes(U_9917)),U_9919))),U_9922))),U_9923)),U_9920)
| ~ class_Rings_Osemiring__0(U_9917) ),
inference(variable_rename,[status(thm)],[f_2744_1]) ).
cnf(f_2744_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9917),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9918,U_9917),U_9919),U_9920)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9921,U_9917),U_9922),U_9923)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9918,U_9917),hAPP(hAPP(c_COMBC(U_9918,tc_fun(U_9921,tc_HOL_Obool),U_9917),hAPP(hAPP(c_COMBB(tc_fun(U_9921,U_9917),tc_fun(tc_fun(U_9921,tc_HOL_Obool),U_9917),U_9918),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9921,U_9917)),hAPP(hAPP(c_COMBC(U_9918,tc_fun(U_9921,U_9917),tc_fun(U_9921,U_9917)),hAPP(hAPP(c_COMBB(tc_fun(U_9917,U_9917),tc_fun(tc_fun(U_9921,U_9917),tc_fun(U_9921,U_9917)),U_9918),c_COMBB(U_9917,U_9917,U_9921)),hAPP(hAPP(c_COMBB(U_9917,tc_fun(U_9917,U_9917),U_9918),c_Groups_Otimes__class_Otimes(U_9917)),U_9919))),U_9922))),U_9923)),U_9920)
| ~ class_Rings_Osemiring__0(U_9917) ),
inference(clausify,[status(thm)],[f_2744_2]) ).
fof(f_2745_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_2745_2,plain,
! [U_9928,U_9927,U_9926,U_9925,U_9924] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9924),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9925,U_9924),U_9926),U_9927)),U_9928) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9925,U_9924),hAPP(hAPP(c_COMBC(U_9925,U_9924,U_9924),hAPP(hAPP(c_COMBB(U_9924,tc_fun(U_9924,U_9924),U_9925),c_Groups_Otimes__class_Otimes(U_9924)),U_9926)),U_9928)),U_9927)
| ~ class_Rings_Osemiring__0(U_9924) ),
inference(variable_rename,[status(thm)],[f_2745_1]) ).
cnf(f_2745_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9924),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9925,U_9924),U_9926),U_9927)),U_9928) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9925,U_9924),hAPP(hAPP(c_COMBC(U_9925,U_9924,U_9924),hAPP(hAPP(c_COMBB(U_9924,tc_fun(U_9924,U_9924),U_9925),c_Groups_Otimes__class_Otimes(U_9924)),U_9926)),U_9928)),U_9927)
| ~ class_Rings_Osemiring__0(U_9924) ),
inference(clausify,[status(thm)],[f_2745_2]) ).
fof(f_2746_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_2746_2,plain,
! [U_9933,U_9932,U_9931,U_9930,U_9929] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9929),U_9930),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9931,U_9929),U_9932),U_9933)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9931,U_9929),hAPP(hAPP(c_COMBB(U_9929,U_9929,U_9931),hAPP(c_Groups_Otimes__class_Otimes(U_9929),U_9930)),U_9932)),U_9933)
| ~ class_Rings_Osemiring__0(U_9929) ),
inference(variable_rename,[status(thm)],[f_2746_1]) ).
cnf(f_2746_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9929),U_9930),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9931,U_9929),U_9932),U_9933)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9931,U_9929),hAPP(hAPP(c_COMBB(U_9929,U_9929,U_9931),hAPP(c_Groups_Otimes__class_Otimes(U_9929),U_9930)),U_9932)),U_9933)
| ~ class_Rings_Osemiring__0(U_9929) ),
inference(clausify,[status(thm)],[f_2746_2]) ).
fof(f_2747_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_2747_2,plain,
! [U_9939,U_9938,U_9937,U_9936,U_9935,U_9934] : hAPP(c_Set_Ovimage(U_9934,U_9935,hAPP(c_Fun_Ocomp(U_9936,U_9935,U_9934,U_9937),U_9938)),U_9939) = hAPP(c_Set_Ovimage(U_9934,U_9936,U_9938),hAPP(c_Set_Ovimage(U_9936,U_9935,U_9937),U_9939)),
inference(variable_rename,[status(thm)],[f_2747_1]) ).
cnf(f_2747_3,plain,
hAPP(c_Set_Ovimage(U_9934,U_9935,hAPP(c_Fun_Ocomp(U_9936,U_9935,U_9934,U_9937),U_9938)),U_9939) = hAPP(c_Set_Ovimage(U_9934,U_9936,U_9938),hAPP(c_Set_Ovimage(U_9936,U_9935,U_9937),U_9939)),
inference(clausify,[status(thm)],[f_2747_2]) ).
fof(f_2748_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_2748_2,plain,
! [U_9946,U_9945,U_9944,U_9943,U_9942,U_9941,U_9940] : hAPP(c_Fun_Ocomp(U_9940,U_9941,U_9942,U_9943),c_Fun_Ofun__upd(U_9942,U_9940,U_9944,U_9945,U_9946)) = c_Fun_Ofun__upd(U_9942,U_9941,hAPP(c_Fun_Ocomp(U_9940,U_9941,U_9942,U_9943),U_9944),U_9945,hAPP(U_9943,U_9946)),
inference(variable_rename,[status(thm)],[f_2748_1]) ).
cnf(f_2748_3,plain,
hAPP(c_Fun_Ocomp(U_9940,U_9941,U_9942,U_9943),c_Fun_Ofun__upd(U_9942,U_9940,U_9944,U_9945,U_9946)) = c_Fun_Ofun__upd(U_9942,U_9941,hAPP(c_Fun_Ocomp(U_9940,U_9941,U_9942,U_9943),U_9944),U_9945,hAPP(U_9943,U_9946)),
inference(clausify,[status(thm)],[f_2748_2]) ).
fof(f_2749_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_2749_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_2749_1]) ).
fof(f_2750_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_2750_2,plain,
! [U_9951,U_9950,U_9949,U_9948,U_9947] :
( hAPP(c_Fun_Ocomp(U_9948,U_9948,U_9948,hAPP(U_9949,U_9950)),hAPP(U_9949,U_9951)) = hAPP(c_Fun_Ocomp(U_9948,U_9948,U_9948,hAPP(U_9949,U_9951)),hAPP(U_9949,U_9950))
| ~ c_Finite__Set_Ofun__left__comm(U_9947,U_9948,U_9949) ),
inference(variable_rename,[status(thm)],[f_2750_1]) ).
fof(f_2750_3,plain,
! [U_9951,U_9950,U_9949,U_9948] :
( ! [U_9947] : ~ c_Finite__Set_Ofun__left__comm(U_9947,U_9948,U_9949)
| hAPP(c_Fun_Ocomp(U_9948,U_9948,U_9948,hAPP(U_9949,U_9950)),hAPP(U_9949,U_9951)) = hAPP(c_Fun_Ocomp(U_9948,U_9948,U_9948,hAPP(U_9949,U_9951)),hAPP(U_9949,U_9950)) ),
inference(miniscope,[status(thm)],[f_2750_2]) ).
cnf(f_2750_4,plain,
( ~ c_Finite__Set_Ofun__left__comm(U_9947,U_9948,U_9949)
| hAPP(c_Fun_Ocomp(U_9948,U_9948,U_9948,hAPP(U_9949,U_9950)),hAPP(U_9949,U_9951)) = hAPP(c_Fun_Ocomp(U_9948,U_9948,U_9948,hAPP(U_9949,U_9951)),hAPP(U_9949,U_9950)) ),
inference(clausify,[status(thm)],[f_2750_3]) ).
fof(f_2751_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_2751_2,plain,
! [U_9955,U_9954,U_9953,U_9952] : hAPP(c_Finite__Set_Ofold__image(U_9952,U_9953,U_9954),U_9955) = c_Finite__Set_Ofold(U_9953,U_9952,hAPP(hAPP(c_COMBB(U_9952,tc_fun(U_9952,U_9952),U_9953),U_9954),U_9955)),
inference(variable_rename,[status(thm)],[f_2751_1]) ).
cnf(f_2751_3,plain,
hAPP(c_Finite__Set_Ofold__image(U_9952,U_9953,U_9954),U_9955) = c_Finite__Set_Ofold(U_9953,U_9952,hAPP(hAPP(c_COMBB(U_9952,tc_fun(U_9952,U_9952),U_9953),U_9954),U_9955)),
inference(clausify,[status(thm)],[f_2751_2]) ).
fof(f_2752_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_2752_2,plain,
! [U_9959,U_9958,U_9957,U_9956] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_9956),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9957,tc_Int_Oint),U_9958),U_9959)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9957,U_9956),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_9956,U_9957),c_Int_Oring__1__class_Oof__int(U_9956)),U_9958)),U_9959)
| ~ class_Rings_Oring__1(U_9956) ),
inference(variable_rename,[status(thm)],[f_2752_1]) ).
cnf(f_2752_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_9956),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9957,tc_Int_Oint),U_9958),U_9959)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9957,U_9956),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_9956,U_9957),c_Int_Oring__1__class_Oof__int(U_9956)),U_9958)),U_9959)
| ~ class_Rings_Oring__1(U_9956) ),
inference(clausify,[status(thm)],[f_2752_2]) ).
fof(f_2753_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_2753_2,plain,
! [U_9964,U_9963,U_9962,U_9961,U_9960] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9960),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9961,U_9960),U_9962),U_9963)),U_9964) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9961,U_9960),hAPP(hAPP(c_COMBC(U_9961,U_9960,U_9960),hAPP(hAPP(c_COMBB(U_9960,tc_fun(U_9960,U_9960),U_9961),c_Rings_Oinverse__class_Odivide(U_9960)),U_9962)),U_9964)),U_9963)
| ~ class_Fields_Ofield(U_9960) ),
inference(variable_rename,[status(thm)],[f_2753_1]) ).
cnf(f_2753_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9960),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9961,U_9960),U_9962),U_9963)),U_9964) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9961,U_9960),hAPP(hAPP(c_COMBC(U_9961,U_9960,U_9960),hAPP(hAPP(c_COMBB(U_9960,tc_fun(U_9960,U_9960),U_9961),c_Rings_Oinverse__class_Odivide(U_9960)),U_9962)),U_9964)),U_9963)
| ~ class_Fields_Ofield(U_9960) ),
inference(clausify,[status(thm)],[f_2753_2]) ).
fof(f_2754_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_2754_2,plain,
! [U_9966,U_9965] : 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_9965),U_9966),
inference(variable_rename,[status(thm)],[f_2754_1]) ).
cnf(f_2754_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_9965),U_9966),
inference(clausify,[status(thm)],[f_2754_2]) ).
fof(f_2755_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_2755_2,plain,
! [U_9973,U_9972,U_9971,U_9970,U_9969] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9969),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9970,U_9969),U_9971),U_9972)),U_9973))
| ? [U_9968] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9969),hAPP(U_9972,U_9968)),U_9973))
& hBOOL(hAPP(hAPP(c_member(U_9970),U_9968),U_9971)) ) )
& ( ! [U_9967] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9969),hAPP(U_9972,U_9967)),U_9973))
| ~ hBOOL(hAPP(hAPP(c_member(U_9970),U_9967),U_9971)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9969),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9970,U_9969),U_9971),U_9972)),U_9973)) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9969) ),
inference(variable_rename,[status(thm)],[f_2755_1]) ).
fof(f_2755_3,plain,
! [U_9973,U_9972,U_9971,U_9970,U_9969] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9969),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9970,U_9969),U_9971),U_9972)),U_9973))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9969),hAPP(U_9972,sK244(U_9973,U_9972,U_9971,U_9970,U_9969))),U_9973))
& hBOOL(hAPP(hAPP(c_member(U_9970),sK244(U_9973,U_9972,U_9971,U_9970,U_9969)),U_9971)) ) )
& ( ! [U_9967] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9969),hAPP(U_9972,U_9967)),U_9973))
| ~ hBOOL(hAPP(hAPP(c_member(U_9970),U_9967),U_9971)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9969),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9970,U_9969),U_9971),U_9972)),U_9973)) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9969) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK244]),skolemize(U_9968,sK244(U_9973,U_9972,U_9971,U_9970,U_9969))],[f_2755_2]) ).
cnf(f_2755_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9969),hAPP(U_9972,U_9967)),U_9973))
| ~ hBOOL(hAPP(hAPP(c_member(U_9970),U_9967),U_9971))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9969),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9970,U_9969),U_9971),U_9972)),U_9973))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9969) ),
inference(clausify,[status(thm)],[f_2755_3]) ).
cnf(f_2755_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_9970),sK244(U_9973,U_9972,U_9971,U_9970,U_9969)),U_9971))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9969),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9970,U_9969),U_9971),U_9972)),U_9973))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9969) ),
inference(clausify,[status(thm)],[f_2755_3]) ).
cnf(f_2755_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9969),hAPP(U_9972,sK244(U_9973,U_9972,U_9971,U_9970,U_9969))),U_9973))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9969),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9970,U_9969),U_9971),U_9972)),U_9973))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9969) ),
inference(clausify,[status(thm)],[f_2755_3]) ).
fof(f_2756_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_2756_2,plain,
! [U_9977,U_9976,U_9975,U_9974] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9974,tc_fun(U_9975,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9974,tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool),tc_fun(U_9975,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9975,tc_fun(tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool),tc_fun(U_9975,tc_HOL_Obool)),U_9974),c_COMBC(U_9975,tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9975,tc_prod(U_9974,U_9975)),tc_fun(U_9975,tc_fun(tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool),tc_HOL_Obool)),U_9974),hAPP(c_COMBB(tc_prod(U_9974,U_9975),tc_fun(tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool),tc_HOL_Obool),U_9975),c_member(tc_prod(U_9974,U_9975)))),c_Product__Type_OPair(U_9974,U_9975)))),U_9976)),hAPP(hAPP(c_COMBC(U_9974,tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool),tc_fun(U_9975,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9975,tc_fun(tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool),tc_fun(U_9975,tc_HOL_Obool)),U_9974),c_COMBC(U_9975,tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9975,tc_prod(U_9974,U_9975)),tc_fun(U_9975,tc_fun(tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool),tc_HOL_Obool)),U_9974),hAPP(c_COMBB(tc_prod(U_9974,U_9975),tc_fun(tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool),tc_HOL_Obool),U_9975),c_member(tc_prod(U_9974,U_9975)))),c_Product__Type_OPair(U_9974,U_9975)))),U_9977)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool)),U_9976),U_9977)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool)),U_9976),U_9977))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9974,tc_fun(U_9975,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9974,tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool),tc_fun(U_9975,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9975,tc_fun(tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool),tc_fun(U_9975,tc_HOL_Obool)),U_9974),c_COMBC(U_9975,tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9975,tc_prod(U_9974,U_9975)),tc_fun(U_9975,tc_fun(tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool),tc_HOL_Obool)),U_9974),hAPP(c_COMBB(tc_prod(U_9974,U_9975),tc_fun(tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool),tc_HOL_Obool),U_9975),c_member(tc_prod(U_9974,U_9975)))),c_Product__Type_OPair(U_9974,U_9975)))),U_9976)),hAPP(hAPP(c_COMBC(U_9974,tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool),tc_fun(U_9975,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9975,tc_fun(tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool),tc_fun(U_9975,tc_HOL_Obool)),U_9974),c_COMBC(U_9975,tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9975,tc_prod(U_9974,U_9975)),tc_fun(U_9975,tc_fun(tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool),tc_HOL_Obool)),U_9974),hAPP(c_COMBB(tc_prod(U_9974,U_9975),tc_fun(tc_fun(tc_prod(U_9974,U_9975),tc_HOL_Obool),tc_HOL_Obool),U_9975),c_member(tc_prod(U_9974,U_9975)))),c_Product__Type_OPair(U_9974,U_9975)))),U_9977))) ) ),
inference(variable_rename,[status(thm)],[f_2756_1]) ).
fof(f_2756_3,plain,
( ! [U_9985,U_9983,U_9981,U_9979] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9979,tc_fun(U_9981,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9979,tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool),tc_fun(U_9981,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9981,tc_fun(tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool),tc_fun(U_9981,tc_HOL_Obool)),U_9979),c_COMBC(U_9981,tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9981,tc_prod(U_9979,U_9981)),tc_fun(U_9981,tc_fun(tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool),tc_HOL_Obool)),U_9979),hAPP(c_COMBB(tc_prod(U_9979,U_9981),tc_fun(tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool),tc_HOL_Obool),U_9981),c_member(tc_prod(U_9979,U_9981)))),c_Product__Type_OPair(U_9979,U_9981)))),U_9983)),hAPP(hAPP(c_COMBC(U_9979,tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool),tc_fun(U_9981,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9981,tc_fun(tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool),tc_fun(U_9981,tc_HOL_Obool)),U_9979),c_COMBC(U_9981,tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9981,tc_prod(U_9979,U_9981)),tc_fun(U_9981,tc_fun(tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool),tc_HOL_Obool)),U_9979),hAPP(c_COMBB(tc_prod(U_9979,U_9981),tc_fun(tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool),tc_HOL_Obool),U_9981),c_member(tc_prod(U_9979,U_9981)))),c_Product__Type_OPair(U_9979,U_9981)))),U_9985)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool)),U_9983),U_9985)) )
& ! [U_9984,U_9982,U_9980,U_9978] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool)),U_9982),U_9984))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9978,tc_fun(U_9980,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9978,tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool),tc_fun(U_9980,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9980,tc_fun(tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool),tc_fun(U_9980,tc_HOL_Obool)),U_9978),c_COMBC(U_9980,tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9980,tc_prod(U_9978,U_9980)),tc_fun(U_9980,tc_fun(tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool),tc_HOL_Obool)),U_9978),hAPP(c_COMBB(tc_prod(U_9978,U_9980),tc_fun(tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool),tc_HOL_Obool),U_9980),c_member(tc_prod(U_9978,U_9980)))),c_Product__Type_OPair(U_9978,U_9980)))),U_9982)),hAPP(hAPP(c_COMBC(U_9978,tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool),tc_fun(U_9980,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9980,tc_fun(tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool),tc_fun(U_9980,tc_HOL_Obool)),U_9978),c_COMBC(U_9980,tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9980,tc_prod(U_9978,U_9980)),tc_fun(U_9980,tc_fun(tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool),tc_HOL_Obool)),U_9978),hAPP(c_COMBB(tc_prod(U_9978,U_9980),tc_fun(tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool),tc_HOL_Obool),U_9980),c_member(tc_prod(U_9978,U_9980)))),c_Product__Type_OPair(U_9978,U_9980)))),U_9984))) ) ),
inference(miniscope,[status(thm)],[f_2756_2]) ).
cnf(f_2756_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool)),U_9982),U_9984))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9978,tc_fun(U_9980,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9978,tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool),tc_fun(U_9980,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9980,tc_fun(tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool),tc_fun(U_9980,tc_HOL_Obool)),U_9978),c_COMBC(U_9980,tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9980,tc_prod(U_9978,U_9980)),tc_fun(U_9980,tc_fun(tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool),tc_HOL_Obool)),U_9978),hAPP(c_COMBB(tc_prod(U_9978,U_9980),tc_fun(tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool),tc_HOL_Obool),U_9980),c_member(tc_prod(U_9978,U_9980)))),c_Product__Type_OPair(U_9978,U_9980)))),U_9982)),hAPP(hAPP(c_COMBC(U_9978,tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool),tc_fun(U_9980,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9980,tc_fun(tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool),tc_fun(U_9980,tc_HOL_Obool)),U_9978),c_COMBC(U_9980,tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9980,tc_prod(U_9978,U_9980)),tc_fun(U_9980,tc_fun(tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool),tc_HOL_Obool)),U_9978),hAPP(c_COMBB(tc_prod(U_9978,U_9980),tc_fun(tc_fun(tc_prod(U_9978,U_9980),tc_HOL_Obool),tc_HOL_Obool),U_9980),c_member(tc_prod(U_9978,U_9980)))),c_Product__Type_OPair(U_9978,U_9980)))),U_9984))) ),
inference(clausify,[status(thm)],[f_2756_3]) ).
cnf(f_2756_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9979,tc_fun(U_9981,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9979,tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool),tc_fun(U_9981,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9981,tc_fun(tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool),tc_fun(U_9981,tc_HOL_Obool)),U_9979),c_COMBC(U_9981,tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9981,tc_prod(U_9979,U_9981)),tc_fun(U_9981,tc_fun(tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool),tc_HOL_Obool)),U_9979),hAPP(c_COMBB(tc_prod(U_9979,U_9981),tc_fun(tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool),tc_HOL_Obool),U_9981),c_member(tc_prod(U_9979,U_9981)))),c_Product__Type_OPair(U_9979,U_9981)))),U_9983)),hAPP(hAPP(c_COMBC(U_9979,tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool),tc_fun(U_9981,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9981,tc_fun(tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool),tc_fun(U_9981,tc_HOL_Obool)),U_9979),c_COMBC(U_9981,tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9981,tc_prod(U_9979,U_9981)),tc_fun(U_9981,tc_fun(tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool),tc_HOL_Obool)),U_9979),hAPP(c_COMBB(tc_prod(U_9979,U_9981),tc_fun(tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool),tc_HOL_Obool),U_9981),c_member(tc_prod(U_9979,U_9981)))),c_Product__Type_OPair(U_9979,U_9981)))),U_9985)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9979,U_9981),tc_HOL_Obool)),U_9983),U_9985)) ),
inference(clausify,[status(thm)],[f_2756_3]) ).
fof(f_2757_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_2757_2,plain,
! [U_9992,U_9991,U_9990,U_9989,U_9988] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9988,tc_HOL_Obool)),U_9989),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9990,tc_fun(U_9988,tc_HOL_Obool)),U_9991),U_9992)))
| ? [U_9987] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9988,tc_HOL_Obool)),U_9989),hAPP(U_9992,U_9987)))
& hBOOL(hAPP(hAPP(c_member(U_9990),U_9987),U_9991)) ) )
& ( ! [U_9986] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9988,tc_HOL_Obool)),U_9989),hAPP(U_9992,U_9986)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9990),U_9986),U_9991)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9988,tc_HOL_Obool)),U_9989),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9990,tc_fun(U_9988,tc_HOL_Obool)),U_9991),U_9992))) ) ),
inference(variable_rename,[status(thm)],[f_2757_1]) ).
fof(f_2757_3,plain,
( ! [U_10002,U_10000,U_9998,U_9996,U_9994] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9994,tc_HOL_Obool)),U_9996),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9998,tc_fun(U_9994,tc_HOL_Obool)),U_10000),U_10002)))
| ? [U_9987] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9994,tc_HOL_Obool)),U_9996),hAPP(U_10002,U_9987)))
& hBOOL(hAPP(hAPP(c_member(U_9998),U_9987),U_10000)) ) )
& ! [U_10001,U_9999,U_9997,U_9995,U_9993] :
( ! [U_9986] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9993,tc_HOL_Obool)),U_9995),hAPP(U_10001,U_9986)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9997),U_9986),U_9999)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9993,tc_HOL_Obool)),U_9995),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9997,tc_fun(U_9993,tc_HOL_Obool)),U_9999),U_10001))) ) ),
inference(miniscope,[status(thm)],[f_2757_2]) ).
fof(f_2757_4,plain,
( ! [U_10002,U_10000,U_9998,U_9996,U_9994] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9994,tc_HOL_Obool)),U_9996),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9998,tc_fun(U_9994,tc_HOL_Obool)),U_10000),U_10002)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9994,tc_HOL_Obool)),U_9996),hAPP(U_10002,sK245(U_10002,U_10000,U_9998,U_9996,U_9994))))
& hBOOL(hAPP(hAPP(c_member(U_9998),sK245(U_10002,U_10000,U_9998,U_9996,U_9994)),U_10000)) ) )
& ! [U_10001,U_9999,U_9997,U_9995,U_9993] :
( ! [U_9986] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9993,tc_HOL_Obool)),U_9995),hAPP(U_10001,U_9986)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9997),U_9986),U_9999)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9993,tc_HOL_Obool)),U_9995),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9997,tc_fun(U_9993,tc_HOL_Obool)),U_9999),U_10001))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK245]),skolemize(U_9987,sK245(U_10002,U_10000,U_9998,U_9996,U_9994))],[f_2757_3]) ).
cnf(f_2757_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9993,tc_HOL_Obool)),U_9995),hAPP(U_10001,U_9986)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9997),U_9986),U_9999))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9993,tc_HOL_Obool)),U_9995),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9997,tc_fun(U_9993,tc_HOL_Obool)),U_9999),U_10001))) ),
inference(clausify,[status(thm)],[f_2757_4]) ).
cnf(f_2757_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_9998),sK245(U_10002,U_10000,U_9998,U_9996,U_9994)),U_10000))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9994,tc_HOL_Obool)),U_9996),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9998,tc_fun(U_9994,tc_HOL_Obool)),U_10000),U_10002))) ),
inference(clausify,[status(thm)],[f_2757_4]) ).
cnf(f_2757_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9994,tc_HOL_Obool)),U_9996),hAPP(U_10002,sK245(U_10002,U_10000,U_9998,U_9996,U_9994))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9994,tc_HOL_Obool)),U_9996),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9998,tc_fun(U_9994,tc_HOL_Obool)),U_10000),U_10002))) ),
inference(clausify,[status(thm)],[f_2757_4]) ).
fof(f_2758_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_2758_2,plain,
! [U_10005,U_10004,U_10003] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10003,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10003,tc_fun(U_10003,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10003)),U_10004)),hAPP(hAPP(c_COMBC(U_10003,tc_fun(U_10003,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10003)),U_10005)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10003,tc_HOL_Obool)),U_10004),U_10005)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10003,tc_HOL_Obool)),U_10004),U_10005))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10003,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10003,tc_fun(U_10003,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10003)),U_10004)),hAPP(hAPP(c_COMBC(U_10003,tc_fun(U_10003,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10003)),U_10005))) ) ),
inference(variable_rename,[status(thm)],[f_2758_1]) ).
fof(f_2758_3,plain,
( ! [U_10011,U_10009,U_10007] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10007,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10007,tc_fun(U_10007,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10007)),U_10009)),hAPP(hAPP(c_COMBC(U_10007,tc_fun(U_10007,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10007)),U_10011)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10007,tc_HOL_Obool)),U_10009),U_10011)) )
& ! [U_10010,U_10008,U_10006] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10006,tc_HOL_Obool)),U_10008),U_10010))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10006,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10006,tc_fun(U_10006,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10006)),U_10008)),hAPP(hAPP(c_COMBC(U_10006,tc_fun(U_10006,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10006)),U_10010))) ) ),
inference(miniscope,[status(thm)],[f_2758_2]) ).
cnf(f_2758_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10006,tc_HOL_Obool)),U_10008),U_10010))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10006,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10006,tc_fun(U_10006,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10006)),U_10008)),hAPP(hAPP(c_COMBC(U_10006,tc_fun(U_10006,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10006)),U_10010))) ),
inference(clausify,[status(thm)],[f_2758_3]) ).
cnf(f_2758_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10007,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10007,tc_fun(U_10007,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10007)),U_10009)),hAPP(hAPP(c_COMBC(U_10007,tc_fun(U_10007,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10007)),U_10011)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10007,tc_HOL_Obool)),U_10009),U_10011)) ),
inference(clausify,[status(thm)],[f_2758_3]) ).
fof(f_2759_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_2759_2,plain,
! [U_10016,U_10015,U_10014,U_10013,U_10012] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10015,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10012,tc_fun(U_10015,tc_HOL_Obool)),U_10014),U_10016)),hAPP(U_10016,U_10013)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10012),U_10013),U_10014)) ),
inference(variable_rename,[status(thm)],[f_2759_1]) ).
cnf(f_2759_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10015,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10012,tc_fun(U_10015,tc_HOL_Obool)),U_10014),U_10016)),hAPP(U_10016,U_10013)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10012),U_10013),U_10014)) ),
inference(clausify,[status(thm)],[f_2759_2]) ).
fof(f_2760_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_2760_2,plain,
! [U_10023,U_10022,U_10021,U_10020,U_10019] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10019),U_10020),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10021,U_10019),U_10022),U_10023)))
| ? [U_10018] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10019),U_10020),hAPP(U_10023,U_10018)))
& hBOOL(hAPP(hAPP(c_member(U_10021),U_10018),U_10022)) ) )
& ( ! [U_10017] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10019),U_10020),hAPP(U_10023,U_10017)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10021),U_10017),U_10022)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10019),U_10020),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10021,U_10019),U_10022),U_10023))) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10019) ),
inference(variable_rename,[status(thm)],[f_2760_1]) ).
fof(f_2760_3,plain,
! [U_10023,U_10022,U_10021,U_10020,U_10019] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10019),U_10020),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10021,U_10019),U_10022),U_10023)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10019),U_10020),hAPP(U_10023,sK246(U_10023,U_10022,U_10021,U_10020,U_10019))))
& hBOOL(hAPP(hAPP(c_member(U_10021),sK246(U_10023,U_10022,U_10021,U_10020,U_10019)),U_10022)) ) )
& ( ! [U_10017] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10019),U_10020),hAPP(U_10023,U_10017)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10021),U_10017),U_10022)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10019),U_10020),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10021,U_10019),U_10022),U_10023))) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10019) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK246]),skolemize(U_10018,sK246(U_10023,U_10022,U_10021,U_10020,U_10019))],[f_2760_2]) ).
cnf(f_2760_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10019),U_10020),hAPP(U_10023,U_10017)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10021),U_10017),U_10022))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10019),U_10020),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10021,U_10019),U_10022),U_10023)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10019) ),
inference(clausify,[status(thm)],[f_2760_3]) ).
cnf(f_2760_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_10021),sK246(U_10023,U_10022,U_10021,U_10020,U_10019)),U_10022))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10019),U_10020),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10021,U_10019),U_10022),U_10023)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10019) ),
inference(clausify,[status(thm)],[f_2760_3]) ).
cnf(f_2760_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10019),U_10020),hAPP(U_10023,sK246(U_10023,U_10022,U_10021,U_10020,U_10019))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10019),U_10020),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10021,U_10019),U_10022),U_10023)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10019) ),
inference(clausify,[status(thm)],[f_2760_3]) ).
fof(f_2761_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_2761_2,plain,
! [U_10025,U_10024] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10024)),U_10025))
| ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10024),U_10025)) )
& ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10024),U_10025))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10024)),U_10025)) ) ),
inference(variable_rename,[status(thm)],[f_2761_1]) ).
fof(f_2761_3,plain,
( ! [U_10029,U_10027] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10027)),U_10029))
| ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10027),U_10029)) )
& ! [U_10028,U_10026] :
( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10026),U_10028))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10026)),U_10028)) ) ),
inference(miniscope,[status(thm)],[f_2761_2]) ).
cnf(f_2761_4,plain,
( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10026),U_10028))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10026)),U_10028)) ),
inference(clausify,[status(thm)],[f_2761_3]) ).
cnf(f_2761_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10027)),U_10029))
| ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10027),U_10029)) ),
inference(clausify,[status(thm)],[f_2761_3]) ).
fof(f_2762_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_2762_2,plain,
! [U_10036,U_10035,U_10034,U_10033,U_10032] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10032,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10033,tc_fun(U_10032,tc_HOL_Obool)),U_10034),U_10035)),U_10036))
| ? [U_10031] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10032,tc_HOL_Obool)),hAPP(U_10035,U_10031)),U_10036))
& hBOOL(hAPP(hAPP(c_member(U_10033),U_10031),U_10034)) ) )
& ( ! [U_10030] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10032,tc_HOL_Obool)),hAPP(U_10035,U_10030)),U_10036))
| ~ hBOOL(hAPP(hAPP(c_member(U_10033),U_10030),U_10034)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10032,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10033,tc_fun(U_10032,tc_HOL_Obool)),U_10034),U_10035)),U_10036)) ) ),
inference(variable_rename,[status(thm)],[f_2762_1]) ).
fof(f_2762_3,plain,
( ! [U_10046,U_10044,U_10042,U_10040,U_10038] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10038,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10040,tc_fun(U_10038,tc_HOL_Obool)),U_10042),U_10044)),U_10046))
| ? [U_10031] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10038,tc_HOL_Obool)),hAPP(U_10044,U_10031)),U_10046))
& hBOOL(hAPP(hAPP(c_member(U_10040),U_10031),U_10042)) ) )
& ! [U_10045,U_10043,U_10041,U_10039,U_10037] :
( ! [U_10030] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10037,tc_HOL_Obool)),hAPP(U_10043,U_10030)),U_10045))
| ~ hBOOL(hAPP(hAPP(c_member(U_10039),U_10030),U_10041)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10037,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10039,tc_fun(U_10037,tc_HOL_Obool)),U_10041),U_10043)),U_10045)) ) ),
inference(miniscope,[status(thm)],[f_2762_2]) ).
fof(f_2762_4,plain,
( ! [U_10046,U_10044,U_10042,U_10040,U_10038] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10038,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10040,tc_fun(U_10038,tc_HOL_Obool)),U_10042),U_10044)),U_10046))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10038,tc_HOL_Obool)),hAPP(U_10044,sK247(U_10046,U_10044,U_10042,U_10040,U_10038))),U_10046))
& hBOOL(hAPP(hAPP(c_member(U_10040),sK247(U_10046,U_10044,U_10042,U_10040,U_10038)),U_10042)) ) )
& ! [U_10045,U_10043,U_10041,U_10039,U_10037] :
( ! [U_10030] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10037,tc_HOL_Obool)),hAPP(U_10043,U_10030)),U_10045))
| ~ hBOOL(hAPP(hAPP(c_member(U_10039),U_10030),U_10041)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10037,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10039,tc_fun(U_10037,tc_HOL_Obool)),U_10041),U_10043)),U_10045)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK247]),skolemize(U_10031,sK247(U_10046,U_10044,U_10042,U_10040,U_10038))],[f_2762_3]) ).
cnf(f_2762_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10037,tc_HOL_Obool)),hAPP(U_10043,U_10030)),U_10045))
| ~ hBOOL(hAPP(hAPP(c_member(U_10039),U_10030),U_10041))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10037,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10039,tc_fun(U_10037,tc_HOL_Obool)),U_10041),U_10043)),U_10045)) ),
inference(clausify,[status(thm)],[f_2762_4]) ).
cnf(f_2762_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_10040),sK247(U_10046,U_10044,U_10042,U_10040,U_10038)),U_10042))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10038,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10040,tc_fun(U_10038,tc_HOL_Obool)),U_10042),U_10044)),U_10046)) ),
inference(clausify,[status(thm)],[f_2762_4]) ).
cnf(f_2762_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10038,tc_HOL_Obool)),hAPP(U_10044,sK247(U_10046,U_10044,U_10042,U_10040,U_10038))),U_10046))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10038,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10040,tc_fun(U_10038,tc_HOL_Obool)),U_10042),U_10044)),U_10046)) ),
inference(clausify,[status(thm)],[f_2762_4]) ).
fof(f_2763_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_2763_2,plain,
! [U_10051,U_10050,U_10049,U_10048,U_10047] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10048,U_10047),hAPP(hAPP(c_COMBS(U_10048,U_10047,U_10047),hAPP(hAPP(c_COMBB(U_10047,tc_fun(U_10047,U_10047),U_10048),c_Groups_Oplus__class_Oplus(U_10047)),U_10049)),U_10050)),U_10051) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10047),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10048,U_10047),U_10049),U_10051)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10048,U_10047),U_10050),U_10051))
| ~ class_Groups_Ocomm__monoid__add(U_10047) ),
inference(variable_rename,[status(thm)],[f_2763_1]) ).
cnf(f_2763_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10048,U_10047),hAPP(hAPP(c_COMBS(U_10048,U_10047,U_10047),hAPP(hAPP(c_COMBB(U_10047,tc_fun(U_10047,U_10047),U_10048),c_Groups_Oplus__class_Oplus(U_10047)),U_10049)),U_10050)),U_10051) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10047),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10048,U_10047),U_10049),U_10051)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10048,U_10047),U_10050),U_10051))
| ~ class_Groups_Ocomm__monoid__add(U_10047) ),
inference(clausify,[status(thm)],[f_2763_2]) ).
fof(f_2764_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_2764_2,plain,
! [U_10058,U_10057,U_10056,U_10055,U_10054] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10054),U_10055),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10056,U_10054),U_10057),U_10058)))
| ! [U_10053] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10054),U_10055),hAPP(U_10058,U_10053)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10056),U_10053),U_10057)) ) )
& ( ? [U_10052] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10054),U_10055),hAPP(U_10058,U_10052)))
& hBOOL(hAPP(hAPP(c_member(U_10056),U_10052),U_10057)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10054),U_10055),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10056,U_10054),U_10057),U_10058))) ) )
| ~ class_Orderings_Olinorder(U_10054)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10054) ),
inference(variable_rename,[status(thm)],[f_2764_1]) ).
fof(f_2764_3,plain,
! [U_10058,U_10057,U_10056,U_10055,U_10054] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10054),U_10055),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10056,U_10054),U_10057),U_10058)))
| ! [U_10053] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10054),U_10055),hAPP(U_10058,U_10053)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10056),U_10053),U_10057)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10054),U_10055),hAPP(U_10058,sK248(U_10058,U_10057,U_10056,U_10055,U_10054))))
& hBOOL(hAPP(hAPP(c_member(U_10056),sK248(U_10058,U_10057,U_10056,U_10055,U_10054)),U_10057)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10054),U_10055),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10056,U_10054),U_10057),U_10058))) ) )
| ~ class_Orderings_Olinorder(U_10054)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10054) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK248]),skolemize(U_10052,sK248(U_10058,U_10057,U_10056,U_10055,U_10054))],[f_2764_2]) ).
cnf(f_2764_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_10056),sK248(U_10058,U_10057,U_10056,U_10055,U_10054)),U_10057))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10054),U_10055),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10056,U_10054),U_10057),U_10058)))
| ~ class_Orderings_Olinorder(U_10054)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10054) ),
inference(clausify,[status(thm)],[f_2764_3]) ).
cnf(f_2764_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10054),U_10055),hAPP(U_10058,sK248(U_10058,U_10057,U_10056,U_10055,U_10054))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10054),U_10055),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10056,U_10054),U_10057),U_10058)))
| ~ class_Orderings_Olinorder(U_10054)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10054) ),
inference(clausify,[status(thm)],[f_2764_3]) ).
cnf(f_2764_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10054),U_10055),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10056,U_10054),U_10057),U_10058)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10054),U_10055),hAPP(U_10058,U_10053)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10056),U_10053),U_10057))
| ~ class_Orderings_Olinorder(U_10054)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10054) ),
inference(clausify,[status(thm)],[f_2764_3]) ).
fof(f_2765_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_2765_2,plain,
! [U_10065,U_10064,U_10063,U_10062,U_10061] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10061),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10062,U_10061),U_10063),U_10064)),U_10065))
| ! [U_10060] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10061),hAPP(U_10064,U_10060)),U_10065))
| ~ hBOOL(hAPP(hAPP(c_member(U_10062),U_10060),U_10063)) ) )
& ( ? [U_10059] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10061),hAPP(U_10064,U_10059)),U_10065))
& hBOOL(hAPP(hAPP(c_member(U_10062),U_10059),U_10063)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10061),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10062,U_10061),U_10063),U_10064)),U_10065)) ) )
| ~ class_Orderings_Olinorder(U_10061)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10061) ),
inference(variable_rename,[status(thm)],[f_2765_1]) ).
fof(f_2765_3,plain,
! [U_10065,U_10064,U_10063,U_10062,U_10061] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10061),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10062,U_10061),U_10063),U_10064)),U_10065))
| ! [U_10060] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10061),hAPP(U_10064,U_10060)),U_10065))
| ~ hBOOL(hAPP(hAPP(c_member(U_10062),U_10060),U_10063)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10061),hAPP(U_10064,sK249(U_10065,U_10064,U_10063,U_10062,U_10061))),U_10065))
& hBOOL(hAPP(hAPP(c_member(U_10062),sK249(U_10065,U_10064,U_10063,U_10062,U_10061)),U_10063)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10061),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10062,U_10061),U_10063),U_10064)),U_10065)) ) )
| ~ class_Orderings_Olinorder(U_10061)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10061) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK249]),skolemize(U_10059,sK249(U_10065,U_10064,U_10063,U_10062,U_10061))],[f_2765_2]) ).
cnf(f_2765_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_10062),sK249(U_10065,U_10064,U_10063,U_10062,U_10061)),U_10063))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10061),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10062,U_10061),U_10063),U_10064)),U_10065))
| ~ class_Orderings_Olinorder(U_10061)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10061) ),
inference(clausify,[status(thm)],[f_2765_3]) ).
cnf(f_2765_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10061),hAPP(U_10064,sK249(U_10065,U_10064,U_10063,U_10062,U_10061))),U_10065))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10061),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10062,U_10061),U_10063),U_10064)),U_10065))
| ~ class_Orderings_Olinorder(U_10061)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10061) ),
inference(clausify,[status(thm)],[f_2765_3]) ).
cnf(f_2765_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10061),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10062,U_10061),U_10063),U_10064)),U_10065))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10061),hAPP(U_10064,U_10060)),U_10065))
| ~ hBOOL(hAPP(hAPP(c_member(U_10062),U_10060),U_10063))
| ~ class_Orderings_Olinorder(U_10061)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10061) ),
inference(clausify,[status(thm)],[f_2765_3]) ).
fof(f_2766_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_2766_2,plain,
! [U_10070,U_10069,U_10068,U_10067,U_10066] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10066),hAPP(U_10070,U_10068)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10067,U_10066),U_10069),U_10070)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10067),U_10068),U_10069))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10066) ),
inference(variable_rename,[status(thm)],[f_2766_1]) ).
cnf(f_2766_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10066),hAPP(U_10070,U_10068)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10067,U_10066),U_10069),U_10070)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10067),U_10068),U_10069))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10066) ),
inference(clausify,[status(thm)],[f_2766_2]) ).
fof(f_2767_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_2767_2,plain,
! [U_10071] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10071) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10071)),
inference(variable_rename,[status(thm)],[f_2767_1]) ).
cnf(f_2767_3,plain,
hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10071) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10071)),
inference(clausify,[status(thm)],[f_2767_2]) ).
fof(f_2768_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_2768_2,plain,
! [U_10076,U_10075,U_10074,U_10073,U_10072] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10075,tc_HOL_Obool)),hAPP(U_10076,U_10073)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10072,tc_fun(U_10075,tc_HOL_Obool)),U_10074),U_10076)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10072),U_10073),U_10074)) ),
inference(variable_rename,[status(thm)],[f_2768_1]) ).
cnf(f_2768_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10075,tc_HOL_Obool)),hAPP(U_10076,U_10073)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10072,tc_fun(U_10075,tc_HOL_Obool)),U_10074),U_10076)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10072),U_10073),U_10074)) ),
inference(clausify,[status(thm)],[f_2768_2]) ).
fof(f_2769_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_2769_2,plain,
! [U_10081,U_10080,U_10079,U_10078,U_10077] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10078,U_10077),hAPP(hAPP(c_COMBS(U_10078,U_10077,U_10077),hAPP(hAPP(c_COMBB(U_10077,tc_fun(U_10077,U_10077),U_10078),c_Groups_Oplus__class_Oplus(U_10077)),U_10080)),U_10081)),U_10079) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10077),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10078,U_10077),U_10080),U_10079)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10078,U_10077),U_10081),U_10079))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10078),U_10079))
| ~ class_Groups_Ocomm__monoid__add(U_10077) ),
inference(variable_rename,[status(thm)],[f_2769_1]) ).
cnf(f_2769_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10078,U_10077),hAPP(hAPP(c_COMBS(U_10078,U_10077,U_10077),hAPP(hAPP(c_COMBB(U_10077,tc_fun(U_10077,U_10077),U_10078),c_Groups_Oplus__class_Oplus(U_10077)),U_10080)),U_10081)),U_10079) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10077),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10078,U_10077),U_10080),U_10079)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10078,U_10077),U_10081),U_10079))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10078),U_10079))
| ~ class_Groups_Ocomm__monoid__add(U_10077) ),
inference(clausify,[status(thm)],[f_2769_2]) ).
fof(f_2770_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_2770_2,plain,
! [U_10086,U_10085,U_10084,U_10083,U_10082] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10082),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10083,U_10082),U_10085),U_10086)),hAPP(U_10086,U_10084)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10083),U_10084),U_10085))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10082) ),
inference(variable_rename,[status(thm)],[f_2770_1]) ).
cnf(f_2770_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10082),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10083,U_10082),U_10085),U_10086)),hAPP(U_10086,U_10084)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10083),U_10084),U_10085))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10082) ),
inference(clausify,[status(thm)],[f_2770_2]) ).
fof(f_2771_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_2771_2,plain,
! [U_10087] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10087)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10087)),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_2771_1]) ).
cnf(f_2771_3,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10087)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10087)),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_2771_2]) ).
fof(f_2772_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_2772_2,plain,
! [U_10093,U_10092,U_10091,U_10090,U_10089,U_10088] :
( ( c_Nitpick_Opair__box_OPairBox(U_10088,U_10089,U_10090,U_10091) = c_Nitpick_Opair__box_OPairBox(U_10088,U_10089,U_10092,U_10093)
| U_10091 != U_10093
| U_10090 != U_10092 )
& ( ( U_10091 = U_10093
& U_10090 = U_10092 )
| c_Nitpick_Opair__box_OPairBox(U_10088,U_10089,U_10090,U_10091) != c_Nitpick_Opair__box_OPairBox(U_10088,U_10089,U_10092,U_10093) ) ),
inference(variable_rename,[status(thm)],[f_2772_1]) ).
fof(f_2772_3,plain,
( ! [U_10105,U_10103,U_10101,U_10099] :
( ! [U_10097,U_10095] : c_Nitpick_Opair__box_OPairBox(U_10095,U_10097,U_10099,U_10101) = c_Nitpick_Opair__box_OPairBox(U_10095,U_10097,U_10103,U_10105)
| U_10101 != U_10105
| U_10099 != U_10103 )
& ! [U_10104,U_10102,U_10100,U_10098] :
( ! [U_10096,U_10094] : c_Nitpick_Opair__box_OPairBox(U_10094,U_10096,U_10098,U_10100) != c_Nitpick_Opair__box_OPairBox(U_10094,U_10096,U_10102,U_10104)
| ( U_10100 = U_10104
& U_10098 = U_10102 ) ) ),
inference(miniscope,[status(thm)],[f_2772_2]) ).
cnf(f_2772_4,plain,
( U_10098 = U_10102
| c_Nitpick_Opair__box_OPairBox(U_10094,U_10096,U_10098,U_10100) != c_Nitpick_Opair__box_OPairBox(U_10094,U_10096,U_10102,U_10104) ),
inference(clausify,[status(thm)],[f_2772_3]) ).
cnf(f_2772_5,plain,
( U_10100 = U_10104
| c_Nitpick_Opair__box_OPairBox(U_10094,U_10096,U_10098,U_10100) != c_Nitpick_Opair__box_OPairBox(U_10094,U_10096,U_10102,U_10104) ),
inference(clausify,[status(thm)],[f_2772_3]) ).
cnf(f_2772_6,plain,
( c_Nitpick_Opair__box_OPairBox(U_10095,U_10097,U_10099,U_10101) = c_Nitpick_Opair__box_OPairBox(U_10095,U_10097,U_10103,U_10105)
| U_10101 != U_10105
| U_10099 != U_10103 ),
inference(clausify,[status(thm)],[f_2772_3]) ).
fof(f_2773_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_2773_2,plain,
! [U_10108,U_10107,U_10106] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10106,tc_HOL_Obool)),U_10107),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10106,tc_HOL_Obool),U_10108)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_10106,tc_HOL_Obool),tc_fun(U_10106,tc_HOL_Obool)),U_10108),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10106,tc_HOL_Obool)),U_10107)),
inference(variable_rename,[status(thm)],[f_2773_1]) ).
cnf(f_2773_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10106,tc_HOL_Obool)),U_10107),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10106,tc_HOL_Obool),U_10108)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_10106,tc_HOL_Obool),tc_fun(U_10106,tc_HOL_Obool)),U_10108),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10106,tc_HOL_Obool)),U_10107)),
inference(clausify,[status(thm)],[f_2773_2]) ).
fof(f_2774_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_2774_2,plain,
! [U_10111,U_10110,U_10109] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10109,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10109,tc_HOL_Obool),U_10110)),U_10111) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_10109,tc_HOL_Obool),tc_fun(U_10109,tc_HOL_Obool)),U_10110),hAPP(hAPP(c_COMBC(tc_fun(U_10109,tc_HOL_Obool),tc_fun(U_10109,tc_HOL_Obool),tc_fun(U_10109,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10109,tc_HOL_Obool))),U_10111)),
inference(variable_rename,[status(thm)],[f_2774_1]) ).
cnf(f_2774_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10109,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10109,tc_HOL_Obool),U_10110)),U_10111) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_10109,tc_HOL_Obool),tc_fun(U_10109,tc_HOL_Obool)),U_10110),hAPP(hAPP(c_COMBC(tc_fun(U_10109,tc_HOL_Obool),tc_fun(U_10109,tc_HOL_Obool),tc_fun(U_10109,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10109,tc_HOL_Obool))),U_10111)),
inference(clausify,[status(thm)],[f_2774_2]) ).
fof(f_2775_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_2775_2,plain,
! [U_10116,U_10115,U_10114,U_10113,U_10112] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10114,tc_HOL_Obool)),U_10115),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10113,tc_fun(U_10114,tc_HOL_Obool)),U_10112),U_10116)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10113,tc_fun(U_10114,tc_HOL_Obool)),U_10112),hAPP(hAPP(c_COMBB(tc_fun(U_10114,tc_HOL_Obool),tc_fun(U_10114,tc_HOL_Obool),U_10113),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10114,tc_HOL_Obool)),U_10115)),U_10116))
| U_10112 = c_Orderings_Obot__class_Obot(tc_fun(U_10113,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10114,tc_HOL_Obool)),U_10115),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10113,tc_fun(U_10114,tc_HOL_Obool)),U_10112),U_10116)) = U_10115
| U_10112 != c_Orderings_Obot__class_Obot(tc_fun(U_10113,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2775_1]) ).
fof(f_2775_3,plain,
( ! [U_10126,U_10124,U_10122,U_10120,U_10118] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10122,tc_HOL_Obool)),U_10124),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10120,tc_fun(U_10122,tc_HOL_Obool)),U_10118),U_10126)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10120,tc_fun(U_10122,tc_HOL_Obool)),U_10118),hAPP(hAPP(c_COMBB(tc_fun(U_10122,tc_HOL_Obool),tc_fun(U_10122,tc_HOL_Obool),U_10120),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10122,tc_HOL_Obool)),U_10124)),U_10126))
| U_10118 = c_Orderings_Obot__class_Obot(tc_fun(U_10120,tc_HOL_Obool)) )
& ! [U_10125,U_10123,U_10121,U_10119,U_10117] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10121,tc_HOL_Obool)),U_10123),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10119,tc_fun(U_10121,tc_HOL_Obool)),U_10117),U_10125)) = U_10123
| U_10117 != c_Orderings_Obot__class_Obot(tc_fun(U_10119,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2775_2]) ).
cnf(f_2775_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10121,tc_HOL_Obool)),U_10123),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10119,tc_fun(U_10121,tc_HOL_Obool)),U_10117),U_10125)) = U_10123
| U_10117 != c_Orderings_Obot__class_Obot(tc_fun(U_10119,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2775_3]) ).
cnf(f_2775_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10122,tc_HOL_Obool)),U_10124),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10120,tc_fun(U_10122,tc_HOL_Obool)),U_10118),U_10126)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10120,tc_fun(U_10122,tc_HOL_Obool)),U_10118),hAPP(hAPP(c_COMBB(tc_fun(U_10122,tc_HOL_Obool),tc_fun(U_10122,tc_HOL_Obool),U_10120),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10122,tc_HOL_Obool)),U_10124)),U_10126))
| U_10118 = c_Orderings_Obot__class_Obot(tc_fun(U_10120,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2775_3]) ).
fof(f_2776_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_2776_2,plain,
! [U_10131,U_10130,U_10129,U_10128,U_10127] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10129,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10128,tc_fun(U_10129,tc_HOL_Obool)),U_10127),U_10130)),U_10131) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10128,tc_fun(U_10129,tc_HOL_Obool)),U_10127),hAPP(hAPP(c_COMBC(U_10128,tc_fun(U_10129,tc_HOL_Obool),tc_fun(U_10129,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10129,tc_HOL_Obool),tc_fun(tc_fun(U_10129,tc_HOL_Obool),tc_fun(U_10129,tc_HOL_Obool)),U_10128),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10129,tc_HOL_Obool))),U_10130)),U_10131))
| U_10127 = c_Orderings_Obot__class_Obot(tc_fun(U_10128,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10129,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10128,tc_fun(U_10129,tc_HOL_Obool)),U_10127),U_10130)),U_10131) = U_10131
| U_10127 != c_Orderings_Obot__class_Obot(tc_fun(U_10128,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2776_1]) ).
fof(f_2776_3,plain,
( ! [U_10141,U_10139,U_10137,U_10135,U_10133] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10137,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10135,tc_fun(U_10137,tc_HOL_Obool)),U_10133),U_10139)),U_10141) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10135,tc_fun(U_10137,tc_HOL_Obool)),U_10133),hAPP(hAPP(c_COMBC(U_10135,tc_fun(U_10137,tc_HOL_Obool),tc_fun(U_10137,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10137,tc_HOL_Obool),tc_fun(tc_fun(U_10137,tc_HOL_Obool),tc_fun(U_10137,tc_HOL_Obool)),U_10135),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10137,tc_HOL_Obool))),U_10139)),U_10141))
| U_10133 = c_Orderings_Obot__class_Obot(tc_fun(U_10135,tc_HOL_Obool)) )
& ! [U_10140,U_10138,U_10136,U_10134,U_10132] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10136,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10134,tc_fun(U_10136,tc_HOL_Obool)),U_10132),U_10138)),U_10140) = U_10140
| U_10132 != c_Orderings_Obot__class_Obot(tc_fun(U_10134,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2776_2]) ).
cnf(f_2776_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10136,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10134,tc_fun(U_10136,tc_HOL_Obool)),U_10132),U_10138)),U_10140) = U_10140
| U_10132 != c_Orderings_Obot__class_Obot(tc_fun(U_10134,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2776_3]) ).
cnf(f_2776_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10137,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10135,tc_fun(U_10137,tc_HOL_Obool)),U_10133),U_10139)),U_10141) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10135,tc_fun(U_10137,tc_HOL_Obool)),U_10133),hAPP(hAPP(c_COMBC(U_10135,tc_fun(U_10137,tc_HOL_Obool),tc_fun(U_10137,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10137,tc_HOL_Obool),tc_fun(tc_fun(U_10137,tc_HOL_Obool),tc_fun(U_10137,tc_HOL_Obool)),U_10135),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10137,tc_HOL_Obool))),U_10139)),U_10141))
| U_10133 = c_Orderings_Obot__class_Obot(tc_fun(U_10135,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2776_3]) ).
fof(f_2777_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_2777_2,plain,
! [U_10146,U_10145,U_10144,U_10143,U_10142] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10142,tc_fun(U_10143,tc_HOL_Obool)),U_10144),hAPP(hAPP(c_COMBS(U_10142,tc_fun(U_10143,tc_HOL_Obool),tc_fun(U_10143,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10143,tc_HOL_Obool),tc_fun(tc_fun(U_10143,tc_HOL_Obool),tc_fun(U_10143,tc_HOL_Obool)),U_10142),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10143,tc_HOL_Obool))),U_10145)),U_10146)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10143,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10142,tc_fun(U_10143,tc_HOL_Obool)),U_10144),U_10145)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10142,tc_fun(U_10143,tc_HOL_Obool)),U_10144),U_10146)),
inference(variable_rename,[status(thm)],[f_2777_1]) ).
cnf(f_2777_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10142,tc_fun(U_10143,tc_HOL_Obool)),U_10144),hAPP(hAPP(c_COMBS(U_10142,tc_fun(U_10143,tc_HOL_Obool),tc_fun(U_10143,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10143,tc_HOL_Obool),tc_fun(tc_fun(U_10143,tc_HOL_Obool),tc_fun(U_10143,tc_HOL_Obool)),U_10142),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10143,tc_HOL_Obool))),U_10145)),U_10146)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10143,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10142,tc_fun(U_10143,tc_HOL_Obool)),U_10144),U_10145)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10142,tc_fun(U_10143,tc_HOL_Obool)),U_10144),U_10146)),
inference(clausify,[status(thm)],[f_2777_2]) ).
fof(f_2778_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_2778_2,plain,
! [U_10151,U_10150,U_10149,U_10148,U_10147] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10147,tc_fun(U_10148,tc_HOL_Obool)),U_10149),hAPP(hAPP(c_COMBB(tc_fun(U_10148,tc_HOL_Obool),tc_fun(U_10148,tc_HOL_Obool),U_10147),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10148,tc_HOL_Obool)),U_10150)),U_10151)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10148,tc_HOL_Obool)),U_10150),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10147,tc_fun(U_10148,tc_HOL_Obool)),U_10149),U_10151)),
inference(variable_rename,[status(thm)],[f_2778_1]) ).
cnf(f_2778_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10147,tc_fun(U_10148,tc_HOL_Obool)),U_10149),hAPP(hAPP(c_COMBB(tc_fun(U_10148,tc_HOL_Obool),tc_fun(U_10148,tc_HOL_Obool),U_10147),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10148,tc_HOL_Obool)),U_10150)),U_10151)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10148,tc_HOL_Obool)),U_10150),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10147,tc_fun(U_10148,tc_HOL_Obool)),U_10149),U_10151)),
inference(clausify,[status(thm)],[f_2778_2]) ).
fof(f_2779_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_2779_2,plain,
! [U_10156,U_10155,U_10154,U_10153,U_10152] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10152,tc_fun(U_10153,tc_HOL_Obool)),U_10154),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__inf__class_Oinf(tc_fun(U_10153,tc_HOL_Obool))),U_10155)),U_10156)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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_10154),U_10155)),U_10156),
inference(variable_rename,[status(thm)],[f_2779_1]) ).
cnf(f_2779_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10152,tc_fun(U_10153,tc_HOL_Obool)),U_10154),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__inf__class_Oinf(tc_fun(U_10153,tc_HOL_Obool))),U_10155)),U_10156)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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_10154),U_10155)),U_10156),
inference(clausify,[status(thm)],[f_2779_2]) ).
fof(f_2780_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_2780_2,plain,
! [U_10161,U_10160,U_10159,U_10158,U_10157] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10157,tc_HOL_Obool)),U_10158),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10159,tc_fun(U_10157,tc_HOL_Obool)),U_10160),U_10161)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10159,tc_fun(U_10157,tc_HOL_Obool)),U_10160),hAPP(hAPP(c_COMBB(tc_fun(U_10157,tc_HOL_Obool),tc_fun(U_10157,tc_HOL_Obool),U_10159),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10157,tc_HOL_Obool)),U_10158)),U_10161)),
inference(variable_rename,[status(thm)],[f_2780_1]) ).
cnf(f_2780_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10157,tc_HOL_Obool)),U_10158),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10159,tc_fun(U_10157,tc_HOL_Obool)),U_10160),U_10161)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10159,tc_fun(U_10157,tc_HOL_Obool)),U_10160),hAPP(hAPP(c_COMBB(tc_fun(U_10157,tc_HOL_Obool),tc_fun(U_10157,tc_HOL_Obool),U_10159),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10157,tc_HOL_Obool)),U_10158)),U_10161)),
inference(clausify,[status(thm)],[f_2780_2]) ).
fof(f_2781_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_2781_2,plain,
! [U_10166,U_10165,U_10164,U_10163,U_10162] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10162,tc_HOL_Obool)),U_10163),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10164,tc_fun(U_10162,tc_HOL_Obool)),U_10165),U_10166)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10164,tc_fun(U_10162,tc_HOL_Obool)),U_10165),hAPP(hAPP(c_COMBB(tc_fun(U_10162,tc_HOL_Obool),tc_fun(U_10162,tc_HOL_Obool),U_10164),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10162,tc_HOL_Obool)),U_10163)),U_10166)),
inference(variable_rename,[status(thm)],[f_2781_1]) ).
cnf(f_2781_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10162,tc_HOL_Obool)),U_10163),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10164,tc_fun(U_10162,tc_HOL_Obool)),U_10165),U_10166)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10164,tc_fun(U_10162,tc_HOL_Obool)),U_10165),hAPP(hAPP(c_COMBB(tc_fun(U_10162,tc_HOL_Obool),tc_fun(U_10162,tc_HOL_Obool),U_10164),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10162,tc_HOL_Obool)),U_10163)),U_10166)),
inference(clausify,[status(thm)],[f_2781_2]) ).
fof(f_2782_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_2782_2,plain,
! [U_10171,U_10170,U_10169,U_10168,U_10167] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10167,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10168,tc_fun(U_10167,tc_HOL_Obool)),U_10169),U_10170)),U_10171) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10168,tc_fun(U_10167,tc_HOL_Obool)),U_10169),hAPP(hAPP(c_COMBC(U_10168,tc_fun(U_10167,tc_HOL_Obool),tc_fun(U_10167,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10167,tc_HOL_Obool),tc_fun(tc_fun(U_10167,tc_HOL_Obool),tc_fun(U_10167,tc_HOL_Obool)),U_10168),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10167,tc_HOL_Obool))),U_10170)),U_10171)),
inference(variable_rename,[status(thm)],[f_2782_1]) ).
cnf(f_2782_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10167,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10168,tc_fun(U_10167,tc_HOL_Obool)),U_10169),U_10170)),U_10171) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10168,tc_fun(U_10167,tc_HOL_Obool)),U_10169),hAPP(hAPP(c_COMBC(U_10168,tc_fun(U_10167,tc_HOL_Obool),tc_fun(U_10167,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10167,tc_HOL_Obool),tc_fun(tc_fun(U_10167,tc_HOL_Obool),tc_fun(U_10167,tc_HOL_Obool)),U_10168),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10167,tc_HOL_Obool))),U_10170)),U_10171)),
inference(clausify,[status(thm)],[f_2782_2]) ).
fof(f_2783_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_2783_2,plain,
! [U_10178,U_10177,U_10176,U_10175,U_10174,U_10173,U_10172] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10172,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10173,tc_fun(U_10172,tc_HOL_Obool)),U_10174),U_10175)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10176,tc_fun(U_10172,tc_HOL_Obool)),U_10177),U_10178)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10173,tc_fun(U_10172,tc_HOL_Obool)),U_10174),hAPP(hAPP(c_COMBB(tc_fun(U_10176,tc_fun(U_10172,tc_HOL_Obool)),tc_fun(U_10172,tc_HOL_Obool),U_10173),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10176,tc_fun(U_10172,tc_HOL_Obool)),U_10177)),hAPP(hAPP(c_COMBC(U_10173,tc_fun(U_10176,tc_fun(U_10172,tc_HOL_Obool)),tc_fun(U_10176,tc_fun(U_10172,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10172,tc_HOL_Obool),tc_fun(U_10172,tc_HOL_Obool)),tc_fun(tc_fun(U_10176,tc_fun(U_10172,tc_HOL_Obool)),tc_fun(U_10176,tc_fun(U_10172,tc_HOL_Obool))),U_10173),c_COMBB(tc_fun(U_10172,tc_HOL_Obool),tc_fun(U_10172,tc_HOL_Obool),U_10176)),hAPP(hAPP(c_COMBB(tc_fun(U_10172,tc_HOL_Obool),tc_fun(tc_fun(U_10172,tc_HOL_Obool),tc_fun(U_10172,tc_HOL_Obool)),U_10173),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10172,tc_HOL_Obool))),U_10175))),U_10178))),
inference(variable_rename,[status(thm)],[f_2783_1]) ).
cnf(f_2783_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10172,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10173,tc_fun(U_10172,tc_HOL_Obool)),U_10174),U_10175)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10176,tc_fun(U_10172,tc_HOL_Obool)),U_10177),U_10178)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10173,tc_fun(U_10172,tc_HOL_Obool)),U_10174),hAPP(hAPP(c_COMBB(tc_fun(U_10176,tc_fun(U_10172,tc_HOL_Obool)),tc_fun(U_10172,tc_HOL_Obool),U_10173),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10176,tc_fun(U_10172,tc_HOL_Obool)),U_10177)),hAPP(hAPP(c_COMBC(U_10173,tc_fun(U_10176,tc_fun(U_10172,tc_HOL_Obool)),tc_fun(U_10176,tc_fun(U_10172,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10172,tc_HOL_Obool),tc_fun(U_10172,tc_HOL_Obool)),tc_fun(tc_fun(U_10176,tc_fun(U_10172,tc_HOL_Obool)),tc_fun(U_10176,tc_fun(U_10172,tc_HOL_Obool))),U_10173),c_COMBB(tc_fun(U_10172,tc_HOL_Obool),tc_fun(U_10172,tc_HOL_Obool),U_10176)),hAPP(hAPP(c_COMBB(tc_fun(U_10172,tc_HOL_Obool),tc_fun(tc_fun(U_10172,tc_HOL_Obool),tc_fun(U_10172,tc_HOL_Obool)),U_10173),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10172,tc_HOL_Obool))),U_10175))),U_10178))),
inference(clausify,[status(thm)],[f_2783_2]) ).
fof(f_2784_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_2784_2,plain,
! [U_10183,U_10182,U_10181,U_10180,U_10179] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10180,U_10179)),U_10181),U_10182),U_10183) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10179),hAPP(U_10181,U_10183)),hAPP(U_10182,U_10183))
| ~ class_Lattices_Olattice(U_10179) ),
inference(variable_rename,[status(thm)],[f_2784_1]) ).
cnf(f_2784_3,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10180,U_10179)),U_10181),U_10182),U_10183) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10179),hAPP(U_10181,U_10183)),hAPP(U_10182,U_10183))
| ~ class_Lattices_Olattice(U_10179) ),
inference(clausify,[status(thm)],[f_2784_2]) ).
fof(f_2785_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_2785_2,plain,
! [U_10188,U_10187,U_10186,U_10185,U_10184] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10184,tc_fun(U_10185,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10184),U_10186),U_10187)),U_10188) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10185,tc_HOL_Obool)),hAPP(U_10188,U_10186)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10184,tc_fun(U_10185,tc_HOL_Obool)),U_10187),U_10188)),
inference(variable_rename,[status(thm)],[f_2785_1]) ).
cnf(f_2785_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10184,tc_fun(U_10185,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10184),U_10186),U_10187)),U_10188) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10185,tc_HOL_Obool)),hAPP(U_10188,U_10186)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10184,tc_fun(U_10185,tc_HOL_Obool)),U_10187),U_10188)),
inference(clausify,[status(thm)],[f_2785_2]) ).
fof(f_2786_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_2786_2,plain,
! [U_10194,U_10193,U_10192,U_10191,U_10190,U_10189] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10189,tc_fun(U_10190,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10189,tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool),tc_fun(U_10190,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10190,tc_fun(tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool),tc_fun(U_10190,tc_HOL_Obool)),U_10189),c_COMBC(U_10190,tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10190,tc_prod(U_10189,U_10190)),tc_fun(U_10190,tc_fun(tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool),tc_HOL_Obool)),U_10189),hAPP(c_COMBB(tc_prod(U_10189,U_10190),tc_fun(tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool),tc_HOL_Obool),U_10190),c_member(tc_prod(U_10189,U_10190)))),c_Product__Type_OPair(U_10189,U_10190)))),U_10191)),hAPP(hAPP(c_COMBC(U_10189,tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool),tc_fun(U_10190,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10190,tc_fun(tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool),tc_fun(U_10190,tc_HOL_Obool)),U_10189),c_COMBC(U_10190,tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10190,tc_prod(U_10189,U_10190)),tc_fun(U_10190,tc_fun(tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool),tc_HOL_Obool)),U_10189),hAPP(c_COMBB(tc_prod(U_10189,U_10190),tc_fun(tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool),tc_HOL_Obool),U_10190),c_member(tc_prod(U_10189,U_10190)))),c_Product__Type_OPair(U_10189,U_10190)))),U_10192)),U_10193),U_10194))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10189,U_10190)),hAPP(hAPP(c_Product__Type_OPair(U_10189,U_10190),U_10193),U_10194)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool)),U_10191),U_10192))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10189,U_10190)),hAPP(hAPP(c_Product__Type_OPair(U_10189,U_10190),U_10193),U_10194)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool)),U_10191),U_10192)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10189,tc_fun(U_10190,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10189,tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool),tc_fun(U_10190,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10190,tc_fun(tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool),tc_fun(U_10190,tc_HOL_Obool)),U_10189),c_COMBC(U_10190,tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10190,tc_prod(U_10189,U_10190)),tc_fun(U_10190,tc_fun(tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool),tc_HOL_Obool)),U_10189),hAPP(c_COMBB(tc_prod(U_10189,U_10190),tc_fun(tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool),tc_HOL_Obool),U_10190),c_member(tc_prod(U_10189,U_10190)))),c_Product__Type_OPair(U_10189,U_10190)))),U_10191)),hAPP(hAPP(c_COMBC(U_10189,tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool),tc_fun(U_10190,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10190,tc_fun(tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool),tc_fun(U_10190,tc_HOL_Obool)),U_10189),c_COMBC(U_10190,tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10190,tc_prod(U_10189,U_10190)),tc_fun(U_10190,tc_fun(tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool),tc_HOL_Obool)),U_10189),hAPP(c_COMBB(tc_prod(U_10189,U_10190),tc_fun(tc_fun(tc_prod(U_10189,U_10190),tc_HOL_Obool),tc_HOL_Obool),U_10190),c_member(tc_prod(U_10189,U_10190)))),c_Product__Type_OPair(U_10189,U_10190)))),U_10192)),U_10193),U_10194)) ) ),
inference(variable_rename,[status(thm)],[f_2786_1]) ).
fof(f_2786_3,plain,
( ! [U_10206,U_10204,U_10202,U_10200,U_10198,U_10196] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10196,tc_fun(U_10198,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10196,tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool),tc_fun(U_10198,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10198,tc_fun(tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool),tc_fun(U_10198,tc_HOL_Obool)),U_10196),c_COMBC(U_10198,tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10198,tc_prod(U_10196,U_10198)),tc_fun(U_10198,tc_fun(tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool),tc_HOL_Obool)),U_10196),hAPP(c_COMBB(tc_prod(U_10196,U_10198),tc_fun(tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool),tc_HOL_Obool),U_10198),c_member(tc_prod(U_10196,U_10198)))),c_Product__Type_OPair(U_10196,U_10198)))),U_10200)),hAPP(hAPP(c_COMBC(U_10196,tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool),tc_fun(U_10198,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10198,tc_fun(tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool),tc_fun(U_10198,tc_HOL_Obool)),U_10196),c_COMBC(U_10198,tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10198,tc_prod(U_10196,U_10198)),tc_fun(U_10198,tc_fun(tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool),tc_HOL_Obool)),U_10196),hAPP(c_COMBB(tc_prod(U_10196,U_10198),tc_fun(tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool),tc_HOL_Obool),U_10198),c_member(tc_prod(U_10196,U_10198)))),c_Product__Type_OPair(U_10196,U_10198)))),U_10202)),U_10204),U_10206))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10196,U_10198)),hAPP(hAPP(c_Product__Type_OPair(U_10196,U_10198),U_10204),U_10206)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool)),U_10200),U_10202))) )
& ! [U_10205,U_10203,U_10201,U_10199,U_10197,U_10195] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10195,U_10197)),hAPP(hAPP(c_Product__Type_OPair(U_10195,U_10197),U_10203),U_10205)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool)),U_10199),U_10201)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10195,tc_fun(U_10197,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10195,tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool),tc_fun(U_10197,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10197,tc_fun(tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool),tc_fun(U_10197,tc_HOL_Obool)),U_10195),c_COMBC(U_10197,tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10197,tc_prod(U_10195,U_10197)),tc_fun(U_10197,tc_fun(tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool),tc_HOL_Obool)),U_10195),hAPP(c_COMBB(tc_prod(U_10195,U_10197),tc_fun(tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool),tc_HOL_Obool),U_10197),c_member(tc_prod(U_10195,U_10197)))),c_Product__Type_OPair(U_10195,U_10197)))),U_10199)),hAPP(hAPP(c_COMBC(U_10195,tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool),tc_fun(U_10197,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10197,tc_fun(tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool),tc_fun(U_10197,tc_HOL_Obool)),U_10195),c_COMBC(U_10197,tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10197,tc_prod(U_10195,U_10197)),tc_fun(U_10197,tc_fun(tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool),tc_HOL_Obool)),U_10195),hAPP(c_COMBB(tc_prod(U_10195,U_10197),tc_fun(tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool),tc_HOL_Obool),U_10197),c_member(tc_prod(U_10195,U_10197)))),c_Product__Type_OPair(U_10195,U_10197)))),U_10201)),U_10203),U_10205)) ) ),
inference(miniscope,[status(thm)],[f_2786_2]) ).
cnf(f_2786_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10195,U_10197)),hAPP(hAPP(c_Product__Type_OPair(U_10195,U_10197),U_10203),U_10205)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool)),U_10199),U_10201)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10195,tc_fun(U_10197,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10195,tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool),tc_fun(U_10197,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10197,tc_fun(tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool),tc_fun(U_10197,tc_HOL_Obool)),U_10195),c_COMBC(U_10197,tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10197,tc_prod(U_10195,U_10197)),tc_fun(U_10197,tc_fun(tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool),tc_HOL_Obool)),U_10195),hAPP(c_COMBB(tc_prod(U_10195,U_10197),tc_fun(tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool),tc_HOL_Obool),U_10197),c_member(tc_prod(U_10195,U_10197)))),c_Product__Type_OPair(U_10195,U_10197)))),U_10199)),hAPP(hAPP(c_COMBC(U_10195,tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool),tc_fun(U_10197,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10197,tc_fun(tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool),tc_fun(U_10197,tc_HOL_Obool)),U_10195),c_COMBC(U_10197,tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10197,tc_prod(U_10195,U_10197)),tc_fun(U_10197,tc_fun(tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool),tc_HOL_Obool)),U_10195),hAPP(c_COMBB(tc_prod(U_10195,U_10197),tc_fun(tc_fun(tc_prod(U_10195,U_10197),tc_HOL_Obool),tc_HOL_Obool),U_10197),c_member(tc_prod(U_10195,U_10197)))),c_Product__Type_OPair(U_10195,U_10197)))),U_10201)),U_10203),U_10205)) ),
inference(clausify,[status(thm)],[f_2786_3]) ).
cnf(f_2786_5,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10196,tc_fun(U_10198,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10196,tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool),tc_fun(U_10198,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10198,tc_fun(tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool),tc_fun(U_10198,tc_HOL_Obool)),U_10196),c_COMBC(U_10198,tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10198,tc_prod(U_10196,U_10198)),tc_fun(U_10198,tc_fun(tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool),tc_HOL_Obool)),U_10196),hAPP(c_COMBB(tc_prod(U_10196,U_10198),tc_fun(tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool),tc_HOL_Obool),U_10198),c_member(tc_prod(U_10196,U_10198)))),c_Product__Type_OPair(U_10196,U_10198)))),U_10200)),hAPP(hAPP(c_COMBC(U_10196,tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool),tc_fun(U_10198,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10198,tc_fun(tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool),tc_fun(U_10198,tc_HOL_Obool)),U_10196),c_COMBC(U_10198,tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10198,tc_prod(U_10196,U_10198)),tc_fun(U_10198,tc_fun(tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool),tc_HOL_Obool)),U_10196),hAPP(c_COMBB(tc_prod(U_10196,U_10198),tc_fun(tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool),tc_HOL_Obool),U_10198),c_member(tc_prod(U_10196,U_10198)))),c_Product__Type_OPair(U_10196,U_10198)))),U_10202)),U_10204),U_10206))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10196,U_10198)),hAPP(hAPP(c_Product__Type_OPair(U_10196,U_10198),U_10204),U_10206)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_10196,U_10198),tc_HOL_Obool)),U_10200),U_10202))) ),
inference(clausify,[status(thm)],[f_2786_3]) ).
fof(f_2787_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_2787_2,plain,
! [U_10211,U_10210,U_10209,U_10208,U_10207] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10210,tc_HOL_Obool)),hAPP(U_10211,U_10208)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10207,tc_fun(U_10210,tc_HOL_Obool)),U_10209),U_10211)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10207,tc_fun(U_10210,tc_HOL_Obool)),U_10209),U_10211)
| ~ hBOOL(hAPP(hAPP(c_member(U_10207),U_10208),U_10209)) ),
inference(variable_rename,[status(thm)],[f_2787_1]) ).
cnf(f_2787_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10210,tc_HOL_Obool)),hAPP(U_10211,U_10208)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10207,tc_fun(U_10210,tc_HOL_Obool)),U_10209),U_10211)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10207,tc_fun(U_10210,tc_HOL_Obool)),U_10209),U_10211)
| ~ hBOOL(hAPP(hAPP(c_member(U_10207),U_10208),U_10209)) ),
inference(clausify,[status(thm)],[f_2787_2]) ).
fof(f_2788_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_2788_2,plain,
! [U_10215,U_10214,U_10213,U_10212] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10212,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10212,tc_fun(U_10212,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10212)),U_10213)),hAPP(hAPP(c_COMBC(U_10212,tc_fun(U_10212,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10212)),U_10214)),U_10215))
| ~ hBOOL(hAPP(hAPP(c_member(U_10212),U_10215),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10212,tc_HOL_Obool)),U_10213),U_10214))) )
& ( hBOOL(hAPP(hAPP(c_member(U_10212),U_10215),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10212,tc_HOL_Obool)),U_10213),U_10214)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10212,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10212,tc_fun(U_10212,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10212)),U_10213)),hAPP(hAPP(c_COMBC(U_10212,tc_fun(U_10212,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10212)),U_10214)),U_10215)) ) ),
inference(variable_rename,[status(thm)],[f_2788_1]) ).
fof(f_2788_3,plain,
( ! [U_10223,U_10221,U_10219,U_10217] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10217,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10217,tc_fun(U_10217,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10217)),U_10219)),hAPP(hAPP(c_COMBC(U_10217,tc_fun(U_10217,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10217)),U_10221)),U_10223))
| ~ hBOOL(hAPP(hAPP(c_member(U_10217),U_10223),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10217,tc_HOL_Obool)),U_10219),U_10221))) )
& ! [U_10222,U_10220,U_10218,U_10216] :
( hBOOL(hAPP(hAPP(c_member(U_10216),U_10222),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10216,tc_HOL_Obool)),U_10218),U_10220)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10216,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10216,tc_fun(U_10216,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10216)),U_10218)),hAPP(hAPP(c_COMBC(U_10216,tc_fun(U_10216,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10216)),U_10220)),U_10222)) ) ),
inference(miniscope,[status(thm)],[f_2788_2]) ).
cnf(f_2788_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_10216),U_10222),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10216,tc_HOL_Obool)),U_10218),U_10220)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10216,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10216,tc_fun(U_10216,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10216)),U_10218)),hAPP(hAPP(c_COMBC(U_10216,tc_fun(U_10216,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10216)),U_10220)),U_10222)) ),
inference(clausify,[status(thm)],[f_2788_3]) ).
cnf(f_2788_5,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10217,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10217,tc_fun(U_10217,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10217)),U_10219)),hAPP(hAPP(c_COMBC(U_10217,tc_fun(U_10217,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10217)),U_10221)),U_10223))
| ~ hBOOL(hAPP(hAPP(c_member(U_10217),U_10223),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10217,tc_HOL_Obool)),U_10219),U_10221))) ),
inference(clausify,[status(thm)],[f_2788_3]) ).
fof(f_2789_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_2789_2,plain,
! [U_10228,U_10227,U_10226,U_10225,U_10224] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10225,tc_fun(U_10226,tc_HOL_Obool)),U_10224),hAPP(hAPP(c_COMBC(U_10225,tc_fun(U_10226,tc_HOL_Obool),tc_fun(U_10226,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10226,tc_HOL_Obool),tc_fun(tc_fun(U_10226,tc_HOL_Obool),tc_fun(U_10226,tc_HOL_Obool)),U_10225),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10226,tc_HOL_Obool))),U_10227)),U_10228)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10226,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10225,tc_fun(U_10226,tc_HOL_Obool)),U_10224),U_10227)),U_10228)
| U_10224 = c_Orderings_Obot__class_Obot(tc_fun(U_10225,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10225,tc_fun(U_10226,tc_HOL_Obool)),U_10224),hAPP(hAPP(c_COMBC(U_10225,tc_fun(U_10226,tc_HOL_Obool),tc_fun(U_10226,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10226,tc_HOL_Obool),tc_fun(tc_fun(U_10226,tc_HOL_Obool),tc_fun(U_10226,tc_HOL_Obool)),U_10225),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10226,tc_HOL_Obool))),U_10227)),U_10228)) = c_Orderings_Otop__class_Otop(tc_fun(U_10226,tc_HOL_Obool))
| U_10224 != c_Orderings_Obot__class_Obot(tc_fun(U_10225,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2789_1]) ).
fof(f_2789_3,plain,
( ! [U_10238,U_10236,U_10234,U_10232,U_10230] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10232,tc_fun(U_10234,tc_HOL_Obool)),U_10230),hAPP(hAPP(c_COMBC(U_10232,tc_fun(U_10234,tc_HOL_Obool),tc_fun(U_10234,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10234,tc_HOL_Obool),tc_fun(tc_fun(U_10234,tc_HOL_Obool),tc_fun(U_10234,tc_HOL_Obool)),U_10232),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10234,tc_HOL_Obool))),U_10236)),U_10238)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10234,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10232,tc_fun(U_10234,tc_HOL_Obool)),U_10230),U_10236)),U_10238)
| U_10230 = c_Orderings_Obot__class_Obot(tc_fun(U_10232,tc_HOL_Obool)) )
& ! [U_10237,U_10235,U_10233,U_10231,U_10229] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10231,tc_fun(U_10233,tc_HOL_Obool)),U_10229),hAPP(hAPP(c_COMBC(U_10231,tc_fun(U_10233,tc_HOL_Obool),tc_fun(U_10233,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10233,tc_HOL_Obool),tc_fun(tc_fun(U_10233,tc_HOL_Obool),tc_fun(U_10233,tc_HOL_Obool)),U_10231),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10233,tc_HOL_Obool))),U_10235)),U_10237)) = c_Orderings_Otop__class_Otop(tc_fun(U_10233,tc_HOL_Obool))
| U_10229 != c_Orderings_Obot__class_Obot(tc_fun(U_10231,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2789_2]) ).
cnf(f_2789_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10231,tc_fun(U_10233,tc_HOL_Obool)),U_10229),hAPP(hAPP(c_COMBC(U_10231,tc_fun(U_10233,tc_HOL_Obool),tc_fun(U_10233,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10233,tc_HOL_Obool),tc_fun(tc_fun(U_10233,tc_HOL_Obool),tc_fun(U_10233,tc_HOL_Obool)),U_10231),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10233,tc_HOL_Obool))),U_10235)),U_10237)) = c_Orderings_Otop__class_Otop(tc_fun(U_10233,tc_HOL_Obool))
| U_10229 != c_Orderings_Obot__class_Obot(tc_fun(U_10231,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2789_3]) ).
cnf(f_2789_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10232,tc_fun(U_10234,tc_HOL_Obool)),U_10230),hAPP(hAPP(c_COMBC(U_10232,tc_fun(U_10234,tc_HOL_Obool),tc_fun(U_10234,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10234,tc_HOL_Obool),tc_fun(tc_fun(U_10234,tc_HOL_Obool),tc_fun(U_10234,tc_HOL_Obool)),U_10232),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10234,tc_HOL_Obool))),U_10236)),U_10238)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10234,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10232,tc_fun(U_10234,tc_HOL_Obool)),U_10230),U_10236)),U_10238)
| U_10230 = c_Orderings_Obot__class_Obot(tc_fun(U_10232,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2789_3]) ).
fof(f_2790_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_2790_2,plain,
! [U_10243,U_10242,U_10241,U_10240,U_10239] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10240,tc_fun(U_10241,tc_HOL_Obool)),U_10239),hAPP(hAPP(c_COMBB(tc_fun(U_10241,tc_HOL_Obool),tc_fun(U_10241,tc_HOL_Obool),U_10240),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10241,tc_HOL_Obool)),U_10242)),U_10243)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10241,tc_HOL_Obool)),U_10242),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10240,tc_fun(U_10241,tc_HOL_Obool)),U_10239),U_10243))
| U_10239 = c_Orderings_Obot__class_Obot(tc_fun(U_10240,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10240,tc_fun(U_10241,tc_HOL_Obool)),U_10239),hAPP(hAPP(c_COMBB(tc_fun(U_10241,tc_HOL_Obool),tc_fun(U_10241,tc_HOL_Obool),U_10240),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10241,tc_HOL_Obool)),U_10242)),U_10243)) = c_Orderings_Otop__class_Otop(tc_fun(U_10241,tc_HOL_Obool))
| U_10239 != c_Orderings_Obot__class_Obot(tc_fun(U_10240,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2790_1]) ).
fof(f_2790_3,plain,
( ! [U_10253,U_10251,U_10249,U_10247,U_10245] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10247,tc_fun(U_10249,tc_HOL_Obool)),U_10245),hAPP(hAPP(c_COMBB(tc_fun(U_10249,tc_HOL_Obool),tc_fun(U_10249,tc_HOL_Obool),U_10247),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10249,tc_HOL_Obool)),U_10251)),U_10253)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10249,tc_HOL_Obool)),U_10251),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10247,tc_fun(U_10249,tc_HOL_Obool)),U_10245),U_10253))
| U_10245 = c_Orderings_Obot__class_Obot(tc_fun(U_10247,tc_HOL_Obool)) )
& ! [U_10252,U_10250,U_10248,U_10246,U_10244] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10246,tc_fun(U_10248,tc_HOL_Obool)),U_10244),hAPP(hAPP(c_COMBB(tc_fun(U_10248,tc_HOL_Obool),tc_fun(U_10248,tc_HOL_Obool),U_10246),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10248,tc_HOL_Obool)),U_10250)),U_10252)) = c_Orderings_Otop__class_Otop(tc_fun(U_10248,tc_HOL_Obool))
| U_10244 != c_Orderings_Obot__class_Obot(tc_fun(U_10246,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2790_2]) ).
cnf(f_2790_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10246,tc_fun(U_10248,tc_HOL_Obool)),U_10244),hAPP(hAPP(c_COMBB(tc_fun(U_10248,tc_HOL_Obool),tc_fun(U_10248,tc_HOL_Obool),U_10246),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10248,tc_HOL_Obool)),U_10250)),U_10252)) = c_Orderings_Otop__class_Otop(tc_fun(U_10248,tc_HOL_Obool))
| U_10244 != c_Orderings_Obot__class_Obot(tc_fun(U_10246,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2790_3]) ).
cnf(f_2790_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10247,tc_fun(U_10249,tc_HOL_Obool)),U_10245),hAPP(hAPP(c_COMBB(tc_fun(U_10249,tc_HOL_Obool),tc_fun(U_10249,tc_HOL_Obool),U_10247),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10249,tc_HOL_Obool)),U_10251)),U_10253)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10249,tc_HOL_Obool)),U_10251),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10247,tc_fun(U_10249,tc_HOL_Obool)),U_10245),U_10253))
| U_10245 = c_Orderings_Obot__class_Obot(tc_fun(U_10247,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2790_3]) ).
fof(f_2791_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_2791_2,plain,
! [U_10257,U_10256,U_10255,U_10254] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10254,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10255,tc_fun(tc_fun(U_10254,tc_HOL_Obool),tc_HOL_Obool)),U_10256),hAPP(hAPP(c_COMBB(tc_fun(U_10254,tc_HOL_Obool),tc_fun(tc_fun(U_10254,tc_HOL_Obool),tc_HOL_Obool),U_10255),c_Set_OPow(U_10254)),U_10257))),hAPP(c_Set_OPow(U_10254),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10255,tc_fun(U_10254,tc_HOL_Obool)),U_10256),U_10257)))),
inference(variable_rename,[status(thm)],[f_2791_1]) ).
cnf(f_2791_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10254,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10255,tc_fun(tc_fun(U_10254,tc_HOL_Obool),tc_HOL_Obool)),U_10256),hAPP(hAPP(c_COMBB(tc_fun(U_10254,tc_HOL_Obool),tc_fun(tc_fun(U_10254,tc_HOL_Obool),tc_HOL_Obool),U_10255),c_Set_OPow(U_10254)),U_10257))),hAPP(c_Set_OPow(U_10254),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10255,tc_fun(U_10254,tc_HOL_Obool)),U_10256),U_10257)))),
inference(clausify,[status(thm)],[f_2791_2]) ).
fof(f_2792_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_2792_2,plain,
! [U_10261,U_10260,U_10259,U_10258] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10258,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10259)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10258,tc_HOL_Obool),tc_Nat_Onat),U_10260),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_10261))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10258,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10261,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10259),U_10261))),U_10260),
inference(variable_rename,[status(thm)],[f_2792_1]) ).
cnf(f_2792_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10258,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10259)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10258,tc_HOL_Obool),tc_Nat_Onat),U_10260),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_10261))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10258,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10261,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10259),U_10261))),U_10260),
inference(clausify,[status(thm)],[f_2792_2]) ).
fof(f_2793_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_2793_2,plain,
! [U_10266,U_10265,U_10264,U_10263,U_10262] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10262,tc_fun(U_10263,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10262,tc_HOL_Obool)),U_10264),U_10265)),U_10266) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10263,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10262,tc_fun(U_10263,tc_HOL_Obool)),U_10264),U_10266)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10262,tc_fun(U_10263,tc_HOL_Obool)),U_10265),U_10266)),
inference(variable_rename,[status(thm)],[f_2793_1]) ).
cnf(f_2793_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10262,tc_fun(U_10263,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10262,tc_HOL_Obool)),U_10264),U_10265)),U_10266) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10263,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10262,tc_fun(U_10263,tc_HOL_Obool)),U_10264),U_10266)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10262,tc_fun(U_10263,tc_HOL_Obool)),U_10265),U_10266)),
inference(clausify,[status(thm)],[f_2793_2]) ).
fof(f_2794_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_2794_2,plain,
! [U_10269,U_10268,U_10267] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10267,tc_HOL_Obool)),U_10268),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10267,tc_HOL_Obool),U_10269)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_10267,tc_HOL_Obool),tc_fun(U_10267,tc_HOL_Obool)),U_10269),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10267,tc_HOL_Obool)),U_10268)),
inference(variable_rename,[status(thm)],[f_2794_1]) ).
cnf(f_2794_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10267,tc_HOL_Obool)),U_10268),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10267,tc_HOL_Obool),U_10269)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_10267,tc_HOL_Obool),tc_fun(U_10267,tc_HOL_Obool)),U_10269),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10267,tc_HOL_Obool)),U_10268)),
inference(clausify,[status(thm)],[f_2794_2]) ).
fof(f_2795_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_2795_2,plain,
! [U_10276,U_10275,U_10274,U_10273,U_10272,U_10271,U_10270] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10270,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10271,tc_fun(U_10270,tc_HOL_Obool)),U_10272),U_10273)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10274,tc_fun(U_10270,tc_HOL_Obool)),U_10275),U_10276)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10271,tc_fun(U_10270,tc_HOL_Obool)),U_10272),hAPP(hAPP(c_COMBB(tc_fun(U_10274,tc_fun(U_10270,tc_HOL_Obool)),tc_fun(U_10270,tc_HOL_Obool),U_10271),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10274,tc_fun(U_10270,tc_HOL_Obool)),U_10275)),hAPP(hAPP(c_COMBC(U_10271,tc_fun(U_10274,tc_fun(U_10270,tc_HOL_Obool)),tc_fun(U_10274,tc_fun(U_10270,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10270,tc_HOL_Obool),tc_fun(U_10270,tc_HOL_Obool)),tc_fun(tc_fun(U_10274,tc_fun(U_10270,tc_HOL_Obool)),tc_fun(U_10274,tc_fun(U_10270,tc_HOL_Obool))),U_10271),c_COMBB(tc_fun(U_10270,tc_HOL_Obool),tc_fun(U_10270,tc_HOL_Obool),U_10274)),hAPP(hAPP(c_COMBB(tc_fun(U_10270,tc_HOL_Obool),tc_fun(tc_fun(U_10270,tc_HOL_Obool),tc_fun(U_10270,tc_HOL_Obool)),U_10271),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10270,tc_HOL_Obool))),U_10273))),U_10276))),
inference(variable_rename,[status(thm)],[f_2795_1]) ).
cnf(f_2795_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10270,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10271,tc_fun(U_10270,tc_HOL_Obool)),U_10272),U_10273)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10274,tc_fun(U_10270,tc_HOL_Obool)),U_10275),U_10276)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10271,tc_fun(U_10270,tc_HOL_Obool)),U_10272),hAPP(hAPP(c_COMBB(tc_fun(U_10274,tc_fun(U_10270,tc_HOL_Obool)),tc_fun(U_10270,tc_HOL_Obool),U_10271),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10274,tc_fun(U_10270,tc_HOL_Obool)),U_10275)),hAPP(hAPP(c_COMBC(U_10271,tc_fun(U_10274,tc_fun(U_10270,tc_HOL_Obool)),tc_fun(U_10274,tc_fun(U_10270,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10270,tc_HOL_Obool),tc_fun(U_10270,tc_HOL_Obool)),tc_fun(tc_fun(U_10274,tc_fun(U_10270,tc_HOL_Obool)),tc_fun(U_10274,tc_fun(U_10270,tc_HOL_Obool))),U_10271),c_COMBB(tc_fun(U_10270,tc_HOL_Obool),tc_fun(U_10270,tc_HOL_Obool),U_10274)),hAPP(hAPP(c_COMBB(tc_fun(U_10270,tc_HOL_Obool),tc_fun(tc_fun(U_10270,tc_HOL_Obool),tc_fun(U_10270,tc_HOL_Obool)),U_10271),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10270,tc_HOL_Obool))),U_10273))),U_10276))),
inference(clausify,[status(thm)],[f_2795_2]) ).
fof(f_2796_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_2796_2,plain,
! [U_10281,U_10280,U_10279,U_10278,U_10277] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10277,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10278,tc_fun(U_10277,tc_HOL_Obool)),U_10279),U_10280)),U_10281) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10278,tc_fun(U_10277,tc_HOL_Obool)),U_10279),hAPP(hAPP(c_COMBC(U_10278,tc_fun(U_10277,tc_HOL_Obool),tc_fun(U_10277,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10277,tc_HOL_Obool),tc_fun(tc_fun(U_10277,tc_HOL_Obool),tc_fun(U_10277,tc_HOL_Obool)),U_10278),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10277,tc_HOL_Obool))),U_10280)),U_10281)),
inference(variable_rename,[status(thm)],[f_2796_1]) ).
cnf(f_2796_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10277,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10278,tc_fun(U_10277,tc_HOL_Obool)),U_10279),U_10280)),U_10281) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10278,tc_fun(U_10277,tc_HOL_Obool)),U_10279),hAPP(hAPP(c_COMBC(U_10278,tc_fun(U_10277,tc_HOL_Obool),tc_fun(U_10277,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10277,tc_HOL_Obool),tc_fun(tc_fun(U_10277,tc_HOL_Obool),tc_fun(U_10277,tc_HOL_Obool)),U_10278),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10277,tc_HOL_Obool))),U_10280)),U_10281)),
inference(clausify,[status(thm)],[f_2796_2]) ).
fof(f_2797_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_2797_2,plain,
! [U_10286,U_10285,U_10284,U_10283,U_10282] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10282,tc_HOL_Obool)),U_10283),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10284,tc_fun(U_10282,tc_HOL_Obool)),U_10285),U_10286)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10284,tc_fun(U_10282,tc_HOL_Obool)),U_10285),hAPP(hAPP(c_COMBB(tc_fun(U_10282,tc_HOL_Obool),tc_fun(U_10282,tc_HOL_Obool),U_10284),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10282,tc_HOL_Obool)),U_10283)),U_10286)),
inference(variable_rename,[status(thm)],[f_2797_1]) ).
cnf(f_2797_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10282,tc_HOL_Obool)),U_10283),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10284,tc_fun(U_10282,tc_HOL_Obool)),U_10285),U_10286)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10284,tc_fun(U_10282,tc_HOL_Obool)),U_10285),hAPP(hAPP(c_COMBB(tc_fun(U_10282,tc_HOL_Obool),tc_fun(U_10282,tc_HOL_Obool),U_10284),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10282,tc_HOL_Obool)),U_10283)),U_10286)),
inference(clausify,[status(thm)],[f_2797_2]) ).
fof(f_2798_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_2798_2,plain,
! [U_10291,U_10290,U_10289,U_10288,U_10287] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10287,tc_HOL_Obool)),U_10288),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10289,tc_fun(U_10287,tc_HOL_Obool)),U_10290),U_10291)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10289,tc_fun(U_10287,tc_HOL_Obool)),U_10290),hAPP(hAPP(c_COMBB(tc_fun(U_10287,tc_HOL_Obool),tc_fun(U_10287,tc_HOL_Obool),U_10289),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10287,tc_HOL_Obool)),U_10288)),U_10291)),
inference(variable_rename,[status(thm)],[f_2798_1]) ).
cnf(f_2798_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10287,tc_HOL_Obool)),U_10288),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10289,tc_fun(U_10287,tc_HOL_Obool)),U_10290),U_10291)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10289,tc_fun(U_10287,tc_HOL_Obool)),U_10290),hAPP(hAPP(c_COMBB(tc_fun(U_10287,tc_HOL_Obool),tc_fun(U_10287,tc_HOL_Obool),U_10289),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10287,tc_HOL_Obool)),U_10288)),U_10291)),
inference(clausify,[status(thm)],[f_2798_2]) ).
fof(f_2799_1,plain,
! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_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_2799_2,plain,
! [U_10296,U_10295,U_10294,U_10293,U_10292] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10292,tc_fun(U_10293,tc_HOL_Obool)),U_10294),hAPP(hAPP(c_COMBC(U_10292,tc_fun(U_10293,tc_HOL_Obool),tc_fun(U_10293,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10293,tc_HOL_Obool),tc_fun(tc_fun(U_10293,tc_HOL_Obool),tc_fun(U_10293,tc_HOL_Obool)),U_10292),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10293,tc_HOL_Obool))),U_10295)),U_10296)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10293,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10292,tc_fun(U_10293,tc_HOL_Obool)),U_10294),U_10295)),U_10296),
inference(variable_rename,[status(thm)],[f_2799_1]) ).
cnf(f_2799_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10292,tc_fun(U_10293,tc_HOL_Obool)),U_10294),hAPP(hAPP(c_COMBC(U_10292,tc_fun(U_10293,tc_HOL_Obool),tc_fun(U_10293,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10293,tc_HOL_Obool),tc_fun(tc_fun(U_10293,tc_HOL_Obool),tc_fun(U_10293,tc_HOL_Obool)),U_10292),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10293,tc_HOL_Obool))),U_10295)),U_10296)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10293,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10292,tc_fun(U_10293,tc_HOL_Obool)),U_10294),U_10295)),U_10296),
inference(clausify,[status(thm)],[f_2799_2]) ).
fof(f_2800_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_2800_2,plain,
! [U_10301,U_10300,U_10299,U_10298,U_10297] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10297,tc_fun(U_10298,tc_HOL_Obool)),U_10299),hAPP(hAPP(c_COMBB(tc_fun(U_10298,tc_HOL_Obool),tc_fun(U_10298,tc_HOL_Obool),U_10297),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10298,tc_HOL_Obool)),U_10300)),U_10301)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10298,tc_HOL_Obool)),U_10300),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10297,tc_fun(U_10298,tc_HOL_Obool)),U_10299),U_10301)),
inference(variable_rename,[status(thm)],[f_2800_1]) ).
cnf(f_2800_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10297,tc_fun(U_10298,tc_HOL_Obool)),U_10299),hAPP(hAPP(c_COMBB(tc_fun(U_10298,tc_HOL_Obool),tc_fun(U_10298,tc_HOL_Obool),U_10297),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10298,tc_HOL_Obool)),U_10300)),U_10301)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10298,tc_HOL_Obool)),U_10300),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10297,tc_fun(U_10298,tc_HOL_Obool)),U_10299),U_10301)),
inference(clausify,[status(thm)],[f_2800_2]) ).
fof(f_2801_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_2801_2,plain,
! [U_10306,U_10305,U_10304,U_10303,U_10302] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10302,tc_fun(U_10303,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10302,tc_HOL_Obool)),U_10304),U_10305)),U_10306) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10303,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10302,tc_fun(U_10303,tc_HOL_Obool)),U_10304),U_10306)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10302,tc_fun(U_10303,tc_HOL_Obool)),U_10305),U_10306)),
inference(variable_rename,[status(thm)],[f_2801_1]) ).
cnf(f_2801_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10302,tc_fun(U_10303,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10302,tc_HOL_Obool)),U_10304),U_10305)),U_10306) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10303,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10302,tc_fun(U_10303,tc_HOL_Obool)),U_10304),U_10306)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10302,tc_fun(U_10303,tc_HOL_Obool)),U_10305),U_10306)),
inference(clausify,[status(thm)],[f_2801_2]) ).
fof(f_2802_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_2802_2,plain,
! [U_10311,U_10310,U_10309,U_10308,U_10307] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10307,tc_fun(U_10308,tc_HOL_Obool)),U_10309),hAPP(hAPP(c_COMBS(U_10307,tc_fun(U_10308,tc_HOL_Obool),tc_fun(U_10308,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10308,tc_HOL_Obool),tc_fun(tc_fun(U_10308,tc_HOL_Obool),tc_fun(U_10308,tc_HOL_Obool)),U_10307),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10308,tc_HOL_Obool))),U_10310)),U_10311)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10308,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10307,tc_fun(U_10308,tc_HOL_Obool)),U_10309),U_10310)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10307,tc_fun(U_10308,tc_HOL_Obool)),U_10309),U_10311)),
inference(variable_rename,[status(thm)],[f_2802_1]) ).
cnf(f_2802_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10307,tc_fun(U_10308,tc_HOL_Obool)),U_10309),hAPP(hAPP(c_COMBS(U_10307,tc_fun(U_10308,tc_HOL_Obool),tc_fun(U_10308,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10308,tc_HOL_Obool),tc_fun(tc_fun(U_10308,tc_HOL_Obool),tc_fun(U_10308,tc_HOL_Obool)),U_10307),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10308,tc_HOL_Obool))),U_10310)),U_10311)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10308,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10307,tc_fun(U_10308,tc_HOL_Obool)),U_10309),U_10310)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10307,tc_fun(U_10308,tc_HOL_Obool)),U_10309),U_10311)),
inference(clausify,[status(thm)],[f_2802_2]) ).
fof(f_2803_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_2803_2,plain,
! [U_10316,U_10315,U_10314,U_10313,U_10312] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10313,U_10312)),U_10314),U_10315),U_10316) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10312),hAPP(U_10314,U_10316)),hAPP(U_10315,U_10316))
| ~ class_Lattices_Olattice(U_10312) ),
inference(variable_rename,[status(thm)],[f_2803_1]) ).
cnf(f_2803_3,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10313,U_10312)),U_10314),U_10315),U_10316) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10312),hAPP(U_10314,U_10316)),hAPP(U_10315,U_10316))
| ~ class_Lattices_Olattice(U_10312) ),
inference(clausify,[status(thm)],[f_2803_2]) ).
fof(f_2804_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_2804_2,plain,
! [U_10322,U_10321,U_10320,U_10319,U_10318,U_10317] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10317,tc_fun(U_10318,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10317,tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool),tc_fun(U_10318,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10318,tc_fun(tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool),tc_fun(U_10318,tc_HOL_Obool)),U_10317),c_COMBC(U_10318,tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10318,tc_prod(U_10317,U_10318)),tc_fun(U_10318,tc_fun(tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool),tc_HOL_Obool)),U_10317),hAPP(c_COMBB(tc_prod(U_10317,U_10318),tc_fun(tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool),tc_HOL_Obool),U_10318),c_member(tc_prod(U_10317,U_10318)))),c_Product__Type_OPair(U_10317,U_10318)))),U_10319)),hAPP(hAPP(c_COMBC(U_10317,tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool),tc_fun(U_10318,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10318,tc_fun(tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool),tc_fun(U_10318,tc_HOL_Obool)),U_10317),c_COMBC(U_10318,tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10318,tc_prod(U_10317,U_10318)),tc_fun(U_10318,tc_fun(tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool),tc_HOL_Obool)),U_10317),hAPP(c_COMBB(tc_prod(U_10317,U_10318),tc_fun(tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool),tc_HOL_Obool),U_10318),c_member(tc_prod(U_10317,U_10318)))),c_Product__Type_OPair(U_10317,U_10318)))),U_10320)),U_10321),U_10322))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10317,U_10318)),hAPP(hAPP(c_Product__Type_OPair(U_10317,U_10318),U_10321),U_10322)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool)),U_10319),U_10320))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10317,U_10318)),hAPP(hAPP(c_Product__Type_OPair(U_10317,U_10318),U_10321),U_10322)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool)),U_10319),U_10320)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10317,tc_fun(U_10318,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10317,tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool),tc_fun(U_10318,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10318,tc_fun(tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool),tc_fun(U_10318,tc_HOL_Obool)),U_10317),c_COMBC(U_10318,tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10318,tc_prod(U_10317,U_10318)),tc_fun(U_10318,tc_fun(tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool),tc_HOL_Obool)),U_10317),hAPP(c_COMBB(tc_prod(U_10317,U_10318),tc_fun(tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool),tc_HOL_Obool),U_10318),c_member(tc_prod(U_10317,U_10318)))),c_Product__Type_OPair(U_10317,U_10318)))),U_10319)),hAPP(hAPP(c_COMBC(U_10317,tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool),tc_fun(U_10318,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10318,tc_fun(tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool),tc_fun(U_10318,tc_HOL_Obool)),U_10317),c_COMBC(U_10318,tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10318,tc_prod(U_10317,U_10318)),tc_fun(U_10318,tc_fun(tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool),tc_HOL_Obool)),U_10317),hAPP(c_COMBB(tc_prod(U_10317,U_10318),tc_fun(tc_fun(tc_prod(U_10317,U_10318),tc_HOL_Obool),tc_HOL_Obool),U_10318),c_member(tc_prod(U_10317,U_10318)))),c_Product__Type_OPair(U_10317,U_10318)))),U_10320)),U_10321),U_10322)) ) ),
inference(variable_rename,[status(thm)],[f_2804_1]) ).
fof(f_2804_3,plain,
( ! [U_10334,U_10332,U_10330,U_10328,U_10326,U_10324] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10324,tc_fun(U_10326,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10324,tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool),tc_fun(U_10326,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10326,tc_fun(tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool),tc_fun(U_10326,tc_HOL_Obool)),U_10324),c_COMBC(U_10326,tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10326,tc_prod(U_10324,U_10326)),tc_fun(U_10326,tc_fun(tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool),tc_HOL_Obool)),U_10324),hAPP(c_COMBB(tc_prod(U_10324,U_10326),tc_fun(tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool),tc_HOL_Obool),U_10326),c_member(tc_prod(U_10324,U_10326)))),c_Product__Type_OPair(U_10324,U_10326)))),U_10328)),hAPP(hAPP(c_COMBC(U_10324,tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool),tc_fun(U_10326,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10326,tc_fun(tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool),tc_fun(U_10326,tc_HOL_Obool)),U_10324),c_COMBC(U_10326,tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10326,tc_prod(U_10324,U_10326)),tc_fun(U_10326,tc_fun(tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool),tc_HOL_Obool)),U_10324),hAPP(c_COMBB(tc_prod(U_10324,U_10326),tc_fun(tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool),tc_HOL_Obool),U_10326),c_member(tc_prod(U_10324,U_10326)))),c_Product__Type_OPair(U_10324,U_10326)))),U_10330)),U_10332),U_10334))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10324,U_10326)),hAPP(hAPP(c_Product__Type_OPair(U_10324,U_10326),U_10332),U_10334)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool)),U_10328),U_10330))) )
& ! [U_10333,U_10331,U_10329,U_10327,U_10325,U_10323] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10323,U_10325)),hAPP(hAPP(c_Product__Type_OPair(U_10323,U_10325),U_10331),U_10333)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool)),U_10327),U_10329)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10323,tc_fun(U_10325,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10323,tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool),tc_fun(U_10325,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10325,tc_fun(tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool),tc_fun(U_10325,tc_HOL_Obool)),U_10323),c_COMBC(U_10325,tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10325,tc_prod(U_10323,U_10325)),tc_fun(U_10325,tc_fun(tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool),tc_HOL_Obool)),U_10323),hAPP(c_COMBB(tc_prod(U_10323,U_10325),tc_fun(tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool),tc_HOL_Obool),U_10325),c_member(tc_prod(U_10323,U_10325)))),c_Product__Type_OPair(U_10323,U_10325)))),U_10327)),hAPP(hAPP(c_COMBC(U_10323,tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool),tc_fun(U_10325,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10325,tc_fun(tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool),tc_fun(U_10325,tc_HOL_Obool)),U_10323),c_COMBC(U_10325,tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10325,tc_prod(U_10323,U_10325)),tc_fun(U_10325,tc_fun(tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool),tc_HOL_Obool)),U_10323),hAPP(c_COMBB(tc_prod(U_10323,U_10325),tc_fun(tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool),tc_HOL_Obool),U_10325),c_member(tc_prod(U_10323,U_10325)))),c_Product__Type_OPair(U_10323,U_10325)))),U_10329)),U_10331),U_10333)) ) ),
inference(miniscope,[status(thm)],[f_2804_2]) ).
cnf(f_2804_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10323,U_10325)),hAPP(hAPP(c_Product__Type_OPair(U_10323,U_10325),U_10331),U_10333)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool)),U_10327),U_10329)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10323,tc_fun(U_10325,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10323,tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool),tc_fun(U_10325,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10325,tc_fun(tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool),tc_fun(U_10325,tc_HOL_Obool)),U_10323),c_COMBC(U_10325,tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10325,tc_prod(U_10323,U_10325)),tc_fun(U_10325,tc_fun(tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool),tc_HOL_Obool)),U_10323),hAPP(c_COMBB(tc_prod(U_10323,U_10325),tc_fun(tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool),tc_HOL_Obool),U_10325),c_member(tc_prod(U_10323,U_10325)))),c_Product__Type_OPair(U_10323,U_10325)))),U_10327)),hAPP(hAPP(c_COMBC(U_10323,tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool),tc_fun(U_10325,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10325,tc_fun(tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool),tc_fun(U_10325,tc_HOL_Obool)),U_10323),c_COMBC(U_10325,tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10325,tc_prod(U_10323,U_10325)),tc_fun(U_10325,tc_fun(tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool),tc_HOL_Obool)),U_10323),hAPP(c_COMBB(tc_prod(U_10323,U_10325),tc_fun(tc_fun(tc_prod(U_10323,U_10325),tc_HOL_Obool),tc_HOL_Obool),U_10325),c_member(tc_prod(U_10323,U_10325)))),c_Product__Type_OPair(U_10323,U_10325)))),U_10329)),U_10331),U_10333)) ),
inference(clausify,[status(thm)],[f_2804_3]) ).
cnf(f_2804_5,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10324,tc_fun(U_10326,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10324,tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool),tc_fun(U_10326,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10326,tc_fun(tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool),tc_fun(U_10326,tc_HOL_Obool)),U_10324),c_COMBC(U_10326,tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10326,tc_prod(U_10324,U_10326)),tc_fun(U_10326,tc_fun(tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool),tc_HOL_Obool)),U_10324),hAPP(c_COMBB(tc_prod(U_10324,U_10326),tc_fun(tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool),tc_HOL_Obool),U_10326),c_member(tc_prod(U_10324,U_10326)))),c_Product__Type_OPair(U_10324,U_10326)))),U_10328)),hAPP(hAPP(c_COMBC(U_10324,tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool),tc_fun(U_10326,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10326,tc_fun(tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool),tc_fun(U_10326,tc_HOL_Obool)),U_10324),c_COMBC(U_10326,tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10326,tc_prod(U_10324,U_10326)),tc_fun(U_10326,tc_fun(tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool),tc_HOL_Obool)),U_10324),hAPP(c_COMBB(tc_prod(U_10324,U_10326),tc_fun(tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool),tc_HOL_Obool),U_10326),c_member(tc_prod(U_10324,U_10326)))),c_Product__Type_OPair(U_10324,U_10326)))),U_10330)),U_10332),U_10334))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10324,U_10326)),hAPP(hAPP(c_Product__Type_OPair(U_10324,U_10326),U_10332),U_10334)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10324,U_10326),tc_HOL_Obool)),U_10328),U_10330))) ),
inference(clausify,[status(thm)],[f_2804_3]) ).
fof(f_2805_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_2805_2,plain,
! [U_10338,U_10337,U_10336,U_10335] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10335,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10335,tc_fun(U_10335,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10335)),U_10336)),hAPP(hAPP(c_COMBC(U_10335,tc_fun(U_10335,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10335)),U_10337)),U_10338))
| ~ hBOOL(hAPP(hAPP(c_member(U_10335),U_10338),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10335,tc_HOL_Obool)),U_10336),U_10337))) )
& ( hBOOL(hAPP(hAPP(c_member(U_10335),U_10338),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10335,tc_HOL_Obool)),U_10336),U_10337)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10335,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10335,tc_fun(U_10335,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10335)),U_10336)),hAPP(hAPP(c_COMBC(U_10335,tc_fun(U_10335,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10335)),U_10337)),U_10338)) ) ),
inference(variable_rename,[status(thm)],[f_2805_1]) ).
fof(f_2805_3,plain,
( ! [U_10346,U_10344,U_10342,U_10340] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10340,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10340,tc_fun(U_10340,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10340)),U_10342)),hAPP(hAPP(c_COMBC(U_10340,tc_fun(U_10340,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10340)),U_10344)),U_10346))
| ~ hBOOL(hAPP(hAPP(c_member(U_10340),U_10346),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10340,tc_HOL_Obool)),U_10342),U_10344))) )
& ! [U_10345,U_10343,U_10341,U_10339] :
( hBOOL(hAPP(hAPP(c_member(U_10339),U_10345),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10339,tc_HOL_Obool)),U_10341),U_10343)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10339,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10339,tc_fun(U_10339,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10339)),U_10341)),hAPP(hAPP(c_COMBC(U_10339,tc_fun(U_10339,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10339)),U_10343)),U_10345)) ) ),
inference(miniscope,[status(thm)],[f_2805_2]) ).
cnf(f_2805_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_10339),U_10345),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10339,tc_HOL_Obool)),U_10341),U_10343)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10339,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10339,tc_fun(U_10339,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10339)),U_10341)),hAPP(hAPP(c_COMBC(U_10339,tc_fun(U_10339,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10339)),U_10343)),U_10345)) ),
inference(clausify,[status(thm)],[f_2805_3]) ).
cnf(f_2805_5,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10340,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10340,tc_fun(U_10340,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10340)),U_10342)),hAPP(hAPP(c_COMBC(U_10340,tc_fun(U_10340,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10340)),U_10344)),U_10346))
| ~ hBOOL(hAPP(hAPP(c_member(U_10340),U_10346),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10340,tc_HOL_Obool)),U_10342),U_10344))) ),
inference(clausify,[status(thm)],[f_2805_3]) ).
fof(f_2806_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_2806_2,plain,
! [U_10351,U_10350,U_10349,U_10348,U_10347] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10347,tc_fun(U_10348,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10347),U_10349),U_10350)),U_10351) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10348,tc_HOL_Obool)),hAPP(U_10351,U_10349)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10347,tc_fun(U_10348,tc_HOL_Obool)),U_10350),U_10351)),
inference(variable_rename,[status(thm)],[f_2806_1]) ).
cnf(f_2806_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10347,tc_fun(U_10348,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10347),U_10349),U_10350)),U_10351) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10348,tc_HOL_Obool)),hAPP(U_10351,U_10349)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10347,tc_fun(U_10348,tc_HOL_Obool)),U_10350),U_10351)),
inference(clausify,[status(thm)],[f_2806_2]) ).
fof(f_2807_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_2807_2,plain,
! [U_10356,U_10355,U_10354,U_10353,U_10352] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10353,tc_fun(U_10354,tc_HOL_Obool)),U_10352),hAPP(hAPP(c_COMBB(tc_fun(U_10354,tc_HOL_Obool),tc_fun(U_10354,tc_HOL_Obool),U_10353),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10354,tc_HOL_Obool)),U_10355)),U_10356)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10354,tc_HOL_Obool)),U_10355),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10353,tc_fun(U_10354,tc_HOL_Obool)),U_10352),U_10356))
| U_10352 = c_Orderings_Obot__class_Obot(tc_fun(U_10353,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10353,tc_fun(U_10354,tc_HOL_Obool)),U_10352),hAPP(hAPP(c_COMBB(tc_fun(U_10354,tc_HOL_Obool),tc_fun(U_10354,tc_HOL_Obool),U_10353),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10354,tc_HOL_Obool)),U_10355)),U_10356)) = c_Orderings_Obot__class_Obot(tc_fun(U_10354,tc_HOL_Obool))
| U_10352 != c_Orderings_Obot__class_Obot(tc_fun(U_10353,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2807_1]) ).
fof(f_2807_3,plain,
( ! [U_10366,U_10364,U_10362,U_10360,U_10358] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10360,tc_fun(U_10362,tc_HOL_Obool)),U_10358),hAPP(hAPP(c_COMBB(tc_fun(U_10362,tc_HOL_Obool),tc_fun(U_10362,tc_HOL_Obool),U_10360),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10362,tc_HOL_Obool)),U_10364)),U_10366)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10362,tc_HOL_Obool)),U_10364),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10360,tc_fun(U_10362,tc_HOL_Obool)),U_10358),U_10366))
| U_10358 = c_Orderings_Obot__class_Obot(tc_fun(U_10360,tc_HOL_Obool)) )
& ! [U_10365,U_10363,U_10361,U_10359,U_10357] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10359,tc_fun(U_10361,tc_HOL_Obool)),U_10357),hAPP(hAPP(c_COMBB(tc_fun(U_10361,tc_HOL_Obool),tc_fun(U_10361,tc_HOL_Obool),U_10359),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10361,tc_HOL_Obool)),U_10363)),U_10365)) = c_Orderings_Obot__class_Obot(tc_fun(U_10361,tc_HOL_Obool))
| U_10357 != c_Orderings_Obot__class_Obot(tc_fun(U_10359,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2807_2]) ).
cnf(f_2807_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10359,tc_fun(U_10361,tc_HOL_Obool)),U_10357),hAPP(hAPP(c_COMBB(tc_fun(U_10361,tc_HOL_Obool),tc_fun(U_10361,tc_HOL_Obool),U_10359),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10361,tc_HOL_Obool)),U_10363)),U_10365)) = c_Orderings_Obot__class_Obot(tc_fun(U_10361,tc_HOL_Obool))
| U_10357 != c_Orderings_Obot__class_Obot(tc_fun(U_10359,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2807_3]) ).
cnf(f_2807_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10360,tc_fun(U_10362,tc_HOL_Obool)),U_10358),hAPP(hAPP(c_COMBB(tc_fun(U_10362,tc_HOL_Obool),tc_fun(U_10362,tc_HOL_Obool),U_10360),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10362,tc_HOL_Obool)),U_10364)),U_10366)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10362,tc_HOL_Obool)),U_10364),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10360,tc_fun(U_10362,tc_HOL_Obool)),U_10358),U_10366))
| U_10358 = c_Orderings_Obot__class_Obot(tc_fun(U_10360,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2807_3]) ).
fof(f_2808_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_2808_2,plain,
! [U_10371,U_10370,U_10369,U_10368,U_10367] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10368,tc_fun(U_10369,tc_HOL_Obool)),U_10367),hAPP(hAPP(c_COMBC(U_10368,tc_fun(U_10369,tc_HOL_Obool),tc_fun(U_10369,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10369,tc_HOL_Obool),tc_fun(tc_fun(U_10369,tc_HOL_Obool),tc_fun(U_10369,tc_HOL_Obool)),U_10368),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10369,tc_HOL_Obool))),U_10370)),U_10371)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10369,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10368,tc_fun(U_10369,tc_HOL_Obool)),U_10367),U_10370)),U_10371)
| U_10367 = c_Orderings_Obot__class_Obot(tc_fun(U_10368,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10368,tc_fun(U_10369,tc_HOL_Obool)),U_10367),hAPP(hAPP(c_COMBC(U_10368,tc_fun(U_10369,tc_HOL_Obool),tc_fun(U_10369,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10369,tc_HOL_Obool),tc_fun(tc_fun(U_10369,tc_HOL_Obool),tc_fun(U_10369,tc_HOL_Obool)),U_10368),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10369,tc_HOL_Obool))),U_10370)),U_10371)) = c_Orderings_Obot__class_Obot(tc_fun(U_10369,tc_HOL_Obool))
| U_10367 != c_Orderings_Obot__class_Obot(tc_fun(U_10368,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2808_1]) ).
fof(f_2808_3,plain,
( ! [U_10381,U_10379,U_10377,U_10375,U_10373] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10375,tc_fun(U_10377,tc_HOL_Obool)),U_10373),hAPP(hAPP(c_COMBC(U_10375,tc_fun(U_10377,tc_HOL_Obool),tc_fun(U_10377,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10377,tc_HOL_Obool),tc_fun(tc_fun(U_10377,tc_HOL_Obool),tc_fun(U_10377,tc_HOL_Obool)),U_10375),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10377,tc_HOL_Obool))),U_10379)),U_10381)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10377,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10375,tc_fun(U_10377,tc_HOL_Obool)),U_10373),U_10379)),U_10381)
| U_10373 = c_Orderings_Obot__class_Obot(tc_fun(U_10375,tc_HOL_Obool)) )
& ! [U_10380,U_10378,U_10376,U_10374,U_10372] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10374,tc_fun(U_10376,tc_HOL_Obool)),U_10372),hAPP(hAPP(c_COMBC(U_10374,tc_fun(U_10376,tc_HOL_Obool),tc_fun(U_10376,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10376,tc_HOL_Obool),tc_fun(tc_fun(U_10376,tc_HOL_Obool),tc_fun(U_10376,tc_HOL_Obool)),U_10374),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10376,tc_HOL_Obool))),U_10378)),U_10380)) = c_Orderings_Obot__class_Obot(tc_fun(U_10376,tc_HOL_Obool))
| U_10372 != c_Orderings_Obot__class_Obot(tc_fun(U_10374,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2808_2]) ).
cnf(f_2808_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10374,tc_fun(U_10376,tc_HOL_Obool)),U_10372),hAPP(hAPP(c_COMBC(U_10374,tc_fun(U_10376,tc_HOL_Obool),tc_fun(U_10376,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10376,tc_HOL_Obool),tc_fun(tc_fun(U_10376,tc_HOL_Obool),tc_fun(U_10376,tc_HOL_Obool)),U_10374),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10376,tc_HOL_Obool))),U_10378)),U_10380)) = c_Orderings_Obot__class_Obot(tc_fun(U_10376,tc_HOL_Obool))
| U_10372 != c_Orderings_Obot__class_Obot(tc_fun(U_10374,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2808_3]) ).
cnf(f_2808_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10375,tc_fun(U_10377,tc_HOL_Obool)),U_10373),hAPP(hAPP(c_COMBC(U_10375,tc_fun(U_10377,tc_HOL_Obool),tc_fun(U_10377,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10377,tc_HOL_Obool),tc_fun(tc_fun(U_10377,tc_HOL_Obool),tc_fun(U_10377,tc_HOL_Obool)),U_10375),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10377,tc_HOL_Obool))),U_10379)),U_10381)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10377,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10375,tc_fun(U_10377,tc_HOL_Obool)),U_10373),U_10379)),U_10381)
| U_10373 = c_Orderings_Obot__class_Obot(tc_fun(U_10375,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2808_3]) ).
fof(f_2809_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_2809_2,plain,
! [U_10386,U_10385,U_10384,U_10383,U_10382] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10384,tc_HOL_Obool)),U_10385),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10383,tc_fun(U_10384,tc_HOL_Obool)),U_10382),U_10386)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10383,tc_fun(U_10384,tc_HOL_Obool)),U_10382),hAPP(hAPP(c_COMBB(tc_fun(U_10384,tc_HOL_Obool),tc_fun(U_10384,tc_HOL_Obool),U_10383),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10384,tc_HOL_Obool)),U_10385)),U_10386))
| U_10382 = c_Orderings_Obot__class_Obot(tc_fun(U_10383,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10384,tc_HOL_Obool)),U_10385),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10383,tc_fun(U_10384,tc_HOL_Obool)),U_10382),U_10386)) = U_10385
| U_10382 != c_Orderings_Obot__class_Obot(tc_fun(U_10383,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2809_1]) ).
fof(f_2809_3,plain,
( ! [U_10396,U_10394,U_10392,U_10390,U_10388] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10392,tc_HOL_Obool)),U_10394),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10390,tc_fun(U_10392,tc_HOL_Obool)),U_10388),U_10396)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10390,tc_fun(U_10392,tc_HOL_Obool)),U_10388),hAPP(hAPP(c_COMBB(tc_fun(U_10392,tc_HOL_Obool),tc_fun(U_10392,tc_HOL_Obool),U_10390),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10392,tc_HOL_Obool)),U_10394)),U_10396))
| U_10388 = c_Orderings_Obot__class_Obot(tc_fun(U_10390,tc_HOL_Obool)) )
& ! [U_10395,U_10393,U_10391,U_10389,U_10387] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10391,tc_HOL_Obool)),U_10393),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10389,tc_fun(U_10391,tc_HOL_Obool)),U_10387),U_10395)) = U_10393
| U_10387 != c_Orderings_Obot__class_Obot(tc_fun(U_10389,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2809_2]) ).
cnf(f_2809_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10391,tc_HOL_Obool)),U_10393),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10389,tc_fun(U_10391,tc_HOL_Obool)),U_10387),U_10395)) = U_10393
| U_10387 != c_Orderings_Obot__class_Obot(tc_fun(U_10389,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2809_3]) ).
cnf(f_2809_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10392,tc_HOL_Obool)),U_10394),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10390,tc_fun(U_10392,tc_HOL_Obool)),U_10388),U_10396)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10390,tc_fun(U_10392,tc_HOL_Obool)),U_10388),hAPP(hAPP(c_COMBB(tc_fun(U_10392,tc_HOL_Obool),tc_fun(U_10392,tc_HOL_Obool),U_10390),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10392,tc_HOL_Obool)),U_10394)),U_10396))
| U_10388 = c_Orderings_Obot__class_Obot(tc_fun(U_10390,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2809_3]) ).
fof(f_2810_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_2810_2,plain,
! [U_10401,U_10400,U_10399,U_10398,U_10397] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10399,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10398,tc_fun(U_10399,tc_HOL_Obool)),U_10397),U_10400)),U_10401) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10398,tc_fun(U_10399,tc_HOL_Obool)),U_10397),hAPP(hAPP(c_COMBC(U_10398,tc_fun(U_10399,tc_HOL_Obool),tc_fun(U_10399,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10399,tc_HOL_Obool),tc_fun(tc_fun(U_10399,tc_HOL_Obool),tc_fun(U_10399,tc_HOL_Obool)),U_10398),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10399,tc_HOL_Obool))),U_10400)),U_10401))
| U_10397 = c_Orderings_Obot__class_Obot(tc_fun(U_10398,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10399,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10398,tc_fun(U_10399,tc_HOL_Obool)),U_10397),U_10400)),U_10401) = U_10401
| U_10397 != c_Orderings_Obot__class_Obot(tc_fun(U_10398,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2810_1]) ).
fof(f_2810_3,plain,
( ! [U_10411,U_10409,U_10407,U_10405,U_10403] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10407,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10405,tc_fun(U_10407,tc_HOL_Obool)),U_10403),U_10409)),U_10411) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10405,tc_fun(U_10407,tc_HOL_Obool)),U_10403),hAPP(hAPP(c_COMBC(U_10405,tc_fun(U_10407,tc_HOL_Obool),tc_fun(U_10407,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10407,tc_HOL_Obool),tc_fun(tc_fun(U_10407,tc_HOL_Obool),tc_fun(U_10407,tc_HOL_Obool)),U_10405),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10407,tc_HOL_Obool))),U_10409)),U_10411))
| U_10403 = c_Orderings_Obot__class_Obot(tc_fun(U_10405,tc_HOL_Obool)) )
& ! [U_10410,U_10408,U_10406,U_10404,U_10402] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10406,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10404,tc_fun(U_10406,tc_HOL_Obool)),U_10402),U_10408)),U_10410) = U_10410
| U_10402 != c_Orderings_Obot__class_Obot(tc_fun(U_10404,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2810_2]) ).
cnf(f_2810_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10406,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10404,tc_fun(U_10406,tc_HOL_Obool)),U_10402),U_10408)),U_10410) = U_10410
| U_10402 != c_Orderings_Obot__class_Obot(tc_fun(U_10404,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2810_3]) ).
cnf(f_2810_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10407,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10405,tc_fun(U_10407,tc_HOL_Obool)),U_10403),U_10409)),U_10411) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10405,tc_fun(U_10407,tc_HOL_Obool)),U_10403),hAPP(hAPP(c_COMBC(U_10405,tc_fun(U_10407,tc_HOL_Obool),tc_fun(U_10407,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10407,tc_HOL_Obool),tc_fun(tc_fun(U_10407,tc_HOL_Obool),tc_fun(U_10407,tc_HOL_Obool)),U_10405),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10407,tc_HOL_Obool))),U_10409)),U_10411))
| U_10403 = c_Orderings_Obot__class_Obot(tc_fun(U_10405,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2810_3]) ).
fof(f_2811_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_2811_2,plain,
! [U_10416,U_10415,U_10414,U_10413,U_10412] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10415,tc_HOL_Obool)),hAPP(U_10416,U_10413)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10412,tc_fun(U_10415,tc_HOL_Obool)),U_10414),U_10416)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10412,tc_fun(U_10415,tc_HOL_Obool)),U_10414),U_10416)
| ~ hBOOL(hAPP(hAPP(c_member(U_10412),U_10413),U_10414)) ),
inference(variable_rename,[status(thm)],[f_2811_1]) ).
cnf(f_2811_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10415,tc_HOL_Obool)),hAPP(U_10416,U_10413)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10412,tc_fun(U_10415,tc_HOL_Obool)),U_10414),U_10416)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10412,tc_fun(U_10415,tc_HOL_Obool)),U_10414),U_10416)
| ~ hBOOL(hAPP(hAPP(c_member(U_10412),U_10413),U_10414)) ),
inference(clausify,[status(thm)],[f_2811_2]) ).
fof(f_2812_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_2812_2,plain,
! [U_10420,U_10419,U_10418,U_10417] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10417),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10418,tc_Nat_Onat),U_10419),U_10420)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10418,U_10417),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10417,U_10418),c_Nat_Osemiring__1__class_Oof__nat(U_10417)),U_10419)),U_10420)
| ~ class_Rings_Osemiring__1(U_10417)
| ~ class_Groups_Ocomm__monoid__mult(U_10417) ),
inference(variable_rename,[status(thm)],[f_2812_1]) ).
cnf(f_2812_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10417),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10418,tc_Nat_Onat),U_10419),U_10420)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10418,U_10417),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10417,U_10418),c_Nat_Osemiring__1__class_Oof__nat(U_10417)),U_10419)),U_10420)
| ~ class_Rings_Osemiring__1(U_10417)
| ~ class_Groups_Ocomm__monoid__mult(U_10417) ),
inference(clausify,[status(thm)],[f_2812_2]) ).
fof(f_2813_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_2813_2,plain,
! [U_10423,U_10422,U_10421] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10421,tc_Nat_Onat),U_10422),U_10423) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10421,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10421),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10422)),U_10423)),
inference(variable_rename,[status(thm)],[f_2813_1]) ).
cnf(f_2813_3,plain,
hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10421,tc_Nat_Onat),U_10422),U_10423) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10421,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10421),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10422)),U_10423)),
inference(clausify,[status(thm)],[f_2813_2]) ).
fof(f_2814_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_2814_2,plain,
! [U_10426,U_10425,U_10424] : 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_10424)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10425),U_10426)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10425),U_10424)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10426),U_10424)),
inference(variable_rename,[status(thm)],[f_2814_1]) ).
cnf(f_2814_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_10424)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10425),U_10426)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10425),U_10424)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10426),U_10424)),
inference(clausify,[status(thm)],[f_2814_2]) ).
fof(f_2815_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_2815_2,plain,
! [U_10429,U_10428,U_10427] : 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_10427)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10428,U_10429)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10428),U_10427),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10429),U_10427)),
inference(variable_rename,[status(thm)],[f_2815_1]) ).
cnf(f_2815_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_10427)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10428,U_10429)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10428),U_10427),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10429),U_10427)),
inference(clausify,[status(thm)],[f_2815_2]) ).
fof(f_2816_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_2816_2,plain,
! [U_10434,U_10433,U_10432,U_10431,U_10430] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10431,U_10430),hAPP(hAPP(c_COMBC(U_10431,U_10430,U_10430),hAPP(hAPP(c_COMBS(U_10431,U_10430,tc_fun(U_10430,U_10430)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10430,tc_fun(U_10430,U_10430)),U_10431),c_If(U_10430)),hAPP(c_fequal,U_10433))),U_10434)),c_Groups_Ozero__class_Ozero(U_10430))),U_10432) = c_Groups_Ozero__class_Ozero(U_10430)
| hBOOL(hAPP(hAPP(c_member(U_10431),U_10433),U_10432)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10431,U_10430),hAPP(hAPP(c_COMBC(U_10431,U_10430,U_10430),hAPP(hAPP(c_COMBS(U_10431,U_10430,tc_fun(U_10430,U_10430)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10430,tc_fun(U_10430,U_10430)),U_10431),c_If(U_10430)),hAPP(c_fequal,U_10433))),U_10434)),c_Groups_Ozero__class_Ozero(U_10430))),U_10432) = hAPP(U_10434,U_10433)
| ~ hBOOL(hAPP(hAPP(c_member(U_10431),U_10433),U_10432)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10431),U_10432))
| ~ class_Groups_Ocomm__monoid__add(U_10430) ),
inference(variable_rename,[status(thm)],[f_2816_1]) ).
cnf(f_2816_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10431,U_10430),hAPP(hAPP(c_COMBC(U_10431,U_10430,U_10430),hAPP(hAPP(c_COMBS(U_10431,U_10430,tc_fun(U_10430,U_10430)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10430,tc_fun(U_10430,U_10430)),U_10431),c_If(U_10430)),hAPP(c_fequal,U_10433))),U_10434)),c_Groups_Ozero__class_Ozero(U_10430))),U_10432) = hAPP(U_10434,U_10433)
| ~ hBOOL(hAPP(hAPP(c_member(U_10431),U_10433),U_10432))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10431),U_10432))
| ~ class_Groups_Ocomm__monoid__add(U_10430) ),
inference(clausify,[status(thm)],[f_2816_2]) ).
cnf(f_2816_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10431,U_10430),hAPP(hAPP(c_COMBC(U_10431,U_10430,U_10430),hAPP(hAPP(c_COMBS(U_10431,U_10430,tc_fun(U_10430,U_10430)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10430,tc_fun(U_10430,U_10430)),U_10431),c_If(U_10430)),hAPP(c_fequal,U_10433))),U_10434)),c_Groups_Ozero__class_Ozero(U_10430))),U_10432) = c_Groups_Ozero__class_Ozero(U_10430)
| hBOOL(hAPP(hAPP(c_member(U_10431),U_10433),U_10432))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10431),U_10432))
| ~ class_Groups_Ocomm__monoid__add(U_10430) ),
inference(clausify,[status(thm)],[f_2816_2]) ).
fof(f_2817_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_2817_2,plain,
! [U_10439,U_10438,U_10437,U_10436,U_10435] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10436,U_10435),hAPP(hAPP(c_COMBC(U_10436,U_10435,U_10435),hAPP(hAPP(c_COMBS(U_10436,U_10435,tc_fun(U_10435,U_10435)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10435,tc_fun(U_10435,U_10435)),U_10436),c_If(U_10435)),hAPP(hAPP(c_COMBC(U_10436,U_10436,tc_HOL_Obool),c_fequal),U_10438))),U_10439)),c_Groups_Ozero__class_Ozero(U_10435))),U_10437) = c_Groups_Ozero__class_Ozero(U_10435)
| hBOOL(hAPP(hAPP(c_member(U_10436),U_10438),U_10437)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10436,U_10435),hAPP(hAPP(c_COMBC(U_10436,U_10435,U_10435),hAPP(hAPP(c_COMBS(U_10436,U_10435,tc_fun(U_10435,U_10435)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10435,tc_fun(U_10435,U_10435)),U_10436),c_If(U_10435)),hAPP(hAPP(c_COMBC(U_10436,U_10436,tc_HOL_Obool),c_fequal),U_10438))),U_10439)),c_Groups_Ozero__class_Ozero(U_10435))),U_10437) = hAPP(U_10439,U_10438)
| ~ hBOOL(hAPP(hAPP(c_member(U_10436),U_10438),U_10437)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10436),U_10437))
| ~ class_Groups_Ocomm__monoid__add(U_10435) ),
inference(variable_rename,[status(thm)],[f_2817_1]) ).
cnf(f_2817_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10436,U_10435),hAPP(hAPP(c_COMBC(U_10436,U_10435,U_10435),hAPP(hAPP(c_COMBS(U_10436,U_10435,tc_fun(U_10435,U_10435)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10435,tc_fun(U_10435,U_10435)),U_10436),c_If(U_10435)),hAPP(hAPP(c_COMBC(U_10436,U_10436,tc_HOL_Obool),c_fequal),U_10438))),U_10439)),c_Groups_Ozero__class_Ozero(U_10435))),U_10437) = hAPP(U_10439,U_10438)
| ~ hBOOL(hAPP(hAPP(c_member(U_10436),U_10438),U_10437))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10436),U_10437))
| ~ class_Groups_Ocomm__monoid__add(U_10435) ),
inference(clausify,[status(thm)],[f_2817_2]) ).
cnf(f_2817_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10436,U_10435),hAPP(hAPP(c_COMBC(U_10436,U_10435,U_10435),hAPP(hAPP(c_COMBS(U_10436,U_10435,tc_fun(U_10435,U_10435)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10435,tc_fun(U_10435,U_10435)),U_10436),c_If(U_10435)),hAPP(hAPP(c_COMBC(U_10436,U_10436,tc_HOL_Obool),c_fequal),U_10438))),U_10439)),c_Groups_Ozero__class_Ozero(U_10435))),U_10437) = c_Groups_Ozero__class_Ozero(U_10435)
| hBOOL(hAPP(hAPP(c_member(U_10436),U_10438),U_10437))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10436),U_10437))
| ~ class_Groups_Ocomm__monoid__add(U_10435) ),
inference(clausify,[status(thm)],[f_2817_2]) ).
fof(f_2818_1,plain,
! [V_c_2,T_c,V_A_2,V_x_2,T_b] :
( hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_image__constant]) ).
fof(f_2818_2,plain,
! [U_10444,U_10443,U_10442,U_10441,U_10440] :
( hAPP(c_Set_Oimage(U_10440,U_10443,hAPP(c_COMBK(U_10443,U_10440),U_10444)),U_10442) = hAPP(hAPP(c_Set_Oinsert(U_10443),U_10444),c_Orderings_Obot__class_Obot(tc_fun(U_10443,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10440),U_10441),U_10442)) ),
inference(variable_rename,[status(thm)],[f_2818_1]) ).
cnf(f_2818_3,plain,
( hAPP(c_Set_Oimage(U_10440,U_10443,hAPP(c_COMBK(U_10443,U_10440),U_10444)),U_10442) = hAPP(hAPP(c_Set_Oinsert(U_10443),U_10444),c_Orderings_Obot__class_Obot(tc_fun(U_10443,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10440),U_10441),U_10442)) ),
inference(clausify,[status(thm)],[f_2818_2]) ).
fof(f_2819_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_2819_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_2819_1]) ).
fof(f_2820_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_2820_2,plain,
! [U_10449,U_10448,U_10447,U_10446,U_10445] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10446,U_10445),hAPP(hAPP(c_COMBC(U_10446,U_10445,U_10445),hAPP(hAPP(c_COMBS(U_10446,U_10445,tc_fun(U_10445,U_10445)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10445,tc_fun(U_10445,U_10445)),U_10446),c_If(U_10445)),hAPP(c_fequal,U_10448))),U_10449)),c_Groups_Oone__class_Oone(U_10445))),U_10447) = c_Groups_Oone__class_Oone(U_10445)
| hBOOL(hAPP(hAPP(c_member(U_10446),U_10448),U_10447)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10446,U_10445),hAPP(hAPP(c_COMBC(U_10446,U_10445,U_10445),hAPP(hAPP(c_COMBS(U_10446,U_10445,tc_fun(U_10445,U_10445)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10445,tc_fun(U_10445,U_10445)),U_10446),c_If(U_10445)),hAPP(c_fequal,U_10448))),U_10449)),c_Groups_Oone__class_Oone(U_10445))),U_10447) = hAPP(U_10449,U_10448)
| ~ hBOOL(hAPP(hAPP(c_member(U_10446),U_10448),U_10447)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10446),U_10447))
| ~ class_Groups_Ocomm__monoid__mult(U_10445) ),
inference(variable_rename,[status(thm)],[f_2820_1]) ).
cnf(f_2820_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10446,U_10445),hAPP(hAPP(c_COMBC(U_10446,U_10445,U_10445),hAPP(hAPP(c_COMBS(U_10446,U_10445,tc_fun(U_10445,U_10445)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10445,tc_fun(U_10445,U_10445)),U_10446),c_If(U_10445)),hAPP(c_fequal,U_10448))),U_10449)),c_Groups_Oone__class_Oone(U_10445))),U_10447) = hAPP(U_10449,U_10448)
| ~ hBOOL(hAPP(hAPP(c_member(U_10446),U_10448),U_10447))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10446),U_10447))
| ~ class_Groups_Ocomm__monoid__mult(U_10445) ),
inference(clausify,[status(thm)],[f_2820_2]) ).
cnf(f_2820_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10446,U_10445),hAPP(hAPP(c_COMBC(U_10446,U_10445,U_10445),hAPP(hAPP(c_COMBS(U_10446,U_10445,tc_fun(U_10445,U_10445)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10445,tc_fun(U_10445,U_10445)),U_10446),c_If(U_10445)),hAPP(c_fequal,U_10448))),U_10449)),c_Groups_Oone__class_Oone(U_10445))),U_10447) = c_Groups_Oone__class_Oone(U_10445)
| hBOOL(hAPP(hAPP(c_member(U_10446),U_10448),U_10447))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10446),U_10447))
| ~ class_Groups_Ocomm__monoid__mult(U_10445) ),
inference(clausify,[status(thm)],[f_2820_2]) ).
fof(f_2821_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_2821_2,plain,
! [U_10454,U_10453,U_10452,U_10451,U_10450] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10451,U_10450),hAPP(hAPP(c_COMBC(U_10451,U_10450,U_10450),hAPP(hAPP(c_COMBS(U_10451,U_10450,tc_fun(U_10450,U_10450)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10450,tc_fun(U_10450,U_10450)),U_10451),c_If(U_10450)),hAPP(hAPP(c_COMBC(U_10451,U_10451,tc_HOL_Obool),c_fequal),U_10453))),U_10454)),c_Groups_Oone__class_Oone(U_10450))),U_10452) = c_Groups_Oone__class_Oone(U_10450)
| hBOOL(hAPP(hAPP(c_member(U_10451),U_10453),U_10452)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10451,U_10450),hAPP(hAPP(c_COMBC(U_10451,U_10450,U_10450),hAPP(hAPP(c_COMBS(U_10451,U_10450,tc_fun(U_10450,U_10450)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10450,tc_fun(U_10450,U_10450)),U_10451),c_If(U_10450)),hAPP(hAPP(c_COMBC(U_10451,U_10451,tc_HOL_Obool),c_fequal),U_10453))),U_10454)),c_Groups_Oone__class_Oone(U_10450))),U_10452) = hAPP(U_10454,U_10453)
| ~ hBOOL(hAPP(hAPP(c_member(U_10451),U_10453),U_10452)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10451),U_10452))
| ~ class_Groups_Ocomm__monoid__mult(U_10450) ),
inference(variable_rename,[status(thm)],[f_2821_1]) ).
cnf(f_2821_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10451,U_10450),hAPP(hAPP(c_COMBC(U_10451,U_10450,U_10450),hAPP(hAPP(c_COMBS(U_10451,U_10450,tc_fun(U_10450,U_10450)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10450,tc_fun(U_10450,U_10450)),U_10451),c_If(U_10450)),hAPP(hAPP(c_COMBC(U_10451,U_10451,tc_HOL_Obool),c_fequal),U_10453))),U_10454)),c_Groups_Oone__class_Oone(U_10450))),U_10452) = hAPP(U_10454,U_10453)
| ~ hBOOL(hAPP(hAPP(c_member(U_10451),U_10453),U_10452))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10451),U_10452))
| ~ class_Groups_Ocomm__monoid__mult(U_10450) ),
inference(clausify,[status(thm)],[f_2821_2]) ).
cnf(f_2821_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10451,U_10450),hAPP(hAPP(c_COMBC(U_10451,U_10450,U_10450),hAPP(hAPP(c_COMBS(U_10451,U_10450,tc_fun(U_10450,U_10450)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10450,tc_fun(U_10450,U_10450)),U_10451),c_If(U_10450)),hAPP(hAPP(c_COMBC(U_10451,U_10451,tc_HOL_Obool),c_fequal),U_10453))),U_10454)),c_Groups_Oone__class_Oone(U_10450))),U_10452) = c_Groups_Oone__class_Oone(U_10450)
| hBOOL(hAPP(hAPP(c_member(U_10451),U_10453),U_10452))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10451),U_10452))
| ~ class_Groups_Ocomm__monoid__mult(U_10450) ),
inference(clausify,[status(thm)],[f_2821_2]) ).
fof(f_2822_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_2822_2,plain,
! [U_10458,U_10457,U_10456,U_10455] : hAPP(c_Set_Oimage(U_10455,U_10456,U_10457),U_10458) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10455,tc_fun(U_10456,tc_HOL_Obool)),U_10458),hAPP(hAPP(c_COMBC(U_10455,tc_fun(U_10456,tc_HOL_Obool),tc_fun(U_10456,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10456,tc_fun(tc_fun(U_10456,tc_HOL_Obool),tc_fun(U_10456,tc_HOL_Obool)),U_10455),c_Set_Oinsert(U_10456)),U_10457)),c_Orderings_Obot__class_Obot(tc_fun(U_10456,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_2822_1]) ).
cnf(f_2822_3,plain,
hAPP(c_Set_Oimage(U_10455,U_10456,U_10457),U_10458) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10455,tc_fun(U_10456,tc_HOL_Obool)),U_10458),hAPP(hAPP(c_COMBC(U_10455,tc_fun(U_10456,tc_HOL_Obool),tc_fun(U_10456,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10456,tc_fun(tc_fun(U_10456,tc_HOL_Obool),tc_fun(U_10456,tc_HOL_Obool)),U_10455),c_Set_Oinsert(U_10456)),U_10457)),c_Orderings_Obot__class_Obot(tc_fun(U_10456,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_2822_2]) ).
fof(f_2823_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_2823_2,plain,
! [U_10463,U_10462,U_10461,U_10460,U_10459] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10460,tc_fun(U_10461,tc_HOL_Obool)),U_10459),hAPP(hAPP(c_COMBB(tc_fun(U_10461,tc_HOL_Obool),tc_fun(U_10461,tc_HOL_Obool),U_10460),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10461,tc_HOL_Obool)),U_10462)),U_10463)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10461,tc_HOL_Obool)),U_10462),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10460,tc_fun(U_10461,tc_HOL_Obool)),U_10459),U_10463))
| U_10459 = c_Orderings_Obot__class_Obot(tc_fun(U_10460,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10460,tc_fun(U_10461,tc_HOL_Obool)),U_10459),hAPP(hAPP(c_COMBB(tc_fun(U_10461,tc_HOL_Obool),tc_fun(U_10461,tc_HOL_Obool),U_10460),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10461,tc_HOL_Obool)),U_10462)),U_10463)) = c_Orderings_Otop__class_Otop(tc_fun(U_10461,tc_HOL_Obool))
| U_10459 != c_Orderings_Obot__class_Obot(tc_fun(U_10460,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2823_1]) ).
fof(f_2823_3,plain,
( ! [U_10473,U_10471,U_10469,U_10467,U_10465] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10467,tc_fun(U_10469,tc_HOL_Obool)),U_10465),hAPP(hAPP(c_COMBB(tc_fun(U_10469,tc_HOL_Obool),tc_fun(U_10469,tc_HOL_Obool),U_10467),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10469,tc_HOL_Obool)),U_10471)),U_10473)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10469,tc_HOL_Obool)),U_10471),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10467,tc_fun(U_10469,tc_HOL_Obool)),U_10465),U_10473))
| U_10465 = c_Orderings_Obot__class_Obot(tc_fun(U_10467,tc_HOL_Obool)) )
& ! [U_10472,U_10470,U_10468,U_10466,U_10464] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10466,tc_fun(U_10468,tc_HOL_Obool)),U_10464),hAPP(hAPP(c_COMBB(tc_fun(U_10468,tc_HOL_Obool),tc_fun(U_10468,tc_HOL_Obool),U_10466),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10468,tc_HOL_Obool)),U_10470)),U_10472)) = c_Orderings_Otop__class_Otop(tc_fun(U_10468,tc_HOL_Obool))
| U_10464 != c_Orderings_Obot__class_Obot(tc_fun(U_10466,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2823_2]) ).
cnf(f_2823_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10466,tc_fun(U_10468,tc_HOL_Obool)),U_10464),hAPP(hAPP(c_COMBB(tc_fun(U_10468,tc_HOL_Obool),tc_fun(U_10468,tc_HOL_Obool),U_10466),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10468,tc_HOL_Obool)),U_10470)),U_10472)) = c_Orderings_Otop__class_Otop(tc_fun(U_10468,tc_HOL_Obool))
| U_10464 != c_Orderings_Obot__class_Obot(tc_fun(U_10466,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2823_3]) ).
cnf(f_2823_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10467,tc_fun(U_10469,tc_HOL_Obool)),U_10465),hAPP(hAPP(c_COMBB(tc_fun(U_10469,tc_HOL_Obool),tc_fun(U_10469,tc_HOL_Obool),U_10467),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10469,tc_HOL_Obool)),U_10471)),U_10473)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10469,tc_HOL_Obool)),U_10471),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10467,tc_fun(U_10469,tc_HOL_Obool)),U_10465),U_10473))
| U_10465 = c_Orderings_Obot__class_Obot(tc_fun(U_10467,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2823_3]) ).
fof(f_2824_1,plain,
! [T_c,V_A_2,V_c_2,T_b] :
( ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
& ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_vimage__const]) ).
fof(f_2824_2,plain,
! [U_10477,U_10476,U_10475,U_10474] :
( ( hAPP(c_Set_Ovimage(U_10477,U_10474,hAPP(c_COMBK(U_10474,U_10477),U_10475)),U_10476) = c_Orderings_Obot__class_Obot(tc_fun(U_10477,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_10474),U_10475),U_10476)) )
& ( hAPP(c_Set_Ovimage(U_10477,U_10474,hAPP(c_COMBK(U_10474,U_10477),U_10475)),U_10476) = c_Orderings_Otop__class_Otop(tc_fun(U_10477,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_10474),U_10475),U_10476)) ) ),
inference(variable_rename,[status(thm)],[f_2824_1]) ).
fof(f_2824_3,plain,
( ! [U_10485,U_10483,U_10481,U_10479] :
( hAPP(c_Set_Ovimage(U_10485,U_10479,hAPP(c_COMBK(U_10479,U_10485),U_10481)),U_10483) = c_Orderings_Obot__class_Obot(tc_fun(U_10485,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_10479),U_10481),U_10483)) )
& ! [U_10484,U_10482,U_10480,U_10478] :
( hAPP(c_Set_Ovimage(U_10484,U_10478,hAPP(c_COMBK(U_10478,U_10484),U_10480)),U_10482) = c_Orderings_Otop__class_Otop(tc_fun(U_10484,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_10478),U_10480),U_10482)) ) ),
inference(miniscope,[status(thm)],[f_2824_2]) ).
cnf(f_2824_4,plain,
( hAPP(c_Set_Ovimage(U_10484,U_10478,hAPP(c_COMBK(U_10478,U_10484),U_10480)),U_10482) = c_Orderings_Otop__class_Otop(tc_fun(U_10484,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_10478),U_10480),U_10482)) ),
inference(clausify,[status(thm)],[f_2824_3]) ).
cnf(f_2824_5,plain,
( hAPP(c_Set_Ovimage(U_10485,U_10479,hAPP(c_COMBK(U_10479,U_10485),U_10481)),U_10483) = c_Orderings_Obot__class_Obot(tc_fun(U_10485,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_10479),U_10481),U_10483)) ),
inference(clausify,[status(thm)],[f_2824_3]) ).
fof(f_2825_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_2825_2,plain,
! [U_10489,U_10488,U_10487,U_10486] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10487,U_10486),hAPP(c_COMBK(U_10486,U_10487),U_10488)),U_10489) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10486),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10486),hAPP(c_Finite__Set_Ocard(U_10487),U_10489))),U_10488)
| ~ class_Rings_Osemiring__1(U_10486) ),
inference(variable_rename,[status(thm)],[f_2825_1]) ).
cnf(f_2825_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10487,U_10486),hAPP(c_COMBK(U_10486,U_10487),U_10488)),U_10489) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10486),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10486),hAPP(c_Finite__Set_Ocard(U_10487),U_10489))),U_10488)
| ~ class_Rings_Osemiring__1(U_10486) ),
inference(clausify,[status(thm)],[f_2825_2]) ).
fof(f_2826_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_2826_2,plain,
! [U_10492,U_10491,U_10490] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10490),U_10491),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10492))) = hAPP(hAPP(c_HOL_OLet(U_10490,U_10490),hAPP(hAPP(c_Power_Opower__class_Opower(U_10490),U_10491),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10492))),hAPP(hAPP(c_COMBS(U_10490,U_10490,U_10490),c_Groups_Otimes__class_Otimes(U_10490)),c_COMBI(U_10490)))
| ~ class_Int_Onumber__ring(U_10490) ),
inference(variable_rename,[status(thm)],[f_2826_1]) ).
cnf(f_2826_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10490),U_10491),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10492))) = hAPP(hAPP(c_HOL_OLet(U_10490,U_10490),hAPP(hAPP(c_Power_Opower__class_Opower(U_10490),U_10491),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10492))),hAPP(hAPP(c_COMBS(U_10490,U_10490,U_10490),c_Groups_Otimes__class_Otimes(U_10490)),c_COMBI(U_10490)))
| ~ class_Int_Onumber__ring(U_10490) ),
inference(clausify,[status(thm)],[f_2826_2]) ).
fof(f_2827_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_2827_2,plain,
! [U_10497,U_10496,U_10495,U_10494,U_10493] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10493,U_10494,c_Groups_Otimes__class_Otimes(U_10493)),hAPP(hAPP(c_COMBS(U_10494,U_10493,U_10493),hAPP(hAPP(c_COMBB(U_10493,tc_fun(U_10493,U_10493),U_10494),c_Groups_Otimes__class_Otimes(U_10493)),U_10496)),U_10497)),c_Groups_Oone__class_Oone(U_10493)),U_10495) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10493),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10493,U_10494,c_Groups_Otimes__class_Otimes(U_10493)),U_10496),c_Groups_Oone__class_Oone(U_10493)),U_10495)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10493,U_10494,c_Groups_Otimes__class_Otimes(U_10493)),U_10497),c_Groups_Oone__class_Oone(U_10493)),U_10495))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10494),U_10495))
| ~ class_Groups_Ocomm__monoid__mult(U_10493) ),
inference(variable_rename,[status(thm)],[f_2827_1]) ).
cnf(f_2827_3,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10493,U_10494,c_Groups_Otimes__class_Otimes(U_10493)),hAPP(hAPP(c_COMBS(U_10494,U_10493,U_10493),hAPP(hAPP(c_COMBB(U_10493,tc_fun(U_10493,U_10493),U_10494),c_Groups_Otimes__class_Otimes(U_10493)),U_10496)),U_10497)),c_Groups_Oone__class_Oone(U_10493)),U_10495) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10493),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10493,U_10494,c_Groups_Otimes__class_Otimes(U_10493)),U_10496),c_Groups_Oone__class_Oone(U_10493)),U_10495)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10493,U_10494,c_Groups_Otimes__class_Otimes(U_10493)),U_10497),c_Groups_Oone__class_Oone(U_10493)),U_10495))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10494),U_10495))
| ~ class_Groups_Ocomm__monoid__mult(U_10493) ),
inference(clausify,[status(thm)],[f_2827_2]) ).
fof(f_2828_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_2828_2,plain,
! [U_10498] :
( c_Orderings_Oord_Omax(U_10498,hAPP(c_COMBC(U_10498,U_10498,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_10498))) = c_Orderings_Oord__class_Omin(U_10498)
| ~ class_Orderings_Olinorder(U_10498) ),
inference(variable_rename,[status(thm)],[f_2828_1]) ).
cnf(f_2828_3,plain,
( c_Orderings_Oord_Omax(U_10498,hAPP(c_COMBC(U_10498,U_10498,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_10498))) = c_Orderings_Oord__class_Omin(U_10498)
| ~ class_Orderings_Olinorder(U_10498) ),
inference(clausify,[status(thm)],[f_2828_2]) ).
fof(f_2829_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_2829_2,plain,
! [U_10499] :
( c_Orderings_Oord_Omin(U_10499,hAPP(c_COMBC(U_10499,U_10499,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_10499))) = c_Orderings_Oord__class_Omax(U_10499)
| ~ class_Orderings_Olinorder(U_10499) ),
inference(variable_rename,[status(thm)],[f_2829_1]) ).
cnf(f_2829_3,plain,
( c_Orderings_Oord_Omin(U_10499,hAPP(c_COMBC(U_10499,U_10499,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_10499))) = c_Orderings_Oord__class_Omax(U_10499)
| ~ class_Orderings_Olinorder(U_10499) ),
inference(clausify,[status(thm)],[f_2829_2]) ).
fof(f_2830_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_2830_2,plain,
! [U_10503,U_10502,U_10501,U_10500] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10501,U_10500),hAPP(c_COMBK(U_10500,U_10501),U_10503)),U_10502) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10500),U_10503),hAPP(c_Finite__Set_Ocard(U_10501),U_10502))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10501),U_10502))
| ~ class_Groups_Ocomm__monoid__mult(U_10500) ),
inference(variable_rename,[status(thm)],[f_2830_1]) ).
cnf(f_2830_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10501,U_10500),hAPP(c_COMBK(U_10500,U_10501),U_10503)),U_10502) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10500),U_10503),hAPP(c_Finite__Set_Ocard(U_10501),U_10502))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10501),U_10502))
| ~ class_Groups_Ocomm__monoid__mult(U_10500) ),
inference(clausify,[status(thm)],[f_2830_2]) ).
fof(f_2831_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_2831_2,plain,
! [U_10508,U_10507,U_10506,U_10505,U_10504] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10504),U_10507),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10505,U_10504),U_10506),U_10508)) = hAPP(hAPP(c_Finite__Set_Ofold(U_10505,U_10504,hAPP(hAPP(c_COMBB(U_10504,tc_fun(U_10504,U_10504),U_10505),c_Lattices_Osemilattice__sup__class_Osup(U_10504)),U_10508)),U_10507),U_10506)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10505),U_10506))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10504) ),
inference(variable_rename,[status(thm)],[f_2831_1]) ).
cnf(f_2831_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10504),U_10507),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10505,U_10504),U_10506),U_10508)) = hAPP(hAPP(c_Finite__Set_Ofold(U_10505,U_10504,hAPP(hAPP(c_COMBB(U_10504,tc_fun(U_10504,U_10504),U_10505),c_Lattices_Osemilattice__sup__class_Osup(U_10504)),U_10508)),U_10507),U_10506)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10505),U_10506))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10504) ),
inference(clausify,[status(thm)],[f_2831_2]) ).
fof(f_2832_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_2832_2,plain,
! [U_10512,U_10511,U_10510,U_10509] : hAPP(c_Set_Ovimage(U_10509,U_10510,U_10511),U_10512) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10510,tc_fun(U_10509,tc_HOL_Obool)),U_10512),hAPP(hAPP(c_COMBB(tc_fun(U_10510,tc_HOL_Obool),tc_fun(U_10509,tc_HOL_Obool),U_10510),c_Set_Ovimage(U_10509,U_10510,U_10511)),hAPP(hAPP(c_COMBC(U_10510,tc_fun(U_10510,tc_HOL_Obool),tc_fun(U_10510,tc_HOL_Obool)),c_Set_Oinsert(U_10510)),c_Orderings_Obot__class_Obot(tc_fun(U_10510,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_2832_1]) ).
cnf(f_2832_3,plain,
hAPP(c_Set_Ovimage(U_10509,U_10510,U_10511),U_10512) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10510,tc_fun(U_10509,tc_HOL_Obool)),U_10512),hAPP(hAPP(c_COMBB(tc_fun(U_10510,tc_HOL_Obool),tc_fun(U_10509,tc_HOL_Obool),U_10510),c_Set_Ovimage(U_10509,U_10510,U_10511)),hAPP(hAPP(c_COMBC(U_10510,tc_fun(U_10510,tc_HOL_Obool),tc_fun(U_10510,tc_HOL_Obool)),c_Set_Oinsert(U_10510)),c_Orderings_Obot__class_Obot(tc_fun(U_10510,tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_2832_2]) ).
fof(f_2833_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_2833_2,plain,
! [U_10517,U_10516,U_10515,U_10514,U_10513] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10513),U_10516),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10514,U_10513),U_10515),U_10517)) = hAPP(hAPP(c_Finite__Set_Ofold(U_10514,U_10513,hAPP(hAPP(c_COMBB(U_10513,tc_fun(U_10513,U_10513),U_10514),c_Lattices_Osemilattice__inf__class_Oinf(U_10513)),U_10517)),U_10516),U_10515)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10514),U_10515))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10513) ),
inference(variable_rename,[status(thm)],[f_2833_1]) ).
cnf(f_2833_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10513),U_10516),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10514,U_10513),U_10515),U_10517)) = hAPP(hAPP(c_Finite__Set_Ofold(U_10514,U_10513,hAPP(hAPP(c_COMBB(U_10513,tc_fun(U_10513,U_10513),U_10514),c_Lattices_Osemilattice__inf__class_Oinf(U_10513)),U_10517)),U_10516),U_10515)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10514),U_10515))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10513) ),
inference(clausify,[status(thm)],[f_2833_2]) ).
fof(f_2834_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_2834_2,plain,
! [U_10519,U_10518] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10518),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10519))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10518),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10519))),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_2834_1]) ).
cnf(f_2834_3,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10518),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10519))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10518),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10519))),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_2834_2]) ).
fof(f_2835_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_2835_2,plain,
! [U_10524,U_10523,U_10522,U_10521,U_10520] :
( hAPP(c_Set_Oimage(U_10520,U_10523,hAPP(c_Fun_Ocomp(U_10521,U_10523,U_10520,U_10524),U_10522)),c_Orderings_Otop__class_Otop(tc_fun(U_10520,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_10523,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_10521,U_10523,U_10524),c_Orderings_Otop__class_Otop(tc_fun(U_10521,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_10523,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_10520,U_10521,U_10522),c_Orderings_Otop__class_Otop(tc_fun(U_10520,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_10521,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_2835_1]) ).
cnf(f_2835_3,plain,
( hAPP(c_Set_Oimage(U_10520,U_10523,hAPP(c_Fun_Ocomp(U_10521,U_10523,U_10520,U_10524),U_10522)),c_Orderings_Otop__class_Otop(tc_fun(U_10520,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_10523,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_10521,U_10523,U_10524),c_Orderings_Otop__class_Otop(tc_fun(U_10521,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_10523,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_10520,U_10521,U_10522),c_Orderings_Otop__class_Otop(tc_fun(U_10520,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_10521,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2835_2]) ).
fof(f_2836_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_2836_2,plain,
! [U_10527,U_10526,U_10525] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10525),U_10526),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10527))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10525),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10525),U_10526),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10527))),hAPP(U_10526,U_10527))
| ~ class_Groups_Ocomm__monoid__add(U_10525) ),
inference(variable_rename,[status(thm)],[f_2836_1]) ).
cnf(f_2836_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10525),U_10526),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10527))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10525),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10525),U_10526),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10527))),hAPP(U_10526,U_10527))
| ~ class_Groups_Ocomm__monoid__add(U_10525) ),
inference(clausify,[status(thm)],[f_2836_2]) ).
fof(f_2837_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_2837_2,plain,
! [U_10533,U_10532,U_10531,U_10530,U_10529,U_10528] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10528,tc_fun(U_10529,tc_HOL_Obool)),U_10530),hAPP(c_Fun_Ocomp(U_10531,tc_fun(U_10529,tc_HOL_Obool),U_10528,U_10532),U_10533)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10531,tc_fun(U_10529,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10528,U_10531,U_10533),U_10530)),U_10532),
inference(variable_rename,[status(thm)],[f_2837_1]) ).
cnf(f_2837_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10528,tc_fun(U_10529,tc_HOL_Obool)),U_10530),hAPP(c_Fun_Ocomp(U_10531,tc_fun(U_10529,tc_HOL_Obool),U_10528,U_10532),U_10533)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10531,tc_fun(U_10529,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10528,U_10531,U_10533),U_10530)),U_10532),
inference(clausify,[status(thm)],[f_2837_2]) ).
fof(f_2838_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_2838_2,plain,
! [U_10538,U_10537,U_10536,U_10535,U_10534] :
( c_Fun_Oinj__on(U_10537,U_10535,hAPP(c_Fun_Ocomp(U_10534,U_10535,U_10537,U_10536),U_10538),c_Orderings_Otop__class_Otop(tc_fun(U_10537,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(U_10537,U_10534,U_10538,c_Orderings_Otop__class_Otop(tc_fun(U_10537,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(U_10534,U_10535,U_10536,c_Orderings_Otop__class_Otop(tc_fun(U_10534,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_2838_1]) ).
cnf(f_2838_3,plain,
( c_Fun_Oinj__on(U_10537,U_10535,hAPP(c_Fun_Ocomp(U_10534,U_10535,U_10537,U_10536),U_10538),c_Orderings_Otop__class_Otop(tc_fun(U_10537,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(U_10537,U_10534,U_10538,c_Orderings_Otop__class_Otop(tc_fun(U_10537,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(U_10534,U_10535,U_10536,c_Orderings_Otop__class_Otop(tc_fun(U_10534,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_2838_2]) ).
fof(f_2839_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_2839_2,plain,
! [U_10544,U_10543,U_10542,U_10541,U_10540,U_10539] :
( c_Fun_Oinj__on(U_10541,U_10540,U_10542,hAPP(c_Set_Oimage(U_10539,U_10541,U_10543),U_10544))
| ~ c_Fun_Oinj__on(U_10539,U_10540,hAPP(c_Fun_Ocomp(U_10541,U_10540,U_10539,U_10542),U_10543),U_10544) ),
inference(variable_rename,[status(thm)],[f_2839_1]) ).
cnf(f_2839_3,plain,
( c_Fun_Oinj__on(U_10541,U_10540,U_10542,hAPP(c_Set_Oimage(U_10539,U_10541,U_10543),U_10544))
| ~ c_Fun_Oinj__on(U_10539,U_10540,hAPP(c_Fun_Ocomp(U_10541,U_10540,U_10539,U_10542),U_10543),U_10544) ),
inference(clausify,[status(thm)],[f_2839_2]) ).
fof(f_2840_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_2840_2,plain,
! [U_10550,U_10549,U_10548,U_10547,U_10546,U_10545] :
( c_Fun_Oinj__on(U_10545,U_10549,hAPP(c_Fun_Ocomp(U_10546,U_10549,U_10545,U_10550),U_10547),U_10548)
| ~ c_Fun_Oinj__on(U_10546,U_10549,U_10550,hAPP(c_Set_Oimage(U_10545,U_10546,U_10547),U_10548))
| ~ c_Fun_Oinj__on(U_10545,U_10546,U_10547,U_10548) ),
inference(variable_rename,[status(thm)],[f_2840_1]) ).
cnf(f_2840_3,plain,
( c_Fun_Oinj__on(U_10545,U_10549,hAPP(c_Fun_Ocomp(U_10546,U_10549,U_10545,U_10550),U_10547),U_10548)
| ~ c_Fun_Oinj__on(U_10546,U_10549,U_10550,hAPP(c_Set_Oimage(U_10545,U_10546,U_10547),U_10548))
| ~ c_Fun_Oinj__on(U_10545,U_10546,U_10547,U_10548) ),
inference(clausify,[status(thm)],[f_2840_2]) ).
fof(f_2841_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_2841_2,plain,
! [U_10556,U_10555,U_10554,U_10553,U_10552,U_10551] :
( ( ( c_Fun_Oinj__on(U_10552,U_10555,U_10556,hAPP(c_Set_Oimage(U_10551,U_10552,U_10553),U_10554))
| ~ c_Fun_Oinj__on(U_10551,U_10555,hAPP(c_Fun_Ocomp(U_10552,U_10555,U_10551,U_10556),U_10553),U_10554) )
& ( c_Fun_Oinj__on(U_10551,U_10555,hAPP(c_Fun_Ocomp(U_10552,U_10555,U_10551,U_10556),U_10553),U_10554)
| ~ c_Fun_Oinj__on(U_10552,U_10555,U_10556,hAPP(c_Set_Oimage(U_10551,U_10552,U_10553),U_10554)) ) )
| ~ c_Fun_Oinj__on(U_10551,U_10552,U_10553,U_10554) ),
inference(variable_rename,[status(thm)],[f_2841_1]) ).
cnf(f_2841_3,plain,
( c_Fun_Oinj__on(U_10551,U_10555,hAPP(c_Fun_Ocomp(U_10552,U_10555,U_10551,U_10556),U_10553),U_10554)
| ~ c_Fun_Oinj__on(U_10552,U_10555,U_10556,hAPP(c_Set_Oimage(U_10551,U_10552,U_10553),U_10554))
| ~ c_Fun_Oinj__on(U_10551,U_10552,U_10553,U_10554) ),
inference(clausify,[status(thm)],[f_2841_2]) ).
cnf(f_2841_4,plain,
( c_Fun_Oinj__on(U_10552,U_10555,U_10556,hAPP(c_Set_Oimage(U_10551,U_10552,U_10553),U_10554))
| ~ c_Fun_Oinj__on(U_10551,U_10555,hAPP(c_Fun_Ocomp(U_10552,U_10555,U_10551,U_10556),U_10553),U_10554)
| ~ c_Fun_Oinj__on(U_10551,U_10552,U_10553,U_10554) ),
inference(clausify,[status(thm)],[f_2841_2]) ).
fof(f_2842_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_2842_2,plain,
! [U_10559,U_10558,U_10557] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10557),U_10558),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10559))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10557),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10557),U_10558),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10559))),hAPP(U_10558,hAPP(c_Nat_OSuc,U_10559)))
| ~ class_Groups_Ocomm__monoid__add(U_10557) ),
inference(variable_rename,[status(thm)],[f_2842_1]) ).
cnf(f_2842_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10557),U_10558),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10559))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10557),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10557),U_10558),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10559))),hAPP(U_10558,hAPP(c_Nat_OSuc,U_10559)))
| ~ class_Groups_Ocomm__monoid__add(U_10557) ),
inference(clausify,[status(thm)],[f_2842_2]) ).
fof(f_2843_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_2843_2,plain,
! [U_10562,U_10561,U_10560] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10560),U_10561),U_10562) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_10560),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10560,tc_Int_Oint),U_10561),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10562))
| ~ class_Groups_Ocomm__monoid__mult(U_10560)
| ~ class_Groups_Ocomm__monoid__add(U_10560) ),
inference(variable_rename,[status(thm)],[f_2843_1]) ).
cnf(f_2843_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10560),U_10561),U_10562) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_10560),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10560,tc_Int_Oint),U_10561),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10562))
| ~ class_Groups_Ocomm__monoid__mult(U_10560)
| ~ class_Groups_Ocomm__monoid__add(U_10560) ),
inference(clausify,[status(thm)],[f_2843_2]) ).
fof(f_2844_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_2844_2,plain,
! [U_10567,U_10566,U_10565,U_10564,U_10563] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10563,tc_fun(U_10564,tc_HOL_Obool)),U_10565),hAPP(hAPP(c_COMBS(U_10563,tc_fun(U_10564,tc_HOL_Obool),tc_fun(U_10564,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10564,tc_HOL_Obool),tc_fun(tc_fun(U_10564,tc_HOL_Obool),tc_fun(U_10564,tc_HOL_Obool)),U_10563),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10564,tc_HOL_Obool))),U_10566)),U_10567)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10564,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10564,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10563,tc_fun(U_10564,tc_HOL_Obool),U_10566),U_10565))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10564,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10563,tc_fun(U_10564,tc_HOL_Obool),U_10567),U_10565))),
inference(variable_rename,[status(thm)],[f_2844_1]) ).
cnf(f_2844_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10563,tc_fun(U_10564,tc_HOL_Obool)),U_10565),hAPP(hAPP(c_COMBS(U_10563,tc_fun(U_10564,tc_HOL_Obool),tc_fun(U_10564,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10564,tc_HOL_Obool),tc_fun(tc_fun(U_10564,tc_HOL_Obool),tc_fun(U_10564,tc_HOL_Obool)),U_10563),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10564,tc_HOL_Obool))),U_10566)),U_10567)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10564,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10564,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10563,tc_fun(U_10564,tc_HOL_Obool),U_10566),U_10565))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10564,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10563,tc_fun(U_10564,tc_HOL_Obool),U_10567),U_10565))),
inference(clausify,[status(thm)],[f_2844_2]) ).
fof(f_2845_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_2845_2,plain,
! [U_10569,U_10568] : 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_10568)),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_10569),U_10568))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_10568),U_10569),
inference(variable_rename,[status(thm)],[f_2845_1]) ).
cnf(f_2845_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_10568)),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_10569),U_10568))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_10568),U_10569),
inference(clausify,[status(thm)],[f_2845_2]) ).
fof(f_2846_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_2846_2,plain,
! [U_10572,U_10571,U_10570] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10570),U_10572),U_10571) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10570),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10570,tc_Nat_Onat),U_10572),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10571))
| ~ c_Nat__Transfer_Onat__set(U_10571)
| ~ class_Groups_Ocomm__monoid__mult(U_10570)
| ~ class_Groups_Ocomm__monoid__add(U_10570) ),
inference(variable_rename,[status(thm)],[f_2846_1]) ).
cnf(f_2846_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10570),U_10572),U_10571) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10570),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10570,tc_Nat_Onat),U_10572),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10571))
| ~ c_Nat__Transfer_Onat__set(U_10571)
| ~ class_Groups_Ocomm__monoid__mult(U_10570)
| ~ class_Groups_Ocomm__monoid__add(U_10570) ),
inference(clausify,[status(thm)],[f_2846_2]) ).
fof(f_2847_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_2847_2,plain,
! [U_10575,U_10574,U_10573] :
( ( hBOOL(hAPP(c_Predicate_OPowp(U_10573,hAPP(hAPP(c_COMBC(U_10573,tc_fun(U_10573,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10573)),U_10574)),U_10575))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10573,tc_HOL_Obool)),U_10575),hAPP(c_Set_OPow(U_10573),U_10574))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10573,tc_HOL_Obool)),U_10575),hAPP(c_Set_OPow(U_10573),U_10574)))
| ~ hBOOL(hAPP(c_Predicate_OPowp(U_10573,hAPP(hAPP(c_COMBC(U_10573,tc_fun(U_10573,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10573)),U_10574)),U_10575)) ) ),
inference(variable_rename,[status(thm)],[f_2847_1]) ).
fof(f_2847_3,plain,
( ! [U_10581,U_10579,U_10577] :
( hBOOL(hAPP(c_Predicate_OPowp(U_10577,hAPP(hAPP(c_COMBC(U_10577,tc_fun(U_10577,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10577)),U_10579)),U_10581))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10577,tc_HOL_Obool)),U_10581),hAPP(c_Set_OPow(U_10577),U_10579))) )
& ! [U_10580,U_10578,U_10576] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10576,tc_HOL_Obool)),U_10580),hAPP(c_Set_OPow(U_10576),U_10578)))
| ~ hBOOL(hAPP(c_Predicate_OPowp(U_10576,hAPP(hAPP(c_COMBC(U_10576,tc_fun(U_10576,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10576)),U_10578)),U_10580)) ) ),
inference(miniscope,[status(thm)],[f_2847_2]) ).
cnf(f_2847_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10576,tc_HOL_Obool)),U_10580),hAPP(c_Set_OPow(U_10576),U_10578)))
| ~ hBOOL(hAPP(c_Predicate_OPowp(U_10576,hAPP(hAPP(c_COMBC(U_10576,tc_fun(U_10576,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10576)),U_10578)),U_10580)) ),
inference(clausify,[status(thm)],[f_2847_3]) ).
cnf(f_2847_5,plain,
( hBOOL(hAPP(c_Predicate_OPowp(U_10577,hAPP(hAPP(c_COMBC(U_10577,tc_fun(U_10577,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10577)),U_10579)),U_10581))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10577,tc_HOL_Obool)),U_10581),hAPP(c_Set_OPow(U_10577),U_10579))) ),
inference(clausify,[status(thm)],[f_2847_3]) ).
fof(f_2848_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_2848_2,plain,
! [U_10586,U_10585,U_10584,U_10583,U_10582] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10583,U_10582),U_10585),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10583,tc_HOL_Obool)),U_10584),U_10586)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10583,U_10582),hAPP(hAPP(c_COMBC(U_10583,U_10582,U_10582),hAPP(hAPP(c_COMBS(U_10583,U_10582,tc_fun(U_10582,U_10582)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10582,tc_fun(U_10582,U_10582)),U_10583),c_If(U_10582)),hAPP(hAPP(c_COMBC(U_10583,tc_fun(U_10583,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10583)),U_10586))),U_10585)),c_Groups_Ozero__class_Ozero(U_10582))),U_10584)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10583),U_10584))
| ~ class_Groups_Ocomm__monoid__add(U_10582) ),
inference(variable_rename,[status(thm)],[f_2848_1]) ).
cnf(f_2848_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10583,U_10582),U_10585),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10583,tc_HOL_Obool)),U_10584),U_10586)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10583,U_10582),hAPP(hAPP(c_COMBC(U_10583,U_10582,U_10582),hAPP(hAPP(c_COMBS(U_10583,U_10582,tc_fun(U_10582,U_10582)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10582,tc_fun(U_10582,U_10582)),U_10583),c_If(U_10582)),hAPP(hAPP(c_COMBC(U_10583,tc_fun(U_10583,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10583)),U_10586))),U_10585)),c_Groups_Ozero__class_Ozero(U_10582))),U_10584)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10583),U_10584))
| ~ class_Groups_Ocomm__monoid__add(U_10582) ),
inference(clausify,[status(thm)],[f_2848_2]) ).
fof(f_2849_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_2849_2,plain,
! [U_10590,U_10589,U_10588,U_10587] :
( hAPP(c_Set_Oimage(U_10587,U_10589,U_10590),U_10588) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_10589,tc_HOL_Obool),U_10587,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10589,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10587,tc_fun(U_10589,tc_HOL_Obool),tc_fun(U_10589,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10589,tc_fun(tc_fun(U_10589,tc_HOL_Obool),tc_fun(U_10589,tc_HOL_Obool)),U_10587),c_Set_Oinsert(U_10589)),U_10590)),c_Orderings_Obot__class_Obot(tc_fun(U_10589,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_10589,tc_HOL_Obool))),U_10588)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10587),U_10588)) ),
inference(variable_rename,[status(thm)],[f_2849_1]) ).
cnf(f_2849_3,plain,
( hAPP(c_Set_Oimage(U_10587,U_10589,U_10590),U_10588) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_10589,tc_HOL_Obool),U_10587,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10589,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10587,tc_fun(U_10589,tc_HOL_Obool),tc_fun(U_10589,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10589,tc_fun(tc_fun(U_10589,tc_HOL_Obool),tc_fun(U_10589,tc_HOL_Obool)),U_10587),c_Set_Oinsert(U_10589)),U_10590)),c_Orderings_Obot__class_Obot(tc_fun(U_10589,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_10589,tc_HOL_Obool))),U_10588)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10587),U_10588)) ),
inference(clausify,[status(thm)],[f_2849_2]) ).
fof(f_2850_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_2850_2,plain,
! [U_10593,U_10592,U_10591] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10591),hAPP(c_Int_Onumber__class_Onumber__of(U_10591),U_10592)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10593))) = hAPP(hAPP(c_HOL_OLet(U_10591,U_10591),hAPP(hAPP(c_Power_Opower__class_Opower(U_10591),hAPP(c_Int_Onumber__class_Onumber__of(U_10591),U_10592)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10593))),hAPP(hAPP(c_COMBS(U_10591,U_10591,U_10591),c_Groups_Otimes__class_Otimes(U_10591)),c_COMBI(U_10591)))
| ~ class_Int_Onumber__ring(U_10591) ),
inference(variable_rename,[status(thm)],[f_2850_1]) ).
cnf(f_2850_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10591),hAPP(c_Int_Onumber__class_Onumber__of(U_10591),U_10592)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10593))) = hAPP(hAPP(c_HOL_OLet(U_10591,U_10591),hAPP(hAPP(c_Power_Opower__class_Opower(U_10591),hAPP(c_Int_Onumber__class_Onumber__of(U_10591),U_10592)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10593))),hAPP(hAPP(c_COMBS(U_10591,U_10591,U_10591),c_Groups_Otimes__class_Otimes(U_10591)),c_COMBI(U_10591)))
| ~ class_Int_Onumber__ring(U_10591) ),
inference(clausify,[status(thm)],[f_2850_2]) ).
fof(f_2851_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_2851_2,plain,
! [U_10597,U_10596,U_10595,U_10594] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10595,U_10594),U_10596),U_10597) = hAPP(hAPP(c_Finite__Set_Ofold(U_10595,U_10594,hAPP(hAPP(c_COMBB(U_10594,tc_fun(U_10594,U_10594),U_10595),c_Lattices_Osemilattice__sup__class_Osup(U_10594)),U_10597)),c_Orderings_Obot__class_Obot(U_10594)),U_10596)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10595),U_10596))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10594) ),
inference(variable_rename,[status(thm)],[f_2851_1]) ).
cnf(f_2851_3,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10595,U_10594),U_10596),U_10597) = hAPP(hAPP(c_Finite__Set_Ofold(U_10595,U_10594,hAPP(hAPP(c_COMBB(U_10594,tc_fun(U_10594,U_10594),U_10595),c_Lattices_Osemilattice__sup__class_Osup(U_10594)),U_10597)),c_Orderings_Obot__class_Obot(U_10594)),U_10596)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10595),U_10596))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10594) ),
inference(clausify,[status(thm)],[f_2851_2]) ).
fof(f_2852_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_2852_2,plain,
! [U_10599,U_10598] :
( ( hAPP(c_Finite__Set_Ocard(U_10598),U_10599) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_10598),U_10599)) )
& ( hAPP(c_Finite__Set_Ocard(U_10598),U_10599) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_10598,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_10598),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10599)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10598),U_10599)) ) ),
inference(variable_rename,[status(thm)],[f_2852_1]) ).
fof(f_2852_3,plain,
( ! [U_10603,U_10601] :
( hAPP(c_Finite__Set_Ocard(U_10601),U_10603) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_10601),U_10603)) )
& ! [U_10602,U_10600] :
( hAPP(c_Finite__Set_Ocard(U_10600),U_10602) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_10600,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_10600),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10602)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10600),U_10602)) ) ),
inference(miniscope,[status(thm)],[f_2852_2]) ).
cnf(f_2852_4,plain,
( hAPP(c_Finite__Set_Ocard(U_10600),U_10602) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_10600,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_10600),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10602)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10600),U_10602)) ),
inference(clausify,[status(thm)],[f_2852_3]) ).
cnf(f_2852_5,plain,
( hAPP(c_Finite__Set_Ocard(U_10601),U_10603) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_10601),U_10603)) ),
inference(clausify,[status(thm)],[f_2852_3]) ).
fof(f_2853_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_2853_2,plain,
! [U_10605,U_10604] :
( hAPP(c_Finite__Set_Ocard(U_10604),U_10605) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_10604,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_10604),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10605)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10604),U_10605)) ),
inference(variable_rename,[status(thm)],[f_2853_1]) ).
cnf(f_2853_3,plain,
( hAPP(c_Finite__Set_Ocard(U_10604),U_10605) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_10604,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_10604),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10605)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10604),U_10605)) ),
inference(clausify,[status(thm)],[f_2853_2]) ).
fof(f_2854_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_2854_2,plain,
! [U_10606] : c_Finite__Set_Ofun__left__comm__idem(U_10606,tc_fun(U_10606,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_10606,tc_HOL_Obool),tc_fun(tc_fun(U_10606,tc_HOL_Obool),tc_fun(U_10606,tc_HOL_Obool)),U_10606),hAPP(c_COMBC(tc_fun(U_10606,tc_HOL_Obool),tc_fun(U_10606,tc_HOL_Obool),tc_fun(U_10606,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_10606,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_10606,tc_fun(U_10606,tc_HOL_Obool),tc_fun(U_10606,tc_HOL_Obool)),c_Set_Oinsert(U_10606)),c_Orderings_Obot__class_Obot(tc_fun(U_10606,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_2854_1]) ).
cnf(f_2854_3,plain,
c_Finite__Set_Ofun__left__comm__idem(U_10606,tc_fun(U_10606,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_10606,tc_HOL_Obool),tc_fun(tc_fun(U_10606,tc_HOL_Obool),tc_fun(U_10606,tc_HOL_Obool)),U_10606),hAPP(c_COMBC(tc_fun(U_10606,tc_HOL_Obool),tc_fun(U_10606,tc_HOL_Obool),tc_fun(U_10606,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_10606,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_10606,tc_fun(U_10606,tc_HOL_Obool),tc_fun(U_10606,tc_HOL_Obool)),c_Set_Oinsert(U_10606)),c_Orderings_Obot__class_Obot(tc_fun(U_10606,tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_2854_2]) ).
fof(f_2855_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_2855_2,plain,
! [U_10610,U_10609,U_10608,U_10607] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10608,U_10607),U_10609),U_10610) = hAPP(hAPP(c_Finite__Set_Ofold(U_10608,U_10607,hAPP(hAPP(c_COMBB(U_10607,tc_fun(U_10607,U_10607),U_10608),c_Lattices_Osemilattice__inf__class_Oinf(U_10607)),U_10610)),c_Orderings_Otop__class_Otop(U_10607)),U_10609)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10608),U_10609))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10607) ),
inference(variable_rename,[status(thm)],[f_2855_1]) ).
cnf(f_2855_3,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10608,U_10607),U_10609),U_10610) = hAPP(hAPP(c_Finite__Set_Ofold(U_10608,U_10607,hAPP(hAPP(c_COMBB(U_10607,tc_fun(U_10607,U_10607),U_10608),c_Lattices_Osemilattice__inf__class_Oinf(U_10607)),U_10610)),c_Orderings_Otop__class_Otop(U_10607)),U_10609)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10608),U_10609))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_10607) ),
inference(clausify,[status(thm)],[f_2855_2]) ).
fof(f_2856_1,plain,
! [V_B_2,T_c,V_d_2,V_A_2,V_c_2,T_b] :
( ( ( ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) )
& ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) ) )
| hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
& ( ( ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = V_B_2
| hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) )
& ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_vimage__if]) ).
fof(f_2856_2,plain,
! [U_10616,U_10615,U_10614,U_10613,U_10612,U_10611] :
( ( ( ( hAPP(c_Set_Ovimage(U_10615,U_10611,hAPP(hAPP(c_COMBC(U_10615,U_10611,U_10611),hAPP(hAPP(c_COMBC(U_10615,U_10611,tc_fun(U_10611,U_10611)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10611,tc_fun(U_10611,U_10611)),U_10615),c_If(U_10611)),hAPP(hAPP(c_COMBC(U_10615,tc_fun(U_10615,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10615)),U_10616))),U_10612)),U_10614)),U_10613) = c_Orderings_Obot__class_Obot(tc_fun(U_10615,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_10611),U_10614),U_10613)) )
& ( hAPP(c_Set_Ovimage(U_10615,U_10611,hAPP(hAPP(c_COMBC(U_10615,U_10611,U_10611),hAPP(hAPP(c_COMBC(U_10615,U_10611,tc_fun(U_10611,U_10611)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10611,tc_fun(U_10611,U_10611)),U_10615),c_If(U_10611)),hAPP(hAPP(c_COMBC(U_10615,tc_fun(U_10615,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10615)),U_10616))),U_10612)),U_10614)),U_10613) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10615,tc_HOL_Obool)),U_10616)
| ~ hBOOL(hAPP(hAPP(c_member(U_10611),U_10614),U_10613)) ) )
| hBOOL(hAPP(hAPP(c_member(U_10611),U_10612),U_10613)) )
& ( ( ( hAPP(c_Set_Ovimage(U_10615,U_10611,hAPP(hAPP(c_COMBC(U_10615,U_10611,U_10611),hAPP(hAPP(c_COMBC(U_10615,U_10611,tc_fun(U_10611,U_10611)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10611,tc_fun(U_10611,U_10611)),U_10615),c_If(U_10611)),hAPP(hAPP(c_COMBC(U_10615,tc_fun(U_10615,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10615)),U_10616))),U_10612)),U_10614)),U_10613) = U_10616
| hBOOL(hAPP(hAPP(c_member(U_10611),U_10614),U_10613)) )
& ( hAPP(c_Set_Ovimage(U_10615,U_10611,hAPP(hAPP(c_COMBC(U_10615,U_10611,U_10611),hAPP(hAPP(c_COMBC(U_10615,U_10611,tc_fun(U_10611,U_10611)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10611,tc_fun(U_10611,U_10611)),U_10615),c_If(U_10611)),hAPP(hAPP(c_COMBC(U_10615,tc_fun(U_10615,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10615)),U_10616))),U_10612)),U_10614)),U_10613) = c_Orderings_Otop__class_Otop(tc_fun(U_10615,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_10611),U_10614),U_10613)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_10611),U_10612),U_10613)) ) ),
inference(variable_rename,[status(thm)],[f_2856_1]) ).
fof(f_2856_3,plain,
( ! [U_10628,U_10626,U_10624,U_10622,U_10620,U_10618] :
( ( ( hAPP(c_Set_Ovimage(U_10626,U_10618,hAPP(hAPP(c_COMBC(U_10626,U_10618,U_10618),hAPP(hAPP(c_COMBC(U_10626,U_10618,tc_fun(U_10618,U_10618)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10618,tc_fun(U_10618,U_10618)),U_10626),c_If(U_10618)),hAPP(hAPP(c_COMBC(U_10626,tc_fun(U_10626,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10626)),U_10628))),U_10620)),U_10624)),U_10622) = c_Orderings_Obot__class_Obot(tc_fun(U_10626,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_10618),U_10624),U_10622)) )
& ( hAPP(c_Set_Ovimage(U_10626,U_10618,hAPP(hAPP(c_COMBC(U_10626,U_10618,U_10618),hAPP(hAPP(c_COMBC(U_10626,U_10618,tc_fun(U_10618,U_10618)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10618,tc_fun(U_10618,U_10618)),U_10626),c_If(U_10618)),hAPP(hAPP(c_COMBC(U_10626,tc_fun(U_10626,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10626)),U_10628))),U_10620)),U_10624)),U_10622) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10626,tc_HOL_Obool)),U_10628)
| ~ hBOOL(hAPP(hAPP(c_member(U_10618),U_10624),U_10622)) ) )
| hBOOL(hAPP(hAPP(c_member(U_10618),U_10620),U_10622)) )
& ! [U_10627,U_10625,U_10623,U_10621,U_10619,U_10617] :
( ( ( hAPP(c_Set_Ovimage(U_10625,U_10617,hAPP(hAPP(c_COMBC(U_10625,U_10617,U_10617),hAPP(hAPP(c_COMBC(U_10625,U_10617,tc_fun(U_10617,U_10617)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10617,tc_fun(U_10617,U_10617)),U_10625),c_If(U_10617)),hAPP(hAPP(c_COMBC(U_10625,tc_fun(U_10625,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10625)),U_10627))),U_10619)),U_10623)),U_10621) = U_10627
| hBOOL(hAPP(hAPP(c_member(U_10617),U_10623),U_10621)) )
& ( hAPP(c_Set_Ovimage(U_10625,U_10617,hAPP(hAPP(c_COMBC(U_10625,U_10617,U_10617),hAPP(hAPP(c_COMBC(U_10625,U_10617,tc_fun(U_10617,U_10617)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10617,tc_fun(U_10617,U_10617)),U_10625),c_If(U_10617)),hAPP(hAPP(c_COMBC(U_10625,tc_fun(U_10625,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10625)),U_10627))),U_10619)),U_10623)),U_10621) = c_Orderings_Otop__class_Otop(tc_fun(U_10625,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_10617),U_10623),U_10621)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_10617),U_10619),U_10621)) ) ),
inference(miniscope,[status(thm)],[f_2856_2]) ).
cnf(f_2856_4,plain,
( hAPP(c_Set_Ovimage(U_10625,U_10617,hAPP(hAPP(c_COMBC(U_10625,U_10617,U_10617),hAPP(hAPP(c_COMBC(U_10625,U_10617,tc_fun(U_10617,U_10617)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10617,tc_fun(U_10617,U_10617)),U_10625),c_If(U_10617)),hAPP(hAPP(c_COMBC(U_10625,tc_fun(U_10625,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10625)),U_10627))),U_10619)),U_10623)),U_10621) = c_Orderings_Otop__class_Otop(tc_fun(U_10625,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_10617),U_10623),U_10621))
| ~ hBOOL(hAPP(hAPP(c_member(U_10617),U_10619),U_10621)) ),
inference(clausify,[status(thm)],[f_2856_3]) ).
cnf(f_2856_5,plain,
( hAPP(c_Set_Ovimage(U_10625,U_10617,hAPP(hAPP(c_COMBC(U_10625,U_10617,U_10617),hAPP(hAPP(c_COMBC(U_10625,U_10617,tc_fun(U_10617,U_10617)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10617,tc_fun(U_10617,U_10617)),U_10625),c_If(U_10617)),hAPP(hAPP(c_COMBC(U_10625,tc_fun(U_10625,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10625)),U_10627))),U_10619)),U_10623)),U_10621) = U_10627
| hBOOL(hAPP(hAPP(c_member(U_10617),U_10623),U_10621))
| ~ hBOOL(hAPP(hAPP(c_member(U_10617),U_10619),U_10621)) ),
inference(clausify,[status(thm)],[f_2856_3]) ).
cnf(f_2856_6,plain,
( hAPP(c_Set_Ovimage(U_10626,U_10618,hAPP(hAPP(c_COMBC(U_10626,U_10618,U_10618),hAPP(hAPP(c_COMBC(U_10626,U_10618,tc_fun(U_10618,U_10618)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10618,tc_fun(U_10618,U_10618)),U_10626),c_If(U_10618)),hAPP(hAPP(c_COMBC(U_10626,tc_fun(U_10626,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10626)),U_10628))),U_10620)),U_10624)),U_10622) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10626,tc_HOL_Obool)),U_10628)
| ~ hBOOL(hAPP(hAPP(c_member(U_10618),U_10624),U_10622))
| hBOOL(hAPP(hAPP(c_member(U_10618),U_10620),U_10622)) ),
inference(clausify,[status(thm)],[f_2856_3]) ).
cnf(f_2856_7,plain,
( hAPP(c_Set_Ovimage(U_10626,U_10618,hAPP(hAPP(c_COMBC(U_10626,U_10618,U_10618),hAPP(hAPP(c_COMBC(U_10626,U_10618,tc_fun(U_10618,U_10618)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10618,tc_fun(U_10618,U_10618)),U_10626),c_If(U_10618)),hAPP(hAPP(c_COMBC(U_10626,tc_fun(U_10626,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10626)),U_10628))),U_10620)),U_10624)),U_10622) = c_Orderings_Obot__class_Obot(tc_fun(U_10626,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_10618),U_10624),U_10622))
| hBOOL(hAPP(hAPP(c_member(U_10618),U_10620),U_10622)) ),
inference(clausify,[status(thm)],[f_2856_3]) ).
fof(f_2857_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_2857_2,plain,
! [U_10630,U_10629] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10630)),hAPP(c_Int_Onat,U_10629)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10630),U_10629)),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_10629)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10630)),hAPP(c_Int_Onat,U_10629)) = hAPP(c_Int_Onat,U_10630)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10629)) ) ),
inference(variable_rename,[status(thm)],[f_2857_1]) ).
fof(f_2857_3,plain,
( ! [U_10634,U_10632] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10634)),hAPP(c_Int_Onat,U_10632)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10634),U_10632)),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_10632)) )
& ! [U_10633,U_10631] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10633)),hAPP(c_Int_Onat,U_10631)) = hAPP(c_Int_Onat,U_10633)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10631)) ) ),
inference(miniscope,[status(thm)],[f_2857_2]) ).
cnf(f_2857_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10633)),hAPP(c_Int_Onat,U_10631)) = hAPP(c_Int_Onat,U_10633)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10631)) ),
inference(clausify,[status(thm)],[f_2857_3]) ).
cnf(f_2857_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10634)),hAPP(c_Int_Onat,U_10632)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10634),U_10632)),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_10632)) ),
inference(clausify,[status(thm)],[f_2857_3]) ).
fof(f_2858_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_2858_2,plain,
! [U_10636,U_10635] :
( c_Divides_OnegDivAlg(U_10635,U_10636) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10635),U_10636)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10635,U_10636))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10636))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10635),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_2858_1]) ).
cnf(f_2858_3,plain,
( c_Divides_OnegDivAlg(U_10635,U_10636) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10635),U_10636)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10635,U_10636))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10636))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10635),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2858_2]) ).
fof(f_2859_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_2859_2,plain,
! [U_10637] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_10637) = 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_10637),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[f_2859_1]) ).
cnf(f_2859_3,plain,
c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_10637) = 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_10637),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_2859_2]) ).
fof(f_2860_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_2860_2,plain,
! [U_10640,U_10639,U_10638] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10638,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10639)),U_10640) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10638,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10638,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_10639)),U_10640)),hAPP(U_10640,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_2860_1]) ).
cnf(f_2860_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10638,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10639)),U_10640) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10638,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10638,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_10639)),U_10640)),hAPP(U_10640,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_2860_2]) ).
fof(f_2861_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_2861_2,plain,
! [U_10643,U_10642,U_10641] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_10641),U_10643),U_10642) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10641),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10641,tc_Nat_Onat),U_10643),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10642))
| ~ c_Nat__Transfer_Onat__set(U_10642)
| ~ class_Groups_Ocomm__monoid__mult(U_10641)
| ~ class_Groups_Ocomm__monoid__add(U_10641) ),
inference(variable_rename,[status(thm)],[f_2861_1]) ).
cnf(f_2861_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_10641),U_10643),U_10642) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10641),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10641,tc_Nat_Onat),U_10643),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10642))
| ~ c_Nat__Transfer_Onat__set(U_10642)
| ~ class_Groups_Ocomm__monoid__mult(U_10641)
| ~ class_Groups_Ocomm__monoid__add(U_10641) ),
inference(clausify,[status(thm)],[f_2861_2]) ).
fof(f_2862_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_2862_2,plain,
! [U_10645,U_10644] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10644),U_10645) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_10644,hAPP(hAPP(c_COMBC(U_10644,U_10644,U_10644),c_Groups_Oplus__class_Oplus(U_10644)),c_Groups_Oone__class_Oone(U_10644)),U_10645,c_Groups_Ozero__class_Ozero(U_10644))
| ~ class_Rings_Osemiring__1(U_10644) ),
inference(variable_rename,[status(thm)],[f_2862_1]) ).
cnf(f_2862_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10644),U_10645) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_10644,hAPP(hAPP(c_COMBC(U_10644,U_10644,U_10644),c_Groups_Oplus__class_Oplus(U_10644)),c_Groups_Oone__class_Oone(U_10644)),U_10645,c_Groups_Ozero__class_Ozero(U_10644))
| ~ class_Rings_Osemiring__1(U_10644) ),
inference(clausify,[status(thm)],[f_2862_2]) ).
fof(f_2863_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_2863_2,plain,
! [U_10648,U_10647,U_10646] : hAPP(c_Divides_Oadjust(U_10646),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10647),U_10648)) = 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_10648),U_10646)),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_10647)),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_10647)),U_10648))),
inference(variable_rename,[status(thm)],[f_2863_1]) ).
cnf(f_2863_3,plain,
hAPP(c_Divides_Oadjust(U_10646),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10647),U_10648)) = 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_10648),U_10646)),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_10647)),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_10647)),U_10648))),
inference(clausify,[status(thm)],[f_2863_2]) ).
fof(f_2864_1,plain,
! [V_P_2,V_n_2,V_m_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_P_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_P_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_P_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__head]) ).
fof(f_2864_2,plain,
! [U_10652,U_10651,U_10650,U_10649] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10649),U_10652),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10650,U_10651)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10649),hAPP(U_10652,U_10650)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10649),U_10652),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10650,U_10651)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10650),U_10651))
| ~ class_Groups_Ocomm__monoid__add(U_10649) ),
inference(variable_rename,[status(thm)],[f_2864_1]) ).
cnf(f_2864_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10649),U_10652),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10650,U_10651)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10649),hAPP(U_10652,U_10650)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10649),U_10652),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10650,U_10651)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10650),U_10651))
| ~ class_Groups_Ocomm__monoid__add(U_10649) ),
inference(clausify,[status(thm)],[f_2864_2]) ).
fof(f_2865_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_2865_2,plain,
! [U_10655,U_10654,U_10653] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10653,tc_HOL_Obool)),U_10655),U_10654) = hAPP(hAPP(c_Finite__Set_Ofold(U_10653,tc_fun(U_10653,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_10653,tc_HOL_Obool),tc_fun(tc_fun(U_10653,tc_HOL_Obool),tc_fun(U_10653,tc_HOL_Obool)),U_10653),hAPP(c_COMBC(tc_fun(U_10653,tc_HOL_Obool),tc_fun(U_10653,tc_HOL_Obool),tc_fun(U_10653,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_10653,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_10653,tc_fun(U_10653,tc_HOL_Obool),tc_fun(U_10653,tc_HOL_Obool)),c_Set_Oinsert(U_10653)),c_Orderings_Obot__class_Obot(tc_fun(U_10653,tc_HOL_Obool))))),U_10655),U_10654)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10653),U_10654)) ),
inference(variable_rename,[status(thm)],[f_2865_1]) ).
cnf(f_2865_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10653,tc_HOL_Obool)),U_10655),U_10654) = hAPP(hAPP(c_Finite__Set_Ofold(U_10653,tc_fun(U_10653,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_10653,tc_HOL_Obool),tc_fun(tc_fun(U_10653,tc_HOL_Obool),tc_fun(U_10653,tc_HOL_Obool)),U_10653),hAPP(c_COMBC(tc_fun(U_10653,tc_HOL_Obool),tc_fun(U_10653,tc_HOL_Obool),tc_fun(U_10653,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_10653,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_10653,tc_fun(U_10653,tc_HOL_Obool),tc_fun(U_10653,tc_HOL_Obool)),c_Set_Oinsert(U_10653)),c_Orderings_Obot__class_Obot(tc_fun(U_10653,tc_HOL_Obool))))),U_10655),U_10654)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10653),U_10654)) ),
inference(clausify,[status(thm)],[f_2865_2]) ).
fof(f_2866_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_2866_2,plain,
! [U_10661,U_10660,U_10659,U_10658,U_10657,U_10656] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10658,U_10656),U_10661),hAPP(c_Set_Oimage(U_10657,U_10658,U_10659),U_10660)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10657,U_10656),hAPP(c_Fun_Ocomp(U_10658,U_10656,U_10657,U_10661),U_10659)),U_10660)
| ~ c_Fun_Oinj__on(U_10657,U_10658,U_10659,U_10660)
| ~ class_Groups_Ocomm__monoid__add(U_10656) ),
inference(variable_rename,[status(thm)],[f_2866_1]) ).
cnf(f_2866_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10658,U_10656),U_10661),hAPP(c_Set_Oimage(U_10657,U_10658,U_10659),U_10660)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10657,U_10656),hAPP(c_Fun_Ocomp(U_10658,U_10656,U_10657,U_10661),U_10659)),U_10660)
| ~ c_Fun_Oinj__on(U_10657,U_10658,U_10659,U_10660)
| ~ class_Groups_Ocomm__monoid__add(U_10656) ),
inference(clausify,[status(thm)],[f_2866_2]) ).
fof(f_2867_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_2867_2,plain,
! [U_10663,U_10662] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10662) = hAPP(c_Nat_OSuc,U_10663)
| ~ 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_10662))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10663))))) )
& ( 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_10662))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10663)))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10662) != hAPP(c_Nat_OSuc,U_10663) ) ),
inference(variable_rename,[status(thm)],[f_2867_1]) ).
fof(f_2867_3,plain,
( ! [U_10667,U_10665] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10665) = hAPP(c_Nat_OSuc,U_10667)
| ~ 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_10665))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10667))))) )
& ! [U_10666,U_10664] :
( 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_10664))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10666)))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10664) != hAPP(c_Nat_OSuc,U_10666) ) ),
inference(miniscope,[status(thm)],[f_2867_2]) ).
cnf(f_2867_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_10664))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10666)))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10664) != hAPP(c_Nat_OSuc,U_10666) ),
inference(clausify,[status(thm)],[f_2867_3]) ).
cnf(f_2867_5,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10665) = hAPP(c_Nat_OSuc,U_10667)
| ~ 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_10665))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10667))))) ),
inference(clausify,[status(thm)],[f_2867_3]) ).
fof(f_2868_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_2868_2,plain,
! [U_10669,U_10668] :
( ( hAPP(c_Nat_OSuc,U_10668) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10669)
| ~ 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_10669))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10668))))) )
& ( 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_10669))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10668)))))
| hAPP(c_Nat_OSuc,U_10668) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10669) ) ),
inference(variable_rename,[status(thm)],[f_2868_1]) ).
fof(f_2868_3,plain,
( ! [U_10673,U_10671] :
( hAPP(c_Nat_OSuc,U_10671) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10673)
| ~ 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_10673))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10671))))) )
& ! [U_10672,U_10670] :
( 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_10672))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10670)))))
| hAPP(c_Nat_OSuc,U_10670) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10672) ) ),
inference(miniscope,[status(thm)],[f_2868_2]) ).
cnf(f_2868_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_10672))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10670)))))
| hAPP(c_Nat_OSuc,U_10670) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10672) ),
inference(clausify,[status(thm)],[f_2868_3]) ).
cnf(f_2868_5,plain,
( hAPP(c_Nat_OSuc,U_10671) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10673)
| ~ 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_10673))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10671))))) ),
inference(clausify,[status(thm)],[f_2868_3]) ).
fof(f_2869_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_2869_2,plain,
! [U_10679,U_10678,U_10677,U_10676,U_10675,U_10674] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10676,U_10674),U_10679),hAPP(c_Set_Oimage(U_10675,U_10676,U_10677),U_10678)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10675,U_10674),hAPP(c_Fun_Ocomp(U_10676,U_10674,U_10675,U_10679),U_10677)),U_10678)
| ~ c_Fun_Oinj__on(U_10675,U_10676,U_10677,U_10678)
| ~ class_Groups_Ocomm__monoid__mult(U_10674) ),
inference(variable_rename,[status(thm)],[f_2869_1]) ).
cnf(f_2869_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10676,U_10674),U_10679),hAPP(c_Set_Oimage(U_10675,U_10676,U_10677),U_10678)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10675,U_10674),hAPP(c_Fun_Ocomp(U_10676,U_10674,U_10675,U_10679),U_10677)),U_10678)
| ~ c_Fun_Oinj__on(U_10675,U_10676,U_10677,U_10678)
| ~ class_Groups_Ocomm__monoid__mult(U_10674) ),
inference(clausify,[status(thm)],[f_2869_2]) ).
fof(f_2870_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_2870_2,plain,
! [U_10687,U_10686,U_10685,U_10684,U_10683,U_10682,U_10681,U_10680] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10682,U_10680),U_10687),U_10685) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10681,U_10680),U_10686),U_10684)
| U_10686 != hAPP(c_Fun_Ocomp(U_10682,U_10680,U_10681,U_10687),U_10683)
| U_10685 != hAPP(c_Set_Oimage(U_10681,U_10682,U_10683),U_10684)
| ~ c_Fun_Oinj__on(U_10681,U_10682,U_10683,U_10684)
| ~ class_Groups_Ocomm__monoid__mult(U_10680) ),
inference(variable_rename,[status(thm)],[f_2870_1]) ).
cnf(f_2870_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10682,U_10680),U_10687),U_10685) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10681,U_10680),U_10686),U_10684)
| U_10686 != hAPP(c_Fun_Ocomp(U_10682,U_10680,U_10681,U_10687),U_10683)
| U_10685 != hAPP(c_Set_Oimage(U_10681,U_10682,U_10683),U_10684)
| ~ c_Fun_Oinj__on(U_10681,U_10682,U_10683,U_10684)
| ~ class_Groups_Ocomm__monoid__mult(U_10680) ),
inference(clausify,[status(thm)],[f_2870_2]) ).
fof(f_2871_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_2871_2,plain,
! [U_10691,U_10690,U_10689,U_10688] : c_Nat_Onat_Onat__case(U_10688,U_10689,U_10690,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10691)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10688),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10691))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10688,U_10688),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10688,tc_fun(U_10688,U_10688)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10688,tc_fun(U_10688,U_10688)),tc_Int_Oint),c_If(U_10688)),c_Nat__Numeral_Oneg)),U_10689)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10688,tc_Int_Oint),U_10690),c_Int_Onat))),
inference(variable_rename,[status(thm)],[f_2871_1]) ).
cnf(f_2871_3,plain,
c_Nat_Onat_Onat__case(U_10688,U_10689,U_10690,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10691)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10688),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10691))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10688,U_10688),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10688,tc_fun(U_10688,U_10688)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10688,tc_fun(U_10688,U_10688)),tc_Int_Oint),c_If(U_10688)),c_Nat__Numeral_Oneg)),U_10689)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10688,tc_Int_Oint),U_10690),c_Int_Onat))),
inference(clausify,[status(thm)],[f_2871_2]) ).
fof(f_2872_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_2872_2,plain,
! [U_10692] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10692)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10692)),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_10692))) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10692)) = 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_10692))) ) ),
inference(variable_rename,[status(thm)],[f_2872_1]) ).
fof(f_2872_3,plain,
( ! [U_10694] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10694)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10694)),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_10694))) )
& ! [U_10693] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10693)) = 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_10693))) ) ),
inference(miniscope,[status(thm)],[f_2872_2]) ).
cnf(f_2872_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10693)) = 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_10693))) ),
inference(clausify,[status(thm)],[f_2872_3]) ).
cnf(f_2872_5,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10694)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10694)),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_10694))) ),
inference(clausify,[status(thm)],[f_2872_3]) ).
fof(f_2873_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_2873_2,plain,
! [U_10697,U_10696,U_10695] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10695),hAPP(c_Power_Opower__class_Opower(U_10695),U_10696)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10697)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10695),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10695),hAPP(hAPP(c_Power_Opower__class_Opower(U_10695),U_10696),U_10697)),c_Groups_Oone__class_Oone(U_10695))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10695),U_10696),c_Groups_Oone__class_Oone(U_10695)))
| U_10696 = c_Groups_Oone__class_Oone(U_10695)
| ~ class_Fields_Ofield(U_10695) ),
inference(variable_rename,[status(thm)],[f_2873_1]) ).
cnf(f_2873_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10695),hAPP(c_Power_Opower__class_Opower(U_10695),U_10696)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10697)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10695),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10695),hAPP(hAPP(c_Power_Opower__class_Opower(U_10695),U_10696),U_10697)),c_Groups_Oone__class_Oone(U_10695))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10695),U_10696),c_Groups_Oone__class_Oone(U_10695)))
| U_10696 = c_Groups_Oone__class_Oone(U_10695)
| ~ class_Fields_Ofield(U_10695) ),
inference(clausify,[status(thm)],[f_2873_2]) ).
fof(f_2874_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_2874_2,plain,
! [U_10699,U_10698] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10698),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10698),c_Groups_Oone__class_Oone(U_10698)),c_Groups_Oone__class_Oone(U_10698))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10698),c_Nat_Osemiring__1__class_Oof__nat(U_10698)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_10699))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10698),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10698),U_10699)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10698),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10698),U_10699)),c_Groups_Oone__class_Oone(U_10698)))
| ~ class_Rings_Ocomm__semiring__1(U_10698) ),
inference(variable_rename,[status(thm)],[f_2874_1]) ).
cnf(f_2874_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10698),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10698),c_Groups_Oone__class_Oone(U_10698)),c_Groups_Oone__class_Oone(U_10698))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10698),c_Nat_Osemiring__1__class_Oof__nat(U_10698)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_10699))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10698),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10698),U_10699)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10698),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10698),U_10699)),c_Groups_Oone__class_Oone(U_10698)))
| ~ class_Rings_Ocomm__semiring__1(U_10698) ),
inference(clausify,[status(thm)],[f_2874_2]) ).
fof(f_2875_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_2875_2,plain,
! [U_10703,U_10702,U_10701,U_10700] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10700),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_10700,U_10700),hAPP(hAPP(c_COMBB(U_10700,tc_fun(U_10700,U_10700),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_10700)),U_10703)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10700,tc_Nat_Onat),U_10703),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_10701,U_10702)) = c_Groups_Ozero__class_Ozero(U_10700)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10701),U_10702)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10700),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_10700,U_10700),hAPP(hAPP(c_COMBB(U_10700,tc_fun(U_10700,U_10700),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_10700)),U_10703)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10700,tc_Nat_Onat),U_10703),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_10701,U_10702)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10700),hAPP(U_10703,U_10701)),hAPP(U_10703,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10702),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10701),U_10702)) ) )
| ~ class_Groups_Oab__group__add(U_10700) ),
inference(variable_rename,[status(thm)],[f_2875_1]) ).
cnf(f_2875_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10700),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_10700,U_10700),hAPP(hAPP(c_COMBB(U_10700,tc_fun(U_10700,U_10700),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_10700)),U_10703)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10700,tc_Nat_Onat),U_10703),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_10701,U_10702)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10700),hAPP(U_10703,U_10701)),hAPP(U_10703,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10702),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10701),U_10702))
| ~ class_Groups_Oab__group__add(U_10700) ),
inference(clausify,[status(thm)],[f_2875_2]) ).
cnf(f_2875_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10700),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_10700,U_10700),hAPP(hAPP(c_COMBB(U_10700,tc_fun(U_10700,U_10700),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_10700)),U_10703)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10700,tc_Nat_Onat),U_10703),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_10701,U_10702)) = c_Groups_Ozero__class_Ozero(U_10700)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10701),U_10702))
| ~ class_Groups_Oab__group__add(U_10700) ),
inference(clausify,[status(thm)],[f_2875_2]) ).
fof(f_2876_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_2876_2,plain,
! [U_10705,U_10704] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10704)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10705)))
| ~ 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_10705))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10704)),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_10705))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10704)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10704)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10705))) ) ),
inference(variable_rename,[status(thm)],[f_2876_1]) ).
fof(f_2876_3,plain,
( ! [U_10709,U_10707] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10707)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10709)))
| ~ 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_10709))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10707)),c_Int_Onat))))) )
& ! [U_10708,U_10706] :
( 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_10708))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10706)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10706)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10708))) ) ),
inference(miniscope,[status(thm)],[f_2876_2]) ).
cnf(f_2876_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_10708))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10706)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10706)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10708))) ),
inference(clausify,[status(thm)],[f_2876_3]) ).
cnf(f_2876_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10707)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10709)))
| ~ 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_10709))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10707)),c_Int_Onat))))) ),
inference(clausify,[status(thm)],[f_2876_3]) ).
fof(f_2877_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_2877_2,plain,
! [U_10711,U_10710] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10710)),hAPP(c_Nat_OSuc,U_10711)))
| ~ 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_10710))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10711)))) )
& ( 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_10710))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10711))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10710)),hAPP(c_Nat_OSuc,U_10711))) ) ),
inference(variable_rename,[status(thm)],[f_2877_1]) ).
fof(f_2877_3,plain,
( ! [U_10715,U_10713] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10713)),hAPP(c_Nat_OSuc,U_10715)))
| ~ 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_10713))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10715)))) )
& ! [U_10714,U_10712] :
( 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_10712))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10714))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10712)),hAPP(c_Nat_OSuc,U_10714))) ) ),
inference(miniscope,[status(thm)],[f_2877_2]) ).
cnf(f_2877_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_10712))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10714))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10712)),hAPP(c_Nat_OSuc,U_10714))) ),
inference(clausify,[status(thm)],[f_2877_3]) ).
cnf(f_2877_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10713)),hAPP(c_Nat_OSuc,U_10715)))
| ~ 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_10713))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10715)))) ),
inference(clausify,[status(thm)],[f_2877_3]) ).
fof(f_2878_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_2878_2,plain,
! [U_10717,U_10716] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10716)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10717)))
| ~ 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_10717))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10716)),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_10717))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10716)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10716)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10717))) ) ),
inference(variable_rename,[status(thm)],[f_2878_1]) ).
fof(f_2878_3,plain,
( ! [U_10721,U_10719] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10719)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10721)))
| ~ 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_10721))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10719)),c_Int_Onat))))) )
& ! [U_10720,U_10718] :
( 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_10720))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10718)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10718)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10720))) ) ),
inference(miniscope,[status(thm)],[f_2878_2]) ).
cnf(f_2878_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_10720))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10718)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10718)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10720))) ),
inference(clausify,[status(thm)],[f_2878_3]) ).
cnf(f_2878_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10719)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10721)))
| ~ 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_10721))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10719)),c_Int_Onat))))) ),
inference(clausify,[status(thm)],[f_2878_3]) ).
fof(f_2879_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_2879_2,plain,
! [U_10723,U_10722] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10722)),hAPP(c_Nat_OSuc,U_10723)))
| ~ 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_10722))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10723)))) )
& ( 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_10722))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10723))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10722)),hAPP(c_Nat_OSuc,U_10723))) ) ),
inference(variable_rename,[status(thm)],[f_2879_1]) ).
fof(f_2879_3,plain,
( ! [U_10727,U_10725] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10725)),hAPP(c_Nat_OSuc,U_10727)))
| ~ 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_10725))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10727)))) )
& ! [U_10726,U_10724] :
( 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_10724))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10726))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10724)),hAPP(c_Nat_OSuc,U_10726))) ) ),
inference(miniscope,[status(thm)],[f_2879_2]) ).
cnf(f_2879_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_10724))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10726))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10724)),hAPP(c_Nat_OSuc,U_10726))) ),
inference(clausify,[status(thm)],[f_2879_3]) ).
cnf(f_2879_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_10725)),hAPP(c_Nat_OSuc,U_10727)))
| ~ 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_10725))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_10727)))) ),
inference(clausify,[status(thm)],[f_2879_3]) ).
fof(f_2880_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_2880_2,plain,
! [U_10729,U_10728] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10728)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10729)) = 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_10729))),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_10728))),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_10728)),c_Int_Onat)))),
inference(variable_rename,[status(thm)],[f_2880_1]) ).
cnf(f_2880_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10728)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10729)) = 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_10729))),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_10728))),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_10728)),c_Int_Onat)))),
inference(clausify,[status(thm)],[f_2880_2]) ).
fof(f_2881_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_2881_2,plain,
! [U_10731,U_10730] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10730)),hAPP(c_Nat_OSuc,U_10731)) = 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_10730))),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_10731))),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_10731)))),
inference(variable_rename,[status(thm)],[f_2881_1]) ).
cnf(f_2881_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10730)),hAPP(c_Nat_OSuc,U_10731)) = 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_10730))),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_10731))),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_10731)))),
inference(clausify,[status(thm)],[f_2881_2]) ).
fof(f_2882_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_2882_2,plain,
! [U_10736,U_10735,U_10734,U_10733,U_10732] : c_Nat_Onat_Onat__case(U_10732,U_10733,U_10734,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10735)),U_10736)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10732),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10735))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10732,U_10732),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10732,tc_fun(U_10732,U_10732)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10732,tc_fun(U_10732,U_10732)),tc_Int_Oint),c_If(U_10732)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_10732,U_10733,U_10734,U_10736))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10732,tc_Int_Oint),U_10734),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_10736)))),
inference(variable_rename,[status(thm)],[f_2882_1]) ).
cnf(f_2882_3,plain,
c_Nat_Onat_Onat__case(U_10732,U_10733,U_10734,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10735)),U_10736)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10732),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10735))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10732,U_10732),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10732,tc_fun(U_10732,U_10732)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10732,tc_fun(U_10732,U_10732)),tc_Int_Oint),c_If(U_10732)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_10732,U_10733,U_10734,U_10736))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10732,tc_Int_Oint),U_10734),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_10736)))),
inference(clausify,[status(thm)],[f_2882_2]) ).
fof(f_2883_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_2883_2,plain,
! [U_10739,U_10738,U_10737] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10737),U_10739),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10738))) = c_Groups_Oone__class_Oone(U_10737)
| 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_10738))) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10737),U_10739),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10738))) = hAPP(hAPP(c_HOL_OLet(U_10737,U_10737),hAPP(hAPP(c_Power_Opower__class_Opower(U_10737),U_10739),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10738))),hAPP(hAPP(c_COMBS(U_10737,U_10737,U_10737),hAPP(hAPP(c_COMBB(U_10737,tc_fun(U_10737,U_10737),U_10737),c_Groups_Otimes__class_Otimes(U_10737)),hAPP(c_Groups_Otimes__class_Otimes(U_10737),U_10739))),c_COMBI(U_10737)))
| ~ 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_10738))) ) )
| ~ class_Int_Onumber__ring(U_10737) ),
inference(variable_rename,[status(thm)],[f_2883_1]) ).
cnf(f_2883_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10737),U_10739),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10738))) = hAPP(hAPP(c_HOL_OLet(U_10737,U_10737),hAPP(hAPP(c_Power_Opower__class_Opower(U_10737),U_10739),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10738))),hAPP(hAPP(c_COMBS(U_10737,U_10737,U_10737),hAPP(hAPP(c_COMBB(U_10737,tc_fun(U_10737,U_10737),U_10737),c_Groups_Otimes__class_Otimes(U_10737)),hAPP(c_Groups_Otimes__class_Otimes(U_10737),U_10739))),c_COMBI(U_10737)))
| ~ 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_10738)))
| ~ class_Int_Onumber__ring(U_10737) ),
inference(clausify,[status(thm)],[f_2883_2]) ).
cnf(f_2883_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10737),U_10739),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10738))) = c_Groups_Oone__class_Oone(U_10737)
| 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_10738)))
| ~ class_Int_Onumber__ring(U_10737) ),
inference(clausify,[status(thm)],[f_2883_2]) ).
fof(f_2884_1,plain,
! [V_c_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__gen__delta]) ).
fof(f_2884_2,plain,
! [U_10745,U_10744,U_10743,U_10742,U_10741,U_10740] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10741,U_10740),hAPP(hAPP(c_COMBC(U_10741,U_10740,U_10740),hAPP(hAPP(c_COMBS(U_10741,U_10740,tc_fun(U_10740,U_10740)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10740,tc_fun(U_10740,U_10740)),U_10741),c_If(U_10740)),hAPP(hAPP(c_COMBC(U_10741,U_10741,tc_HOL_Obool),c_fequal),U_10743))),U_10744)),U_10745)),U_10742) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10740),U_10745),hAPP(c_Finite__Set_Ocard(U_10741),U_10742))
| hBOOL(hAPP(hAPP(c_member(U_10741),U_10743),U_10742)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10741,U_10740),hAPP(hAPP(c_COMBC(U_10741,U_10740,U_10740),hAPP(hAPP(c_COMBS(U_10741,U_10740,tc_fun(U_10740,U_10740)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10740,tc_fun(U_10740,U_10740)),U_10741),c_If(U_10740)),hAPP(hAPP(c_COMBC(U_10741,U_10741,tc_HOL_Obool),c_fequal),U_10743))),U_10744)),U_10745)),U_10742) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10740),hAPP(U_10744,U_10743)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10740),U_10745),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10741),U_10742)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_member(U_10741),U_10743),U_10742)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10741),U_10742))
| ~ class_Groups_Ocomm__monoid__mult(U_10740) ),
inference(variable_rename,[status(thm)],[f_2884_1]) ).
cnf(f_2884_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10741,U_10740),hAPP(hAPP(c_COMBC(U_10741,U_10740,U_10740),hAPP(hAPP(c_COMBS(U_10741,U_10740,tc_fun(U_10740,U_10740)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10740,tc_fun(U_10740,U_10740)),U_10741),c_If(U_10740)),hAPP(hAPP(c_COMBC(U_10741,U_10741,tc_HOL_Obool),c_fequal),U_10743))),U_10744)),U_10745)),U_10742) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10740),hAPP(U_10744,U_10743)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10740),U_10745),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10741),U_10742)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_member(U_10741),U_10743),U_10742))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10741),U_10742))
| ~ class_Groups_Ocomm__monoid__mult(U_10740) ),
inference(clausify,[status(thm)],[f_2884_2]) ).
cnf(f_2884_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10741,U_10740),hAPP(hAPP(c_COMBC(U_10741,U_10740,U_10740),hAPP(hAPP(c_COMBS(U_10741,U_10740,tc_fun(U_10740,U_10740)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10740,tc_fun(U_10740,U_10740)),U_10741),c_If(U_10740)),hAPP(hAPP(c_COMBC(U_10741,U_10741,tc_HOL_Obool),c_fequal),U_10743))),U_10744)),U_10745)),U_10742) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10740),U_10745),hAPP(c_Finite__Set_Ocard(U_10741),U_10742))
| hBOOL(hAPP(hAPP(c_member(U_10741),U_10743),U_10742))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10741),U_10742))
| ~ class_Groups_Ocomm__monoid__mult(U_10740) ),
inference(clausify,[status(thm)],[f_2884_2]) ).
fof(f_2885_1,plain,
! [V_x_2,V_y_2,V_c_2] :
( ( ( ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) )
& ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2)) )
& ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_c_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_image__minus__const__atLeastLessThan__nat]) ).
fof(f_2885_2,plain,
! [U_10748,U_10747,U_10746] :
( ( ( ( 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_10746)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10748),U_10747)) = 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_10748),U_10747)) )
& ( 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_10746)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10748),U_10747)) = 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_10748),U_10747)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10746),U_10747)) )
& ( 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_10746)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10748),U_10747)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10748),U_10746)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10747),U_10746))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10746),U_10747)) ) ),
inference(variable_rename,[status(thm)],[f_2885_1]) ).
fof(f_2885_3,plain,
( ! [U_10754,U_10752,U_10750] :
( ( ( 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_10750)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10754),U_10752)) = 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_10754),U_10752)) )
& ( 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_10750)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10754),U_10752)) = 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_10754),U_10752)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10750),U_10752)) )
& ! [U_10753,U_10751,U_10749] :
( 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_10749)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10753),U_10751)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10753),U_10749)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10751),U_10749))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10749),U_10751)) ) ),
inference(miniscope,[status(thm)],[f_2885_2]) ).
cnf(f_2885_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_10749)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10753),U_10751)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10753),U_10749)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10751),U_10749))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10749),U_10751)) ),
inference(clausify,[status(thm)],[f_2885_3]) ).
cnf(f_2885_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_10750)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10754),U_10752)) = 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_10754),U_10752))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10750),U_10752)) ),
inference(clausify,[status(thm)],[f_2885_3]) ).
cnf(f_2885_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_10750)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10754),U_10752)) = 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_10754),U_10752))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10750),U_10752)) ),
inference(clausify,[status(thm)],[f_2885_3]) ).
fof(f_2886_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_2886_2,plain,
! [U_10759,U_10758,U_10757,U_10756,U_10755] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10756,U_10755),U_10759),hAPP(c_Set_Oimage(U_10756,U_10756,U_10758),U_10757)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10756,U_10755),hAPP(c_Fun_Ocomp(U_10756,U_10755,U_10756,U_10759),U_10758)),U_10757)
| ~ c_Fun_Oinj__on(U_10756,U_10756,U_10758,U_10757)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10756),U_10757))
| ~ class_Groups_Ocomm__monoid__add(U_10755) ),
inference(variable_rename,[status(thm)],[f_2886_1]) ).
cnf(f_2886_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10756,U_10755),U_10759),hAPP(c_Set_Oimage(U_10756,U_10756,U_10758),U_10757)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10756,U_10755),hAPP(c_Fun_Ocomp(U_10756,U_10755,U_10756,U_10759),U_10758)),U_10757)
| ~ c_Fun_Oinj__on(U_10756,U_10756,U_10758,U_10757)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10756),U_10757))
| ~ class_Groups_Ocomm__monoid__add(U_10755) ),
inference(clausify,[status(thm)],[f_2886_2]) ).
fof(f_2887_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_2887_2,plain,
! [U_10761,U_10760] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10761),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10760))) = 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_10760))) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10761),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10760))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10761),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10760))),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_10761))),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_10760))) ) ),
inference(variable_rename,[status(thm)],[f_2887_1]) ).
fof(f_2887_3,plain,
( ! [U_10765,U_10763] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10765),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10763))) = 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_10763))) )
& ! [U_10764,U_10762] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10764),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10762))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10764),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10762))),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_10764))),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_10762))) ) ),
inference(miniscope,[status(thm)],[f_2887_2]) ).
cnf(f_2887_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10764),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10762))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10764),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10762))),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_10764))),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_10762))) ),
inference(clausify,[status(thm)],[f_2887_3]) ).
cnf(f_2887_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10765),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10763))) = 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_10763))) ),
inference(clausify,[status(thm)],[f_2887_3]) ).
fof(f_2888_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_2888_2,plain,
! [U_10770,U_10769,U_10768,U_10767,U_10766] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10767,U_10766),U_10770),hAPP(c_Set_Oimage(U_10767,U_10767,U_10769),U_10768)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10767,U_10766),hAPP(c_Fun_Ocomp(U_10767,U_10766,U_10767,U_10770),U_10769)),U_10768)
| ~ c_Fun_Oinj__on(U_10767,U_10767,U_10769,U_10768)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10767),U_10768))
| ~ class_Groups_Ocomm__monoid__mult(U_10766) ),
inference(variable_rename,[status(thm)],[f_2888_1]) ).
cnf(f_2888_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10767,U_10766),U_10770),hAPP(c_Set_Oimage(U_10767,U_10767,U_10769),U_10768)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10767,U_10766),hAPP(c_Fun_Ocomp(U_10767,U_10766,U_10767,U_10770),U_10769)),U_10768)
| ~ c_Fun_Oinj__on(U_10767,U_10767,U_10769,U_10768)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10767),U_10768))
| ~ class_Groups_Ocomm__monoid__mult(U_10766) ),
inference(clausify,[status(thm)],[f_2888_2]) ).
fof(f_2889_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_2889_2,plain,
! [U_10774,U_10773,U_10772,U_10771] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10771),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10771),c_Groups_Oone__class_Oone(U_10771)),c_Groups_Oone__class_Oone(U_10771))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10771),hAPP(hAPP(c_COMBB(U_10771,U_10771,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_10771),U_10772)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_10771,U_10771),hAPP(hAPP(c_COMBB(U_10771,tc_fun(U_10771,U_10771),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_10771)),c_Nat_Osemiring__1__class_Oof__nat(U_10771))),U_10773))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10774))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10771),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10771),U_10774)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10771),U_10772),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10771),U_10772),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10771),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10771),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10774),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_10773))))
| ~ class_Rings_Ocomm__semiring__1(U_10771) ),
inference(variable_rename,[status(thm)],[f_2889_1]) ).
cnf(f_2889_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10771),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10771),c_Groups_Oone__class_Oone(U_10771)),c_Groups_Oone__class_Oone(U_10771))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10771),hAPP(hAPP(c_COMBB(U_10771,U_10771,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_10771),U_10772)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_10771,U_10771),hAPP(hAPP(c_COMBB(U_10771,tc_fun(U_10771,U_10771),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_10771)),c_Nat_Osemiring__1__class_Oof__nat(U_10771))),U_10773))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10774))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10771),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10771),U_10774)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10771),U_10772),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10771),U_10772),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10771),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10771),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10774),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_10773))))
| ~ class_Rings_Ocomm__semiring__1(U_10771) ),
inference(clausify,[status(thm)],[f_2889_2]) ).
fof(f_2890_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_2890_2,plain,
! [U_10776,U_10775] :
( ( c_Divides_OnegDivAlg(U_10775,U_10776) = hAPP(c_Divides_Oadjust(U_10776),c_Divides_OnegDivAlg(U_10775,hAPP(hAPP(c_Groups_Otimes__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_10776)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10776),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_10775),U_10776))) )
& ( c_Divides_OnegDivAlg(U_10775,U_10776) = 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_10775),U_10776))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10776),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_10775),U_10776))) ) ) ),
inference(variable_rename,[status(thm)],[f_2890_1]) ).
fof(f_2890_3,plain,
( ! [U_10780,U_10778] :
( c_Divides_OnegDivAlg(U_10778,U_10780) = hAPP(c_Divides_Oadjust(U_10780),c_Divides_OnegDivAlg(U_10778,hAPP(hAPP(c_Groups_Otimes__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_10780)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10780),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_10778),U_10780))) )
& ! [U_10779,U_10777] :
( c_Divides_OnegDivAlg(U_10777,U_10779) = 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_10777),U_10779))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10779),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_10777),U_10779))) ) ) ),
inference(miniscope,[status(thm)],[f_2890_2]) ).
cnf(f_2890_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_10777),U_10779)))
| c_Divides_OnegDivAlg(U_10777,U_10779) = 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_10777),U_10779)) ),
inference(clausify,[status(thm)],[f_2890_3]) ).
cnf(f_2890_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10779),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OnegDivAlg(U_10777,U_10779) = 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_10777),U_10779)) ),
inference(clausify,[status(thm)],[f_2890_3]) ).
cnf(f_2890_6,plain,
( c_Divides_OnegDivAlg(U_10778,U_10780) = hAPP(c_Divides_Oadjust(U_10780),c_Divides_OnegDivAlg(U_10778,hAPP(hAPP(c_Groups_Otimes__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_10780)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10780),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_10778),U_10780))) ),
inference(clausify,[status(thm)],[f_2890_3]) ).
fof(f_2891_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_2891_2,plain,
! [U_10782,U_10781] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10781)),hAPP(c_Nat_OSuc,U_10782)) = 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_10781))),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_10782)))),
inference(variable_rename,[status(thm)],[f_2891_1]) ).
cnf(f_2891_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10781)),hAPP(c_Nat_OSuc,U_10782)) = 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_10781))),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_10782)))),
inference(clausify,[status(thm)],[f_2891_2]) ).
fof(f_2892_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_2892_2,plain,
! [U_10784,U_10783] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10783)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10784)) = 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_10784))),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_10783)),c_Int_Onat)))),
inference(variable_rename,[status(thm)],[f_2892_1]) ).
cnf(f_2892_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10783)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10784)) = 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_10784))),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_10783)),c_Int_Onat)))),
inference(clausify,[status(thm)],[f_2892_2]) ).
fof(f_2893_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_2893_2,plain,
! [U_10787,U_10786,U_10785] : 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_10785)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_10786))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10787))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10787),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10785),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10787),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_10786)))),
inference(variable_rename,[status(thm)],[f_2893_1]) ).
cnf(f_2893_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_10785)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_10786))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10787))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10787),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10785),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10787),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_10786)))),
inference(clausify,[status(thm)],[f_2893_2]) ).
fof(f_2894_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_2894_2,plain,
! [U_10794,U_10793,U_10792,U_10791,U_10790,U_10789,U_10788] :
( hAPP(c_Fun_Othe__inv__into(U_10791,U_10789,U_10793,hAPP(c_Fun_Ocomp(U_10788,U_10789,U_10791,U_10790),U_10792)),U_10794) = hAPP(hAPP(c_Fun_Ocomp(U_10788,U_10791,U_10789,c_Fun_Othe__inv__into(U_10791,U_10788,U_10793,U_10792)),c_Fun_Othe__inv__into(U_10788,U_10789,hAPP(c_Set_Oimage(U_10791,U_10788,U_10792),U_10793),U_10790)),U_10794)
| ~ hBOOL(hAPP(hAPP(c_member(U_10789),U_10794),hAPP(c_Set_Oimage(U_10788,U_10789,U_10790),hAPP(c_Set_Oimage(U_10791,U_10788,U_10792),U_10793))))
| ~ c_Fun_Oinj__on(U_10791,U_10788,U_10792,U_10793)
| ~ c_Fun_Oinj__on(U_10788,U_10789,U_10790,hAPP(c_Set_Oimage(U_10791,U_10788,U_10792),U_10793)) ),
inference(variable_rename,[status(thm)],[f_2894_1]) ).
cnf(f_2894_3,plain,
( hAPP(c_Fun_Othe__inv__into(U_10791,U_10789,U_10793,hAPP(c_Fun_Ocomp(U_10788,U_10789,U_10791,U_10790),U_10792)),U_10794) = hAPP(hAPP(c_Fun_Ocomp(U_10788,U_10791,U_10789,c_Fun_Othe__inv__into(U_10791,U_10788,U_10793,U_10792)),c_Fun_Othe__inv__into(U_10788,U_10789,hAPP(c_Set_Oimage(U_10791,U_10788,U_10792),U_10793),U_10790)),U_10794)
| ~ hBOOL(hAPP(hAPP(c_member(U_10789),U_10794),hAPP(c_Set_Oimage(U_10788,U_10789,U_10790),hAPP(c_Set_Oimage(U_10791,U_10788,U_10792),U_10793))))
| ~ c_Fun_Oinj__on(U_10791,U_10788,U_10792,U_10793)
| ~ c_Fun_Oinj__on(U_10788,U_10789,U_10790,hAPP(c_Set_Oimage(U_10791,U_10788,U_10792),U_10793)) ),
inference(clausify,[status(thm)],[f_2894_2]) ).
fof(f_2895_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_2895_2,plain,
! [U_10797,U_10796,U_10795] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10795),hAPP(c_Int_Onumber__class_Onumber__of(U_10795),U_10797)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10796))) = c_Groups_Oone__class_Oone(U_10795)
| 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_10796))) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10795),hAPP(c_Int_Onumber__class_Onumber__of(U_10795),U_10797)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10796))) = hAPP(hAPP(c_HOL_OLet(U_10795,U_10795),hAPP(hAPP(c_Power_Opower__class_Opower(U_10795),hAPP(c_Int_Onumber__class_Onumber__of(U_10795),U_10797)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10796))),hAPP(hAPP(c_COMBS(U_10795,U_10795,U_10795),hAPP(hAPP(c_COMBB(U_10795,tc_fun(U_10795,U_10795),U_10795),c_Groups_Otimes__class_Otimes(U_10795)),hAPP(c_Groups_Otimes__class_Otimes(U_10795),hAPP(c_Int_Onumber__class_Onumber__of(U_10795),U_10797)))),c_COMBI(U_10795)))
| ~ 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_10796))) ) )
| ~ class_Int_Onumber__ring(U_10795) ),
inference(variable_rename,[status(thm)],[f_2895_1]) ).
cnf(f_2895_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10795),hAPP(c_Int_Onumber__class_Onumber__of(U_10795),U_10797)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10796))) = hAPP(hAPP(c_HOL_OLet(U_10795,U_10795),hAPP(hAPP(c_Power_Opower__class_Opower(U_10795),hAPP(c_Int_Onumber__class_Onumber__of(U_10795),U_10797)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10796))),hAPP(hAPP(c_COMBS(U_10795,U_10795,U_10795),hAPP(hAPP(c_COMBB(U_10795,tc_fun(U_10795,U_10795),U_10795),c_Groups_Otimes__class_Otimes(U_10795)),hAPP(c_Groups_Otimes__class_Otimes(U_10795),hAPP(c_Int_Onumber__class_Onumber__of(U_10795),U_10797)))),c_COMBI(U_10795)))
| ~ 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_10796)))
| ~ class_Int_Onumber__ring(U_10795) ),
inference(clausify,[status(thm)],[f_2895_2]) ).
cnf(f_2895_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10795),hAPP(c_Int_Onumber__class_Onumber__of(U_10795),U_10797)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10796))) = c_Groups_Oone__class_Oone(U_10795)
| 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_10796)))
| ~ class_Int_Onumber__ring(U_10795) ),
inference(clausify,[status(thm)],[f_2895_2]) ).
fof(f_2896_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_2896_2,plain,
! [U_10799,U_10798] :
( ( ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10799),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10798)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10798)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10799),hAPP(hAPP(c_Groups_Otimes__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_10798))))
| 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_10799)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10798)))) )
& ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10799),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10798)) = 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_10799)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10798)))
| ~ 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_10799)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10798)))) ) )
| ~ 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_10798))) ),
inference(variable_rename,[status(thm)],[f_2896_1]) ).
cnf(f_2896_3,plain,
( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10799),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10798)) = 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_10799)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10798)))
| ~ 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_10799)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10798))))
| ~ 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_10798))) ),
inference(clausify,[status(thm)],[f_2896_2]) ).
cnf(f_2896_4,plain,
( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10799),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10798)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10798)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10799),hAPP(hAPP(c_Groups_Otimes__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_10798))))
| 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_10799)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10798))))
| ~ 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_10798))) ),
inference(clausify,[status(thm)],[f_2896_2]) ).
fof(f_2897_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_2897_2,plain,
! [U_10801,U_10800] :
( ( ( c_Divides_OnegDivAlg(U_10801,U_10800) = hAPP(c_Divides_Oadjust(U_10800),c_Divides_OnegDivAlg(U_10801,hAPP(hAPP(c_Groups_Otimes__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_10800)))
| 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_10801),U_10800))) )
& ( c_Divides_OnegDivAlg(U_10801,U_10800) = 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_10801),U_10800))
| ~ 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_10801),U_10800))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10800)) ),
inference(variable_rename,[status(thm)],[f_2897_1]) ).
cnf(f_2897_3,plain,
( c_Divides_OnegDivAlg(U_10801,U_10800) = 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_10801),U_10800))
| ~ 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_10801),U_10800)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10800)) ),
inference(clausify,[status(thm)],[f_2897_2]) ).
cnf(f_2897_4,plain,
( c_Divides_OnegDivAlg(U_10801,U_10800) = hAPP(c_Divides_Oadjust(U_10800),c_Divides_OnegDivAlg(U_10801,hAPP(hAPP(c_Groups_Otimes__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_10800)))
| 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_10801),U_10800)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10800)) ),
inference(clausify,[status(thm)],[f_2897_2]) ).
fof(f_2898_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_2898_2,plain,
! [U_10803,U_10802] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10803)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10802)) = 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_10803),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10802)))),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_10802),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10803)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10802)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10803)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10802),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_2898_1]) ).
fof(f_2898_3,plain,
( ! [U_10807,U_10805] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10807)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10805)) = 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_10807),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10805)))),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_10805),c_Int_OPls)) )
& ! [U_10806,U_10804] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10806)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10804)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10806)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10804),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_2898_2]) ).
cnf(f_2898_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10806)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10804)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10806)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10804),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2898_3]) ).
cnf(f_2898_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10807)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10805)) = 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_10807),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10805)))),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_10805),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2898_3]) ).
fof(f_2899_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_2899_2,plain,
! [U_10809,U_10808] :
( ( ( ( c_Nitpick_Onorm__frac(U_10809,U_10808) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_10809),U_10808)),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_10809))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10808)))
| U_10808 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_10809 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Nitpick_Onorm__frac(U_10809,U_10808) = 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_10808 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& U_10809 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10808),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( c_Nitpick_Onorm__frac(U_10809,U_10808) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10809),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10808))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10808),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_2899_1]) ).
fof(f_2899_3,plain,
( ! [U_10813,U_10811] :
( ( ( c_Nitpick_Onorm__frac(U_10813,U_10811) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_10813),U_10811)),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_10813))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10811)))
| U_10811 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_10813 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Nitpick_Onorm__frac(U_10813,U_10811) = 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_10811 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& U_10813 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10811),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_10812,U_10810] :
( c_Nitpick_Onorm__frac(U_10812,U_10810) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10812),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10810))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10810),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_2899_2]) ).
cnf(f_2899_4,plain,
( c_Nitpick_Onorm__frac(U_10812,U_10810) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10812),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10810))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10810),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2899_3]) ).
cnf(f_2899_5,plain,
( U_10813 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nitpick_Onorm__frac(U_10813,U_10811) = 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_10811),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2899_3]) ).
cnf(f_2899_6,plain,
( U_10811 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nitpick_Onorm__frac(U_10813,U_10811) = 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_10811),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2899_3]) ).
cnf(f_2899_7,plain,
( c_Nitpick_Onorm__frac(U_10813,U_10811) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_10813),U_10811)),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_10813))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10811)))
| U_10811 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_10813 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10811),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2899_3]) ).
fof(f_2900_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_2900_2,plain,
! [U_10814] :
( ( ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10814)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10814)),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_10814))))
| 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_10814))) )
& ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10814)) = 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_10814))) ) )
| ~ 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_10814))) ),
inference(variable_rename,[status(thm)],[f_2900_1]) ).
cnf(f_2900_3,plain,
( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10814)) = 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_10814)))
| ~ 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_10814))) ),
inference(clausify,[status(thm)],[f_2900_2]) ).
cnf(f_2900_4,plain,
( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10814)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10814)),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_10814))))
| 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_10814)))
| ~ 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_10814))) ),
inference(clausify,[status(thm)],[f_2900_2]) ).
fof(f_2901_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_2901_2,plain,
! [U_10816,U_10815] :
( ( c_Divides_OposDivAlg(U_10815,U_10816) = hAPP(c_Divides_Oadjust(U_10816),c_Divides_OposDivAlg(U_10815,hAPP(hAPP(c_Groups_Otimes__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_10816)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10816),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10815),U_10816)) )
& ( c_Divides_OposDivAlg(U_10815,U_10816) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10815)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10816),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10815),U_10816)) ) ) ),
inference(variable_rename,[status(thm)],[f_2901_1]) ).
fof(f_2901_3,plain,
( ! [U_10820,U_10818] :
( c_Divides_OposDivAlg(U_10818,U_10820) = hAPP(c_Divides_Oadjust(U_10820),c_Divides_OposDivAlg(U_10818,hAPP(hAPP(c_Groups_Otimes__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_10820)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10820),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10818),U_10820)) )
& ! [U_10819,U_10817] :
( c_Divides_OposDivAlg(U_10817,U_10819) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10817)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10819),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10817),U_10819)) ) ) ),
inference(miniscope,[status(thm)],[f_2901_2]) ).
cnf(f_2901_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10817),U_10819))
| c_Divides_OposDivAlg(U_10817,U_10819) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10817) ),
inference(clausify,[status(thm)],[f_2901_3]) ).
cnf(f_2901_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10819),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OposDivAlg(U_10817,U_10819) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10817) ),
inference(clausify,[status(thm)],[f_2901_3]) ).
cnf(f_2901_6,plain,
( c_Divides_OposDivAlg(U_10818,U_10820) = hAPP(c_Divides_Oadjust(U_10820),c_Divides_OposDivAlg(U_10818,hAPP(hAPP(c_Groups_Otimes__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_10820)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10820),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10818),U_10820)) ),
inference(clausify,[status(thm)],[f_2901_3]) ).
fof(f_2902_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_2902_2,plain,
! [U_10821] : c_Divides_Oadjust(U_10821) = 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_10821))))),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_10821))))),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_2902_1]) ).
cnf(f_2902_3,plain,
c_Divides_Oadjust(U_10821) = 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_10821))))),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_10821))))),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_2902_2]) ).
fof(f_2903_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_2903_2,plain,
! [U_10827,U_10826,U_10825,U_10824,U_10823,U_10822] :
( hBOOL(hAPP(hAPP(U_10825,U_10826),U_10827))
| hBOOL(hAPP(hAPP(U_10824,U_10826),U_10827))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10822,tc_fun(U_10823,tc_HOL_Obool))),U_10824),U_10825),U_10826),U_10827)) ),
inference(variable_rename,[status(thm)],[f_2903_1]) ).
fof(f_2903_3,plain,
! [U_10827,U_10826,U_10825,U_10824] :
( ! [U_10823,U_10822] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10822,tc_fun(U_10823,tc_HOL_Obool))),U_10824),U_10825),U_10826),U_10827))
| hBOOL(hAPP(hAPP(U_10825,U_10826),U_10827))
| hBOOL(hAPP(hAPP(U_10824,U_10826),U_10827)) ),
inference(miniscope,[status(thm)],[f_2903_2]) ).
cnf(f_2903_4,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10822,tc_fun(U_10823,tc_HOL_Obool))),U_10824),U_10825),U_10826),U_10827))
| hBOOL(hAPP(hAPP(U_10825,U_10826),U_10827))
| hBOOL(hAPP(hAPP(U_10824,U_10826),U_10827)) ),
inference(clausify,[status(thm)],[f_2903_3]) ).
fof(f_2904_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_2904_2,plain,
! [U_10833,U_10832,U_10831,U_10830,U_10829,U_10828] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10832,tc_fun(U_10833,tc_HOL_Obool))),U_10831),U_10828),U_10829),U_10830))
| ( ~ hBOOL(hAPP(hAPP(U_10831,U_10829),U_10830))
& ~ hBOOL(hAPP(hAPP(U_10828,U_10829),U_10830)) ) ),
inference(variable_rename,[status(thm)],[f_2904_1]) ).
cnf(f_2904_3,plain,
( ~ hBOOL(hAPP(hAPP(U_10828,U_10829),U_10830))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10832,tc_fun(U_10833,tc_HOL_Obool))),U_10831),U_10828),U_10829),U_10830)) ),
inference(clausify,[status(thm)],[f_2904_2]) ).
cnf(f_2904_4,plain,
( ~ hBOOL(hAPP(hAPP(U_10831,U_10829),U_10830))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10832,tc_fun(U_10833,tc_HOL_Obool))),U_10831),U_10828),U_10829),U_10830)) ),
inference(clausify,[status(thm)],[f_2904_2]) ).
fof(f_2905_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_2905_2,plain,
! [U_10839,U_10838,U_10837,U_10836,U_10835,U_10834] :
( ( hBOOL(hAPP(hAPP(U_10837,U_10838),U_10839))
& hBOOL(hAPP(hAPP(U_10836,U_10838),U_10839)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10834,tc_fun(U_10835,tc_HOL_Obool))),U_10836),U_10837),U_10838),U_10839)) ),
inference(variable_rename,[status(thm)],[f_2905_1]) ).
fof(f_2905_3,plain,
! [U_10839,U_10838,U_10837,U_10836] :
( ! [U_10835,U_10834] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10834,tc_fun(U_10835,tc_HOL_Obool))),U_10836),U_10837),U_10838),U_10839))
| ( hBOOL(hAPP(hAPP(U_10837,U_10838),U_10839))
& hBOOL(hAPP(hAPP(U_10836,U_10838),U_10839)) ) ),
inference(miniscope,[status(thm)],[f_2905_2]) ).
cnf(f_2905_4,plain,
( hBOOL(hAPP(hAPP(U_10836,U_10838),U_10839))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10834,tc_fun(U_10835,tc_HOL_Obool))),U_10836),U_10837),U_10838),U_10839)) ),
inference(clausify,[status(thm)],[f_2905_3]) ).
cnf(f_2905_5,plain,
( hBOOL(hAPP(hAPP(U_10837,U_10838),U_10839))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10834,tc_fun(U_10835,tc_HOL_Obool))),U_10836),U_10837),U_10838),U_10839)) ),
inference(clausify,[status(thm)],[f_2905_3]) ).
fof(f_2906_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_2906_2,plain,
! [U_10845,U_10844,U_10843,U_10842,U_10841,U_10840] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10844,tc_fun(U_10845,tc_HOL_Obool))),U_10840),U_10843),U_10841),U_10842))
| ~ hBOOL(hAPP(hAPP(U_10843,U_10841),U_10842))
| ~ hBOOL(hAPP(hAPP(U_10840,U_10841),U_10842)) ),
inference(variable_rename,[status(thm)],[f_2906_1]) ).
cnf(f_2906_3,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10844,tc_fun(U_10845,tc_HOL_Obool))),U_10840),U_10843),U_10841),U_10842))
| ~ hBOOL(hAPP(hAPP(U_10843,U_10841),U_10842))
| ~ hBOOL(hAPP(hAPP(U_10840,U_10841),U_10842)) ),
inference(clausify,[status(thm)],[f_2906_2]) ).
fof(f_2907_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_2907_2,plain,
! [U_10849,U_10848,U_10847,U_10846] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_10846,tc_fun(U_10847,tc_HOL_Obool))),U_10848),U_10849)),
inference(variable_rename,[status(thm)],[f_2907_1]) ).
cnf(f_2907_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_10846,tc_fun(U_10847,tc_HOL_Obool))),U_10848),U_10849)),
inference(clausify,[status(thm)],[f_2907_2]) ).
fof(f_2908_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_2908_2,plain,
! [U_10856,U_10855,U_10854,U_10853,U_10852] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10852,tc_fun(U_10853,tc_HOL_Obool)),U_10854),U_10855),U_10856))
| ? [U_10851] :
( ~ hBOOL(hAPP(hAPP(U_10855,U_10851),U_10856))
& hBOOL(hAPP(hAPP(c_member(U_10852),U_10851),U_10854)) ) )
& ( ! [U_10850] :
( hBOOL(hAPP(hAPP(U_10855,U_10850),U_10856))
| ~ hBOOL(hAPP(hAPP(c_member(U_10852),U_10850),U_10854)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10852,tc_fun(U_10853,tc_HOL_Obool)),U_10854),U_10855),U_10856)) ) ),
inference(variable_rename,[status(thm)],[f_2908_1]) ).
fof(f_2908_3,plain,
( ! [U_10866,U_10864,U_10862,U_10860,U_10858] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10858,tc_fun(U_10860,tc_HOL_Obool)),U_10862),U_10864),U_10866))
| ? [U_10851] :
( ~ hBOOL(hAPP(hAPP(U_10864,U_10851),U_10866))
& hBOOL(hAPP(hAPP(c_member(U_10858),U_10851),U_10862)) ) )
& ! [U_10865,U_10863,U_10861,U_10859,U_10857] :
( ! [U_10850] :
( hBOOL(hAPP(hAPP(U_10863,U_10850),U_10865))
| ~ hBOOL(hAPP(hAPP(c_member(U_10857),U_10850),U_10861)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10857,tc_fun(U_10859,tc_HOL_Obool)),U_10861),U_10863),U_10865)) ) ),
inference(miniscope,[status(thm)],[f_2908_2]) ).
fof(f_2908_4,plain,
( ! [U_10866,U_10864,U_10862,U_10860,U_10858] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10858,tc_fun(U_10860,tc_HOL_Obool)),U_10862),U_10864),U_10866))
| ( ~ hBOOL(hAPP(hAPP(U_10864,sK250(U_10866,U_10864,U_10862,U_10860,U_10858)),U_10866))
& hBOOL(hAPP(hAPP(c_member(U_10858),sK250(U_10866,U_10864,U_10862,U_10860,U_10858)),U_10862)) ) )
& ! [U_10865,U_10863,U_10861,U_10859,U_10857] :
( ! [U_10850] :
( hBOOL(hAPP(hAPP(U_10863,U_10850),U_10865))
| ~ hBOOL(hAPP(hAPP(c_member(U_10857),U_10850),U_10861)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10857,tc_fun(U_10859,tc_HOL_Obool)),U_10861),U_10863),U_10865)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK250]),skolemize(U_10851,sK250(U_10866,U_10864,U_10862,U_10860,U_10858))],[f_2908_3]) ).
cnf(f_2908_5,plain,
( hBOOL(hAPP(hAPP(U_10863,U_10850),U_10865))
| ~ hBOOL(hAPP(hAPP(c_member(U_10857),U_10850),U_10861))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10857,tc_fun(U_10859,tc_HOL_Obool)),U_10861),U_10863),U_10865)) ),
inference(clausify,[status(thm)],[f_2908_4]) ).
cnf(f_2908_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_10858),sK250(U_10866,U_10864,U_10862,U_10860,U_10858)),U_10862))
| hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10858,tc_fun(U_10860,tc_HOL_Obool)),U_10862),U_10864),U_10866)) ),
inference(clausify,[status(thm)],[f_2908_4]) ).
cnf(f_2908_7,plain,
( ~ hBOOL(hAPP(hAPP(U_10864,sK250(U_10866,U_10864,U_10862,U_10860,U_10858)),U_10866))
| hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10858,tc_fun(U_10860,tc_HOL_Obool)),U_10862),U_10864),U_10866)) ),
inference(clausify,[status(thm)],[f_2908_4]) ).
fof(f_2909_1,plain,
! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_INF2__iff]) ).
fof(f_2909_2,plain,
! [U_10875,U_10874,U_10873,U_10872,U_10871,U_10870,U_10869] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10869,tc_fun(U_10870,tc_fun(U_10871,tc_HOL_Obool))),U_10872),U_10873),U_10874),U_10875))
| ? [U_10868] :
( ~ hBOOL(hAPP(hAPP(hAPP(U_10873,U_10868),U_10874),U_10875))
& hBOOL(hAPP(hAPP(c_member(U_10869),U_10868),U_10872)) ) )
& ( ! [U_10867] :
( hBOOL(hAPP(hAPP(hAPP(U_10873,U_10867),U_10874),U_10875))
| ~ hBOOL(hAPP(hAPP(c_member(U_10869),U_10867),U_10872)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10869,tc_fun(U_10870,tc_fun(U_10871,tc_HOL_Obool))),U_10872),U_10873),U_10874),U_10875)) ) ),
inference(variable_rename,[status(thm)],[f_2909_1]) ).
fof(f_2909_3,plain,
( ! [U_10889,U_10887,U_10885,U_10883,U_10881,U_10879,U_10877] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10877,tc_fun(U_10879,tc_fun(U_10881,tc_HOL_Obool))),U_10883),U_10885),U_10887),U_10889))
| ? [U_10868] :
( ~ hBOOL(hAPP(hAPP(hAPP(U_10885,U_10868),U_10887),U_10889))
& hBOOL(hAPP(hAPP(c_member(U_10877),U_10868),U_10883)) ) )
& ! [U_10888,U_10886,U_10884,U_10882,U_10880,U_10878,U_10876] :
( ! [U_10867] :
( hBOOL(hAPP(hAPP(hAPP(U_10884,U_10867),U_10886),U_10888))
| ~ hBOOL(hAPP(hAPP(c_member(U_10876),U_10867),U_10882)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10876,tc_fun(U_10878,tc_fun(U_10880,tc_HOL_Obool))),U_10882),U_10884),U_10886),U_10888)) ) ),
inference(miniscope,[status(thm)],[f_2909_2]) ).
fof(f_2909_4,plain,
( ! [U_10889,U_10887,U_10885,U_10883,U_10881,U_10879,U_10877] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10877,tc_fun(U_10879,tc_fun(U_10881,tc_HOL_Obool))),U_10883),U_10885),U_10887),U_10889))
| ( ~ hBOOL(hAPP(hAPP(hAPP(U_10885,sK251(U_10889,U_10887,U_10885,U_10883,U_10881,U_10879,U_10877)),U_10887),U_10889))
& hBOOL(hAPP(hAPP(c_member(U_10877),sK251(U_10889,U_10887,U_10885,U_10883,U_10881,U_10879,U_10877)),U_10883)) ) )
& ! [U_10888,U_10886,U_10884,U_10882,U_10880,U_10878,U_10876] :
( ! [U_10867] :
( hBOOL(hAPP(hAPP(hAPP(U_10884,U_10867),U_10886),U_10888))
| ~ hBOOL(hAPP(hAPP(c_member(U_10876),U_10867),U_10882)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10876,tc_fun(U_10878,tc_fun(U_10880,tc_HOL_Obool))),U_10882),U_10884),U_10886),U_10888)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK251]),skolemize(U_10868,sK251(U_10889,U_10887,U_10885,U_10883,U_10881,U_10879,U_10877))],[f_2909_3]) ).
cnf(f_2909_5,plain,
( hBOOL(hAPP(hAPP(hAPP(U_10884,U_10867),U_10886),U_10888))
| ~ hBOOL(hAPP(hAPP(c_member(U_10876),U_10867),U_10882))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10876,tc_fun(U_10878,tc_fun(U_10880,tc_HOL_Obool))),U_10882),U_10884),U_10886),U_10888)) ),
inference(clausify,[status(thm)],[f_2909_4]) ).
cnf(f_2909_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_10877),sK251(U_10889,U_10887,U_10885,U_10883,U_10881,U_10879,U_10877)),U_10883))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10877,tc_fun(U_10879,tc_fun(U_10881,tc_HOL_Obool))),U_10883),U_10885),U_10887),U_10889)) ),
inference(clausify,[status(thm)],[f_2909_4]) ).
cnf(f_2909_7,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(U_10885,sK251(U_10889,U_10887,U_10885,U_10883,U_10881,U_10879,U_10877)),U_10887),U_10889))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10877,tc_fun(U_10879,tc_fun(U_10881,tc_HOL_Obool))),U_10883),U_10885),U_10887),U_10889)) ),
inference(clausify,[status(thm)],[f_2909_4]) ).
fof(f_2910_1,plain,
! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_SUP2__iff]) ).
fof(f_2910_2,plain,
! [U_10898,U_10897,U_10896,U_10895,U_10894,U_10893,U_10892] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10892,tc_fun(U_10893,tc_fun(U_10894,tc_HOL_Obool))),U_10895),U_10896),U_10897),U_10898))
| ! [U_10891] :
( ~ hBOOL(hAPP(hAPP(hAPP(U_10896,U_10891),U_10897),U_10898))
| ~ hBOOL(hAPP(hAPP(c_member(U_10892),U_10891),U_10895)) ) )
& ( ? [U_10890] :
( hBOOL(hAPP(hAPP(hAPP(U_10896,U_10890),U_10897),U_10898))
& hBOOL(hAPP(hAPP(c_member(U_10892),U_10890),U_10895)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10892,tc_fun(U_10893,tc_fun(U_10894,tc_HOL_Obool))),U_10895),U_10896),U_10897),U_10898)) ) ),
inference(variable_rename,[status(thm)],[f_2910_1]) ).
fof(f_2910_3,plain,
( ! [U_10912,U_10910,U_10908,U_10906,U_10904,U_10902,U_10900] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10900,tc_fun(U_10902,tc_fun(U_10904,tc_HOL_Obool))),U_10906),U_10908),U_10910),U_10912))
| ! [U_10891] :
( ~ hBOOL(hAPP(hAPP(hAPP(U_10908,U_10891),U_10910),U_10912))
| ~ hBOOL(hAPP(hAPP(c_member(U_10900),U_10891),U_10906)) ) )
& ! [U_10911,U_10909,U_10907,U_10905,U_10903,U_10901,U_10899] :
( ? [U_10890] :
( hBOOL(hAPP(hAPP(hAPP(U_10907,U_10890),U_10909),U_10911))
& hBOOL(hAPP(hAPP(c_member(U_10899),U_10890),U_10905)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10899,tc_fun(U_10901,tc_fun(U_10903,tc_HOL_Obool))),U_10905),U_10907),U_10909),U_10911)) ) ),
inference(miniscope,[status(thm)],[f_2910_2]) ).
fof(f_2910_4,plain,
( ! [U_10912,U_10910,U_10908,U_10906,U_10904,U_10902,U_10900] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10900,tc_fun(U_10902,tc_fun(U_10904,tc_HOL_Obool))),U_10906),U_10908),U_10910),U_10912))
| ! [U_10891] :
( ~ hBOOL(hAPP(hAPP(hAPP(U_10908,U_10891),U_10910),U_10912))
| ~ hBOOL(hAPP(hAPP(c_member(U_10900),U_10891),U_10906)) ) )
& ! [U_10911,U_10909,U_10907,U_10905,U_10903,U_10901,U_10899] :
( ( hBOOL(hAPP(hAPP(hAPP(U_10907,sK252(U_10911,U_10909,U_10907,U_10905,U_10903,U_10901,U_10899)),U_10909),U_10911))
& hBOOL(hAPP(hAPP(c_member(U_10899),sK252(U_10911,U_10909,U_10907,U_10905,U_10903,U_10901,U_10899)),U_10905)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10899,tc_fun(U_10901,tc_fun(U_10903,tc_HOL_Obool))),U_10905),U_10907),U_10909),U_10911)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK252]),skolemize(U_10890,sK252(U_10911,U_10909,U_10907,U_10905,U_10903,U_10901,U_10899))],[f_2910_3]) ).
cnf(f_2910_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_10899),sK252(U_10911,U_10909,U_10907,U_10905,U_10903,U_10901,U_10899)),U_10905))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10899,tc_fun(U_10901,tc_fun(U_10903,tc_HOL_Obool))),U_10905),U_10907),U_10909),U_10911)) ),
inference(clausify,[status(thm)],[f_2910_4]) ).
cnf(f_2910_6,plain,
( hBOOL(hAPP(hAPP(hAPP(U_10907,sK252(U_10911,U_10909,U_10907,U_10905,U_10903,U_10901,U_10899)),U_10909),U_10911))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10899,tc_fun(U_10901,tc_fun(U_10903,tc_HOL_Obool))),U_10905),U_10907),U_10909),U_10911)) ),
inference(clausify,[status(thm)],[f_2910_4]) ).
cnf(f_2910_7,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10900,tc_fun(U_10902,tc_fun(U_10904,tc_HOL_Obool))),U_10906),U_10908),U_10910),U_10912))
| ~ hBOOL(hAPP(hAPP(hAPP(U_10908,U_10891),U_10910),U_10912))
| ~ hBOOL(hAPP(hAPP(c_member(U_10900),U_10891),U_10906)) ),
inference(clausify,[status(thm)],[f_2910_4]) ).
fof(f_2911_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_2911_2,plain,
! [U_10918,U_10917,U_10916,U_10915,U_10914,U_10913] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10916,tc_fun(U_10917,tc_HOL_Obool))),U_10913),U_10918),U_10914),U_10915))
| ~ hBOOL(hAPP(hAPP(U_10913,U_10914),U_10915)) ),
inference(variable_rename,[status(thm)],[f_2911_1]) ).
cnf(f_2911_3,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10916,tc_fun(U_10917,tc_HOL_Obool))),U_10913),U_10918),U_10914),U_10915))
| ~ hBOOL(hAPP(hAPP(U_10913,U_10914),U_10915)) ),
inference(clausify,[status(thm)],[f_2911_2]) ).
fof(f_2912_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_2912_2,plain,
! [U_10924,U_10923,U_10922,U_10921,U_10920,U_10919] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10922,tc_fun(U_10923,tc_HOL_Obool))),U_10924),U_10919),U_10920),U_10921))
| ~ hBOOL(hAPP(hAPP(U_10919,U_10920),U_10921)) ),
inference(variable_rename,[status(thm)],[f_2912_1]) ).
cnf(f_2912_3,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10922,tc_fun(U_10923,tc_HOL_Obool))),U_10924),U_10919),U_10920),U_10921))
| ~ hBOOL(hAPP(hAPP(U_10919,U_10920),U_10921)) ),
inference(clausify,[status(thm)],[f_2912_2]) ).
fof(f_2913_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_2913_2,plain,
! [U_10930,U_10929,U_10928,U_10927,U_10926,U_10925] :
( hBOOL(hAPP(hAPP(U_10928,U_10929),U_10930))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10925,tc_fun(U_10926,tc_HOL_Obool))),U_10927),U_10928),U_10929),U_10930)) ),
inference(variable_rename,[status(thm)],[f_2913_1]) ).
fof(f_2913_3,plain,
! [U_10930,U_10929,U_10928] :
( ! [U_10927,U_10926,U_10925] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10925,tc_fun(U_10926,tc_HOL_Obool))),U_10927),U_10928),U_10929),U_10930))
| hBOOL(hAPP(hAPP(U_10928,U_10929),U_10930)) ),
inference(miniscope,[status(thm)],[f_2913_2]) ).
cnf(f_2913_4,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10925,tc_fun(U_10926,tc_HOL_Obool))),U_10927),U_10928),U_10929),U_10930))
| hBOOL(hAPP(hAPP(U_10928,U_10929),U_10930)) ),
inference(clausify,[status(thm)],[f_2913_3]) ).
fof(f_2914_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_2914_2,plain,
! [U_10936,U_10935,U_10934,U_10933,U_10932,U_10931] :
( hBOOL(hAPP(hAPP(U_10933,U_10935),U_10936))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10931,tc_fun(U_10932,tc_HOL_Obool))),U_10933),U_10934),U_10935),U_10936)) ),
inference(variable_rename,[status(thm)],[f_2914_1]) ).
fof(f_2914_3,plain,
! [U_10936,U_10935,U_10934,U_10933] :
( ! [U_10932,U_10931] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10931,tc_fun(U_10932,tc_HOL_Obool))),U_10933),U_10934),U_10935),U_10936))
| hBOOL(hAPP(hAPP(U_10933,U_10935),U_10936)) ),
inference(miniscope,[status(thm)],[f_2914_2]) ).
cnf(f_2914_4,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10931,tc_fun(U_10932,tc_HOL_Obool))),U_10933),U_10934),U_10935),U_10936))
| hBOOL(hAPP(hAPP(U_10933,U_10935),U_10936)) ),
inference(clausify,[status(thm)],[f_2914_3]) ).
fof(f_2915_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_2915_2,plain,
! [U_10939,U_10938,U_10937] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10938,U_10938),tc_HOL_Obool)),U_10937),U_10939))
| U_10937 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10938,U_10938),tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_2915_1]) ).
cnf(f_2915_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10938,U_10938),tc_HOL_Obool)),U_10937),U_10939))
| U_10937 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10938,U_10938),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2915_2]) ).
fof(f_2916_1,plain,
! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_P_2] :
( hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Q_2))
| ~ hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_rev__predicate2D]) ).
fof(f_2916_2,plain,
! [U_10945,U_10944,U_10943,U_10942,U_10941,U_10940] :
( hBOOL(hAPP(hAPP(U_10945,U_10941),U_10942))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10943,tc_fun(U_10944,tc_HOL_Obool))),U_10940),U_10945))
| ~ hBOOL(hAPP(hAPP(U_10940,U_10941),U_10942)) ),
inference(variable_rename,[status(thm)],[f_2916_1]) ).
cnf(f_2916_3,plain,
( hBOOL(hAPP(hAPP(U_10945,U_10941),U_10942))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10943,tc_fun(U_10944,tc_HOL_Obool))),U_10940),U_10945))
| ~ hBOOL(hAPP(hAPP(U_10940,U_10941),U_10942)) ),
inference(clausify,[status(thm)],[f_2916_2]) ).
fof(f_2917_1,plain,
! [V_y_2,V_x_2,V_Q_2,V_P_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Q_2)) ),
inference(fof_nnf,[status(thm)],[fact_predicate2D]) ).
fof(f_2917_2,plain,
! [U_10951,U_10950,U_10949,U_10948,U_10947,U_10946] :
( hBOOL(hAPP(hAPP(U_10949,U_10950),U_10951))
| ~ hBOOL(hAPP(hAPP(U_10948,U_10950),U_10951))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10946,tc_fun(U_10947,tc_HOL_Obool))),U_10948),U_10949)) ),
inference(variable_rename,[status(thm)],[f_2917_1]) ).
fof(f_2917_3,plain,
! [U_10951,U_10950,U_10949,U_10948] :
( ! [U_10947,U_10946] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10946,tc_fun(U_10947,tc_HOL_Obool))),U_10948),U_10949))
| hBOOL(hAPP(hAPP(U_10949,U_10950),U_10951))
| ~ hBOOL(hAPP(hAPP(U_10948,U_10950),U_10951)) ),
inference(miniscope,[status(thm)],[f_2917_2]) ).
cnf(f_2917_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10946,tc_fun(U_10947,tc_HOL_Obool))),U_10948),U_10949))
| hBOOL(hAPP(hAPP(U_10949,U_10950),U_10951))
| ~ hBOOL(hAPP(hAPP(U_10948,U_10950),U_10951)) ),
inference(clausify,[status(thm)],[f_2917_3]) ).
fof(f_2918_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_2918_2,plain,
! [U_10952] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_10952) = 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_2918_1]) ).
cnf(f_2918_3,plain,
c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_10952) = 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_2918_2]) ).
fof(f_2919_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_2919_2,plain,
! [U_10954,U_10953] :
( c_Divides_OposDivAlg(U_10953,U_10954) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10953),U_10954)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10953,U_10954))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10954))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10953)) ),
inference(variable_rename,[status(thm)],[f_2919_1]) ).
cnf(f_2919_3,plain,
( c_Divides_OposDivAlg(U_10953,U_10954) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10953),U_10954)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10953,U_10954))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10954))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10953)) ),
inference(clausify,[status(thm)],[f_2919_2]) ).
fof(f_2920_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_2920_2,plain,
! [U_10956,U_10955] :
( ( ( c_Divides_OposDivAlg(U_10956,U_10955) = hAPP(c_Divides_Oadjust(U_10955),c_Divides_OposDivAlg(U_10956,hAPP(hAPP(c_Groups_Otimes__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_10955)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10956),U_10955)) )
& ( c_Divides_OposDivAlg(U_10956,U_10955) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10956)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10956),U_10955)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10955)) ),
inference(variable_rename,[status(thm)],[f_2920_1]) ).
cnf(f_2920_3,plain,
( c_Divides_OposDivAlg(U_10956,U_10955) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10956)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10956),U_10955))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10955)) ),
inference(clausify,[status(thm)],[f_2920_2]) ).
cnf(f_2920_4,plain,
( c_Divides_OposDivAlg(U_10956,U_10955) = hAPP(c_Divides_Oadjust(U_10955),c_Divides_OposDivAlg(U_10956,hAPP(hAPP(c_Groups_Otimes__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_10955)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10956),U_10955))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10955)) ),
inference(clausify,[status(thm)],[f_2920_2]) ).
fof(f_2921_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_2921_2,plain,
! [U_10958,U_10957] :
( ( ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10958),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10957)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10957)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10958),hAPP(hAPP(c_Groups_Otimes__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_10957))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10958)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10957))) )
& ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10958),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10957)) = 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_10958))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10958)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10957))) ) )
| ~ 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_10957))) ),
inference(variable_rename,[status(thm)],[f_2921_1]) ).
cnf(f_2921_3,plain,
( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10958),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10957)) = 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_10958))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10958)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10957)))
| ~ 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_10957))) ),
inference(clausify,[status(thm)],[f_2921_2]) ).
cnf(f_2921_4,plain,
( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10958),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10957)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10957)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10958),hAPP(hAPP(c_Groups_Otimes__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_10957))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10958)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10957)))
| ~ 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_10957))) ),
inference(clausify,[status(thm)],[f_2921_2]) ).
fof(f_2922_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_2922_2,plain,
! [U_10965,U_10964,U_10963,U_10962,U_10961,U_10960,U_10959] :
( hBOOL(hAPP(hAPP(c_member(U_10964),hAPP(hAPP(U_10965,U_10961),U_10962)),hAPP(c_Set_Oimage(tc_prod(U_10959,U_10960),U_10964,hAPP(c_Product__Type_Oprod_Oprod__case(U_10959,U_10960,U_10964),U_10965)),U_10963)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10959,U_10960)),hAPP(hAPP(c_Product__Type_OPair(U_10959,U_10960),U_10961),U_10962)),U_10963)) ),
inference(variable_rename,[status(thm)],[f_2922_1]) ).
cnf(f_2922_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_10964),hAPP(hAPP(U_10965,U_10961),U_10962)),hAPP(c_Set_Oimage(tc_prod(U_10959,U_10960),U_10964,hAPP(c_Product__Type_Oprod_Oprod__case(U_10959,U_10960,U_10964),U_10965)),U_10963)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10959,U_10960)),hAPP(hAPP(c_Product__Type_OPair(U_10959,U_10960),U_10961),U_10962)),U_10963)) ),
inference(clausify,[status(thm)],[f_2922_2]) ).
fof(f_2923_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_2923_2,plain,
! [U_10967,U_10966] :
( ( ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_10966),U_10967) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_10966),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_10966,U_10966)),tc_fun(tc_Int_Oint,U_10966)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10966,U_10966),U_10966),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_10966,U_10966)),tc_fun(tc_Int_Oint,U_10966)),tc_Int_Oint),c_COMBB(tc_fun(U_10966,U_10966),U_10966,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_10966,tc_fun(tc_fun(U_10966,U_10966),U_10966),tc_Int_Oint),c_HOL_OLet(U_10966,U_10966)),c_Int_Oring__1__class_Oof__int(U_10966)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_10966,U_10966),tc_fun(U_10966,U_10966)),hAPP(hAPP(c_COMBB(tc_fun(U_10966,tc_fun(U_10966,U_10966)),tc_fun(tc_fun(U_10966,U_10966),tc_fun(U_10966,U_10966)),tc_Int_Oint),c_COMBS(U_10966,U_10966,U_10966)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_10966,U_10966),tc_fun(U_10966,tc_fun(U_10966,U_10966))),hAPP(hAPP(c_COMBB(tc_fun(U_10966,tc_fun(U_10966,U_10966)),tc_fun(tc_fun(U_10966,U_10966),tc_fun(U_10966,tc_fun(U_10966,U_10966))),tc_Int_Oint),c_COMBB(U_10966,tc_fun(U_10966,U_10966),U_10966)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10966,tc_fun(U_10966,U_10966)),tc_Int_Oint),c_If(U_10966)),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_10966,U_10966,U_10966),c_Groups_Oplus__class_Oplus(U_10966)),c_COMBI(U_10966))))),hAPP(hAPP(c_COMBC(U_10966,U_10966,U_10966),hAPP(hAPP(c_COMBB(U_10966,tc_fun(U_10966,U_10966),U_10966),c_Groups_Oplus__class_Oplus(U_10966)),hAPP(hAPP(c_COMBS(U_10966,U_10966,U_10966),c_Groups_Oplus__class_Oplus(U_10966)),c_COMBI(U_10966)))),c_Groups_Oone__class_Oone(U_10966))))),c_Divides_Odivmod__int(U_10967,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_10967),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hAPP(c_Int_Oring__1__class_Oof__int(U_10966),U_10967) = hAPP(c_Groups_Ouminus__class_Ouminus(U_10966),hAPP(c_Int_Oring__1__class_Oof__int(U_10966),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10967)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10967),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
| U_10967 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hAPP(c_Int_Oring__1__class_Oof__int(U_10966),U_10967) = c_Groups_Ozero__class_Ozero(U_10966)
| U_10967 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ class_Rings_Oring__1(U_10966) ),
inference(variable_rename,[status(thm)],[f_2923_1]) ).
cnf(f_2923_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_10966),U_10967) = c_Groups_Ozero__class_Ozero(U_10966)
| U_10967 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ class_Rings_Oring__1(U_10966) ),
inference(clausify,[status(thm)],[f_2923_2]) ).
cnf(f_2923_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_10966),U_10967) = hAPP(c_Groups_Ouminus__class_Ouminus(U_10966),hAPP(c_Int_Oring__1__class_Oof__int(U_10966),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10967)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10967),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_10967 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ class_Rings_Oring__1(U_10966) ),
inference(clausify,[status(thm)],[f_2923_2]) ).
cnf(f_2923_5,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_10966),U_10967) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_10966),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_10966,U_10966)),tc_fun(tc_Int_Oint,U_10966)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10966,U_10966),U_10966),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_10966,U_10966)),tc_fun(tc_Int_Oint,U_10966)),tc_Int_Oint),c_COMBB(tc_fun(U_10966,U_10966),U_10966,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_10966,tc_fun(tc_fun(U_10966,U_10966),U_10966),tc_Int_Oint),c_HOL_OLet(U_10966,U_10966)),c_Int_Oring__1__class_Oof__int(U_10966)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_10966,U_10966),tc_fun(U_10966,U_10966)),hAPP(hAPP(c_COMBB(tc_fun(U_10966,tc_fun(U_10966,U_10966)),tc_fun(tc_fun(U_10966,U_10966),tc_fun(U_10966,U_10966)),tc_Int_Oint),c_COMBS(U_10966,U_10966,U_10966)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_10966,U_10966),tc_fun(U_10966,tc_fun(U_10966,U_10966))),hAPP(hAPP(c_COMBB(tc_fun(U_10966,tc_fun(U_10966,U_10966)),tc_fun(tc_fun(U_10966,U_10966),tc_fun(U_10966,tc_fun(U_10966,U_10966))),tc_Int_Oint),c_COMBB(U_10966,tc_fun(U_10966,U_10966),U_10966)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10966,tc_fun(U_10966,U_10966)),tc_Int_Oint),c_If(U_10966)),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_10966,U_10966,U_10966),c_Groups_Oplus__class_Oplus(U_10966)),c_COMBI(U_10966))))),hAPP(hAPP(c_COMBC(U_10966,U_10966,U_10966),hAPP(hAPP(c_COMBB(U_10966,tc_fun(U_10966,U_10966),U_10966),c_Groups_Oplus__class_Oplus(U_10966)),hAPP(hAPP(c_COMBS(U_10966,U_10966,U_10966),c_Groups_Oplus__class_Oplus(U_10966)),c_COMBI(U_10966)))),c_Groups_Oone__class_Oone(U_10966))))),c_Divides_Odivmod__int(U_10967,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_10967),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_10967 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ class_Rings_Oring__1(U_10966) ),
inference(clausify,[status(thm)],[f_2923_2]) ).
fof(f_2924_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_2924_2,plain,
! [U_10972,U_10971,U_10970,U_10969,U_10968] :
( ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_10968,U_10969,U_10970),U_10971),U_10972))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10968,U_10969)),hAPP(hAPP(c_Product__Type_OPair(U_10968,U_10969),U_10971),U_10972)),U_10970)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10968,U_10969)),hAPP(hAPP(c_Product__Type_OPair(U_10968,U_10969),U_10971),U_10972)),U_10970))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_10968,U_10969,U_10970),U_10971),U_10972)) ) ),
inference(variable_rename,[status(thm)],[f_2924_1]) ).
fof(f_2924_3,plain,
( ! [U_10982,U_10980,U_10978,U_10976,U_10974] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_10974,U_10976,U_10978),U_10980),U_10982))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10974,U_10976)),hAPP(hAPP(c_Product__Type_OPair(U_10974,U_10976),U_10980),U_10982)),U_10978)) )
& ! [U_10981,U_10979,U_10977,U_10975,U_10973] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10973,U_10975)),hAPP(hAPP(c_Product__Type_OPair(U_10973,U_10975),U_10979),U_10981)),U_10977))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_10973,U_10975,U_10977),U_10979),U_10981)) ) ),
inference(miniscope,[status(thm)],[f_2924_2]) ).
cnf(f_2924_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10973,U_10975)),hAPP(hAPP(c_Product__Type_OPair(U_10973,U_10975),U_10979),U_10981)),U_10977))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_10973,U_10975,U_10977),U_10979),U_10981)) ),
inference(clausify,[status(thm)],[f_2924_3]) ).
cnf(f_2924_5,plain,
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_10974,U_10976,U_10978),U_10980),U_10982))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10974,U_10976)),hAPP(hAPP(c_Product__Type_OPair(U_10974,U_10976),U_10980),U_10982)),U_10978)) ),
inference(clausify,[status(thm)],[f_2924_3]) ).
fof(f_2925_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_2925_2,plain,
! [U_10987,U_10986,U_10985,U_10984,U_10983] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10986,U_10987,tc_HOL_Obool),U_10983),hAPP(hAPP(c_Product__Type_OPair(U_10986,U_10987),U_10984),U_10985)))
| ~ hBOOL(hAPP(hAPP(U_10983,U_10984),U_10985)) ),
inference(variable_rename,[status(thm)],[f_2925_1]) ).
cnf(f_2925_3,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10986,U_10987,tc_HOL_Obool),U_10983),hAPP(hAPP(c_Product__Type_OPair(U_10986,U_10987),U_10984),U_10985)))
| ~ hBOOL(hAPP(hAPP(U_10983,U_10984),U_10985)) ),
inference(clausify,[status(thm)],[f_2925_2]) ).
fof(f_2926_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_2926_2,plain,
! [U_10992,U_10991,U_10990,U_10989,U_10988] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10991,U_10992,tc_HOL_Obool),U_10988),hAPP(hAPP(c_Product__Type_OPair(U_10991,U_10992),U_10989),U_10990)))
| ~ hBOOL(hAPP(hAPP(U_10988,U_10989),U_10990)) ),
inference(variable_rename,[status(thm)],[f_2926_1]) ).
cnf(f_2926_3,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10991,U_10992,tc_HOL_Obool),U_10988),hAPP(hAPP(c_Product__Type_OPair(U_10991,U_10992),U_10989),U_10990)))
| ~ hBOOL(hAPP(hAPP(U_10988,U_10989),U_10990)) ),
inference(clausify,[status(thm)],[f_2926_2]) ).
fof(f_2927_1,plain,
! [T_d,T_c,V_b_2,V_a_2,V_c_2,V_z_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2))) ),
inference(fof_nnf,[status(thm)],[fact_mem__splitI]) ).
fof(f_2927_2,plain,
! [U_10999,U_10998,U_10997,U_10996,U_10995,U_10994,U_10993] :
( hBOOL(hAPP(hAPP(c_member(U_10993),U_10994),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10998,U_10999,tc_fun(U_10993,tc_HOL_Obool)),U_10995),hAPP(hAPP(c_Product__Type_OPair(U_10998,U_10999),U_10996),U_10997))))
| ~ hBOOL(hAPP(hAPP(c_member(U_10993),U_10994),hAPP(hAPP(U_10995,U_10996),U_10997))) ),
inference(variable_rename,[status(thm)],[f_2927_1]) ).
cnf(f_2927_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_10993),U_10994),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10998,U_10999,tc_fun(U_10993,tc_HOL_Obool)),U_10995),hAPP(hAPP(c_Product__Type_OPair(U_10998,U_10999),U_10996),U_10997))))
| ~ hBOOL(hAPP(hAPP(c_member(U_10993),U_10994),hAPP(hAPP(U_10995,U_10996),U_10997))) ),
inference(clausify,[status(thm)],[f_2927_2]) ).
fof(f_2928_1,plain,
! [V_c_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_c_2)) ),
inference(fof_nnf,[status(thm)],[fact_splitD_H]) ).
fof(f_2928_2,plain,
! [U_11006,U_11005,U_11004,U_11003,U_11002,U_11001,U_11000] :
( hBOOL(hAPP(hAPP(hAPP(U_11003,U_11004),U_11005),U_11006))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11000,U_11001,tc_fun(U_11002,tc_HOL_Obool)),U_11003),hAPP(hAPP(c_Product__Type_OPair(U_11000,U_11001),U_11004),U_11005)),U_11006)) ),
inference(variable_rename,[status(thm)],[f_2928_1]) ).
fof(f_2928_3,plain,
! [U_11006,U_11005,U_11004,U_11003] :
( ! [U_11002,U_11001,U_11000] : ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11000,U_11001,tc_fun(U_11002,tc_HOL_Obool)),U_11003),hAPP(hAPP(c_Product__Type_OPair(U_11000,U_11001),U_11004),U_11005)),U_11006))
| hBOOL(hAPP(hAPP(hAPP(U_11003,U_11004),U_11005),U_11006)) ),
inference(miniscope,[status(thm)],[f_2928_2]) ).
cnf(f_2928_4,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11000,U_11001,tc_fun(U_11002,tc_HOL_Obool)),U_11003),hAPP(hAPP(c_Product__Type_OPair(U_11000,U_11001),U_11004),U_11005)),U_11006))
| hBOOL(hAPP(hAPP(hAPP(U_11003,U_11004),U_11005),U_11006)) ),
inference(clausify,[status(thm)],[f_2928_3]) ).
fof(f_2929_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_2929_2,plain,
! [U_11011,U_11010,U_11009,U_11008,U_11007] :
( hBOOL(hAPP(hAPP(U_11009,U_11010),U_11011))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11007,U_11008,tc_HOL_Obool),U_11009),hAPP(hAPP(c_Product__Type_OPair(U_11007,U_11008),U_11010),U_11011))) ),
inference(variable_rename,[status(thm)],[f_2929_1]) ).
fof(f_2929_3,plain,
! [U_11011,U_11010,U_11009] :
( ! [U_11008,U_11007] : ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11007,U_11008,tc_HOL_Obool),U_11009),hAPP(hAPP(c_Product__Type_OPair(U_11007,U_11008),U_11010),U_11011)))
| hBOOL(hAPP(hAPP(U_11009,U_11010),U_11011)) ),
inference(miniscope,[status(thm)],[f_2929_2]) ).
cnf(f_2929_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11007,U_11008,tc_HOL_Obool),U_11009),hAPP(hAPP(c_Product__Type_OPair(U_11007,U_11008),U_11010),U_11011)))
| hBOOL(hAPP(hAPP(U_11009,U_11010),U_11011)) ),
inference(clausify,[status(thm)],[f_2929_3]) ).
fof(f_2930_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_2930_2,plain,
! [U_11017,U_11016,U_11015,U_11014,U_11013,U_11012] :
( ( U_11015 = U_11017
& U_11014 = U_11016 )
| hAPP(hAPP(c_Product__Type_OPair(U_11012,U_11013),U_11014),U_11015) != hAPP(hAPP(c_Product__Type_OPair(U_11012,U_11013),U_11016),U_11017) ),
inference(variable_rename,[status(thm)],[f_2930_1]) ).
fof(f_2930_3,plain,
! [U_11017,U_11016,U_11015,U_11014] :
( ! [U_11013,U_11012] : hAPP(hAPP(c_Product__Type_OPair(U_11012,U_11013),U_11014),U_11015) != hAPP(hAPP(c_Product__Type_OPair(U_11012,U_11013),U_11016),U_11017)
| ( U_11015 = U_11017
& U_11014 = U_11016 ) ),
inference(miniscope,[status(thm)],[f_2930_2]) ).
cnf(f_2930_4,plain,
( U_11014 = U_11016
| hAPP(hAPP(c_Product__Type_OPair(U_11012,U_11013),U_11014),U_11015) != hAPP(hAPP(c_Product__Type_OPair(U_11012,U_11013),U_11016),U_11017) ),
inference(clausify,[status(thm)],[f_2930_3]) ).
cnf(f_2930_5,plain,
( U_11015 = U_11017
| hAPP(hAPP(c_Product__Type_OPair(U_11012,U_11013),U_11014),U_11015) != hAPP(hAPP(c_Product__Type_OPair(U_11012,U_11013),U_11016),U_11017) ),
inference(clausify,[status(thm)],[f_2930_3]) ).
fof(f_2931_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_2931_2,plain,
! [U_11023,U_11022,U_11021,U_11020,U_11019,U_11018] :
( ( hAPP(hAPP(c_Product__Type_OPair(U_11018,U_11019),U_11020),U_11021) = hAPP(hAPP(c_Product__Type_OPair(U_11018,U_11019),U_11022),U_11023)
| U_11021 != U_11023
| U_11020 != U_11022 )
& ( ( U_11021 = U_11023
& U_11020 = U_11022 )
| hAPP(hAPP(c_Product__Type_OPair(U_11018,U_11019),U_11020),U_11021) != hAPP(hAPP(c_Product__Type_OPair(U_11018,U_11019),U_11022),U_11023) ) ),
inference(variable_rename,[status(thm)],[f_2931_1]) ).
fof(f_2931_3,plain,
( ! [U_11035,U_11033,U_11031,U_11029] :
( ! [U_11027,U_11025] : hAPP(hAPP(c_Product__Type_OPair(U_11025,U_11027),U_11029),U_11031) = hAPP(hAPP(c_Product__Type_OPair(U_11025,U_11027),U_11033),U_11035)
| U_11031 != U_11035
| U_11029 != U_11033 )
& ! [U_11034,U_11032,U_11030,U_11028] :
( ! [U_11026,U_11024] : hAPP(hAPP(c_Product__Type_OPair(U_11024,U_11026),U_11028),U_11030) != hAPP(hAPP(c_Product__Type_OPair(U_11024,U_11026),U_11032),U_11034)
| ( U_11030 = U_11034
& U_11028 = U_11032 ) ) ),
inference(miniscope,[status(thm)],[f_2931_2]) ).
cnf(f_2931_4,plain,
( U_11028 = U_11032
| hAPP(hAPP(c_Product__Type_OPair(U_11024,U_11026),U_11028),U_11030) != hAPP(hAPP(c_Product__Type_OPair(U_11024,U_11026),U_11032),U_11034) ),
inference(clausify,[status(thm)],[f_2931_3]) ).
cnf(f_2931_5,plain,
( U_11030 = U_11034
| hAPP(hAPP(c_Product__Type_OPair(U_11024,U_11026),U_11028),U_11030) != hAPP(hAPP(c_Product__Type_OPair(U_11024,U_11026),U_11032),U_11034) ),
inference(clausify,[status(thm)],[f_2931_3]) ).
cnf(f_2931_6,plain,
( hAPP(hAPP(c_Product__Type_OPair(U_11025,U_11027),U_11029),U_11031) = hAPP(hAPP(c_Product__Type_OPair(U_11025,U_11027),U_11033),U_11035)
| U_11031 != U_11035
| U_11029 != U_11033 ),
inference(clausify,[status(thm)],[f_2931_3]) ).
fof(f_2932_1,plain,
! [T_c,T_b,V_P_2] :
( ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
| ? [B_a,B_b] : ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) )
& ( ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)))
| ? [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ) ),
inference(fof_nnf,[status(thm)],[fact_split__paired__All]) ).
fof(f_2932_2,plain,
! [U_11044,U_11043,U_11042] :
( ( ! [U_11041] : hBOOL(hAPP(U_11042,U_11041))
| ? [U_11040,U_11039] : ~ hBOOL(hAPP(U_11042,hAPP(hAPP(c_Product__Type_OPair(U_11043,U_11044),U_11040),U_11039))) )
& ( ! [U_11038,U_11037] : hBOOL(hAPP(U_11042,hAPP(hAPP(c_Product__Type_OPair(U_11043,U_11044),U_11038),U_11037)))
| ? [U_11036] : ~ hBOOL(hAPP(U_11042,U_11036)) ) ),
inference(variable_rename,[status(thm)],[f_2932_1]) ).
fof(f_2932_3,plain,
( ! [U_11050,U_11048,U_11046] :
( ! [U_11041] : hBOOL(hAPP(U_11046,U_11041))
| ? [U_11040,U_11039] : ~ hBOOL(hAPP(U_11046,hAPP(hAPP(c_Product__Type_OPair(U_11048,U_11050),U_11040),U_11039))) )
& ! [U_11049,U_11047,U_11045] :
( ! [U_11038,U_11037] : hBOOL(hAPP(U_11045,hAPP(hAPP(c_Product__Type_OPair(U_11047,U_11049),U_11038),U_11037)))
| ? [U_11036] : ~ hBOOL(hAPP(U_11045,U_11036)) ) ),
inference(miniscope,[status(thm)],[f_2932_2]) ).
fof(f_2932_4,plain,
( ! [U_11050,U_11048,U_11046] :
( ! [U_11041] : hBOOL(hAPP(U_11046,U_11041))
| ? [U_11040,U_11039] : ~ hBOOL(hAPP(U_11046,hAPP(hAPP(c_Product__Type_OPair(U_11048,U_11050),U_11040),U_11039))) )
& ! [U_11049,U_11047,U_11045] :
( ! [U_11038,U_11037] : hBOOL(hAPP(U_11045,hAPP(hAPP(c_Product__Type_OPair(U_11047,U_11049),U_11038),U_11037)))
| ~ hBOOL(hAPP(U_11045,sK253(U_11049,U_11047,U_11045))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK253]),skolemize(U_11036,sK253(U_11049,U_11047,U_11045))],[f_2932_3]) ).
fof(f_2932_5,plain,
( ! [U_11050,U_11048,U_11046] :
( ! [U_11041] : hBOOL(hAPP(U_11046,U_11041))
| ? [U_11039] : ~ hBOOL(hAPP(U_11046,hAPP(hAPP(c_Product__Type_OPair(U_11048,U_11050),sK254(U_11050,U_11048,U_11046)),U_11039))) )
& ! [U_11049,U_11047,U_11045] :
( ! [U_11038,U_11037] : hBOOL(hAPP(U_11045,hAPP(hAPP(c_Product__Type_OPair(U_11047,U_11049),U_11038),U_11037)))
| ~ hBOOL(hAPP(U_11045,sK253(U_11049,U_11047,U_11045))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK254]),skolemize(U_11040,sK254(U_11050,U_11048,U_11046))],[f_2932_4]) ).
fof(f_2932_6,plain,
( ! [U_11050,U_11048,U_11046] :
( ! [U_11041] : hBOOL(hAPP(U_11046,U_11041))
| ~ hBOOL(hAPP(U_11046,hAPP(hAPP(c_Product__Type_OPair(U_11048,U_11050),sK254(U_11050,U_11048,U_11046)),sK255(U_11050,U_11048,U_11046)))) )
& ! [U_11049,U_11047,U_11045] :
( ! [U_11038,U_11037] : hBOOL(hAPP(U_11045,hAPP(hAPP(c_Product__Type_OPair(U_11047,U_11049),U_11038),U_11037)))
| ~ hBOOL(hAPP(U_11045,sK253(U_11049,U_11047,U_11045))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK255]),skolemize(U_11039,sK255(U_11050,U_11048,U_11046))],[f_2932_5]) ).
cnf(f_2932_7,plain,
( hBOOL(hAPP(U_11045,hAPP(hAPP(c_Product__Type_OPair(U_11047,U_11049),U_11038),U_11037)))
| ~ hBOOL(hAPP(U_11045,sK253(U_11049,U_11047,U_11045))) ),
inference(clausify,[status(thm)],[f_2932_6]) ).
cnf(f_2932_8,plain,
( hBOOL(hAPP(U_11046,U_11041))
| ~ hBOOL(hAPP(U_11046,hAPP(hAPP(c_Product__Type_OPair(U_11048,U_11050),sK254(U_11050,U_11048,U_11046)),sK255(U_11050,U_11048,U_11046)))) ),
inference(clausify,[status(thm)],[f_2932_6]) ).
fof(f_2933_1,plain,
! [V_c_2,T_d,T_c,T_b,V_q_2,V_p_2] :
( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_q_2)
| V_p_2 != V_q_2 ),
inference(fof_nnf,[status(thm)],[fact_split__weak__cong]) ).
fof(f_2933_2,plain,
! [U_11056,U_11055,U_11054,U_11053,U_11052,U_11051] :
( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11053,U_11054,U_11055),U_11056),U_11051) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11053,U_11054,U_11055),U_11056),U_11052)
| U_11051 != U_11052 ),
inference(variable_rename,[status(thm)],[f_2933_1]) ).
cnf(f_2933_3,plain,
( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11053,U_11054,U_11055),U_11056),U_11051) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11053,U_11054,U_11055),U_11056),U_11052)
| U_11051 != U_11052 ),
inference(clausify,[status(thm)],[f_2933_2]) ).
fof(f_2934_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_2934_2,plain,
! [U_11058,U_11057] : c_Divides_Odivmod__int(U_11057,U_11058) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11057),U_11058)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11057,U_11058)),
inference(variable_rename,[status(thm)],[f_2934_1]) ).
cnf(f_2934_3,plain,
c_Divides_Odivmod__int(U_11057,U_11058) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11057),U_11058)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11057,U_11058)),
inference(clausify,[status(thm)],[f_2934_2]) ).
fof(f_2935_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_2935_2,plain,
! [U_11064,U_11063,U_11062,U_11061,U_11060,U_11059] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11059,U_11060,U_11061),U_11062),hAPP(hAPP(c_Product__Type_OPair(U_11059,U_11060),U_11063),U_11064)) = hAPP(hAPP(U_11062,U_11063),U_11064),
inference(variable_rename,[status(thm)],[f_2935_1]) ).
cnf(f_2935_3,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11059,U_11060,U_11061),U_11062),hAPP(hAPP(c_Product__Type_OPair(U_11059,U_11060),U_11063),U_11064)) = hAPP(hAPP(U_11062,U_11063),U_11064),
inference(clausify,[status(thm)],[f_2935_2]) ).
fof(f_2936_1,plain,
! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : 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_2936_2,plain,
! [U_11070,U_11069,U_11068,U_11067,U_11066,U_11065] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11065,U_11066,U_11067),U_11068),hAPP(hAPP(c_Product__Type_OPair(U_11065,U_11066),U_11069),U_11070)) = hAPP(hAPP(U_11068,U_11069),U_11070),
inference(variable_rename,[status(thm)],[f_2936_1]) ).
cnf(f_2936_3,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11065,U_11066,U_11067),U_11068),hAPP(hAPP(c_Product__Type_OPair(U_11065,U_11066),U_11069),U_11070)) = hAPP(hAPP(U_11068,U_11069),U_11070),
inference(clausify,[status(thm)],[f_2936_2]) ).
fof(f_2937_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_2937_2,plain,
! [U_11074,U_11073,U_11072,U_11071] : hAPP(c_Product__Type_Oprod_Oprod__case(U_11071,U_11072,U_11073),hAPP(hAPP(c_COMBB(tc_fun(U_11072,tc_prod(U_11071,U_11072)),tc_fun(U_11072,U_11073),U_11071),hAPP(c_COMBB(tc_prod(U_11071,U_11072),U_11073,U_11072),U_11074)),c_Product__Type_OPair(U_11071,U_11072))) = U_11074,
inference(variable_rename,[status(thm)],[f_2937_1]) ).
cnf(f_2937_3,plain,
hAPP(c_Product__Type_Oprod_Oprod__case(U_11071,U_11072,U_11073),hAPP(hAPP(c_COMBB(tc_fun(U_11072,tc_prod(U_11071,U_11072)),tc_fun(U_11072,U_11073),U_11071),hAPP(c_COMBB(tc_prod(U_11071,U_11072),U_11073,U_11072),U_11074)),c_Product__Type_OPair(U_11071,U_11072))) = U_11074,
inference(clausify,[status(thm)],[f_2937_2]) ).
fof(f_2938_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_2938_2,plain,
! [U_11077,U_11076,U_11075] : c_Fun_Oinj__on(tc_prod(U_11075,U_11076),tc_prod(U_11076,U_11075),hAPP(c_Product__Type_Oprod_Oprod__case(U_11075,U_11076,tc_prod(U_11076,U_11075)),hAPP(c_COMBC(U_11076,U_11075,tc_prod(U_11076,U_11075)),c_Product__Type_OPair(U_11076,U_11075))),U_11077),
inference(variable_rename,[status(thm)],[f_2938_1]) ).
cnf(f_2938_3,plain,
c_Fun_Oinj__on(tc_prod(U_11075,U_11076),tc_prod(U_11076,U_11075),hAPP(c_Product__Type_Oprod_Oprod__case(U_11075,U_11076,tc_prod(U_11076,U_11075)),hAPP(c_COMBC(U_11076,U_11075,tc_prod(U_11076,U_11075)),c_Product__Type_OPair(U_11076,U_11075))),U_11077),
inference(clausify,[status(thm)],[f_2938_2]) ).
fof(f_2939_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_2939_2,plain,
! [U_11085,U_11084,U_11083,U_11082,U_11081,U_11080,U_11079,U_11078] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11078,U_11079,U_11080),U_11081),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11082,U_11083,tc_prod(U_11078,U_11079)),U_11084),U_11085)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11082,U_11083,U_11080),hAPP(hAPP(c_COMBB(tc_fun(U_11083,tc_prod(U_11078,U_11079)),tc_fun(U_11083,U_11080),U_11082),hAPP(c_COMBB(tc_prod(U_11078,U_11079),U_11080,U_11083),hAPP(c_Product__Type_Oprod_Oprod__case(U_11078,U_11079,U_11080),U_11081))),U_11084)),U_11085),
inference(variable_rename,[status(thm)],[f_2939_1]) ).
cnf(f_2939_3,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11078,U_11079,U_11080),U_11081),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11082,U_11083,tc_prod(U_11078,U_11079)),U_11084),U_11085)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11082,U_11083,U_11080),hAPP(hAPP(c_COMBB(tc_fun(U_11083,tc_prod(U_11078,U_11079)),tc_fun(U_11083,U_11080),U_11082),hAPP(c_COMBB(tc_prod(U_11078,U_11079),U_11080,U_11083),hAPP(c_Product__Type_Oprod_Oprod__case(U_11078,U_11079,U_11080),U_11081))),U_11084)),U_11085),
inference(clausify,[status(thm)],[f_2939_2]) ).
fof(f_2940_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_2940_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_2940_1]) ).
fof(f_2941_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_2941_2,plain,
! [U_11087,U_11086] : c_Code__Numeral_Odiv__mod__code__numeral(U_11086,U_11087) = 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_11086),U_11087)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_11086,U_11087)),
inference(variable_rename,[status(thm)],[f_2941_1]) ).
cnf(f_2941_3,plain,
c_Code__Numeral_Odiv__mod__code__numeral(U_11086,U_11087) = 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_11086),U_11087)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_11086,U_11087)),
inference(clausify,[status(thm)],[f_2941_2]) ).
fof(f_2942_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_2942_2,plain,
! [U_11089,U_11088] :
( ( ( ( c_Divides_Odivmod__int(U_11088,U_11089) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11088),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11089)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11089)) )
& ( c_Divides_Odivmod__int(U_11088,U_11089) = c_Divides_OnegDivAlg(U_11088,U_11089)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11089)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11088)) )
& ( ( ( ( ( c_Divides_Odivmod__int(U_11088,U_11089) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11088),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11089)))
| U_11088 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_11088,U_11089) = 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_11088 != 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_11089)) )
& ( c_Divides_Odivmod__int(U_11088,U_11089) = c_Divides_OposDivAlg(U_11088,U_11089)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11089)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11088)) ) ),
inference(variable_rename,[status(thm)],[f_2942_1]) ).
fof(f_2942_3,plain,
( ! [U_11093,U_11091] :
( ( ( c_Divides_Odivmod__int(U_11091,U_11093) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11091),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11093)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11093)) )
& ( c_Divides_Odivmod__int(U_11091,U_11093) = c_Divides_OnegDivAlg(U_11091,U_11093)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11093)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11091)) )
& ! [U_11092,U_11090] :
( ( ( ( ( c_Divides_Odivmod__int(U_11090,U_11092) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11090),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11092)))
| U_11090 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_11090,U_11092) = 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_11090 != 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_11092)) )
& ( c_Divides_Odivmod__int(U_11090,U_11092) = c_Divides_OposDivAlg(U_11090,U_11092)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11092)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11090)) ) ),
inference(miniscope,[status(thm)],[f_2942_2]) ).
cnf(f_2942_4,plain,
( c_Divides_Odivmod__int(U_11090,U_11092) = c_Divides_OposDivAlg(U_11090,U_11092)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11092))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11090)) ),
inference(clausify,[status(thm)],[f_2942_3]) ).
cnf(f_2942_5,plain,
( c_Divides_Odivmod__int(U_11090,U_11092) = 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_11090 != 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_11092))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11090)) ),
inference(clausify,[status(thm)],[f_2942_3]) ).
cnf(f_2942_6,plain,
( c_Divides_Odivmod__int(U_11090,U_11092) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11090),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11092)))
| U_11090 = 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_11092))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11090)) ),
inference(clausify,[status(thm)],[f_2942_3]) ).
cnf(f_2942_7,plain,
( c_Divides_Odivmod__int(U_11091,U_11093) = c_Divides_OnegDivAlg(U_11091,U_11093)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11093))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11091)) ),
inference(clausify,[status(thm)],[f_2942_3]) ).
cnf(f_2942_8,plain,
( c_Divides_Odivmod__int(U_11091,U_11093) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11091),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11093)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11093))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11091)) ),
inference(clausify,[status(thm)],[f_2942_3]) ).
fof(f_2943_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_2943_2,plain,
! [U_11095,U_11094] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11094),U_11095)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11094),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11095)),
inference(variable_rename,[status(thm)],[f_2943_1]) ).
cnf(f_2943_3,plain,
hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11094),U_11095)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11094),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11095)),
inference(clausify,[status(thm)],[f_2943_2]) ).
fof(f_2944_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_2944_2,plain,
! [U_11099,U_11098] :
( ( c_Nitpick_Orefl_H(U_11098,U_11099)
| ? [U_11097] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11098,U_11098)),hAPP(hAPP(c_Product__Type_OPair(U_11098,U_11098),U_11097),U_11097)),U_11099)) )
& ( ! [U_11096] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_11098,U_11098)),hAPP(hAPP(c_Product__Type_OPair(U_11098,U_11098),U_11096),U_11096)),U_11099))
| ~ c_Nitpick_Orefl_H(U_11098,U_11099) ) ),
inference(variable_rename,[status(thm)],[f_2944_1]) ).
fof(f_2944_3,plain,
( ! [U_11103,U_11101] :
( c_Nitpick_Orefl_H(U_11101,U_11103)
| ? [U_11097] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11101,U_11101)),hAPP(hAPP(c_Product__Type_OPair(U_11101,U_11101),U_11097),U_11097)),U_11103)) )
& ! [U_11102,U_11100] :
( ! [U_11096] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_11100,U_11100)),hAPP(hAPP(c_Product__Type_OPair(U_11100,U_11100),U_11096),U_11096)),U_11102))
| ~ c_Nitpick_Orefl_H(U_11100,U_11102) ) ),
inference(miniscope,[status(thm)],[f_2944_2]) ).
fof(f_2944_4,plain,
( ! [U_11103,U_11101] :
( c_Nitpick_Orefl_H(U_11101,U_11103)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11101,U_11101)),hAPP(hAPP(c_Product__Type_OPair(U_11101,U_11101),sK256(U_11103,U_11101)),sK256(U_11103,U_11101))),U_11103)) )
& ! [U_11102,U_11100] :
( ! [U_11096] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_11100,U_11100)),hAPP(hAPP(c_Product__Type_OPair(U_11100,U_11100),U_11096),U_11096)),U_11102))
| ~ c_Nitpick_Orefl_H(U_11100,U_11102) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK256]),skolemize(U_11097,sK256(U_11103,U_11101))],[f_2944_3]) ).
cnf(f_2944_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11100,U_11100)),hAPP(hAPP(c_Product__Type_OPair(U_11100,U_11100),U_11096),U_11096)),U_11102))
| ~ c_Nitpick_Orefl_H(U_11100,U_11102) ),
inference(clausify,[status(thm)],[f_2944_4]) ).
cnf(f_2944_6,plain,
( c_Nitpick_Orefl_H(U_11101,U_11103)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11101,U_11101)),hAPP(hAPP(c_Product__Type_OPair(U_11101,U_11101),sK256(U_11103,U_11101)),sK256(U_11103,U_11101))),U_11103)) ),
inference(clausify,[status(thm)],[f_2944_4]) ).
fof(f_2945_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_2945_2,plain,
! [U_11105,U_11104] :
( c_Divides_Odivmod__nat(U_11105,U_11104) = 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_11105),U_11104)),U_11104))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11105),U_11104),U_11104))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11104),U_11105))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11104)) ),
inference(variable_rename,[status(thm)],[f_2945_1]) ).
cnf(f_2945_3,plain,
( c_Divides_Odivmod__nat(U_11105,U_11104) = 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_11105),U_11104)),U_11104))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11105),U_11104),U_11104))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11104),U_11105))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11104)) ),
inference(clausify,[status(thm)],[f_2945_2]) ).
fof(f_2946_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_2946_2,plain,
! [U_11107,U_11106] :
( ( ( ( c_Divides_Odivmod__int(U_11106,U_11107) = 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_11107))),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_11107)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11106))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11107),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11106),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_11106,U_11107)),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_11107))))),c_Divides_Opdivmod(U_11106,U_11107))))
| U_11107 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_11106,U_11107) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11106)
| U_11107 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| U_11106 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_11106,U_11107) = 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_11106 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_2946_1]) ).
fof(f_2946_3,plain,
( ! [U_11111,U_11109] :
( ( ( c_Divides_Odivmod__int(U_11109,U_11111) = 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_11111))),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_11111)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11109))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11111),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11109),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_11109,U_11111)),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_11111))))),c_Divides_Opdivmod(U_11109,U_11111))))
| U_11111 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_11109,U_11111) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11109)
| U_11111 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| U_11109 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_11110,U_11108] :
( c_Divides_Odivmod__int(U_11108,U_11110) = 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_11108 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_2946_2]) ).
cnf(f_2946_4,plain,
( c_Divides_Odivmod__int(U_11108,U_11110) = 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_11108 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2946_3]) ).
cnf(f_2946_5,plain,
( c_Divides_Odivmod__int(U_11109,U_11111) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11109)
| U_11111 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_11109 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2946_3]) ).
cnf(f_2946_6,plain,
( c_Divides_Odivmod__int(U_11109,U_11111) = 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_11111))),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_11111)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11109))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11111),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11109),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_11109,U_11111)),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_11111))))),c_Divides_Opdivmod(U_11109,U_11111))))
| U_11111 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_11109 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2946_3]) ).
fof(f_2947_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_2947_2,plain,
! [U_11117,U_11116,U_11115,U_11114,U_11113,U_11112] : hAPP(c_Product__Type_Oapsnd(U_11112,U_11113,U_11114,U_11115),hAPP(hAPP(c_Product__Type_OPair(U_11114,U_11112),U_11116),U_11117)) = hAPP(hAPP(c_Product__Type_OPair(U_11114,U_11113),U_11116),hAPP(U_11115,U_11117)),
inference(variable_rename,[status(thm)],[f_2947_1]) ).
cnf(f_2947_3,plain,
hAPP(c_Product__Type_Oapsnd(U_11112,U_11113,U_11114,U_11115),hAPP(hAPP(c_Product__Type_OPair(U_11114,U_11112),U_11116),U_11117)) = hAPP(hAPP(c_Product__Type_OPair(U_11114,U_11113),U_11116),hAPP(U_11115,U_11117)),
inference(clausify,[status(thm)],[f_2947_2]) ).
fof(f_2948_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_2948_2,plain,
! [U_11124,U_11123,U_11122,U_11121,U_11120,U_11119,U_11118] : hAPP(c_Product__Type_Oapsnd(U_11118,U_11119,U_11120,U_11121),hAPP(c_Product__Type_Oapsnd(U_11122,U_11118,U_11120,U_11123),U_11124)) = hAPP(c_Product__Type_Oapsnd(U_11122,U_11119,U_11120,hAPP(c_Fun_Ocomp(U_11118,U_11119,U_11122,U_11121),U_11123)),U_11124),
inference(variable_rename,[status(thm)],[f_2948_1]) ).
cnf(f_2948_3,plain,
hAPP(c_Product__Type_Oapsnd(U_11118,U_11119,U_11120,U_11121),hAPP(c_Product__Type_Oapsnd(U_11122,U_11118,U_11120,U_11123),U_11124)) = hAPP(c_Product__Type_Oapsnd(U_11122,U_11119,U_11120,hAPP(c_Fun_Ocomp(U_11118,U_11119,U_11122,U_11121),U_11123)),U_11124),
inference(clausify,[status(thm)],[f_2948_2]) ).
fof(f_2949_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_2949_2,plain,
! [U_11125] : c_Divides_Odivmod__nat(U_11125,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_11125),
inference(variable_rename,[status(thm)],[f_2949_1]) ).
cnf(f_2949_3,plain,
c_Divides_Odivmod__nat(U_11125,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_11125),
inference(clausify,[status(thm)],[f_2949_2]) ).
fof(f_2950_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_2950_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_2950_1]) ).
fof(f_2951_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_2951_2,plain,
! [U_11127,U_11126] :
( c_Divides_Odivmod__nat(U_11126,U_11127) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11126)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11126),U_11127)) ),
inference(variable_rename,[status(thm)],[f_2951_1]) ).
cnf(f_2951_3,plain,
( c_Divides_Odivmod__nat(U_11126,U_11127) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11126)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11126),U_11127)) ),
inference(clausify,[status(thm)],[f_2951_2]) ).
fof(f_2952_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_2952_2,plain,
! [U_11129,U_11128] : c_Divides_Odivmod__nat(U_11128,U_11129) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11128),U_11129)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11128,U_11129)),
inference(variable_rename,[status(thm)],[f_2952_1]) ).
cnf(f_2952_3,plain,
c_Divides_Odivmod__nat(U_11128,U_11129) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11128),U_11129)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11128,U_11129)),
inference(clausify,[status(thm)],[f_2952_2]) ).
fof(f_2953_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_2953_2,plain,
! [U_11131,U_11130] :
( ( c_Divides_Odivmod__nat(U_11131,U_11130) = 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_11131),U_11130),U_11130))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11131),U_11130))
| U_11130 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Divides_Odivmod__nat(U_11131,U_11130) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11131)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11131),U_11130))
& U_11130 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(variable_rename,[status(thm)],[f_2953_1]) ).
fof(f_2953_3,plain,
( ! [U_11135,U_11133] :
( c_Divides_Odivmod__nat(U_11135,U_11133) = 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_11135),U_11133),U_11133))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11135),U_11133))
| U_11133 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_11134,U_11132] :
( c_Divides_Odivmod__nat(U_11134,U_11132) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11134)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11134),U_11132))
& U_11132 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(miniscope,[status(thm)],[f_2953_2]) ).
cnf(f_2953_4,plain,
( U_11132 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Divides_Odivmod__nat(U_11134,U_11132) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11134) ),
inference(clausify,[status(thm)],[f_2953_3]) ).
cnf(f_2953_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11134),U_11132))
| c_Divides_Odivmod__nat(U_11134,U_11132) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11134) ),
inference(clausify,[status(thm)],[f_2953_3]) ).
cnf(f_2953_6,plain,
( c_Divides_Odivmod__nat(U_11135,U_11133) = 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_11135),U_11133),U_11133))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11135),U_11133))
| U_11133 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_2953_3]) ).
fof(f_2954_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_2954_2,plain,
! [U_11137,U_11136] : c_Divides_Opdivmod(U_11136,U_11137) = 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_11136)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11137))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11136),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11137))),
inference(variable_rename,[status(thm)],[f_2954_1]) ).
cnf(f_2954_3,plain,
c_Divides_Opdivmod(U_11136,U_11137) = 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_11136)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11137))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11136),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11137))),
inference(clausify,[status(thm)],[f_2954_2]) ).
fof(f_2955_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_2955_2,plain,
! [U_11139,U_11138] :
( ( c_Divides_Opdivmod(U_11139,U_11138) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11139),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11138))
| U_11138 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Opdivmod(U_11139,U_11138) = 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_11139))
| U_11138 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_2955_1]) ).
fof(f_2955_3,plain,
( ! [U_11143,U_11141] :
( c_Divides_Opdivmod(U_11143,U_11141) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11143),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11141))
| U_11141 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_11142,U_11140] :
( c_Divides_Opdivmod(U_11142,U_11140) = 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_11142))
| U_11140 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_2955_2]) ).
cnf(f_2955_4,plain,
( c_Divides_Opdivmod(U_11142,U_11140) = 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_11142))
| U_11140 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2955_3]) ).
cnf(f_2955_5,plain,
( c_Divides_Opdivmod(U_11143,U_11141) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11143),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11141))
| U_11141 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2955_3]) ).
fof(f_2956_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_2956_2,plain,
! [U_11145,U_11144] :
( ( ( ( c_Divides_Odivmod__int(U_11144,U_11145) = 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_11145))),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_11144)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_11145))),c_Divides_Opdivmod(U_11144,U_11145)),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_11145))))),c_Divides_Opdivmod(U_11144,U_11145))))
| U_11145 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_11144,U_11145) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11144)
| U_11145 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| U_11144 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_11144,U_11145) = 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_11144 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_2956_1]) ).
fof(f_2956_3,plain,
( ! [U_11149,U_11147] :
( ( ( c_Divides_Odivmod__int(U_11147,U_11149) = 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_11149))),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_11147)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_11149))),c_Divides_Opdivmod(U_11147,U_11149)),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_11149))))),c_Divides_Opdivmod(U_11147,U_11149))))
| U_11149 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_11147,U_11149) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11147)
| U_11149 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| U_11147 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_11148,U_11146] :
( c_Divides_Odivmod__int(U_11146,U_11148) = 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_11146 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_2956_2]) ).
cnf(f_2956_4,plain,
( c_Divides_Odivmod__int(U_11146,U_11148) = 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_11146 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2956_3]) ).
cnf(f_2956_5,plain,
( c_Divides_Odivmod__int(U_11147,U_11149) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11147)
| U_11149 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_11147 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2956_3]) ).
cnf(f_2956_6,plain,
( c_Divides_Odivmod__int(U_11147,U_11149) = 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_11149))),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_11147)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_11149))),c_Divides_Opdivmod(U_11147,U_11149)),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_11149))))),c_Divides_Opdivmod(U_11147,U_11149))))
| U_11149 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_11147 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2956_3]) ).
fof(f_2957_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_2957_2,plain,
! [U_11154,U_11153,U_11152,U_11151,U_11150] : hAPP(c_Nat_Onat_Onat__rec(U_11150,U_11151,U_11152),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11153)),U_11154)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_11150),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_11153))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_11150,U_11150),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_11150,tc_fun(U_11150,U_11150)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_11150,tc_fun(U_11150,U_11150)),tc_Int_Oint),c_If(U_11150)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_11150,U_11151,U_11152),U_11154))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_11150,U_11150),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_11150,U_11150),tc_Int_Oint),U_11152),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_11154))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_11150,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_11150,U_11151,U_11152)),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_11154))))),
inference(variable_rename,[status(thm)],[f_2957_1]) ).
cnf(f_2957_3,plain,
hAPP(c_Nat_Onat_Onat__rec(U_11150,U_11151,U_11152),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11153)),U_11154)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_11150),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_11153))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_11150,U_11150),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_11150,tc_fun(U_11150,U_11150)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_11150,tc_fun(U_11150,U_11150)),tc_Int_Oint),c_If(U_11150)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_11150,U_11151,U_11152),U_11154))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_11150,U_11150),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_11150,U_11150),tc_Int_Oint),U_11152),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_11154))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_11150,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_11150,U_11151,U_11152)),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_11154))))),
inference(clausify,[status(thm)],[f_2957_2]) ).
fof(f_2958_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_2958_2,plain,
! [U_11159,U_11158,U_11157,U_11156,U_11155] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11159),U_11155),U_11156),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_11159),U_11157)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11159),U_11158)),U_11156))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11159),U_11158),U_11156))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11156))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11155,U_11156),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11157),U_11158))) ),
inference(variable_rename,[status(thm)],[f_2958_1]) ).
cnf(f_2958_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11159),U_11155),U_11156),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_11159),U_11157)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11159),U_11158)),U_11156))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11159),U_11158),U_11156))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11156))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11155,U_11156),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11157),U_11158))) ),
inference(clausify,[status(thm)],[f_2958_2]) ).
fof(f_2959_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_2959_2,plain,
! [U_11164,U_11163,U_11162,U_11161,U_11160] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11160,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11161),U_11164)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11162),U_11164)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11161),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11162,U_11164))),U_11163))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11164))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11161))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11160,U_11161),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11162),U_11163))) ),
inference(variable_rename,[status(thm)],[f_2959_1]) ).
cnf(f_2959_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11160,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11161),U_11164)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11162),U_11164)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11161),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11162,U_11164))),U_11163))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11164))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11161))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11160,U_11161),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11162),U_11163))) ),
inference(clausify,[status(thm)],[f_2959_2]) ).
fof(f_2960_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_2960_2,plain,
! [U_11168,U_11167,U_11166,U_11165] :
( U_11167 = U_11168
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11165,U_11166),U_11168))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11165,U_11166),U_11167)) ),
inference(variable_rename,[status(thm)],[f_2960_1]) ).
cnf(f_2960_3,plain,
( U_11167 = U_11168
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11165,U_11166),U_11168))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11165,U_11166),U_11167)) ),
inference(clausify,[status(thm)],[f_2960_2]) ).
fof(f_2961_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_2961_2,plain,
! [U_11171,U_11170,U_11169] : hAPP(c_Nat_Onat_Onat__rec(U_11169,U_11170,U_11171),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_11170,
inference(variable_rename,[status(thm)],[f_2961_1]) ).
cnf(f_2961_3,plain,
hAPP(c_Nat_Onat_Onat__rec(U_11169,U_11170,U_11171),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_11170,
inference(clausify,[status(thm)],[f_2961_2]) ).
fof(f_2962_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_2962_2,plain,
! [U_11175,U_11174,U_11173,U_11172] : hAPP(c_Nat_Onat_Onat__rec(U_11172,U_11173,U_11174),hAPP(c_Nat_OSuc,U_11175)) = hAPP(hAPP(U_11174,U_11175),hAPP(c_Nat_Onat_Onat__rec(U_11172,U_11173,U_11174),U_11175)),
inference(variable_rename,[status(thm)],[f_2962_1]) ).
cnf(f_2962_3,plain,
hAPP(c_Nat_Onat_Onat__rec(U_11172,U_11173,U_11174),hAPP(c_Nat_OSuc,U_11175)) = hAPP(hAPP(U_11174,U_11175),hAPP(c_Nat_Onat_Onat__rec(U_11172,U_11173,U_11174),U_11175)),
inference(clausify,[status(thm)],[f_2962_2]) ).
fof(f_2963_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_2963_2,plain,
! [U_11178,U_11177,U_11176] :
( c_Divides_Odivmod__nat(U_11176,U_11177) = U_11178
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11176,U_11177),U_11178)) ),
inference(variable_rename,[status(thm)],[f_2963_1]) ).
cnf(f_2963_3,plain,
( c_Divides_Odivmod__nat(U_11176,U_11177) = U_11178
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11176,U_11177),U_11178)) ),
inference(clausify,[status(thm)],[f_2963_2]) ).
fof(f_2964_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_2964_2,plain,
! [U_11180,U_11179] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11179,U_11180),c_Divides_Odivmod__nat(U_11179,U_11180))),
inference(variable_rename,[status(thm)],[f_2964_1]) ).
cnf(f_2964_3,plain,
hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11179,U_11180),c_Divides_Odivmod__nat(U_11179,U_11180))),
inference(clausify,[status(thm)],[f_2964_2]) ).
fof(f_2965_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_2965_2,plain,
! [U_11184,U_11183,U_11182,U_11181] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11181,U_11182) = U_11184
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11181,U_11182),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11183),U_11184))) ),
inference(variable_rename,[status(thm)],[f_2965_1]) ).
cnf(f_2965_3,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11181,U_11182) = U_11184
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11181,U_11182),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11183),U_11184))) ),
inference(clausify,[status(thm)],[f_2965_2]) ).
fof(f_2966_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_2966_2,plain,
! [U_11188,U_11187,U_11186,U_11185] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11185),U_11186) = U_11187
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11185,U_11186),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11187),U_11188))) ),
inference(variable_rename,[status(thm)],[f_2966_1]) ).
cnf(f_2966_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11185),U_11186) = U_11187
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11185,U_11186),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11187),U_11188))) ),
inference(clausify,[status(thm)],[f_2966_2]) ).
fof(f_2967_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_2967_2,plain,
! [U_11190,U_11189] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11189,U_11190),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11189),U_11190)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11189,U_11190)))),
inference(variable_rename,[status(thm)],[f_2967_1]) ).
cnf(f_2967_3,plain,
hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11189,U_11190),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11189),U_11190)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11189,U_11190)))),
inference(clausify,[status(thm)],[f_2967_2]) ).
fof(f_2968_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_2968_2,plain,
! [U_11197,U_11196,U_11195,U_11194,U_11193,U_11192,U_11191] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11191),U_11195),U_11192),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_11193),U_11196)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11194),U_11197)),U_11192))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11194),U_11197),U_11192))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11192))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11195,U_11192),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11196),U_11197)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11191,U_11192),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11193),U_11194))) ),
inference(variable_rename,[status(thm)],[f_2968_1]) ).
cnf(f_2968_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11191),U_11195),U_11192),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_11193),U_11196)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11194),U_11197)),U_11192))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11194),U_11197),U_11192))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11192))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11195,U_11192),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11196),U_11197)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11191,U_11192),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11193),U_11194))) ),
inference(clausify,[status(thm)],[f_2968_2]) ).
fof(f_2969_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_2969_2,plain,
! [U_11201,U_11200,U_11199,U_11198] : hAPP(c_Nat_Onat_Onat__rec(U_11198,U_11199,U_11200),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11201)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_11198),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_11201))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_11198,U_11198),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_11198,tc_fun(U_11198,U_11198)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_11198,tc_fun(U_11198,U_11198)),tc_Int_Oint),c_If(U_11198)),c_Nat__Numeral_Oneg)),U_11199)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_11198,U_11198),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_11198,U_11198),tc_Int_Oint),U_11200),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_11198,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_11198,U_11199,U_11200)),c_Int_Onat)))),
inference(variable_rename,[status(thm)],[f_2969_1]) ).
cnf(f_2969_3,plain,
hAPP(c_Nat_Onat_Onat__rec(U_11198,U_11199,U_11200),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_11201)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_11198),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_11201))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_11198,U_11198),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_11198,tc_fun(U_11198,U_11198)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_11198,tc_fun(U_11198,U_11198)),tc_Int_Oint),c_If(U_11198)),c_Nat__Numeral_Oneg)),U_11199)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_11198,U_11198),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_11198,U_11198),tc_Int_Oint),U_11200),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_11198,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_11198,U_11199,U_11200)),c_Int_Onat)))),
inference(clausify,[status(thm)],[f_2969_2]) ).
fof(f_2970_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_2970_2,plain,
! [U_11205,U_11204,U_11203,U_11202] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(U_11202,U_11203)),c_Nitpick_Opair__box_OPairBox(U_11202,U_11203,U_11204,U_11205)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_2970_1]) ).
cnf(f_2970_3,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(U_11202,U_11203)),c_Nitpick_Opair__box_OPairBox(U_11202,U_11203,U_11204,U_11205)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_2970_2]) ).
fof(f_2971_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_2971_2,plain,
! [U_11211,U_11210,U_11209,U_11208,U_11207,U_11206] : c_Nitpick_Opair__box_Opair__box__case(U_11206,U_11207,U_11208,U_11209,c_Nitpick_Opair__box_OPairBox(U_11206,U_11207,U_11210,U_11211)) = hAPP(hAPP(U_11209,U_11210),U_11211),
inference(variable_rename,[status(thm)],[f_2971_1]) ).
cnf(f_2971_3,plain,
c_Nitpick_Opair__box_Opair__box__case(U_11206,U_11207,U_11208,U_11209,c_Nitpick_Opair__box_OPairBox(U_11206,U_11207,U_11210,U_11211)) = hAPP(hAPP(U_11209,U_11210),U_11211),
inference(clausify,[status(thm)],[f_2971_2]) ).
fof(f_2972_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_2972_2,plain,
! [U_11217,U_11216,U_11215,U_11214,U_11213,U_11212] : c_Nitpick_Opair__box_Opair__box__rec(U_11212,U_11213,U_11214,U_11215,c_Nitpick_Opair__box_OPairBox(U_11212,U_11213,U_11216,U_11217)) = hAPP(hAPP(U_11215,U_11216),U_11217),
inference(variable_rename,[status(thm)],[f_2972_1]) ).
cnf(f_2972_3,plain,
c_Nitpick_Opair__box_Opair__box__rec(U_11212,U_11213,U_11214,U_11215,c_Nitpick_Opair__box_OPairBox(U_11212,U_11213,U_11216,U_11217)) = hAPP(hAPP(U_11215,U_11216),U_11217),
inference(clausify,[status(thm)],[f_2972_2]) ).
fof(f_2973_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_2973_2,plain,
! [U_11219,U_11218] :
( ( ( c_Divides_OnegDivAlg(U_11218,U_11219) = hAPP(c_Divides_Oadjust(U_11219),c_Divides_OnegDivAlg(U_11218,hAPP(hAPP(c_Groups_Otimes__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_11219)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11219),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_11218),U_11219))) )
& ( c_Divides_OnegDivAlg(U_11218,U_11219) = 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_11218),U_11219))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11219),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_11218),U_11219))) ) ) )
| ~ 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_11218),U_11219))) ),
inference(variable_rename,[status(thm)],[f_2973_1]) ).
cnf(f_2973_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_11218),U_11219)))
| c_Divides_OnegDivAlg(U_11218,U_11219) = 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_11218),U_11219))
| ~ 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_11218),U_11219))) ),
inference(clausify,[status(thm)],[f_2973_2]) ).
cnf(f_2973_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11219),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OnegDivAlg(U_11218,U_11219) = 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_11218),U_11219))
| ~ 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_11218),U_11219))) ),
inference(clausify,[status(thm)],[f_2973_2]) ).
cnf(f_2973_5,plain,
( c_Divides_OnegDivAlg(U_11218,U_11219) = hAPP(c_Divides_Oadjust(U_11219),c_Divides_OnegDivAlg(U_11218,hAPP(hAPP(c_Groups_Otimes__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_11219)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11219),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_11218),U_11219)))
| ~ 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_11218),U_11219))) ),
inference(clausify,[status(thm)],[f_2973_2]) ).
fof(f_2974_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_2974_2,plain,
! [U_11224,U_11223,U_11222,U_11221,U_11220] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11220,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11221),U_11224)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11222),U_11224)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11221),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11222,U_11224))),U_11223))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11224))
| U_11221 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11220,U_11221),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11222),U_11223))) ),
inference(variable_rename,[status(thm)],[f_2974_1]) ).
cnf(f_2974_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11220,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11221),U_11224)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11222),U_11224)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11221),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11222,U_11224))),U_11223))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11224))
| U_11221 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11220,U_11221),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11222),U_11223))) ),
inference(clausify,[status(thm)],[f_2974_2]) ).
fof(f_2975_1,plain,
! [V_B_2,V_X_2,V_f_2,T_c,T_b] :
( c_Orderings_Oorder__class_Omono(T_b,tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_f_2)),V_X_2))),V_B_2))
| ~ c_Orderings_Oorder__class_Omono(T_b,tc_fun(T_c,tc_HOL_Obool),V_f_2)
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_coinduct3__mono__lemma]) ).
fof(f_2975_2,plain,
! [U_11229,U_11228,U_11227,U_11226,U_11225] :
( c_Orderings_Oorder__class_Omono(U_11225,tc_fun(U_11226,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11225,tc_fun(U_11226,tc_HOL_Obool),tc_fun(U_11226,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11226,tc_HOL_Obool),tc_fun(tc_fun(U_11226,tc_HOL_Obool),tc_fun(U_11226,tc_HOL_Obool)),U_11225),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11226,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11225,tc_fun(U_11226,tc_HOL_Obool),tc_fun(U_11226,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11226,tc_HOL_Obool),tc_fun(tc_fun(U_11226,tc_HOL_Obool),tc_fun(U_11226,tc_HOL_Obool)),U_11225),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11226,tc_HOL_Obool))),U_11227)),U_11228))),U_11229))
| ~ c_Orderings_Oorder__class_Omono(U_11225,tc_fun(U_11226,tc_HOL_Obool),U_11227)
| ~ class_Orderings_Oorder(U_11225) ),
inference(variable_rename,[status(thm)],[f_2975_1]) ).
cnf(f_2975_3,plain,
( c_Orderings_Oorder__class_Omono(U_11225,tc_fun(U_11226,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11225,tc_fun(U_11226,tc_HOL_Obool),tc_fun(U_11226,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11226,tc_HOL_Obool),tc_fun(tc_fun(U_11226,tc_HOL_Obool),tc_fun(U_11226,tc_HOL_Obool)),U_11225),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11226,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11225,tc_fun(U_11226,tc_HOL_Obool),tc_fun(U_11226,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11226,tc_HOL_Obool),tc_fun(tc_fun(U_11226,tc_HOL_Obool),tc_fun(U_11226,tc_HOL_Obool)),U_11225),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11226,tc_HOL_Obool))),U_11227)),U_11228))),U_11229))
| ~ c_Orderings_Oorder__class_Omono(U_11225,tc_fun(U_11226,tc_HOL_Obool),U_11227)
| ~ class_Orderings_Oorder(U_11225) ),
inference(clausify,[status(thm)],[f_2975_2]) ).
fof(f_2976_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_2976_2,plain,
! [U_11235,U_11234,U_11233,U_11232,U_11231,U_11230] :
( U_11233 = U_11235
| U_11231 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11230,U_11231),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11234),U_11235)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11230,U_11231),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11232),U_11233))) ),
inference(variable_rename,[status(thm)],[f_2976_1]) ).
cnf(f_2976_3,plain,
( U_11233 = U_11235
| U_11231 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11230,U_11231),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11234),U_11235)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11230,U_11231),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11232),U_11233))) ),
inference(clausify,[status(thm)],[f_2976_2]) ).
fof(f_2977_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_2977_2,plain,
! [U_11241,U_11240,U_11239,U_11238,U_11237,U_11236] :
( U_11238 = U_11240
| U_11237 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11236,U_11237),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11240),U_11241)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11236,U_11237),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11238),U_11239))) ),
inference(variable_rename,[status(thm)],[f_2977_1]) ).
cnf(f_2977_3,plain,
( U_11238 = U_11240
| U_11237 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11236,U_11237),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11240),U_11241)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11236,U_11237),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11238),U_11239))) ),
inference(clausify,[status(thm)],[f_2977_2]) ).
fof(f_2978_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_2978_2,plain,
! [U_11244,U_11243,U_11242] :
( U_11244 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_11242 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11242,U_11242),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11243),U_11244))) ),
inference(variable_rename,[status(thm)],[f_2978_1]) ).
cnf(f_2978_3,plain,
( U_11244 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_11242 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11242,U_11242),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11243),U_11244))) ),
inference(clausify,[status(thm)],[f_2978_2]) ).
fof(f_2979_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_2979_2,plain,
! [U_11245] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_11245),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_11245 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_2979_1]) ).
cnf(f_2979_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_11245),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_11245 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2979_2]) ).
fof(f_2980_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_2980_2,plain,
! [U_11248,U_11247,U_11246] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11246,U_11247),hAPP(c_Divides_OnegateSnd,U_11248)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11246),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11247)),U_11248)) ),
inference(variable_rename,[status(thm)],[f_2980_1]) ).
cnf(f_2980_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11246,U_11247),hAPP(c_Divides_OnegateSnd,U_11248)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11246),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11247)),U_11248)) ),
inference(clausify,[status(thm)],[f_2980_2]) ).
fof(f_2981_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_2981_2,plain,
! [U_11250,U_11249] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11250,U_11249),c_Divides_Odivmod__int(U_11250,U_11249)))
| U_11249 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_2981_1]) ).
cnf(f_2981_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11250,U_11249),c_Divides_Odivmod__int(U_11250,U_11249)))
| U_11249 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2981_2]) ).
fof(f_2982_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_2982_2,plain,
! [U_11253,U_11252,U_11251] :
( U_11252 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_11251 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11251,U_11251),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11252),U_11253))) ),
inference(variable_rename,[status(thm)],[f_2982_1]) ).
cnf(f_2982_3,plain,
( U_11252 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_11251 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11251,U_11251),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11252),U_11253))) ),
inference(clausify,[status(thm)],[f_2982_2]) ).
fof(f_2983_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_2983_2,plain,
! [U_11257,U_11256,U_11255,U_11254] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11254,U_11255) = U_11257
| U_11255 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11254,U_11255),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11256),U_11257))) ),
inference(variable_rename,[status(thm)],[f_2983_1]) ).
cnf(f_2983_3,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11254,U_11255) = U_11257
| U_11255 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11254,U_11255),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11256),U_11257))) ),
inference(clausify,[status(thm)],[f_2983_2]) ).
fof(f_2984_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_2984_2,plain,
! [U_11261,U_11260,U_11259,U_11258] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11258),U_11259) = U_11260
| U_11259 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11258,U_11259),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11260),U_11261))) ),
inference(variable_rename,[status(thm)],[f_2984_1]) ).
cnf(f_2984_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11258),U_11259) = U_11260
| U_11259 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11258,U_11259),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11260),U_11261))) ),
inference(clausify,[status(thm)],[f_2984_2]) ).
fof(f_2985_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_2985_2,plain,
! [U_11263,U_11262] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11262,U_11263),c_Divides_OnegDivAlg(U_11262,U_11263)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11263))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11262),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_2985_1]) ).
cnf(f_2985_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11262,U_11263),c_Divides_OnegDivAlg(U_11262,U_11263)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11263))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11262),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2985_2]) ).
fof(f_2986_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_2986_2,plain,
! [U_11265,U_11264] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11265,U_11264),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11265),U_11264)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11265,U_11264))))
| U_11264 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_2986_1]) ).
cnf(f_2986_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11265,U_11264),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11265),U_11264)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11265,U_11264))))
| U_11264 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2986_2]) ).
fof(f_2987_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_2987_2,plain,
! [U_11267,U_11266] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11266,U_11267),c_Divides_OposDivAlg(U_11266,U_11267)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11267))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11266)) ),
inference(variable_rename,[status(thm)],[f_2987_1]) ).
cnf(f_2987_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11266,U_11267),c_Divides_OposDivAlg(U_11266,U_11267)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11267))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11266)) ),
inference(clausify,[status(thm)],[f_2987_2]) ).
fof(f_2988_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_2988_2,plain,
! [U_11274,U_11273,U_11272,U_11271,U_11270,U_11269,U_11268] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11268),U_11272),U_11269),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_11270),U_11273)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11271),U_11274)),U_11269))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11271),U_11274),U_11269))))
| U_11269 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11272,U_11269),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11273),U_11274)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11268,U_11269),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11270),U_11271))) ),
inference(variable_rename,[status(thm)],[f_2988_1]) ).
cnf(f_2988_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11268),U_11272),U_11269),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_11270),U_11273)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11271),U_11274)),U_11269))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11271),U_11274),U_11269))))
| U_11269 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11272,U_11269),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11273),U_11274)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11268,U_11269),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11270),U_11271))) ),
inference(clausify,[status(thm)],[f_2988_2]) ).
fof(f_2989_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_2989_2,plain,
! [U_11278,U_11277,U_11276,U_11275] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11275),U_11276),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_11278),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11277)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11277)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_11278),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_11276),U_11278)))))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11275,U_11276),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11277),U_11278))) ),
inference(variable_rename,[status(thm)],[f_2989_1]) ).
cnf(f_2989_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11275),U_11276),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_11278),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11277)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11277)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_11278),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_11276),U_11278)))))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11275,U_11276),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11277),U_11278))) ),
inference(clausify,[status(thm)],[f_2989_2]) ).
fof(f_2990_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_2990_2,plain,
! [U_11282,U_11281,U_11280,U_11279] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11279,U_11280),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11281),U_11282)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11282),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11280),U_11282)) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11280)) )
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11282),U_11280))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11282)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11280)) )
| U_11279 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11280),U_11281)),U_11282) ),
inference(variable_rename,[status(thm)],[f_2990_1]) ).
cnf(f_2990_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11280))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11280))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11279,U_11280),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11281),U_11282)))
| U_11279 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11280),U_11281)),U_11282) ),
inference(clausify,[status(thm)],[f_2990_2]) ).
cnf(f_2990_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11282),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11280),U_11282))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11280))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11279,U_11280),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11281),U_11282)))
| U_11279 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11280),U_11281)),U_11282) ),
inference(clausify,[status(thm)],[f_2990_2]) ).
cnf(f_2990_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11280))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11282),U_11280))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11282))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11279,U_11280),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11281),U_11282)))
| U_11279 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11280),U_11281)),U_11282) ),
inference(clausify,[status(thm)],[f_2990_2]) ).
cnf(f_2990_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11282),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11280),U_11282))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11282),U_11280))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11282))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11279,U_11280),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11281),U_11282)))
| U_11279 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11280),U_11281)),U_11282) ),
inference(clausify,[status(thm)],[f_2990_2]) ).
fof(f_2991_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_2991_2,plain,
! [U_11287,U_11286,U_11285,U_11284,U_11283] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11287),U_11283),U_11284),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_11287),U_11285)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11287),U_11286)),U_11284))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11287),U_11286),U_11284))))
| U_11284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11283,U_11284),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11285),U_11286))) ),
inference(variable_rename,[status(thm)],[f_2991_1]) ).
cnf(f_2991_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11287),U_11283),U_11284),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_11287),U_11285)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11287),U_11286)),U_11284))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11287),U_11286),U_11284))))
| U_11284 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11283,U_11284),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11285),U_11286))) ),
inference(clausify,[status(thm)],[f_2991_2]) ).
fof(f_2992_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_2992_2,plain,
! [U_11289,U_11288] : c_Divides_Odivmod__int__rel(U_11288,U_11289) = 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_11288))),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_11289)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_11289))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_11289))))),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_11289)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_11289))),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_2992_1]) ).
cnf(f_2992_3,plain,
c_Divides_Odivmod__int__rel(U_11288,U_11289) = 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_11288))),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_11289)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_11289))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_11289))))),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_11289)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_11289))),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_2992_2]) ).
fof(f_2993_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_2993_2,plain,
! [U_11291,U_11290] :
( ( ( c_Divides_OposDivAlg(U_11290,U_11291) = hAPP(c_Divides_Oadjust(U_11291),c_Divides_OposDivAlg(U_11290,hAPP(hAPP(c_Groups_Otimes__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_11291)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11291),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11290),U_11291)) )
& ( c_Divides_OposDivAlg(U_11290,U_11291) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11290)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11291),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11290),U_11291)) ) ) )
| ~ 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_11290),U_11291))) ),
inference(variable_rename,[status(thm)],[f_2993_1]) ).
cnf(f_2993_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11290),U_11291))
| c_Divides_OposDivAlg(U_11290,U_11291) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11290)
| ~ 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_11290),U_11291))) ),
inference(clausify,[status(thm)],[f_2993_2]) ).
cnf(f_2993_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11291),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OposDivAlg(U_11290,U_11291) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11290)
| ~ 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_11290),U_11291))) ),
inference(clausify,[status(thm)],[f_2993_2]) ).
cnf(f_2993_5,plain,
( c_Divides_OposDivAlg(U_11290,U_11291) = hAPP(c_Divides_Oadjust(U_11291),c_Divides_OposDivAlg(U_11290,hAPP(hAPP(c_Groups_Otimes__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_11291)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11291),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11290),U_11291))
| ~ 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_11290),U_11291))) ),
inference(clausify,[status(thm)],[f_2993_2]) ).
fof(f_2994_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_2994_2,plain,
! [U_11293,U_11292] :
( ( ( ( ( c_Nitpick_Onorm__frac(U_11292,U_11293) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_11292),U_11293)),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_11292))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11293)))
| U_11293 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_11292 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Nitpick_Onorm__frac(U_11292,U_11293) = 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_11293 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& U_11292 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11293),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( c_Nitpick_Onorm__frac(U_11292,U_11293) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11292),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11293))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11293),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_11292),U_11293))) ),
inference(variable_rename,[status(thm)],[f_2994_1]) ).
cnf(f_2994_3,plain,
( c_Nitpick_Onorm__frac(U_11292,U_11293) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11292),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11293))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11293),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_11292),U_11293))) ),
inference(clausify,[status(thm)],[f_2994_2]) ).
cnf(f_2994_4,plain,
( U_11292 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nitpick_Onorm__frac(U_11292,U_11293) = 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_11293),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_11292),U_11293))) ),
inference(clausify,[status(thm)],[f_2994_2]) ).
cnf(f_2994_5,plain,
( U_11293 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nitpick_Onorm__frac(U_11292,U_11293) = 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_11293),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_11292),U_11293))) ),
inference(clausify,[status(thm)],[f_2994_2]) ).
cnf(f_2994_6,plain,
( c_Nitpick_Onorm__frac(U_11292,U_11293) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_11292),U_11293)),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_11292))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11293)))
| U_11293 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_11292 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11293),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_11292),U_11293))) ),
inference(clausify,[status(thm)],[f_2994_2]) ).
fof(f_2995_1,plain,
! [V_P_2,V_a1_2,V_a0_2] :
( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
| ? [B_a,B_b] :
( ~ hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
& ( hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_a),B_b))) )
& hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) ),
inference(fof_nnf,[status(thm)],[fact_negDivAlg_Opinduct]) ).
fof(f_2995_2,plain,
! [U_11298,U_11297,U_11296] :
( hBOOL(hAPP(hAPP(U_11298,U_11296),U_11297))
| ? [U_11295,U_11294] :
( ~ hBOOL(hAPP(hAPP(U_11298,U_11295),U_11294))
& ( hBOOL(hAPP(hAPP(U_11298,U_11295),hAPP(hAPP(c_Groups_Otimes__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_11294)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11294),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_11295),U_11294))) )
& 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_11295),U_11294))) )
| ~ 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_11296),U_11297))) ),
inference(variable_rename,[status(thm)],[f_2995_1]) ).
fof(f_2995_3,plain,
! [U_11298,U_11297,U_11296] :
( hBOOL(hAPP(hAPP(U_11298,U_11296),U_11297))
| ? [U_11294] :
( ~ hBOOL(hAPP(hAPP(U_11298,sK257(U_11298,U_11297,U_11296)),U_11294))
& ( hBOOL(hAPP(hAPP(U_11298,sK257(U_11298,U_11297,U_11296)),hAPP(hAPP(c_Groups_Otimes__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_11294)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11294),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),sK257(U_11298,U_11297,U_11296)),U_11294))) )
& 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),sK257(U_11298,U_11297,U_11296)),U_11294))) )
| ~ 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_11296),U_11297))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK257]),skolemize(U_11295,sK257(U_11298,U_11297,U_11296))],[f_2995_2]) ).
fof(f_2995_4,plain,
! [U_11298,U_11297,U_11296] :
( hBOOL(hAPP(hAPP(U_11298,U_11296),U_11297))
| ( ~ hBOOL(hAPP(hAPP(U_11298,sK257(U_11298,U_11297,U_11296)),sK258(U_11298,U_11297,U_11296)))
& ( hBOOL(hAPP(hAPP(U_11298,sK257(U_11298,U_11297,U_11296)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK258(U_11298,U_11297,U_11296))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK258(U_11298,U_11297,U_11296)),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),sK257(U_11298,U_11297,U_11296)),sK258(U_11298,U_11297,U_11296)))) )
& 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),sK257(U_11298,U_11297,U_11296)),sK258(U_11298,U_11297,U_11296)))) )
| ~ 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_11296),U_11297))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK258]),skolemize(U_11294,sK258(U_11298,U_11297,U_11296))],[f_2995_3]) ).
cnf(f_2995_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),sK257(U_11298,U_11297,U_11296)),sK258(U_11298,U_11297,U_11296))))
| hBOOL(hAPP(hAPP(U_11298,U_11296),U_11297))
| ~ 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_11296),U_11297))) ),
inference(clausify,[status(thm)],[f_2995_4]) ).
cnf(f_2995_6,plain,
( hBOOL(hAPP(hAPP(U_11298,sK257(U_11298,U_11297,U_11296)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK258(U_11298,U_11297,U_11296))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK258(U_11298,U_11297,U_11296)),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),sK257(U_11298,U_11297,U_11296)),sK258(U_11298,U_11297,U_11296))))
| hBOOL(hAPP(hAPP(U_11298,U_11296),U_11297))
| ~ 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_11296),U_11297))) ),
inference(clausify,[status(thm)],[f_2995_4]) ).
cnf(f_2995_7,plain,
( ~ hBOOL(hAPP(hAPP(U_11298,sK257(U_11298,U_11297,U_11296)),sK258(U_11298,U_11297,U_11296)))
| hBOOL(hAPP(hAPP(U_11298,U_11296),U_11297))
| ~ 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_11296),U_11297))) ),
inference(clausify,[status(thm)],[f_2995_4]) ).
fof(f_2996_1,plain,
! [V_P_2,V_a1_2,V_a0_2] :
( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
| ? [B_a,B_b] :
( ~ hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
& ( hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) )
& hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) ),
inference(fof_nnf,[status(thm)],[fact_posDivAlg_Opinduct]) ).
fof(f_2996_2,plain,
! [U_11303,U_11302,U_11301] :
( hBOOL(hAPP(hAPP(U_11303,U_11301),U_11302))
| ? [U_11300,U_11299] :
( ~ hBOOL(hAPP(hAPP(U_11303,U_11300),U_11299))
& ( hBOOL(hAPP(hAPP(U_11303,U_11300),hAPP(hAPP(c_Groups_Otimes__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_11299)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11299),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11300),U_11299)) )
& 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_11300),U_11299))) )
| ~ 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_11301),U_11302))) ),
inference(variable_rename,[status(thm)],[f_2996_1]) ).
fof(f_2996_3,plain,
! [U_11303,U_11302,U_11301] :
( hBOOL(hAPP(hAPP(U_11303,U_11301),U_11302))
| ? [U_11299] :
( ~ hBOOL(hAPP(hAPP(U_11303,sK259(U_11303,U_11302,U_11301)),U_11299))
& ( hBOOL(hAPP(hAPP(U_11303,sK259(U_11303,U_11302,U_11301)),hAPP(hAPP(c_Groups_Otimes__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_11299)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11299),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK259(U_11303,U_11302,U_11301)),U_11299)) )
& 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),sK259(U_11303,U_11302,U_11301)),U_11299))) )
| ~ 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_11301),U_11302))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK259]),skolemize(U_11300,sK259(U_11303,U_11302,U_11301))],[f_2996_2]) ).
fof(f_2996_4,plain,
! [U_11303,U_11302,U_11301] :
( hBOOL(hAPP(hAPP(U_11303,U_11301),U_11302))
| ( ~ hBOOL(hAPP(hAPP(U_11303,sK259(U_11303,U_11302,U_11301)),sK260(U_11303,U_11302,U_11301)))
& ( hBOOL(hAPP(hAPP(U_11303,sK259(U_11303,U_11302,U_11301)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK260(U_11303,U_11302,U_11301))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK260(U_11303,U_11302,U_11301)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK259(U_11303,U_11302,U_11301)),sK260(U_11303,U_11302,U_11301))) )
& 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),sK259(U_11303,U_11302,U_11301)),sK260(U_11303,U_11302,U_11301)))) )
| ~ 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_11301),U_11302))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK260]),skolemize(U_11299,sK260(U_11303,U_11302,U_11301))],[f_2996_3]) ).
cnf(f_2996_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),sK259(U_11303,U_11302,U_11301)),sK260(U_11303,U_11302,U_11301))))
| hBOOL(hAPP(hAPP(U_11303,U_11301),U_11302))
| ~ 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_11301),U_11302))) ),
inference(clausify,[status(thm)],[f_2996_4]) ).
cnf(f_2996_6,plain,
( hBOOL(hAPP(hAPP(U_11303,sK259(U_11303,U_11302,U_11301)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK260(U_11303,U_11302,U_11301))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK260(U_11303,U_11302,U_11301)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK259(U_11303,U_11302,U_11301)),sK260(U_11303,U_11302,U_11301)))
| hBOOL(hAPP(hAPP(U_11303,U_11301),U_11302))
| ~ 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_11301),U_11302))) ),
inference(clausify,[status(thm)],[f_2996_4]) ).
cnf(f_2996_7,plain,
( ~ hBOOL(hAPP(hAPP(U_11303,sK259(U_11303,U_11302,U_11301)),sK260(U_11303,U_11302,U_11301)))
| hBOOL(hAPP(hAPP(U_11303,U_11301),U_11302))
| ~ 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_11301),U_11302))) ),
inference(clausify,[status(thm)],[f_2996_4]) ).
fof(f_2997_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_2997_2,plain,
! [U_11306,U_11305,U_11304] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11304,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_11304,U_11306)),c_Wellfounded_Oaccp(U_11304,U_11305)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11304,tc_fun(U_11304,tc_HOL_Obool))),U_11305),U_11306)) ),
inference(variable_rename,[status(thm)],[f_2997_1]) ).
cnf(f_2997_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11304,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_11304,U_11306)),c_Wellfounded_Oaccp(U_11304,U_11305)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11304,tc_fun(U_11304,tc_HOL_Obool))),U_11305),U_11306)) ),
inference(clausify,[status(thm)],[f_2997_2]) ).
fof(f_2998_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_2998_2,plain,
! [U_11310,U_11309,U_11308] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11308,tc_Int_Oint),U_11310),U_11309) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11308,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_11308),c_Int_Onat),U_11310)),U_11309))
| ? [U_11307] :
( ~ c_Nat__Transfer_Ois__nat(hAPP(U_11310,U_11307))
& hBOOL(hAPP(hAPP(c_member(U_11308),U_11307),U_11309)) ) ),
inference(variable_rename,[status(thm)],[f_2998_1]) ).
fof(f_2998_3,plain,
! [U_11310,U_11309,U_11308] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11308,tc_Int_Oint),U_11310),U_11309) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11308,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_11308),c_Int_Onat),U_11310)),U_11309))
| ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_11310,sK261(U_11310,U_11309,U_11308)))
& hBOOL(hAPP(hAPP(c_member(U_11308),sK261(U_11310,U_11309,U_11308)),U_11309)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK261]),skolemize(U_11307,sK261(U_11310,U_11309,U_11308))],[f_2998_2]) ).
cnf(f_2998_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11308),sK261(U_11310,U_11309,U_11308)),U_11309))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11308,tc_Int_Oint),U_11310),U_11309) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11308,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_11308),c_Int_Onat),U_11310)),U_11309)) ),
inference(clausify,[status(thm)],[f_2998_3]) ).
cnf(f_2998_5,plain,
( ~ c_Nat__Transfer_Ois__nat(hAPP(U_11310,sK261(U_11310,U_11309,U_11308)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11308,tc_Int_Oint),U_11310),U_11309) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11308,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_11308),c_Int_Onat),U_11310)),U_11309)) ),
inference(clausify,[status(thm)],[f_2998_3]) ).
fof(f_2999_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_2999_2,plain,
! [U_11315,U_11314,U_11313] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11313,U_11314),U_11315))
| ? [U_11312] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11313,U_11314),U_11312))
& hBOOL(hAPP(hAPP(U_11314,U_11312),U_11315)) ) )
& ( ! [U_11311] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11313,U_11314),U_11311))
| ~ hBOOL(hAPP(hAPP(U_11314,U_11311),U_11315)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11313,U_11314),U_11315)) ) ),
inference(variable_rename,[status(thm)],[f_2999_1]) ).
fof(f_2999_3,plain,
( ! [U_11321,U_11319,U_11317] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11317,U_11319),U_11321))
| ? [U_11312] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11317,U_11319),U_11312))
& hBOOL(hAPP(hAPP(U_11319,U_11312),U_11321)) ) )
& ! [U_11320,U_11318,U_11316] :
( ! [U_11311] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11316,U_11318),U_11311))
| ~ hBOOL(hAPP(hAPP(U_11318,U_11311),U_11320)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11316,U_11318),U_11320)) ) ),
inference(miniscope,[status(thm)],[f_2999_2]) ).
fof(f_2999_4,plain,
( ! [U_11321,U_11319,U_11317] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11317,U_11319),U_11321))
| ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11317,U_11319),sK262(U_11321,U_11319,U_11317)))
& hBOOL(hAPP(hAPP(U_11319,sK262(U_11321,U_11319,U_11317)),U_11321)) ) )
& ! [U_11320,U_11318,U_11316] :
( ! [U_11311] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11316,U_11318),U_11311))
| ~ hBOOL(hAPP(hAPP(U_11318,U_11311),U_11320)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11316,U_11318),U_11320)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK262]),skolemize(U_11312,sK262(U_11321,U_11319,U_11317))],[f_2999_3]) ).
cnf(f_2999_5,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11316,U_11318),U_11311))
| ~ hBOOL(hAPP(hAPP(U_11318,U_11311),U_11320))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11316,U_11318),U_11320)) ),
inference(clausify,[status(thm)],[f_2999_4]) ).
cnf(f_2999_6,plain,
( hBOOL(hAPP(hAPP(U_11319,sK262(U_11321,U_11319,U_11317)),U_11321))
| hBOOL(hAPP(c_Wellfounded_Oaccp(U_11317,U_11319),U_11321)) ),
inference(clausify,[status(thm)],[f_2999_4]) ).
cnf(f_2999_7,plain,
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11317,U_11319),sK262(U_11321,U_11319,U_11317)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(U_11317,U_11319),U_11321)) ),
inference(clausify,[status(thm)],[f_2999_4]) ).
fof(f_3000_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_3000_2,plain,
! [U_11326,U_11325,U_11324] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11324,U_11325),U_11326))
| ? [U_11323] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11324,U_11325),U_11323))
& hBOOL(hAPP(hAPP(U_11325,U_11323),U_11326)) ) )
& ( ! [U_11322] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11324,U_11325),U_11322))
| ~ hBOOL(hAPP(hAPP(U_11325,U_11322),U_11326)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11324,U_11325),U_11326)) ) ),
inference(variable_rename,[status(thm)],[f_3000_1]) ).
fof(f_3000_3,plain,
( ! [U_11332,U_11330,U_11328] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11328,U_11330),U_11332))
| ? [U_11323] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11328,U_11330),U_11323))
& hBOOL(hAPP(hAPP(U_11330,U_11323),U_11332)) ) )
& ! [U_11331,U_11329,U_11327] :
( ! [U_11322] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11327,U_11329),U_11322))
| ~ hBOOL(hAPP(hAPP(U_11329,U_11322),U_11331)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11327,U_11329),U_11331)) ) ),
inference(miniscope,[status(thm)],[f_3000_2]) ).
fof(f_3000_4,plain,
( ! [U_11332,U_11330,U_11328] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11328,U_11330),U_11332))
| ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11328,U_11330),sK263(U_11332,U_11330,U_11328)))
& hBOOL(hAPP(hAPP(U_11330,sK263(U_11332,U_11330,U_11328)),U_11332)) ) )
& ! [U_11331,U_11329,U_11327] :
( ! [U_11322] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11327,U_11329),U_11322))
| ~ hBOOL(hAPP(hAPP(U_11329,U_11322),U_11331)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11327,U_11329),U_11331)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK263]),skolemize(U_11323,sK263(U_11332,U_11330,U_11328))],[f_3000_3]) ).
cnf(f_3000_5,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11327,U_11329),U_11322))
| ~ hBOOL(hAPP(hAPP(U_11329,U_11322),U_11331))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11327,U_11329),U_11331)) ),
inference(clausify,[status(thm)],[f_3000_4]) ).
cnf(f_3000_6,plain,
( hBOOL(hAPP(hAPP(U_11330,sK263(U_11332,U_11330,U_11328)),U_11332))
| hBOOL(hAPP(c_Wellfounded_Oaccp(U_11328,U_11330),U_11332)) ),
inference(clausify,[status(thm)],[f_3000_4]) ).
cnf(f_3000_7,plain,
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11328,U_11330),sK263(U_11332,U_11330,U_11328)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(U_11328,U_11330),U_11332)) ),
inference(clausify,[status(thm)],[f_3000_4]) ).
fof(f_3001_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_3001_2,plain,
! [U_11336,U_11335,U_11334,U_11333] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11333,U_11334),U_11336))
| ~ hBOOL(hAPP(hAPP(U_11334,U_11336),U_11335))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11333,U_11334),U_11335)) ),
inference(variable_rename,[status(thm)],[f_3001_1]) ).
cnf(f_3001_3,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11333,U_11334),U_11336))
| ~ hBOOL(hAPP(hAPP(U_11334,U_11336),U_11335))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11333,U_11334),U_11335)) ),
inference(clausify,[status(thm)],[f_3001_2]) ).
fof(f_3002_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_3002_2,plain,
! [U_11338,U_11337] :
( ( ( c_Nitpick_Onat__gcd(U_11337,U_11338) = c_Nitpick_Onat__gcd(U_11338,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11337,U_11338))
| U_11338 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Nitpick_Onat__gcd(U_11337,U_11338) = U_11337
| U_11338 != 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_11337),U_11338))) ),
inference(variable_rename,[status(thm)],[f_3002_1]) ).
cnf(f_3002_3,plain,
( c_Nitpick_Onat__gcd(U_11337,U_11338) = U_11337
| U_11338 != 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_11337),U_11338))) ),
inference(clausify,[status(thm)],[f_3002_2]) ).
cnf(f_3002_4,plain,
( c_Nitpick_Onat__gcd(U_11337,U_11338) = c_Nitpick_Onat__gcd(U_11338,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11337,U_11338))
| U_11338 = 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_11337),U_11338))) ),
inference(clausify,[status(thm)],[f_3002_2]) ).
fof(f_3003_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_3003_2,plain,
! [U_11339] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,U_11339)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(U_11339)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_3003_1]) ).
cnf(f_3003_3,plain,
c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,U_11339)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(U_11339)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_3003_2]) ).
fof(f_3004_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_3004_2,plain,
! [U_11340] :
( 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_11340)) = 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_11340)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11340)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_3004_1]) ).
cnf(f_3004_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_11340)) = 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_11340)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11340)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_3004_2]) ).
fof(f_3005_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_3005_2,plain,
! [U_11345,U_11344,U_11343,U_11342,U_11341] : hAPP(c_Product__Type_Osnd(U_11341,U_11342),hAPP(c_Product__Type_Oapsnd(U_11343,U_11342,U_11341,U_11344),U_11345)) = hAPP(U_11344,hAPP(c_Product__Type_Osnd(U_11341,U_11343),U_11345)),
inference(variable_rename,[status(thm)],[f_3005_1]) ).
cnf(f_3005_3,plain,
hAPP(c_Product__Type_Osnd(U_11341,U_11342),hAPP(c_Product__Type_Oapsnd(U_11343,U_11342,U_11341,U_11344),U_11345)) = hAPP(U_11344,hAPP(c_Product__Type_Osnd(U_11341,U_11343),U_11345)),
inference(clausify,[status(thm)],[f_3005_2]) ).
fof(f_3006_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_3006_2,plain,
! [U_11351,U_11350,U_11349,U_11348,U_11347,U_11346] :
( ( hAPP(c_Product__Type_Oapsnd(U_11346,U_11347,U_11348,U_11349),U_11350) = hAPP(c_Product__Type_Oapsnd(U_11346,U_11347,U_11348,U_11351),U_11350)
| hAPP(U_11349,hAPP(c_Product__Type_Osnd(U_11348,U_11346),U_11350)) != hAPP(U_11351,hAPP(c_Product__Type_Osnd(U_11348,U_11346),U_11350)) )
& ( hAPP(U_11349,hAPP(c_Product__Type_Osnd(U_11348,U_11346),U_11350)) = hAPP(U_11351,hAPP(c_Product__Type_Osnd(U_11348,U_11346),U_11350))
| hAPP(c_Product__Type_Oapsnd(U_11346,U_11347,U_11348,U_11349),U_11350) != hAPP(c_Product__Type_Oapsnd(U_11346,U_11347,U_11348,U_11351),U_11350) ) ),
inference(variable_rename,[status(thm)],[f_3006_1]) ).
fof(f_3006_3,plain,
( ! [U_11363,U_11361,U_11359,U_11357,U_11355,U_11353] :
( hAPP(c_Product__Type_Oapsnd(U_11353,U_11355,U_11357,U_11359),U_11361) = hAPP(c_Product__Type_Oapsnd(U_11353,U_11355,U_11357,U_11363),U_11361)
| hAPP(U_11359,hAPP(c_Product__Type_Osnd(U_11357,U_11353),U_11361)) != hAPP(U_11363,hAPP(c_Product__Type_Osnd(U_11357,U_11353),U_11361)) )
& ! [U_11362,U_11360,U_11358,U_11356,U_11354,U_11352] :
( hAPP(U_11358,hAPP(c_Product__Type_Osnd(U_11356,U_11352),U_11360)) = hAPP(U_11362,hAPP(c_Product__Type_Osnd(U_11356,U_11352),U_11360))
| hAPP(c_Product__Type_Oapsnd(U_11352,U_11354,U_11356,U_11358),U_11360) != hAPP(c_Product__Type_Oapsnd(U_11352,U_11354,U_11356,U_11362),U_11360) ) ),
inference(miniscope,[status(thm)],[f_3006_2]) ).
cnf(f_3006_4,plain,
( hAPP(U_11358,hAPP(c_Product__Type_Osnd(U_11356,U_11352),U_11360)) = hAPP(U_11362,hAPP(c_Product__Type_Osnd(U_11356,U_11352),U_11360))
| hAPP(c_Product__Type_Oapsnd(U_11352,U_11354,U_11356,U_11358),U_11360) != hAPP(c_Product__Type_Oapsnd(U_11352,U_11354,U_11356,U_11362),U_11360) ),
inference(clausify,[status(thm)],[f_3006_3]) ).
cnf(f_3006_5,plain,
( hAPP(c_Product__Type_Oapsnd(U_11353,U_11355,U_11357,U_11359),U_11361) = hAPP(c_Product__Type_Oapsnd(U_11353,U_11355,U_11357,U_11363),U_11361)
| hAPP(U_11359,hAPP(c_Product__Type_Osnd(U_11357,U_11353),U_11361)) != hAPP(U_11363,hAPP(c_Product__Type_Osnd(U_11357,U_11353),U_11361)) ),
inference(clausify,[status(thm)],[f_3006_3]) ).
fof(f_3007_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_3007_2,plain,
! [U_11366,U_11365,U_11364] : hAPP(c_Product__Type_Osnd(U_11364,U_11365),U_11366) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11364,U_11365,U_11365),hAPP(c_COMBK(tc_fun(U_11365,U_11365),U_11364),c_COMBI(U_11365))),U_11366),
inference(variable_rename,[status(thm)],[f_3007_1]) ).
cnf(f_3007_3,plain,
hAPP(c_Product__Type_Osnd(U_11364,U_11365),U_11366) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11364,U_11365,U_11365),hAPP(c_COMBK(tc_fun(U_11365,U_11365),U_11364),c_COMBI(U_11365))),U_11366),
inference(clausify,[status(thm)],[f_3007_2]) ).
fof(f_3008_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_3008_2,plain,
! [U_11370,U_11369,U_11368,U_11367] : hAPP(c_Product__Type_Osnd(U_11367,U_11368),hAPP(hAPP(c_Product__Type_OPair(U_11367,U_11368),U_11369),U_11370)) = U_11370,
inference(variable_rename,[status(thm)],[f_3008_1]) ).
cnf(f_3008_3,plain,
hAPP(c_Product__Type_Osnd(U_11367,U_11368),hAPP(hAPP(c_Product__Type_OPair(U_11367,U_11368),U_11369),U_11370)) = U_11370,
inference(clausify,[status(thm)],[f_3008_2]) ).
fof(f_3009_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_3009_2,plain,
! [U_11375,U_11374,U_11373,U_11372,U_11371] :
( U_11374 = U_11375
| hAPP(c_Product__Type_Osnd(U_11371,U_11372),hAPP(hAPP(c_Product__Type_OPair(U_11371,U_11372),U_11373),U_11374)) != U_11375 ),
inference(variable_rename,[status(thm)],[f_3009_1]) ).
fof(f_3009_3,plain,
! [U_11375,U_11374] :
( ! [U_11373,U_11372,U_11371] : hAPP(c_Product__Type_Osnd(U_11371,U_11372),hAPP(hAPP(c_Product__Type_OPair(U_11371,U_11372),U_11373),U_11374)) != U_11375
| U_11374 = U_11375 ),
inference(miniscope,[status(thm)],[f_3009_2]) ).
cnf(f_3009_4,plain,
( hAPP(c_Product__Type_Osnd(U_11371,U_11372),hAPP(hAPP(c_Product__Type_OPair(U_11371,U_11372),U_11373),U_11374)) != U_11375
| U_11374 = U_11375 ),
inference(clausify,[status(thm)],[f_3009_3]) ).
fof(f_3010_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_3010_2,plain,
! [U_11377,U_11376] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11376,U_11377) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_11376,U_11377)),
inference(variable_rename,[status(thm)],[f_3010_1]) ).
cnf(f_3010_3,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11376,U_11377) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_11376,U_11377)),
inference(clausify,[status(thm)],[f_3010_2]) ).
fof(f_3011_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_3011_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_3011_1]) ).
fof(f_3012_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_3012_2,plain,
! [U_11379,U_11378] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11378,U_11379) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_11378,U_11379))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11379))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11378),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_3012_1]) ).
cnf(f_3012_3,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11378,U_11379) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_11378,U_11379))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11379))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11378),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_3012_2]) ).
fof(f_3013_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_3013_2,plain,
! [U_11381,U_11380] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11380,U_11381) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_11380,U_11381))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11381))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11380)) ),
inference(variable_rename,[status(thm)],[f_3013_1]) ).
cnf(f_3013_3,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11380,U_11381) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_11380,U_11381))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11381))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11380)) ),
inference(clausify,[status(thm)],[f_3013_2]) ).
fof(f_3014_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_3014_2,plain,
! [U_11382] :
( 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_11382)) = 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_11382)))
| ~ 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_11382))) ),
inference(variable_rename,[status(thm)],[f_3014_1]) ).
cnf(f_3014_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_11382)) = 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_11382)))
| ~ 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_11382))) ),
inference(clausify,[status(thm)],[f_3014_2]) ).
fof(f_3015_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_3015_2,plain,
! [U_11384,U_11383] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11383,U_11384) = 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_11383),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11384))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11384),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_11383)) ),
inference(variable_rename,[status(thm)],[f_3015_1]) ).
cnf(f_3015_3,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11383,U_11384) = 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_11383),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11384))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11384),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_11383)) ),
inference(clausify,[status(thm)],[f_3015_2]) ).
fof(f_3016_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_3016_2,plain,
! [U_11386,U_11385] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11385,U_11386) = 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_11385),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11386))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11386),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11385),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_3016_1]) ).
cnf(f_3016_3,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11385,U_11386) = 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_11385),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11386))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11386),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11385),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_3016_2]) ).
fof(f_3017_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_3017_2,plain,
! [U_11390,U_11389,U_11388,U_11387] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11387,U_11387)),hAPP(hAPP(c_Product__Type_OPair(U_11387,U_11387),U_11388),U_11389)),hAPP(c_Wellfounded_Omeasure(U_11387),U_11390)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_11390,U_11388)),hAPP(U_11390,U_11389))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_11390,U_11388)),hAPP(U_11390,U_11389)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11387,U_11387)),hAPP(hAPP(c_Product__Type_OPair(U_11387,U_11387),U_11388),U_11389)),hAPP(c_Wellfounded_Omeasure(U_11387),U_11390))) ) ),
inference(variable_rename,[status(thm)],[f_3017_1]) ).
fof(f_3017_3,plain,
( ! [U_11398,U_11396,U_11394] :
( ! [U_11392] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_11392,U_11392)),hAPP(hAPP(c_Product__Type_OPair(U_11392,U_11392),U_11394),U_11396)),hAPP(c_Wellfounded_Omeasure(U_11392),U_11398)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_11398,U_11394)),hAPP(U_11398,U_11396))) )
& ! [U_11397,U_11395,U_11393] :
( ! [U_11391] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11391,U_11391)),hAPP(hAPP(c_Product__Type_OPair(U_11391,U_11391),U_11393),U_11395)),hAPP(c_Wellfounded_Omeasure(U_11391),U_11397)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_11397,U_11393)),hAPP(U_11397,U_11395))) ) ),
inference(miniscope,[status(thm)],[f_3017_2]) ).
cnf(f_3017_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11391,U_11391)),hAPP(hAPP(c_Product__Type_OPair(U_11391,U_11391),U_11393),U_11395)),hAPP(c_Wellfounded_Omeasure(U_11391),U_11397)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_11397,U_11393)),hAPP(U_11397,U_11395))) ),
inference(clausify,[status(thm)],[f_3017_3]) ).
cnf(f_3017_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11392,U_11392)),hAPP(hAPP(c_Product__Type_OPair(U_11392,U_11392),U_11394),U_11396)),hAPP(c_Wellfounded_Omeasure(U_11392),U_11398)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_11398,U_11394)),hAPP(U_11398,U_11396))) ),
inference(clausify,[status(thm)],[f_3017_3]) ).
fof(f_3018_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_3018_2,plain,
! [U_11402,U_11401,U_11400] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11400,tc_Int_Oint),U_11402),U_11401) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11400,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_11400),c_Int_Onat),U_11402)),U_11401))
| ? [U_11399] :
( ~ c_Nat__Transfer_Ois__nat(hAPP(U_11402,U_11399))
& hBOOL(hAPP(hAPP(c_member(U_11400),U_11399),U_11401)) ) ),
inference(variable_rename,[status(thm)],[f_3018_1]) ).
fof(f_3018_3,plain,
! [U_11402,U_11401,U_11400] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11400,tc_Int_Oint),U_11402),U_11401) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11400,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_11400),c_Int_Onat),U_11402)),U_11401))
| ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_11402,sK264(U_11402,U_11401,U_11400)))
& hBOOL(hAPP(hAPP(c_member(U_11400),sK264(U_11402,U_11401,U_11400)),U_11401)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK264]),skolemize(U_11399,sK264(U_11402,U_11401,U_11400))],[f_3018_2]) ).
cnf(f_3018_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11400),sK264(U_11402,U_11401,U_11400)),U_11401))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11400,tc_Int_Oint),U_11402),U_11401) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11400,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_11400),c_Int_Onat),U_11402)),U_11401)) ),
inference(clausify,[status(thm)],[f_3018_3]) ).
cnf(f_3018_5,plain,
( ~ c_Nat__Transfer_Ois__nat(hAPP(U_11402,sK264(U_11402,U_11401,U_11400)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11400,tc_Int_Oint),U_11402),U_11401) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11400,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_11400),c_Int_Onat),U_11402)),U_11401)) ),
inference(clausify,[status(thm)],[f_3018_3]) ).
fof(f_3019_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_3019_2,plain,
! [U_11408,U_11407,U_11406,U_11405,U_11404,U_11403] :
( hAPP(U_11406,U_11407) = hAPP(c_Fun_Ocomp(U_11404,U_11404,U_11404,hAPP(U_11406,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11403,tc_HOL_Obool)),U_11407),hAPP(hAPP(c_Set_Oinsert(U_11403),U_11408),c_Orderings_Obot__class_Obot(tc_fun(U_11403,tc_HOL_Obool)))))),hAPP(U_11405,U_11408))
| ~ hBOOL(hAPP(hAPP(c_member(U_11403),U_11408),U_11407))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11403),U_11407))
| ~ c_Finite__Set_Ofolding(U_11403,U_11404,U_11405,U_11406) ),
inference(variable_rename,[status(thm)],[f_3019_1]) ).
cnf(f_3019_3,plain,
( hAPP(U_11406,U_11407) = hAPP(c_Fun_Ocomp(U_11404,U_11404,U_11404,hAPP(U_11406,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11403,tc_HOL_Obool)),U_11407),hAPP(hAPP(c_Set_Oinsert(U_11403),U_11408),c_Orderings_Obot__class_Obot(tc_fun(U_11403,tc_HOL_Obool)))))),hAPP(U_11405,U_11408))
| ~ hBOOL(hAPP(hAPP(c_member(U_11403),U_11408),U_11407))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11403),U_11407))
| ~ c_Finite__Set_Ofolding(U_11403,U_11404,U_11405,U_11406) ),
inference(clausify,[status(thm)],[f_3019_2]) ).
fof(f_3020_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_3020_2,plain,
! [U_11416,U_11415,U_11414,U_11413,U_11412,U_11411,U_11410,U_11409] :
( hAPP(c_Fun_Ocomp(U_11410,U_11410,U_11413,hAPP(U_11411,U_11414)),hAPP(c_Fun_Ocomp(U_11410,U_11410,U_11413,hAPP(U_11411,U_11415)),U_11416)) = hAPP(c_Fun_Ocomp(U_11410,U_11410,U_11413,hAPP(U_11411,U_11415)),hAPP(c_Fun_Ocomp(U_11410,U_11410,U_11413,hAPP(U_11411,U_11414)),U_11416))
| ~ c_Finite__Set_Ofolding(U_11409,U_11410,U_11411,U_11412) ),
inference(variable_rename,[status(thm)],[f_3020_1]) ).
fof(f_3020_3,plain,
! [U_11416,U_11415,U_11414,U_11413,U_11412,U_11411,U_11410] :
( ! [U_11409] : ~ c_Finite__Set_Ofolding(U_11409,U_11410,U_11411,U_11412)
| hAPP(c_Fun_Ocomp(U_11410,U_11410,U_11413,hAPP(U_11411,U_11414)),hAPP(c_Fun_Ocomp(U_11410,U_11410,U_11413,hAPP(U_11411,U_11415)),U_11416)) = hAPP(c_Fun_Ocomp(U_11410,U_11410,U_11413,hAPP(U_11411,U_11415)),hAPP(c_Fun_Ocomp(U_11410,U_11410,U_11413,hAPP(U_11411,U_11414)),U_11416)) ),
inference(miniscope,[status(thm)],[f_3020_2]) ).
cnf(f_3020_4,plain,
( ~ c_Finite__Set_Ofolding(U_11409,U_11410,U_11411,U_11412)
| hAPP(c_Fun_Ocomp(U_11410,U_11410,U_11413,hAPP(U_11411,U_11414)),hAPP(c_Fun_Ocomp(U_11410,U_11410,U_11413,hAPP(U_11411,U_11415)),U_11416)) = hAPP(c_Fun_Ocomp(U_11410,U_11410,U_11413,hAPP(U_11411,U_11415)),hAPP(c_Fun_Ocomp(U_11410,U_11410,U_11413,hAPP(U_11411,U_11414)),U_11416)) ),
inference(clausify,[status(thm)],[f_3020_3]) ).
fof(f_3021_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_3021_2,plain,
! [U_11422,U_11421,U_11420,U_11419,U_11418,U_11417] :
( hAPP(c_Fun_Ocomp(U_11418,U_11418,U_11418,hAPP(U_11419,U_11421)),hAPP(U_11419,U_11422)) = hAPP(c_Fun_Ocomp(U_11418,U_11418,U_11418,hAPP(U_11419,U_11422)),hAPP(U_11419,U_11421))
| ~ c_Finite__Set_Ofolding(U_11417,U_11418,U_11419,U_11420) ),
inference(variable_rename,[status(thm)],[f_3021_1]) ).
fof(f_3021_3,plain,
! [U_11422,U_11421,U_11420,U_11419,U_11418] :
( ! [U_11417] : ~ c_Finite__Set_Ofolding(U_11417,U_11418,U_11419,U_11420)
| hAPP(c_Fun_Ocomp(U_11418,U_11418,U_11418,hAPP(U_11419,U_11421)),hAPP(U_11419,U_11422)) = hAPP(c_Fun_Ocomp(U_11418,U_11418,U_11418,hAPP(U_11419,U_11422)),hAPP(U_11419,U_11421)) ),
inference(miniscope,[status(thm)],[f_3021_2]) ).
cnf(f_3021_4,plain,
( ~ c_Finite__Set_Ofolding(U_11417,U_11418,U_11419,U_11420)
| hAPP(c_Fun_Ocomp(U_11418,U_11418,U_11418,hAPP(U_11419,U_11421)),hAPP(U_11419,U_11422)) = hAPP(c_Fun_Ocomp(U_11418,U_11418,U_11418,hAPP(U_11419,U_11422)),hAPP(U_11419,U_11421)) ),
inference(clausify,[status(thm)],[f_3021_3]) ).
fof(f_3022_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_3022_2,plain,
! [U_11433,U_11432,U_11431,U_11430,U_11429,U_11428,U_11427,U_11426,U_11425,U_11424,U_11423] :
( hAPP(c_Fun_Ocomp(U_11427,U_11428,U_11429,U_11430),hAPP(c_Fun_Ocomp(U_11431,U_11427,U_11429,U_11432),U_11433)) = hAPP(c_Fun_Ocomp(U_11431,U_11428,U_11429,hAPP(c_Fun_Ocomp(U_11427,U_11428,U_11431,U_11430),U_11432)),U_11433)
| ~ c_Finite__Set_Ofolding(U_11423,U_11424,U_11425,U_11426) ),
inference(variable_rename,[status(thm)],[f_3022_1]) ).
fof(f_3022_3,plain,
( ! [U_11433,U_11432,U_11431,U_11430,U_11429,U_11428,U_11427] : hAPP(c_Fun_Ocomp(U_11427,U_11428,U_11429,U_11430),hAPP(c_Fun_Ocomp(U_11431,U_11427,U_11429,U_11432),U_11433)) = hAPP(c_Fun_Ocomp(U_11431,U_11428,U_11429,hAPP(c_Fun_Ocomp(U_11427,U_11428,U_11431,U_11430),U_11432)),U_11433)
| ! [U_11426,U_11425,U_11424,U_11423] : ~ c_Finite__Set_Ofolding(U_11423,U_11424,U_11425,U_11426) ),
inference(miniscope,[status(thm)],[f_3022_2]) ).
cnf(f_3022_4,plain,
( hAPP(c_Fun_Ocomp(U_11427,U_11428,U_11429,U_11430),hAPP(c_Fun_Ocomp(U_11431,U_11427,U_11429,U_11432),U_11433)) = hAPP(c_Fun_Ocomp(U_11431,U_11428,U_11429,hAPP(c_Fun_Ocomp(U_11427,U_11428,U_11431,U_11430),U_11432)),U_11433)
| ~ c_Finite__Set_Ofolding(U_11423,U_11424,U_11425,U_11426) ),
inference(clausify,[status(thm)],[f_3022_3]) ).
fof(f_3023_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_3023_2,plain,
! [U_11435,U_11434] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11434,U_11435) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_11434,U_11435)),
inference(variable_rename,[status(thm)],[f_3023_1]) ).
cnf(f_3023_3,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11434,U_11435) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_11434,U_11435)),
inference(clausify,[status(thm)],[f_3023_2]) ).
fof(f_3024_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_3024_2,plain,
! [U_11441,U_11440,U_11439,U_11438,U_11437,U_11436] :
( hAPP(c_Fun_Ocomp(U_11437,U_11437,U_11437,hAPP(U_11438,U_11441)),hAPP(U_11439,U_11440)) = hAPP(c_Fun_Ocomp(U_11437,U_11437,U_11437,hAPP(U_11439,U_11440)),hAPP(U_11438,U_11441))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11436),U_11440))
| ~ c_Finite__Set_Ofolding(U_11436,U_11437,U_11438,U_11439) ),
inference(variable_rename,[status(thm)],[f_3024_1]) ).
cnf(f_3024_3,plain,
( hAPP(c_Fun_Ocomp(U_11437,U_11437,U_11437,hAPP(U_11438,U_11441)),hAPP(U_11439,U_11440)) = hAPP(c_Fun_Ocomp(U_11437,U_11437,U_11437,hAPP(U_11439,U_11440)),hAPP(U_11438,U_11441))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11436),U_11440))
| ~ c_Finite__Set_Ofolding(U_11436,U_11437,U_11438,U_11439) ),
inference(clausify,[status(thm)],[f_3024_2]) ).
fof(f_3025_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_3025_2,plain,
! [U_11449,U_11448,U_11447,U_11446,U_11445,U_11444,U_11443,U_11442] :
( hAPP(c_Fun_Ocomp(U_11443,U_11443,U_11447,hAPP(U_11444,U_11448)),hAPP(c_Fun_Ocomp(U_11443,U_11443,U_11447,hAPP(U_11445,U_11446)),U_11449)) = hAPP(c_Fun_Ocomp(U_11443,U_11443,U_11447,hAPP(U_11445,U_11446)),hAPP(c_Fun_Ocomp(U_11443,U_11443,U_11447,hAPP(U_11444,U_11448)),U_11449))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11442),U_11446))
| ~ c_Finite__Set_Ofolding(U_11442,U_11443,U_11444,U_11445) ),
inference(variable_rename,[status(thm)],[f_3025_1]) ).
cnf(f_3025_3,plain,
( hAPP(c_Fun_Ocomp(U_11443,U_11443,U_11447,hAPP(U_11444,U_11448)),hAPP(c_Fun_Ocomp(U_11443,U_11443,U_11447,hAPP(U_11445,U_11446)),U_11449)) = hAPP(c_Fun_Ocomp(U_11443,U_11443,U_11447,hAPP(U_11445,U_11446)),hAPP(c_Fun_Ocomp(U_11443,U_11443,U_11447,hAPP(U_11444,U_11448)),U_11449))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11442),U_11446))
| ~ c_Finite__Set_Ofolding(U_11442,U_11443,U_11444,U_11445) ),
inference(clausify,[status(thm)],[f_3025_2]) ).
fof(f_3026_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_3026_2,plain,
! [U_11455,U_11454,U_11453,U_11452,U_11451,U_11450] :
( hAPP(c_Fun_Ocomp(U_11451,U_11451,U_11451,hAPP(U_11453,U_11455)),hAPP(U_11453,U_11454)) = hAPP(c_Fun_Ocomp(U_11451,U_11451,U_11451,hAPP(U_11453,U_11454)),hAPP(U_11453,U_11455))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11450),U_11455))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11450),U_11454))
| ~ c_Finite__Set_Ofolding(U_11450,U_11451,U_11452,U_11453) ),
inference(variable_rename,[status(thm)],[f_3026_1]) ).
cnf(f_3026_3,plain,
( hAPP(c_Fun_Ocomp(U_11451,U_11451,U_11451,hAPP(U_11453,U_11455)),hAPP(U_11453,U_11454)) = hAPP(c_Fun_Ocomp(U_11451,U_11451,U_11451,hAPP(U_11453,U_11454)),hAPP(U_11453,U_11455))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11450),U_11455))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11450),U_11454))
| ~ c_Finite__Set_Ofolding(U_11450,U_11451,U_11452,U_11453) ),
inference(clausify,[status(thm)],[f_3026_2]) ).
fof(f_3027_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_3027_2,plain,
! [U_11463,U_11462,U_11461,U_11460,U_11459,U_11458,U_11457,U_11456] :
( hAPP(c_Fun_Ocomp(U_11457,U_11457,U_11462,hAPP(U_11459,U_11461)),hAPP(c_Fun_Ocomp(U_11457,U_11457,U_11462,hAPP(U_11459,U_11460)),U_11463)) = hAPP(c_Fun_Ocomp(U_11457,U_11457,U_11462,hAPP(U_11459,U_11460)),hAPP(c_Fun_Ocomp(U_11457,U_11457,U_11462,hAPP(U_11459,U_11461)),U_11463))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11456),U_11461))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11456),U_11460))
| ~ c_Finite__Set_Ofolding(U_11456,U_11457,U_11458,U_11459) ),
inference(variable_rename,[status(thm)],[f_3027_1]) ).
cnf(f_3027_3,plain,
( hAPP(c_Fun_Ocomp(U_11457,U_11457,U_11462,hAPP(U_11459,U_11461)),hAPP(c_Fun_Ocomp(U_11457,U_11457,U_11462,hAPP(U_11459,U_11460)),U_11463)) = hAPP(c_Fun_Ocomp(U_11457,U_11457,U_11462,hAPP(U_11459,U_11460)),hAPP(c_Fun_Ocomp(U_11457,U_11457,U_11462,hAPP(U_11459,U_11461)),U_11463))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11456),U_11461))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11456),U_11460))
| ~ c_Finite__Set_Ofolding(U_11456,U_11457,U_11458,U_11459) ),
inference(clausify,[status(thm)],[f_3027_2]) ).
fof(f_3028_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_3028_2,plain,
! [U_11469,U_11468,U_11467,U_11466,U_11465,U_11464] :
( hAPP(hAPP(U_11467,U_11468),U_11469) = hAPP(hAPP(c_Finite__Set_Ofold(U_11464,U_11465,U_11466),U_11469),U_11468)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11464),U_11468))
| ~ c_Finite__Set_Ofolding(U_11464,U_11465,U_11466,U_11467) ),
inference(variable_rename,[status(thm)],[f_3028_1]) ).
cnf(f_3028_3,plain,
( hAPP(hAPP(U_11467,U_11468),U_11469) = hAPP(hAPP(c_Finite__Set_Ofold(U_11464,U_11465,U_11466),U_11469),U_11468)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11464),U_11468))
| ~ c_Finite__Set_Ofolding(U_11464,U_11465,U_11466,U_11467) ),
inference(clausify,[status(thm)],[f_3028_2]) ).
fof(f_3029_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_3029_2,plain,
! [U_11475,U_11474,U_11473,U_11472,U_11471,U_11470] :
( hAPP(U_11473,hAPP(hAPP(c_Set_Oinsert(U_11470),U_11475),U_11474)) = hAPP(c_Fun_Ocomp(U_11471,U_11471,U_11471,hAPP(U_11473,U_11474)),hAPP(U_11472,U_11475))
| hBOOL(hAPP(hAPP(c_member(U_11470),U_11475),U_11474))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11470),U_11474))
| ~ c_Finite__Set_Ofolding(U_11470,U_11471,U_11472,U_11473) ),
inference(variable_rename,[status(thm)],[f_3029_1]) ).
cnf(f_3029_3,plain,
( hAPP(U_11473,hAPP(hAPP(c_Set_Oinsert(U_11470),U_11475),U_11474)) = hAPP(c_Fun_Ocomp(U_11471,U_11471,U_11471,hAPP(U_11473,U_11474)),hAPP(U_11472,U_11475))
| hBOOL(hAPP(hAPP(c_member(U_11470),U_11475),U_11474))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11470),U_11474))
| ~ c_Finite__Set_Ofolding(U_11470,U_11471,U_11472,U_11473) ),
inference(clausify,[status(thm)],[f_3029_2]) ).
fof(f_3030_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_3030_2,plain,
! [U_11481,U_11480,U_11479,U_11478,U_11477,U_11476] :
( hAPP(c_Fun_Ocomp(U_11477,U_11477,U_11477,hAPP(U_11479,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11476,tc_HOL_Obool)),U_11480),U_11481))),hAPP(U_11479,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11476,tc_HOL_Obool)),U_11480),U_11481))) = hAPP(c_Fun_Ocomp(U_11477,U_11477,U_11477,hAPP(U_11479,U_11480)),hAPP(U_11479,U_11481))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11476),U_11481))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11476),U_11480))
| ~ c_Finite__Set_Ofolding(U_11476,U_11477,U_11478,U_11479) ),
inference(variable_rename,[status(thm)],[f_3030_1]) ).
cnf(f_3030_3,plain,
( hAPP(c_Fun_Ocomp(U_11477,U_11477,U_11477,hAPP(U_11479,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11476,tc_HOL_Obool)),U_11480),U_11481))),hAPP(U_11479,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11476,tc_HOL_Obool)),U_11480),U_11481))) = hAPP(c_Fun_Ocomp(U_11477,U_11477,U_11477,hAPP(U_11479,U_11480)),hAPP(U_11479,U_11481))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11476),U_11481))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11476),U_11480))
| ~ c_Finite__Set_Ofolding(U_11476,U_11477,U_11478,U_11479) ),
inference(clausify,[status(thm)],[f_3030_2]) ).
fof(f_3031_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_3031_2,plain,
! [U_11487,U_11486,U_11485,U_11484,U_11483,U_11482] :
( hAPP(U_11485,hAPP(hAPP(c_Set_Oinsert(U_11482),U_11487),U_11486)) = hAPP(c_Fun_Ocomp(U_11483,U_11483,U_11483,hAPP(U_11485,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11482,tc_HOL_Obool)),U_11486),hAPP(hAPP(c_Set_Oinsert(U_11482),U_11487),c_Orderings_Obot__class_Obot(tc_fun(U_11482,tc_HOL_Obool)))))),hAPP(U_11484,U_11487))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11482),U_11486))
| ~ c_Finite__Set_Ofolding(U_11482,U_11483,U_11484,U_11485) ),
inference(variable_rename,[status(thm)],[f_3031_1]) ).
cnf(f_3031_3,plain,
( hAPP(U_11485,hAPP(hAPP(c_Set_Oinsert(U_11482),U_11487),U_11486)) = hAPP(c_Fun_Ocomp(U_11483,U_11483,U_11483,hAPP(U_11485,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11482,tc_HOL_Obool)),U_11486),hAPP(hAPP(c_Set_Oinsert(U_11482),U_11487),c_Orderings_Obot__class_Obot(tc_fun(U_11482,tc_HOL_Obool)))))),hAPP(U_11484,U_11487))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11482),U_11486))
| ~ c_Finite__Set_Ofolding(U_11482,U_11483,U_11484,U_11485) ),
inference(clausify,[status(thm)],[f_3031_2]) ).
fof(f_3032_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_3032_2,plain,
! [U_11493,U_11492,U_11491,U_11490,U_11489,U_11488] :
( hAPP(U_11491,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11488,tc_HOL_Obool)),U_11492),U_11493)) = hAPP(c_Fun_Ocomp(U_11489,U_11489,U_11489,hAPP(U_11491,U_11492)),hAPP(U_11491,U_11493))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11488,tc_HOL_Obool)),U_11492),U_11493) != c_Orderings_Obot__class_Obot(tc_fun(U_11488,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11488),U_11493))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11488),U_11492))
| ~ c_Finite__Set_Ofolding(U_11488,U_11489,U_11490,U_11491) ),
inference(variable_rename,[status(thm)],[f_3032_1]) ).
cnf(f_3032_3,plain,
( hAPP(U_11491,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11488,tc_HOL_Obool)),U_11492),U_11493)) = hAPP(c_Fun_Ocomp(U_11489,U_11489,U_11489,hAPP(U_11491,U_11492)),hAPP(U_11491,U_11493))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11488,tc_HOL_Obool)),U_11492),U_11493) != c_Orderings_Obot__class_Obot(tc_fun(U_11488,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11488),U_11493))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11488),U_11492))
| ~ c_Finite__Set_Ofolding(U_11488,U_11489,U_11490,U_11491) ),
inference(clausify,[status(thm)],[f_3032_2]) ).
fof(f_3033_1,plain,
! [V_P_2,V_a1_2,V_a0_2] :
( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
| ? [B_a,B_b] :
( ~ hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
& ( hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) ),
inference(fof_nnf,[status(thm)],[fact_norm__frac_Opinduct]) ).
fof(f_3033_2,plain,
! [U_11498,U_11497,U_11496] :
( hBOOL(hAPP(hAPP(U_11498,U_11496),U_11497))
| ? [U_11495,U_11494] :
( ~ hBOOL(hAPP(hAPP(U_11498,U_11495),U_11494))
& ( hBOOL(hAPP(hAPP(U_11498,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11495)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11494)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11494),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_11495),U_11494))) )
| ~ 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_11496),U_11497))) ),
inference(variable_rename,[status(thm)],[f_3033_1]) ).
fof(f_3033_3,plain,
! [U_11498,U_11497,U_11496] :
( hBOOL(hAPP(hAPP(U_11498,U_11496),U_11497))
| ? [U_11494] :
( ~ hBOOL(hAPP(hAPP(U_11498,sK265(U_11498,U_11497,U_11496)),U_11494))
& ( hBOOL(hAPP(hAPP(U_11498,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK265(U_11498,U_11497,U_11496))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11494)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11494),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),sK265(U_11498,U_11497,U_11496)),U_11494))) )
| ~ 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_11496),U_11497))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK265]),skolemize(U_11495,sK265(U_11498,U_11497,U_11496))],[f_3033_2]) ).
fof(f_3033_4,plain,
! [U_11498,U_11497,U_11496] :
( hBOOL(hAPP(hAPP(U_11498,U_11496),U_11497))
| ( ~ hBOOL(hAPP(hAPP(U_11498,sK265(U_11498,U_11497,U_11496)),sK266(U_11498,U_11497,U_11496)))
& ( hBOOL(hAPP(hAPP(U_11498,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK265(U_11498,U_11497,U_11496))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK266(U_11498,U_11497,U_11496))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK266(U_11498,U_11497,U_11496)),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),sK265(U_11498,U_11497,U_11496)),sK266(U_11498,U_11497,U_11496)))) )
| ~ 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_11496),U_11497))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK266]),skolemize(U_11494,sK266(U_11498,U_11497,U_11496))],[f_3033_3]) ).
cnf(f_3033_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),sK265(U_11498,U_11497,U_11496)),sK266(U_11498,U_11497,U_11496))))
| hBOOL(hAPP(hAPP(U_11498,U_11496),U_11497))
| ~ 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_11496),U_11497))) ),
inference(clausify,[status(thm)],[f_3033_4]) ).
cnf(f_3033_6,plain,
( hBOOL(hAPP(hAPP(U_11498,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK265(U_11498,U_11497,U_11496))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK266(U_11498,U_11497,U_11496))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK266(U_11498,U_11497,U_11496)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(U_11498,U_11496),U_11497))
| ~ 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_11496),U_11497))) ),
inference(clausify,[status(thm)],[f_3033_4]) ).
cnf(f_3033_7,plain,
( ~ hBOOL(hAPP(hAPP(U_11498,sK265(U_11498,U_11497,U_11496)),sK266(U_11498,U_11497,U_11496)))
| hBOOL(hAPP(hAPP(U_11498,U_11496),U_11497))
| ~ 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_11496),U_11497))) ),
inference(clausify,[status(thm)],[f_3033_4]) ).
fof(f_3034_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_3034_2,plain,
! [U_11499] :
( 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_11499)) = 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_11499)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11499)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_3034_1]) ).
cnf(f_3034_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_11499)) = 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_11499)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11499)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_3034_2]) ).
fof(f_3035_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_3035_2,plain,
! [U_11500] : hAPP(c_Int_Onat,U_11500) = 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_11500)),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_3035_1]) ).
cnf(f_3035_3,plain,
hAPP(c_Int_Onat,U_11500) = 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_11500)),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_3035_2]) ).
fof(f_3036_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_3036_2,plain,
! [U_11504,U_11503,U_11502,U_11501] :
( ( U_11501 = U_11502
| hAPP(c_Product__Type_Osnd(U_11503,U_11504),U_11501) != hAPP(c_Product__Type_Osnd(U_11503,U_11504),U_11502)
| hAPP(c_Product__Type_Ofst(U_11503,U_11504),U_11501) != hAPP(c_Product__Type_Ofst(U_11503,U_11504),U_11502) )
& ( ( hAPP(c_Product__Type_Osnd(U_11503,U_11504),U_11501) = hAPP(c_Product__Type_Osnd(U_11503,U_11504),U_11502)
& hAPP(c_Product__Type_Ofst(U_11503,U_11504),U_11501) = hAPP(c_Product__Type_Ofst(U_11503,U_11504),U_11502) )
| U_11501 != U_11502 ) ),
inference(variable_rename,[status(thm)],[f_3036_1]) ).
fof(f_3036_3,plain,
( ! [U_11512,U_11510,U_11508,U_11506] :
( U_11506 = U_11508
| hAPP(c_Product__Type_Osnd(U_11510,U_11512),U_11506) != hAPP(c_Product__Type_Osnd(U_11510,U_11512),U_11508)
| hAPP(c_Product__Type_Ofst(U_11510,U_11512),U_11506) != hAPP(c_Product__Type_Ofst(U_11510,U_11512),U_11508) )
& ! [U_11511,U_11509,U_11507,U_11505] :
( ( hAPP(c_Product__Type_Osnd(U_11509,U_11511),U_11505) = hAPP(c_Product__Type_Osnd(U_11509,U_11511),U_11507)
& hAPP(c_Product__Type_Ofst(U_11509,U_11511),U_11505) = hAPP(c_Product__Type_Ofst(U_11509,U_11511),U_11507) )
| U_11505 != U_11507 ) ),
inference(miniscope,[status(thm)],[f_3036_2]) ).
cnf(f_3036_4,plain,
( hAPP(c_Product__Type_Ofst(U_11509,U_11511),U_11505) = hAPP(c_Product__Type_Ofst(U_11509,U_11511),U_11507)
| U_11505 != U_11507 ),
inference(clausify,[status(thm)],[f_3036_3]) ).
cnf(f_3036_5,plain,
( hAPP(c_Product__Type_Osnd(U_11509,U_11511),U_11505) = hAPP(c_Product__Type_Osnd(U_11509,U_11511),U_11507)
| U_11505 != U_11507 ),
inference(clausify,[status(thm)],[f_3036_3]) ).
cnf(f_3036_6,plain,
( U_11506 = U_11508
| hAPP(c_Product__Type_Osnd(U_11510,U_11512),U_11506) != hAPP(c_Product__Type_Osnd(U_11510,U_11512),U_11508)
| hAPP(c_Product__Type_Ofst(U_11510,U_11512),U_11506) != hAPP(c_Product__Type_Ofst(U_11510,U_11512),U_11508) ),
inference(clausify,[status(thm)],[f_3036_3]) ).
fof(f_3037_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_3037_2,plain,
! [U_11516,U_11515,U_11514,U_11513] :
( U_11515 = U_11516
| hAPP(c_Product__Type_Osnd(U_11513,U_11514),U_11515) != hAPP(c_Product__Type_Osnd(U_11513,U_11514),U_11516)
| hAPP(c_Product__Type_Ofst(U_11513,U_11514),U_11515) != hAPP(c_Product__Type_Ofst(U_11513,U_11514),U_11516) ),
inference(variable_rename,[status(thm)],[f_3037_1]) ).
cnf(f_3037_3,plain,
( U_11515 = U_11516
| hAPP(c_Product__Type_Osnd(U_11513,U_11514),U_11515) != hAPP(c_Product__Type_Osnd(U_11513,U_11514),U_11516)
| hAPP(c_Product__Type_Ofst(U_11513,U_11514),U_11515) != hAPP(c_Product__Type_Ofst(U_11513,U_11514),U_11516) ),
inference(clausify,[status(thm)],[f_3037_2]) ).
fof(f_3038_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_3038_2,plain,
! [U_11521,U_11520,U_11519,U_11518,U_11517] : hAPP(c_Product__Type_Ofst(U_11517,U_11518),hAPP(c_Product__Type_Oapsnd(U_11519,U_11518,U_11517,U_11520),U_11521)) = hAPP(c_Product__Type_Ofst(U_11517,U_11519),U_11521),
inference(variable_rename,[status(thm)],[f_3038_1]) ).
cnf(f_3038_3,plain,
hAPP(c_Product__Type_Ofst(U_11517,U_11518),hAPP(c_Product__Type_Oapsnd(U_11519,U_11518,U_11517,U_11520),U_11521)) = hAPP(c_Product__Type_Ofst(U_11517,U_11519),U_11521),
inference(clausify,[status(thm)],[f_3038_2]) ).
fof(f_3039_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_3039_2,plain,
! [U_11524,U_11523,U_11522] : hAPP(c_Product__Type_Ofst(U_11522,U_11523),U_11524) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11522,U_11523,U_11522),c_COMBK(U_11522,U_11523)),U_11524),
inference(variable_rename,[status(thm)],[f_3039_1]) ).
cnf(f_3039_3,plain,
hAPP(c_Product__Type_Ofst(U_11522,U_11523),U_11524) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11522,U_11523,U_11522),c_COMBK(U_11522,U_11523)),U_11524),
inference(clausify,[status(thm)],[f_3039_2]) ).
fof(f_3040_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_3040_2,plain,
! [U_11526,U_11525] :
( ( hAPP(c_Int_ORep__Integ,U_11525) = hAPP(c_Int_ORep__Integ,U_11526)
| U_11525 != U_11526 )
& ( U_11525 = U_11526
| hAPP(c_Int_ORep__Integ,U_11525) != hAPP(c_Int_ORep__Integ,U_11526) ) ),
inference(variable_rename,[status(thm)],[f_3040_1]) ).
fof(f_3040_3,plain,
( ! [U_11530,U_11528] :
( hAPP(c_Int_ORep__Integ,U_11528) = hAPP(c_Int_ORep__Integ,U_11530)
| U_11528 != U_11530 )
& ! [U_11529,U_11527] :
( U_11527 = U_11529
| hAPP(c_Int_ORep__Integ,U_11527) != hAPP(c_Int_ORep__Integ,U_11529) ) ),
inference(miniscope,[status(thm)],[f_3040_2]) ).
cnf(f_3040_4,plain,
( U_11527 = U_11529
| hAPP(c_Int_ORep__Integ,U_11527) != hAPP(c_Int_ORep__Integ,U_11529) ),
inference(clausify,[status(thm)],[f_3040_3]) ).
cnf(f_3040_5,plain,
( hAPP(c_Int_ORep__Integ,U_11528) = hAPP(c_Int_ORep__Integ,U_11530)
| U_11528 != U_11530 ),
inference(clausify,[status(thm)],[f_3040_3]) ).
fof(f_3041_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_3041_2,plain,
! [U_11534,U_11533,U_11532,U_11531] : hAPP(c_Product__Type_Ofst(U_11531,U_11532),hAPP(hAPP(c_Product__Type_OPair(U_11531,U_11532),U_11533),U_11534)) = U_11533,
inference(variable_rename,[status(thm)],[f_3041_1]) ).
cnf(f_3041_3,plain,
hAPP(c_Product__Type_Ofst(U_11531,U_11532),hAPP(hAPP(c_Product__Type_OPair(U_11531,U_11532),U_11533),U_11534)) = U_11533,
inference(clausify,[status(thm)],[f_3041_2]) ).
fof(f_3042_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_3042_2,plain,
! [U_11539,U_11538,U_11537,U_11536,U_11535] :
( U_11537 = U_11539
| hAPP(c_Product__Type_Ofst(U_11535,U_11536),hAPP(hAPP(c_Product__Type_OPair(U_11535,U_11536),U_11537),U_11538)) != U_11539 ),
inference(variable_rename,[status(thm)],[f_3042_1]) ).
fof(f_3042_3,plain,
! [U_11539,U_11538,U_11537] :
( ! [U_11536,U_11535] : hAPP(c_Product__Type_Ofst(U_11535,U_11536),hAPP(hAPP(c_Product__Type_OPair(U_11535,U_11536),U_11537),U_11538)) != U_11539
| U_11537 = U_11539 ),
inference(miniscope,[status(thm)],[f_3042_2]) ).
cnf(f_3042_4,plain,
( hAPP(c_Product__Type_Ofst(U_11535,U_11536),hAPP(hAPP(c_Product__Type_OPair(U_11535,U_11536),U_11537),U_11538)) != U_11539
| U_11537 = U_11539 ),
inference(clausify,[status(thm)],[f_3042_3]) ).
fof(f_3043_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_3043_2,plain,
! [U_11542,U_11541,U_11540] : U_11540 = hAPP(hAPP(c_Product__Type_OPair(U_11541,U_11542),hAPP(c_Product__Type_Ofst(U_11541,U_11542),U_11540)),hAPP(c_Product__Type_Osnd(U_11541,U_11542),U_11540)),
inference(variable_rename,[status(thm)],[f_3043_1]) ).
cnf(f_3043_3,plain,
U_11540 = hAPP(hAPP(c_Product__Type_OPair(U_11541,U_11542),hAPP(c_Product__Type_Ofst(U_11541,U_11542),U_11540)),hAPP(c_Product__Type_Osnd(U_11541,U_11542),U_11540)),
inference(clausify,[status(thm)],[f_3043_2]) ).
fof(f_3044_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_3044_2,plain,
! [U_11545,U_11544,U_11543] : hAPP(hAPP(c_Product__Type_OPair(U_11543,U_11544),hAPP(c_Product__Type_Ofst(U_11543,U_11544),U_11545)),hAPP(c_Product__Type_Osnd(U_11543,U_11544),U_11545)) = U_11545,
inference(variable_rename,[status(thm)],[f_3044_1]) ).
cnf(f_3044_3,plain,
hAPP(hAPP(c_Product__Type_OPair(U_11543,U_11544),hAPP(c_Product__Type_Ofst(U_11543,U_11544),U_11545)),hAPP(c_Product__Type_Osnd(U_11543,U_11544),U_11545)) = U_11545,
inference(clausify,[status(thm)],[f_3044_2]) ).
fof(f_3045_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_3045_2,plain,
! [U_11550,U_11549,U_11548,U_11547,U_11546] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11546,U_11547,U_11548),U_11549),U_11550) = hAPP(hAPP(U_11549,hAPP(c_Product__Type_Ofst(U_11546,U_11547),U_11550)),hAPP(c_Product__Type_Osnd(U_11546,U_11547),U_11550)),
inference(variable_rename,[status(thm)],[f_3045_1]) ).
cnf(f_3045_3,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11546,U_11547,U_11548),U_11549),U_11550) = hAPP(hAPP(U_11549,hAPP(c_Product__Type_Ofst(U_11546,U_11547),U_11550)),hAPP(c_Product__Type_Osnd(U_11546,U_11547),U_11550)),
inference(clausify,[status(thm)],[f_3045_2]) ).
fof(f_3046_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_3046_2,plain,
! [U_11552,U_11551] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11551),U_11552) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_11551,U_11552)),
inference(variable_rename,[status(thm)],[f_3046_1]) ).
cnf(f_3046_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11551),U_11552) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_11551,U_11552)),
inference(clausify,[status(thm)],[f_3046_2]) ).
fof(f_3047_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_3047_2,plain,
! [U_11558,U_11557,U_11556,U_11555,U_11554,U_11553] : hAPP(hAPP(c_COMBS(tc_prod(U_11553,U_11554),U_11554,U_11555),hAPP(hAPP(c_COMBB(U_11556,tc_fun(U_11554,U_11555),tc_prod(U_11553,U_11554)),U_11557),hAPP(hAPP(c_COMBB(U_11553,U_11556,tc_prod(U_11553,U_11554)),U_11558),c_Product__Type_Ofst(U_11553,U_11554)))),c_Product__Type_Osnd(U_11553,U_11554)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_11553,U_11554,U_11555),hAPP(hAPP(c_COMBB(U_11556,tc_fun(U_11554,U_11555),U_11553),U_11557),U_11558)),
inference(variable_rename,[status(thm)],[f_3047_1]) ).
cnf(f_3047_3,plain,
hAPP(hAPP(c_COMBS(tc_prod(U_11553,U_11554),U_11554,U_11555),hAPP(hAPP(c_COMBB(U_11556,tc_fun(U_11554,U_11555),tc_prod(U_11553,U_11554)),U_11557),hAPP(hAPP(c_COMBB(U_11553,U_11556,tc_prod(U_11553,U_11554)),U_11558),c_Product__Type_Ofst(U_11553,U_11554)))),c_Product__Type_Osnd(U_11553,U_11554)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_11553,U_11554,U_11555),hAPP(hAPP(c_COMBB(U_11556,tc_fun(U_11554,U_11555),U_11553),U_11557),U_11558)),
inference(clausify,[status(thm)],[f_3047_2]) ).
fof(f_3048_1,plain,
! [V_z_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_P_2),V_z_2) = hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_z_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_z_2)),
inference(fof_nnf,[status(thm)],[fact_split__beta]) ).
fof(f_3048_2,plain,
! [U_11563,U_11562,U_11561,U_11560,U_11559] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11559,U_11560,U_11561),U_11562),U_11563) = hAPP(hAPP(U_11562,hAPP(c_Product__Type_Ofst(U_11559,U_11560),U_11563)),hAPP(c_Product__Type_Osnd(U_11559,U_11560),U_11563)),
inference(variable_rename,[status(thm)],[f_3048_1]) ).
cnf(f_3048_3,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11559,U_11560,U_11561),U_11562),U_11563) = hAPP(hAPP(U_11562,hAPP(c_Product__Type_Ofst(U_11559,U_11560),U_11563)),hAPP(c_Product__Type_Osnd(U_11559,U_11560),U_11563)),
inference(clausify,[status(thm)],[f_3048_2]) ).
fof(f_3049_1,plain,
! [V_p_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_c_2),V_p_2) = hAPP(hAPP(V_c_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)),
inference(fof_nnf,[status(thm)],[fact_split__def]) ).
fof(f_3049_2,plain,
! [U_11568,U_11567,U_11566,U_11565,U_11564] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11564,U_11565,U_11566),U_11567),U_11568) = hAPP(hAPP(U_11567,hAPP(c_Product__Type_Ofst(U_11564,U_11565),U_11568)),hAPP(c_Product__Type_Osnd(U_11564,U_11565),U_11568)),
inference(variable_rename,[status(thm)],[f_3049_1]) ).
cnf(f_3049_3,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11564,U_11565,U_11566),U_11567),U_11568) = hAPP(hAPP(U_11567,hAPP(c_Product__Type_Ofst(U_11564,U_11565),U_11568)),hAPP(c_Product__Type_Osnd(U_11564,U_11565),U_11568)),
inference(clausify,[status(thm)],[f_3049_2]) ).
fof(f_3050_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_3050_2,plain,
! [U_11575,U_11574,U_11573,U_11572,U_11571,U_11570,U_11569] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11569,U_11570,U_11571),hAPP(c_Fun_Ocomp(U_11572,tc_fun(U_11570,U_11571),U_11569,U_11573),U_11574)),U_11575) = hAPP(hAPP(U_11573,hAPP(U_11574,hAPP(c_Product__Type_Ofst(U_11569,U_11570),U_11575))),hAPP(c_Product__Type_Osnd(U_11569,U_11570),U_11575)),
inference(variable_rename,[status(thm)],[f_3050_1]) ).
cnf(f_3050_3,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11569,U_11570,U_11571),hAPP(c_Fun_Ocomp(U_11572,tc_fun(U_11570,U_11571),U_11569,U_11573),U_11574)),U_11575) = hAPP(hAPP(U_11573,hAPP(U_11574,hAPP(c_Product__Type_Ofst(U_11569,U_11570),U_11575))),hAPP(c_Product__Type_Osnd(U_11569,U_11570),U_11575)),
inference(clausify,[status(thm)],[f_3050_2]) ).
fof(f_3051_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_3051_2,plain,
! [U_11577,U_11576] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11576),U_11577) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_11576,U_11577))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11577))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11576),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_3051_1]) ).
cnf(f_3051_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11576),U_11577) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_11576,U_11577))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11577))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11576),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_3051_2]) ).
fof(f_3052_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_3052_2,plain,
! [U_11579,U_11578] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11578),U_11579) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_11578,U_11579))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11579))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11578)) ),
inference(variable_rename,[status(thm)],[f_3052_1]) ).
cnf(f_3052_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11578),U_11579) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_11578,U_11579))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11579))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11578)) ),
inference(clausify,[status(thm)],[f_3052_2]) ).
fof(f_3053_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_3053_2,plain,
! [U_11580] :
( 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_11580)) = 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_11580)))
| ~ 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_11580))) ),
inference(variable_rename,[status(thm)],[f_3053_1]) ).
cnf(f_3053_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_11580)) = 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_11580)))
| ~ 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_11580))) ),
inference(clausify,[status(thm)],[f_3053_2]) ).
fof(f_3054_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_3054_2,plain,
! [U_11582,U_11581] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11581),U_11582) = 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_11581),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11582))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11582),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_11581)) ),
inference(variable_rename,[status(thm)],[f_3054_1]) ).
cnf(f_3054_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11581),U_11582) = 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_11581),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11582))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11582),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_11581)) ),
inference(clausify,[status(thm)],[f_3054_2]) ).
fof(f_3055_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_3055_2,plain,
! [U_11584,U_11583] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11583),U_11584) = 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_11583),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11584))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11584),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11583),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_3055_1]) ).
cnf(f_3055_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11583),U_11584) = 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_11583),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11584))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11584),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11583),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_3055_2]) ).
fof(f_3056_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_3056_2,plain,
! [U_11589,U_11588,U_11587,U_11586,U_11585] : c_Product__Type_Oprod_Oprod__size(U_11585,U_11586,U_11587,U_11588,U_11589) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_11587,hAPP(c_Product__Type_Ofst(U_11585,U_11586),U_11589))),hAPP(U_11588,hAPP(c_Product__Type_Osnd(U_11585,U_11586),U_11589)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_3056_1]) ).
cnf(f_3056_3,plain,
c_Product__Type_Oprod_Oprod__size(U_11585,U_11586,U_11587,U_11588,U_11589) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_11587,hAPP(c_Product__Type_Ofst(U_11585,U_11586),U_11589))),hAPP(U_11588,hAPP(c_Product__Type_Osnd(U_11585,U_11586),U_11589)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_3056_2]) ).
fof(f_3057_1,plain,
! [T_b,T_c,V_x_2,V_y_2,V_P_2] :
( hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))))
| ~ hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_exI__realizer]) ).
fof(f_3057_2,plain,
! [U_11594,U_11593,U_11592,U_11591,U_11590] :
( hBOOL(hAPP(hAPP(U_11590,hAPP(c_Product__Type_Osnd(U_11593,U_11594),hAPP(hAPP(c_Product__Type_OPair(U_11593,U_11594),U_11592),U_11591))),hAPP(c_Product__Type_Ofst(U_11593,U_11594),hAPP(hAPP(c_Product__Type_OPair(U_11593,U_11594),U_11592),U_11591))))
| ~ hBOOL(hAPP(hAPP(U_11590,U_11591),U_11592)) ),
inference(variable_rename,[status(thm)],[f_3057_1]) ).
cnf(f_3057_3,plain,
( hBOOL(hAPP(hAPP(U_11590,hAPP(c_Product__Type_Osnd(U_11593,U_11594),hAPP(hAPP(c_Product__Type_OPair(U_11593,U_11594),U_11592),U_11591))),hAPP(c_Product__Type_Ofst(U_11593,U_11594),hAPP(hAPP(c_Product__Type_OPair(U_11593,U_11594),U_11592),U_11591))))
| ~ hBOOL(hAPP(hAPP(U_11590,U_11591),U_11592)) ),
inference(clausify,[status(thm)],[f_3057_2]) ).
fof(f_3058_1,plain,
! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_P_2] :
( ( hBOOL(hAPP(V_Q_2,hAPP(c_Product__Type_Osnd(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2))))
& hBOOL(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2)))) )
| ~ hBOOL(hAPP(V_Q_2,V_q_2))
| ~ hBOOL(hAPP(V_P_2,V_p_2)) ),
inference(fof_nnf,[status(thm)],[fact_conjI__realizer]) ).
fof(f_3058_2,plain,
! [U_11600,U_11599,U_11598,U_11597,U_11596,U_11595] :
( ( hBOOL(hAPP(U_11597,hAPP(c_Product__Type_Osnd(U_11599,U_11600),hAPP(hAPP(c_Product__Type_OPair(U_11599,U_11600),U_11596),U_11598))))
& hBOOL(hAPP(U_11595,hAPP(c_Product__Type_Ofst(U_11599,U_11600),hAPP(hAPP(c_Product__Type_OPair(U_11599,U_11600),U_11596),U_11598)))) )
| ~ hBOOL(hAPP(U_11597,U_11598))
| ~ hBOOL(hAPP(U_11595,U_11596)) ),
inference(variable_rename,[status(thm)],[f_3058_1]) ).
cnf(f_3058_3,plain,
( hBOOL(hAPP(U_11595,hAPP(c_Product__Type_Ofst(U_11599,U_11600),hAPP(hAPP(c_Product__Type_OPair(U_11599,U_11600),U_11596),U_11598))))
| ~ hBOOL(hAPP(U_11597,U_11598))
| ~ hBOOL(hAPP(U_11595,U_11596)) ),
inference(clausify,[status(thm)],[f_3058_2]) ).
cnf(f_3058_4,plain,
( hBOOL(hAPP(U_11597,hAPP(c_Product__Type_Osnd(U_11599,U_11600),hAPP(hAPP(c_Product__Type_OPair(U_11599,U_11600),U_11596),U_11598))))
| ~ hBOOL(hAPP(U_11597,U_11598))
| ~ hBOOL(hAPP(U_11595,U_11596)) ),
inference(clausify,[status(thm)],[f_3058_2]) ).
fof(f_3059_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_3059_2,plain,
! [U_11602,U_11601] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11601),U_11602) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_11601,U_11602)),
inference(variable_rename,[status(thm)],[f_3059_1]) ).
cnf(f_3059_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11601),U_11602) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_11601,U_11602)),
inference(clausify,[status(thm)],[f_3059_2]) ).
fof(f_3060_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_3060_2,plain,
! [U_11605,U_11604,U_11603] :
( ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11603,U_11604),U_11605))
| ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11605)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11604),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11605))) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11604)) )
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11605)),U_11604))
| ~ 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_11605))) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11604)) ) )
& U_11604 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11605) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_11604 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| U_11603 != 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_11605)),U_11604)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11605)) )
& ( ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11605)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11604),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11605))) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11604)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11605)),U_11604))
& 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_11605))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11604)) ) )
| U_11604 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11605) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_11604 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& U_11603 = 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_11605)),U_11604)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11605)) )
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11603,U_11604),U_11605)) ) ),
inference(variable_rename,[status(thm)],[f_3060_1]) ).
fof(f_3060_3,plain,
( ! [U_11611,U_11609,U_11607] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11607,U_11609),U_11611))
| ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11611)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11609),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11611))) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11609)) )
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11611)),U_11609))
| ~ 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_11611))) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11609)) ) )
& U_11609 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11611) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_11609 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| U_11607 != 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_11611)),U_11609)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11611)) )
& ! [U_11610,U_11608,U_11606] :
( ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11610)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11608),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11610))) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11608)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11610)),U_11608))
& 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_11610))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11608)) ) )
| U_11608 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11610) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_11608 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& U_11606 = 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_11610)),U_11608)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11610)) )
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11606,U_11608),U_11610)) ) ),
inference(miniscope,[status(thm)],[f_3060_2]) ).
cnf(f_3060_4,plain,
( U_11606 = 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_11610)),U_11608)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11610))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11606,U_11608),U_11610)) ),
inference(clausify,[status(thm)],[f_3060_3]) ).
cnf(f_3060_5,plain,
( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11610) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_11608 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11606,U_11608),U_11610)) ),
inference(clausify,[status(thm)],[f_3060_3]) ).
cnf(f_3060_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_11610)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11608))
| U_11608 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11606,U_11608),U_11610)) ),
inference(clausify,[status(thm)],[f_3060_3]) ).
cnf(f_3060_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_11610)),U_11608))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11608))
| U_11608 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11606,U_11608),U_11610)) ),
inference(clausify,[status(thm)],[f_3060_3]) ).
cnf(f_3060_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11608),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11610)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11608))
| U_11608 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11606,U_11608),U_11610)) ),
inference(clausify,[status(thm)],[f_3060_3]) ).
cnf(f_3060_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_11610)),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_11608))
| U_11608 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11606,U_11608),U_11610)) ),
inference(clausify,[status(thm)],[f_3060_3]) ).
cnf(f_3060_10,plain,
( U_11609 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_11609 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_11607 != 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_11611)),U_11609)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11611))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11607,U_11609),U_11611)) ),
inference(clausify,[status(thm)],[f_3060_3]) ).
cnf(f_3060_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11609))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11609))
| U_11609 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_11607 != 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_11611)),U_11609)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11611))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11607,U_11609),U_11611)) ),
inference(clausify,[status(thm)],[f_3060_3]) ).
cnf(f_3060_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_11611)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11609),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11611)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11609))
| U_11609 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_11607 != 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_11611)),U_11609)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11611))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11607,U_11609),U_11611)) ),
inference(clausify,[status(thm)],[f_3060_3]) ).
cnf(f_3060_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11609))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11611)),U_11609))
| ~ 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_11611)))
| U_11609 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_11607 != 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_11611)),U_11609)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11611))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11607,U_11609),U_11611)) ),
inference(clausify,[status(thm)],[f_3060_3]) ).
cnf(f_3060_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_11611)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11609),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11611)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11611)),U_11609))
| ~ 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_11611)))
| U_11609 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_11607 != 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_11611)),U_11609)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11611))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11607,U_11609),U_11611)) ),
inference(clausify,[status(thm)],[f_3060_3]) ).
cnf(f_3060_15,plain,
( U_11609 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11611) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_11607 != 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_11611)),U_11609)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11611))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11607,U_11609),U_11611)) ),
inference(clausify,[status(thm)],[f_3060_3]) ).
cnf(f_3060_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11609))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11609))
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11611) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_11607 != 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_11611)),U_11609)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11611))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11607,U_11609),U_11611)) ),
inference(clausify,[status(thm)],[f_3060_3]) ).
cnf(f_3060_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_11611)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11609),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11611)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11609))
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11611) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_11607 != 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_11611)),U_11609)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11611))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11607,U_11609),U_11611)) ),
inference(clausify,[status(thm)],[f_3060_3]) ).
cnf(f_3060_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11609))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11611)),U_11609))
| ~ 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_11611)))
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11611) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_11607 != 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_11611)),U_11609)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11611))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11607,U_11609),U_11611)) ),
inference(clausify,[status(thm)],[f_3060_3]) ).
cnf(f_3060_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_11611)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11609),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11611)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11611)),U_11609))
| ~ 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_11611)))
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11611) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_11607 != 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_11611)),U_11609)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11611))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11607,U_11609),U_11611)) ),
inference(clausify,[status(thm)],[f_3060_3]) ).
fof(f_3061_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_3061_2,plain,
! [U_11615,U_11614,U_11613,U_11612] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11612,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_11612,U_11613,U_11614),hAPP(hAPP(c_Set_Oinsert(U_11613),U_11615),c_Orderings_Obot__class_Obot(tc_fun(U_11613,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_11612),c_HOL_OThe(U_11612,hAPP(hAPP(c_COMBC(U_11612,U_11613,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_11613,tc_fun(U_11613,tc_HOL_Obool),U_11612),c_fequal),U_11614)),U_11615))),c_Orderings_Obot__class_Obot(tc_fun(U_11612,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(U_11612,U_11613,U_11614,c_Orderings_Otop__class_Otop(tc_fun(U_11612,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_3061_1]) ).
cnf(f_3061_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11612,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_11612,U_11613,U_11614),hAPP(hAPP(c_Set_Oinsert(U_11613),U_11615),c_Orderings_Obot__class_Obot(tc_fun(U_11613,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_11612),c_HOL_OThe(U_11612,hAPP(hAPP(c_COMBC(U_11612,U_11613,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_11613,tc_fun(U_11613,tc_HOL_Obool),U_11612),c_fequal),U_11614)),U_11615))),c_Orderings_Obot__class_Obot(tc_fun(U_11612,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(U_11612,U_11613,U_11614,c_Orderings_Otop__class_Otop(tc_fun(U_11612,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_3061_2]) ).
fof(f_3062_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_3062_2,plain,
! [U_11620,U_11619,U_11618,U_11617] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11617,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11617,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11618)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11617,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11620)))
| ? [U_11616] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11617,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11617,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11616)),U_11618)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11617,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_11616),U_11619))),U_11620))) ),
inference(variable_rename,[status(thm)],[f_3062_1]) ).
fof(f_3062_3,plain,
! [U_11620,U_11619,U_11618,U_11617] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11617,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11617,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11618)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11617,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11620)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11617,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11617,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK267(U_11620,U_11619,U_11618,U_11617))),U_11618)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11617,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK267(U_11620,U_11619,U_11618,U_11617)),U_11619))),U_11620))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK267]),skolemize(U_11616,sK267(U_11620,U_11619,U_11618,U_11617))],[f_3062_2]) ).
cnf(f_3062_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11617,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11617,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11618)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11617,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11620)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11617,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11617,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK267(U_11620,U_11619,U_11618,U_11617))),U_11618)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11617,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK267(U_11620,U_11619,U_11618,U_11617)),U_11619))),U_11620))) ),
inference(clausify,[status(thm)],[f_3062_3]) ).
fof(f_3063_1,plain,
! [V_P_2,V_a1_2,V_a0_2] :
( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
| ? [B_x,B_y] :
( ~ hBOOL(hAPP(hAPP(V_P_2,B_x),B_y))
& ( hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y)))
| B_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y))) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a0_2),V_a1_2))) ),
inference(fof_nnf,[status(thm)],[fact_nat__gcd_Opinduct]) ).
fof(f_3063_2,plain,
! [U_11625,U_11624,U_11623] :
( hBOOL(hAPP(hAPP(U_11625,U_11623),U_11624))
| ? [U_11622,U_11621] :
( ~ hBOOL(hAPP(hAPP(U_11625,U_11622),U_11621))
& ( hBOOL(hAPP(hAPP(U_11625,U_11621),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11622,U_11621)))
| U_11621 = 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_11622),U_11621))) )
| ~ 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_11623),U_11624))) ),
inference(variable_rename,[status(thm)],[f_3063_1]) ).
fof(f_3063_3,plain,
! [U_11625,U_11624,U_11623] :
( hBOOL(hAPP(hAPP(U_11625,U_11623),U_11624))
| ? [U_11621] :
( ~ hBOOL(hAPP(hAPP(U_11625,sK268(U_11625,U_11624,U_11623)),U_11621))
& ( hBOOL(hAPP(hAPP(U_11625,U_11621),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK268(U_11625,U_11624,U_11623),U_11621)))
| U_11621 = 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),sK268(U_11625,U_11624,U_11623)),U_11621))) )
| ~ 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_11623),U_11624))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK268]),skolemize(U_11622,sK268(U_11625,U_11624,U_11623))],[f_3063_2]) ).
fof(f_3063_4,plain,
! [U_11625,U_11624,U_11623] :
( hBOOL(hAPP(hAPP(U_11625,U_11623),U_11624))
| ( ~ hBOOL(hAPP(hAPP(U_11625,sK268(U_11625,U_11624,U_11623)),sK269(U_11625,U_11624,U_11623)))
& ( hBOOL(hAPP(hAPP(U_11625,sK269(U_11625,U_11624,U_11623)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK268(U_11625,U_11624,U_11623),sK269(U_11625,U_11624,U_11623))))
| sK269(U_11625,U_11624,U_11623) = 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),sK268(U_11625,U_11624,U_11623)),sK269(U_11625,U_11624,U_11623)))) )
| ~ 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_11623),U_11624))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK269]),skolemize(U_11621,sK269(U_11625,U_11624,U_11623))],[f_3063_3]) ).
cnf(f_3063_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),sK268(U_11625,U_11624,U_11623)),sK269(U_11625,U_11624,U_11623))))
| hBOOL(hAPP(hAPP(U_11625,U_11623),U_11624))
| ~ 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_11623),U_11624))) ),
inference(clausify,[status(thm)],[f_3063_4]) ).
cnf(f_3063_6,plain,
( hBOOL(hAPP(hAPP(U_11625,sK269(U_11625,U_11624,U_11623)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK268(U_11625,U_11624,U_11623),sK269(U_11625,U_11624,U_11623))))
| sK269(U_11625,U_11624,U_11623) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(U_11625,U_11623),U_11624))
| ~ 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_11623),U_11624))) ),
inference(clausify,[status(thm)],[f_3063_4]) ).
cnf(f_3063_7,plain,
( ~ hBOOL(hAPP(hAPP(U_11625,sK268(U_11625,U_11624,U_11623)),sK269(U_11625,U_11624,U_11623)))
| hBOOL(hAPP(hAPP(U_11625,U_11623),U_11624))
| ~ 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_11623),U_11624))) ),
inference(clausify,[status(thm)],[f_3063_4]) ).
fof(f_3064_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_3064_2,plain,
! [U_11629,U_11628,U_11627,U_11626] : c_HOL_OThe(tc_prod(U_11626,U_11627),hAPP(c_Product__Type_Oprod_Oprod__case(U_11626,U_11627,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11626,tc_fun(U_11627,tc_HOL_Obool),tc_fun(U_11627,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11627,tc_HOL_Obool),tc_fun(U_11627,tc_HOL_Obool)),U_11626),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11627)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11626),c_fconj),hAPP(c_fequal,U_11628)))),hAPP(c_fequal,U_11629)))) = hAPP(hAPP(c_Product__Type_OPair(U_11626,U_11627),U_11628),U_11629),
inference(variable_rename,[status(thm)],[f_3064_1]) ).
cnf(f_3064_3,plain,
c_HOL_OThe(tc_prod(U_11626,U_11627),hAPP(c_Product__Type_Oprod_Oprod__case(U_11626,U_11627,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11626,tc_fun(U_11627,tc_HOL_Obool),tc_fun(U_11627,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11627,tc_HOL_Obool),tc_fun(U_11627,tc_HOL_Obool)),U_11626),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11627)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11626),c_fconj),hAPP(c_fequal,U_11628)))),hAPP(c_fequal,U_11629)))) = hAPP(hAPP(c_Product__Type_OPair(U_11626,U_11627),U_11628),U_11629),
inference(clausify,[status(thm)],[f_3064_2]) ).
fof(f_3065_1,plain,
! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_P_2) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))),
inference(fof_nnf,[status(thm)],[fact_split__paired__The]) ).
fof(f_3065_2,plain,
! [U_11632,U_11631,U_11630] : c_HOL_OThe(tc_prod(U_11630,U_11631),U_11632) = c_HOL_OThe(tc_prod(U_11630,U_11631),hAPP(c_Product__Type_Oprod_Oprod__case(U_11630,U_11631,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_11631,tc_prod(U_11630,U_11631)),tc_fun(U_11631,tc_HOL_Obool),U_11630),hAPP(c_COMBB(tc_prod(U_11630,U_11631),tc_HOL_Obool,U_11631),U_11632)),c_Product__Type_OPair(U_11630,U_11631)))),
inference(variable_rename,[status(thm)],[f_3065_1]) ).
cnf(f_3065_3,plain,
c_HOL_OThe(tc_prod(U_11630,U_11631),U_11632) = c_HOL_OThe(tc_prod(U_11630,U_11631),hAPP(c_Product__Type_Oprod_Oprod__case(U_11630,U_11631,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_11631,tc_prod(U_11630,U_11631)),tc_fun(U_11631,tc_HOL_Obool),U_11630),hAPP(c_COMBB(tc_prod(U_11630,U_11631),tc_HOL_Obool,U_11631),U_11632)),c_Product__Type_OPair(U_11630,U_11631)))),
inference(clausify,[status(thm)],[f_3065_2]) ).
fof(f_3066_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_3066_2,plain,
! [U_11637,U_11636,U_11635,U_11634,U_11633] : hAPP(c_Fun_Othe__inv__into(U_11633,U_11634,U_11635,U_11636),U_11637) = c_HOL_OThe(U_11633,hAPP(hAPP(c_COMBS(U_11633,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11633),c_fconj),hAPP(hAPP(c_COMBC(U_11633,tc_fun(U_11633,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11633)),U_11635))),hAPP(hAPP(c_COMBC(U_11633,U_11634,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_11634,tc_fun(U_11634,tc_HOL_Obool),U_11633),c_fequal),U_11636)),U_11637))),
inference(variable_rename,[status(thm)],[f_3066_1]) ).
cnf(f_3066_3,plain,
hAPP(c_Fun_Othe__inv__into(U_11633,U_11634,U_11635,U_11636),U_11637) = c_HOL_OThe(U_11633,hAPP(hAPP(c_COMBS(U_11633,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11633),c_fconj),hAPP(hAPP(c_COMBC(U_11633,tc_fun(U_11633,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11633)),U_11635))),hAPP(hAPP(c_COMBC(U_11633,U_11634,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_11634,tc_fun(U_11634,tc_HOL_Obool),U_11633),c_fequal),U_11636)),U_11637))),
inference(clausify,[status(thm)],[f_3066_2]) ).
fof(f_3067_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_3067_2,plain,
! [U_11642,U_11641,U_11640,U_11639,U_11638] : hAPP(hAPP(c_Finite__Set_Ofold(U_11638,U_11639,U_11640),U_11641),U_11642) = c_HOL_OThe(U_11639,c_Finite__Set_Ofold__graph(U_11638,U_11639,U_11640,U_11641,U_11642)),
inference(variable_rename,[status(thm)],[f_3067_1]) ).
cnf(f_3067_3,plain,
hAPP(hAPP(c_Finite__Set_Ofold(U_11638,U_11639,U_11640),U_11641),U_11642) = c_HOL_OThe(U_11639,c_Finite__Set_Ofold__graph(U_11638,U_11639,U_11640,U_11641,U_11642)),
inference(clausify,[status(thm)],[f_3067_2]) ).
fof(f_3068_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_3068_2,plain,
! [U_11644,U_11643] : c_Divides_Odivmod__nat(U_11643,U_11644) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(U_11643,U_11644)),
inference(variable_rename,[status(thm)],[f_3068_1]) ).
cnf(f_3068_3,plain,
c_Divides_Odivmod__nat(U_11643,U_11644) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(U_11643,U_11644)),
inference(clausify,[status(thm)],[f_3068_2]) ).
fof(f_3069_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_3069_2,plain,
! [U_11647,U_11646,U_11645] : hAPP(c_Finite__Set_Ofold1(U_11645,U_11646),U_11647) = c_HOL_OThe(U_11645,c_Finite__Set_Ofold1Set(U_11645,U_11646,U_11647)),
inference(variable_rename,[status(thm)],[f_3069_1]) ).
cnf(f_3069_3,plain,
hAPP(c_Finite__Set_Ofold1(U_11645,U_11646),U_11647) = c_HOL_OThe(U_11645,c_Finite__Set_Ofold1Set(U_11645,U_11646,U_11647)),
inference(clausify,[status(thm)],[f_3069_2]) ).
fof(f_3070_1,plain,
! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))),
inference(fof_nnf,[status(thm)],[fact_The__split]) ).
fof(f_3070_2,plain,
! [U_11650,U_11649,U_11648] : c_HOL_OThe(tc_prod(U_11648,U_11649),hAPP(c_Product__Type_Oprod_Oprod__case(U_11648,U_11649,tc_HOL_Obool),U_11650)) = c_HOL_OThe(tc_prod(U_11648,U_11649),hAPP(hAPP(c_COMBS(tc_prod(U_11648,U_11649),U_11649,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_11648,tc_fun(U_11649,tc_HOL_Obool),tc_prod(U_11648,U_11649)),U_11650),c_Product__Type_Ofst(U_11648,U_11649))),c_Product__Type_Osnd(U_11648,U_11649))),
inference(variable_rename,[status(thm)],[f_3070_1]) ).
cnf(f_3070_3,plain,
c_HOL_OThe(tc_prod(U_11648,U_11649),hAPP(c_Product__Type_Oprod_Oprod__case(U_11648,U_11649,tc_HOL_Obool),U_11650)) = c_HOL_OThe(tc_prod(U_11648,U_11649),hAPP(hAPP(c_COMBS(tc_prod(U_11648,U_11649),U_11649,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_11648,tc_fun(U_11649,tc_HOL_Obool),tc_prod(U_11648,U_11649)),U_11650),c_Product__Type_Ofst(U_11648,U_11649))),c_Product__Type_Osnd(U_11648,U_11649))),
inference(clausify,[status(thm)],[f_3070_2]) ).
fof(f_3071_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_3071_2,plain,
! [U_11652,U_11651] : c_Set_Othe__elem(U_11651,U_11652) = c_HOL_OThe(U_11651,hAPP(hAPP(c_COMBB(tc_fun(U_11651,tc_HOL_Obool),tc_HOL_Obool,U_11651),hAPP(c_fequal,U_11652)),hAPP(hAPP(c_COMBC(U_11651,tc_fun(U_11651,tc_HOL_Obool),tc_fun(U_11651,tc_HOL_Obool)),c_Set_Oinsert(U_11651)),c_Orderings_Obot__class_Obot(tc_fun(U_11651,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_3071_1]) ).
cnf(f_3071_3,plain,
c_Set_Othe__elem(U_11651,U_11652) = c_HOL_OThe(U_11651,hAPP(hAPP(c_COMBB(tc_fun(U_11651,tc_HOL_Obool),tc_HOL_Obool,U_11651),hAPP(c_fequal,U_11652)),hAPP(hAPP(c_COMBC(U_11651,tc_fun(U_11651,tc_HOL_Obool),tc_fun(U_11651,tc_HOL_Obool)),c_Set_Oinsert(U_11651)),c_Orderings_Obot__class_Obot(tc_fun(U_11651,tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_3071_2]) ).
fof(f_3072_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_3072_2,plain,
! [U_11654,U_11653] :
( 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_11653),U_11654))),U_11653))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_11653)) ),
inference(variable_rename,[status(thm)],[f_3072_1]) ).
cnf(f_3072_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_11653),U_11654))),U_11653))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_11653)) ),
inference(clausify,[status(thm)],[f_3072_2]) ).
fof(f_3073_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_3073_2,plain,
! [U_11657,U_11656,U_11655] :
( ( c_Partial__Function_Oflat__lub(U_11655,U_11657,U_11656) = c_HOL_OThe(U_11655,hAPP(hAPP(c_COMBC(U_11655,tc_fun(U_11655,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11655)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11655,tc_HOL_Obool)),U_11656),hAPP(hAPP(c_Set_Oinsert(U_11655),U_11657),c_Orderings_Obot__class_Obot(tc_fun(U_11655,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11655,tc_HOL_Obool)),U_11656),hAPP(hAPP(c_Set_Oinsert(U_11655),U_11657),c_Orderings_Obot__class_Obot(tc_fun(U_11655,tc_HOL_Obool))))) )
& ( c_Partial__Function_Oflat__lub(U_11655,U_11657,U_11656) = U_11657
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11655,tc_HOL_Obool)),U_11656),hAPP(hAPP(c_Set_Oinsert(U_11655),U_11657),c_Orderings_Obot__class_Obot(tc_fun(U_11655,tc_HOL_Obool))))) ) ),
inference(variable_rename,[status(thm)],[f_3073_1]) ).
fof(f_3073_3,plain,
( ! [U_11663,U_11661,U_11659] :
( c_Partial__Function_Oflat__lub(U_11659,U_11663,U_11661) = c_HOL_OThe(U_11659,hAPP(hAPP(c_COMBC(U_11659,tc_fun(U_11659,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11659)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11659,tc_HOL_Obool)),U_11661),hAPP(hAPP(c_Set_Oinsert(U_11659),U_11663),c_Orderings_Obot__class_Obot(tc_fun(U_11659,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11659,tc_HOL_Obool)),U_11661),hAPP(hAPP(c_Set_Oinsert(U_11659),U_11663),c_Orderings_Obot__class_Obot(tc_fun(U_11659,tc_HOL_Obool))))) )
& ! [U_11662,U_11660,U_11658] :
( c_Partial__Function_Oflat__lub(U_11658,U_11662,U_11660) = U_11662
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11658,tc_HOL_Obool)),U_11660),hAPP(hAPP(c_Set_Oinsert(U_11658),U_11662),c_Orderings_Obot__class_Obot(tc_fun(U_11658,tc_HOL_Obool))))) ) ),
inference(miniscope,[status(thm)],[f_3073_2]) ).
cnf(f_3073_4,plain,
( c_Partial__Function_Oflat__lub(U_11658,U_11662,U_11660) = U_11662
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11658,tc_HOL_Obool)),U_11660),hAPP(hAPP(c_Set_Oinsert(U_11658),U_11662),c_Orderings_Obot__class_Obot(tc_fun(U_11658,tc_HOL_Obool))))) ),
inference(clausify,[status(thm)],[f_3073_3]) ).
cnf(f_3073_5,plain,
( c_Partial__Function_Oflat__lub(U_11659,U_11663,U_11661) = c_HOL_OThe(U_11659,hAPP(hAPP(c_COMBC(U_11659,tc_fun(U_11659,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11659)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11659,tc_HOL_Obool)),U_11661),hAPP(hAPP(c_Set_Oinsert(U_11659),U_11663),c_Orderings_Obot__class_Obot(tc_fun(U_11659,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11659,tc_HOL_Obool)),U_11661),hAPP(hAPP(c_Set_Oinsert(U_11659),U_11663),c_Orderings_Obot__class_Obot(tc_fun(U_11659,tc_HOL_Obool))))) ),
inference(clausify,[status(thm)],[f_3073_3]) ).
fof(f_3074_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_3074_2,plain,
! [U_11668,U_11667,U_11666,U_11665,U_11664] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11667,U_11667)),hAPP(hAPP(c_Product__Type_OPair(U_11667,U_11667),U_11665),U_11666)),c_Wellfounded_Omlex__prod(U_11667,U_11664,U_11668)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11667,U_11667)),hAPP(hAPP(c_Product__Type_OPair(U_11667,U_11667),U_11665),U_11666)),U_11668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_11664,U_11665)),hAPP(U_11664,U_11666))) ),
inference(variable_rename,[status(thm)],[f_3074_1]) ).
cnf(f_3074_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11667,U_11667)),hAPP(hAPP(c_Product__Type_OPair(U_11667,U_11667),U_11665),U_11666)),c_Wellfounded_Omlex__prod(U_11667,U_11664,U_11668)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11667,U_11667)),hAPP(hAPP(c_Product__Type_OPair(U_11667,U_11667),U_11665),U_11666)),U_11668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_11664,U_11665)),hAPP(U_11664,U_11666))) ),
inference(clausify,[status(thm)],[f_3074_2]) ).
fof(f_3075_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_3075_2,plain,
! [U_11673,U_11672,U_11671,U_11670,U_11669] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11672,U_11672)),hAPP(hAPP(c_Product__Type_OPair(U_11672,U_11672),U_11670),U_11671)),c_Wellfounded_Omlex__prod(U_11672,U_11669,U_11673)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_11669,U_11670)),hAPP(U_11669,U_11671))) ),
inference(variable_rename,[status(thm)],[f_3075_1]) ).
cnf(f_3075_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11672,U_11672)),hAPP(hAPP(c_Product__Type_OPair(U_11672,U_11672),U_11670),U_11671)),c_Wellfounded_Omlex__prod(U_11672,U_11669,U_11673)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_11669,U_11670)),hAPP(U_11669,U_11671))) ),
inference(clausify,[status(thm)],[f_3075_2]) ).
fof(f_3076_1,plain,
! [V_S_2,V_f_2,T_b,T_c] :
( c_Orderings_Oord__class_OLeast(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2))) = hAPP(V_f_2,c_Orderings_Oord__class_OLeast(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))
| ! [B_x] :
( ? [B_xa] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa))
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_S_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
| ~ c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
| ~ class_Orderings_Oorder(T_b)
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Least__mono]) ).
fof(f_3076_2,plain,
! [U_11679,U_11678,U_11677,U_11676] :
( c_Orderings_Oord__class_OLeast(U_11676,hAPP(hAPP(c_COMBC(U_11676,tc_fun(U_11676,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11676)),hAPP(c_Set_Oimage(U_11677,U_11676,U_11678),U_11679))) = hAPP(U_11678,c_Orderings_Oord__class_OLeast(U_11677,hAPP(hAPP(c_COMBC(U_11677,tc_fun(U_11677,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11677)),U_11679)))
| ! [U_11675] :
( ? [U_11674] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11677),U_11675),U_11674))
& hBOOL(hAPP(hAPP(c_member(U_11677),U_11674),U_11679)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_11677),U_11675),U_11679)) )
| ~ c_Orderings_Oorder__class_Omono(U_11677,U_11676,U_11678)
| ~ class_Orderings_Oorder(U_11677)
| ~ class_Orderings_Oorder(U_11676) ),
inference(variable_rename,[status(thm)],[f_3076_1]) ).
fof(f_3076_3,plain,
! [U_11679,U_11678,U_11677,U_11676] :
( c_Orderings_Oord__class_OLeast(U_11676,hAPP(hAPP(c_COMBC(U_11676,tc_fun(U_11676,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11676)),hAPP(c_Set_Oimage(U_11677,U_11676,U_11678),U_11679))) = hAPP(U_11678,c_Orderings_Oord__class_OLeast(U_11677,hAPP(hAPP(c_COMBC(U_11677,tc_fun(U_11677,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11677)),U_11679)))
| ! [U_11675] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11677),U_11675),sK270(U_11679,U_11678,U_11677,U_11676,U_11675)))
& hBOOL(hAPP(hAPP(c_member(U_11677),sK270(U_11679,U_11678,U_11677,U_11676,U_11675)),U_11679)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_11677),U_11675),U_11679)) )
| ~ c_Orderings_Oorder__class_Omono(U_11677,U_11676,U_11678)
| ~ class_Orderings_Oorder(U_11677)
| ~ class_Orderings_Oorder(U_11676) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK270]),skolemize(U_11674,sK270(U_11679,U_11678,U_11677,U_11676,U_11675))],[f_3076_2]) ).
cnf(f_3076_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11677),sK270(U_11679,U_11678,U_11677,U_11676,U_11675)),U_11679))
| ~ hBOOL(hAPP(hAPP(c_member(U_11677),U_11675),U_11679))
| c_Orderings_Oord__class_OLeast(U_11676,hAPP(hAPP(c_COMBC(U_11676,tc_fun(U_11676,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11676)),hAPP(c_Set_Oimage(U_11677,U_11676,U_11678),U_11679))) = hAPP(U_11678,c_Orderings_Oord__class_OLeast(U_11677,hAPP(hAPP(c_COMBC(U_11677,tc_fun(U_11677,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11677)),U_11679)))
| ~ c_Orderings_Oorder__class_Omono(U_11677,U_11676,U_11678)
| ~ class_Orderings_Oorder(U_11677)
| ~ class_Orderings_Oorder(U_11676) ),
inference(clausify,[status(thm)],[f_3076_3]) ).
cnf(f_3076_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11677),U_11675),sK270(U_11679,U_11678,U_11677,U_11676,U_11675)))
| ~ hBOOL(hAPP(hAPP(c_member(U_11677),U_11675),U_11679))
| c_Orderings_Oord__class_OLeast(U_11676,hAPP(hAPP(c_COMBC(U_11676,tc_fun(U_11676,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11676)),hAPP(c_Set_Oimage(U_11677,U_11676,U_11678),U_11679))) = hAPP(U_11678,c_Orderings_Oord__class_OLeast(U_11677,hAPP(hAPP(c_COMBC(U_11677,tc_fun(U_11677,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11677)),U_11679)))
| ~ c_Orderings_Oorder__class_Omono(U_11677,U_11676,U_11678)
| ~ class_Orderings_Oorder(U_11677)
| ~ class_Orderings_Oorder(U_11676) ),
inference(clausify,[status(thm)],[f_3076_3]) ).
fof(f_3077_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_3077_2,plain,
! [U_11687,U_11686,U_11685,U_11684,U_11683,U_11682,U_11681,U_11680] :
( hAPP(hAPP(U_11684,U_11687),hAPP(c_Set_Oimage(U_11681,U_11681,U_11686),U_11685)) = hAPP(hAPP(U_11684,hAPP(c_Fun_Ocomp(U_11681,U_11680,U_11681,U_11687),U_11686)),U_11685)
| ~ c_Fun_Oinj__on(U_11681,U_11681,U_11686,U_11685)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11681),U_11685))
| ~ c_Finite__Set_Ofolding__image(U_11680,U_11681,U_11682,U_11683,U_11684) ),
inference(variable_rename,[status(thm)],[f_3077_1]) ).
cnf(f_3077_3,plain,
( hAPP(hAPP(U_11684,U_11687),hAPP(c_Set_Oimage(U_11681,U_11681,U_11686),U_11685)) = hAPP(hAPP(U_11684,hAPP(c_Fun_Ocomp(U_11681,U_11680,U_11681,U_11687),U_11686)),U_11685)
| ~ c_Fun_Oinj__on(U_11681,U_11681,U_11686,U_11685)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11681),U_11685))
| ~ c_Finite__Set_Ofolding__image(U_11680,U_11681,U_11682,U_11683,U_11684) ),
inference(clausify,[status(thm)],[f_3077_2]) ).
fof(f_3078_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_3078_2,plain,
! [U_11688] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11688)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_11688)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_3078_1]) ).
cnf(f_3078_3,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11688)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_11688)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_3078_2]) ).
fof(f_3079_1,plain,
! [V_k_2,V_P_2,T_b] :
( hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2)))
| ~ hBOOL(hAPP(V_P_2,V_k_2))
| ~ class_Orderings_Owellorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_LeastI]) ).
fof(f_3079_2,plain,
! [U_11691,U_11690,U_11689] :
( hBOOL(hAPP(U_11690,c_Orderings_Oord__class_OLeast(U_11689,U_11690)))
| ~ hBOOL(hAPP(U_11690,U_11691))
| ~ class_Orderings_Owellorder(U_11689) ),
inference(variable_rename,[status(thm)],[f_3079_1]) ).
cnf(f_3079_3,plain,
( hBOOL(hAPP(U_11690,c_Orderings_Oord__class_OLeast(U_11689,U_11690)))
| ~ hBOOL(hAPP(U_11690,U_11691))
| ~ class_Orderings_Owellorder(U_11689) ),
inference(clausify,[status(thm)],[f_3079_2]) ).
fof(f_3080_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_3080_2,plain,
! [U_11692] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_11692) = U_11692,
inference(variable_rename,[status(thm)],[f_3080_1]) ).
cnf(f_3080_3,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_11692) = U_11692,
inference(clausify,[status(thm)],[f_3080_2]) ).
fof(f_3081_1,plain,
! [V_P_2,T_b] :
( hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2)))
| ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1))
| ~ class_Orderings_Owellorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_LeastI__ex]) ).
fof(f_3081_2,plain,
! [U_11695,U_11694] :
( hBOOL(hAPP(U_11695,c_Orderings_Oord__class_OLeast(U_11694,U_11695)))
| ! [U_11693] : ~ hBOOL(hAPP(U_11695,U_11693))
| ~ class_Orderings_Owellorder(U_11694) ),
inference(variable_rename,[status(thm)],[f_3081_1]) ).
cnf(f_3081_3,plain,
( hBOOL(hAPP(U_11695,c_Orderings_Oord__class_OLeast(U_11694,U_11695)))
| ~ hBOOL(hAPP(U_11695,U_11693))
| ~ class_Orderings_Owellorder(U_11694) ),
inference(clausify,[status(thm)],[f_3081_2]) ).
fof(f_3082_1,plain,
! [V_k_2,V_P_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Orderings_Oord__class_OLeast(T_b,V_P_2)),V_k_2))
| ~ hBOOL(hAPP(V_P_2,V_k_2))
| ~ class_Orderings_Owellorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Least__le]) ).
fof(f_3082_2,plain,
! [U_11698,U_11697,U_11696] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11696),c_Orderings_Oord__class_OLeast(U_11696,U_11697)),U_11698))
| ~ hBOOL(hAPP(U_11697,U_11698))
| ~ class_Orderings_Owellorder(U_11696) ),
inference(variable_rename,[status(thm)],[f_3082_1]) ).
cnf(f_3082_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11696),c_Orderings_Oord__class_OLeast(U_11696,U_11697)),U_11698))
| ~ hBOOL(hAPP(U_11697,U_11698))
| ~ class_Orderings_Owellorder(U_11696) ),
inference(clausify,[status(thm)],[f_3082_2]) ).
fof(f_3083_1,plain,
! [V_P_2,V_k_2,T_b] :
( ~ hBOOL(hAPP(V_P_2,V_k_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),c_Orderings_Oord__class_OLeast(T_b,V_P_2)))
| ~ class_Orderings_Owellorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_not__less__Least]) ).
fof(f_3083_2,plain,
! [U_11701,U_11700,U_11699] :
( ~ hBOOL(hAPP(U_11701,U_11700))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11699),U_11700),c_Orderings_Oord__class_OLeast(U_11699,U_11701)))
| ~ class_Orderings_Owellorder(U_11699) ),
inference(variable_rename,[status(thm)],[f_3083_1]) ).
cnf(f_3083_3,plain,
( ~ hBOOL(hAPP(U_11701,U_11700))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11699),U_11700),c_Orderings_Oord__class_OLeast(U_11699,U_11701)))
| ~ class_Orderings_Owellorder(U_11699) ),
inference(clausify,[status(thm)],[f_3083_2]) ).
fof(f_3084_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_3084_2,plain,
! [U_11709,U_11708,U_11707,U_11706,U_11705,U_11704,U_11703,U_11702] :
( hAPP(hAPP(U_11706,hAPP(hAPP(c_COMBS(U_11703,U_11702,U_11702),hAPP(hAPP(c_COMBB(U_11702,tc_fun(U_11702,U_11702),U_11703),U_11704),U_11708)),U_11709)),U_11707) = hAPP(hAPP(U_11704,hAPP(hAPP(U_11706,U_11708),U_11707)),hAPP(hAPP(U_11706,U_11709),U_11707))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11703),U_11707))
| ~ c_Finite__Set_Ofolding__image(U_11702,U_11703,U_11704,U_11705,U_11706) ),
inference(variable_rename,[status(thm)],[f_3084_1]) ).
cnf(f_3084_3,plain,
( hAPP(hAPP(U_11706,hAPP(hAPP(c_COMBS(U_11703,U_11702,U_11702),hAPP(hAPP(c_COMBB(U_11702,tc_fun(U_11702,U_11702),U_11703),U_11704),U_11708)),U_11709)),U_11707) = hAPP(hAPP(U_11704,hAPP(hAPP(U_11706,U_11708),U_11707)),hAPP(hAPP(U_11706,U_11709),U_11707))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11703),U_11707))
| ~ c_Finite__Set_Ofolding__image(U_11702,U_11703,U_11704,U_11705,U_11706) ),
inference(clausify,[status(thm)],[f_3084_2]) ).
fof(f_3085_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_3085_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_3085_1]) ).
fof(f_3086_1,plain,
! [V_n_2,V_P_2] :
( c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_P_2) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_OSuc)))
| hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(V_P_2,V_n_2)) ),
inference(fof_nnf,[status(thm)],[fact_Least__Suc]) ).
fof(f_3086_2,plain,
! [U_11711,U_11710] :
( c_Orderings_Oord__class_OLeast(tc_Nat_Onat,U_11710) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),U_11710),c_Nat_OSuc)))
| hBOOL(hAPP(U_11710,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(U_11710,U_11711)) ),
inference(variable_rename,[status(thm)],[f_3086_1]) ).
cnf(f_3086_3,plain,
( c_Orderings_Oord__class_OLeast(tc_Nat_Onat,U_11710) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),U_11710),c_Nat_OSuc)))
| hBOOL(hAPP(U_11710,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(U_11710,U_11711)) ),
inference(clausify,[status(thm)],[f_3086_2]) ).
fof(f_3087_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_3087_2,plain,
! [U_11718,U_11717,U_11716,U_11715,U_11714,U_11713,U_11712] :
( hAPP(hAPP(U_11716,U_11718),U_11717) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11712,U_11713,U_11714),U_11718),U_11715),U_11717)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11713),U_11717))
| ~ c_Finite__Set_Ofolding__image(U_11712,U_11713,U_11714,U_11715,U_11716) ),
inference(variable_rename,[status(thm)],[f_3087_1]) ).
cnf(f_3087_3,plain,
( hAPP(hAPP(U_11716,U_11718),U_11717) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11712,U_11713,U_11714),U_11718),U_11715),U_11717)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11713),U_11717))
| ~ c_Finite__Set_Ofolding__image(U_11712,U_11713,U_11714,U_11715,U_11716) ),
inference(clausify,[status(thm)],[f_3087_2]) ).
fof(f_3088_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_3088_2,plain,
! [U_11724,U_11723,U_11722,U_11721,U_11720,U_11719] : c_Product__Type_Oprod_Oprod__rec(U_11719,U_11720,U_11721,U_11722,hAPP(hAPP(c_Product__Type_OPair(U_11719,U_11720),U_11723),U_11724)) = hAPP(hAPP(U_11722,U_11723),U_11724),
inference(variable_rename,[status(thm)],[f_3088_1]) ).
cnf(f_3088_3,plain,
c_Product__Type_Oprod_Oprod__rec(U_11719,U_11720,U_11721,U_11722,hAPP(hAPP(c_Product__Type_OPair(U_11719,U_11720),U_11723),U_11724)) = hAPP(hAPP(U_11722,U_11723),U_11724),
inference(clausify,[status(thm)],[f_3088_2]) ).
fof(f_3089_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_3089_2,plain,
! [U_11732,U_11731,U_11730,U_11729,U_11728,U_11727] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11732,U_11727),U_11731),hAPP(c_Set_Oimage(U_11728,U_11732,U_11730),U_11729)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11728,U_11727),hAPP(c_Fun_Ocomp(U_11732,U_11727,U_11728,U_11731),U_11730)),U_11729)
| ? [U_11726] :
( ? [U_11725] :
( hAPP(U_11731,hAPP(U_11730,U_11726)) != c_Groups_Ozero__class_Ozero(U_11727)
& hAPP(U_11730,U_11726) = hAPP(U_11730,U_11725)
& U_11726 != U_11725
& hBOOL(hAPP(hAPP(c_member(U_11728),U_11725),U_11729)) )
& hBOOL(hAPP(hAPP(c_member(U_11728),U_11726),U_11729)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11728),U_11729))
| ~ class_Groups_Ocomm__monoid__add(U_11727) ),
inference(variable_rename,[status(thm)],[f_3089_1]) ).
fof(f_3089_3,plain,
! [U_11732,U_11731,U_11730,U_11729,U_11728,U_11727] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11732,U_11727),U_11731),hAPP(c_Set_Oimage(U_11728,U_11732,U_11730),U_11729)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11728,U_11727),hAPP(c_Fun_Ocomp(U_11732,U_11727,U_11728,U_11731),U_11730)),U_11729)
| ( ? [U_11725] :
( hAPP(U_11731,hAPP(U_11730,sK271(U_11732,U_11731,U_11730,U_11729,U_11728,U_11727))) != c_Groups_Ozero__class_Ozero(U_11727)
& hAPP(U_11730,sK271(U_11732,U_11731,U_11730,U_11729,U_11728,U_11727)) = hAPP(U_11730,U_11725)
& sK271(U_11732,U_11731,U_11730,U_11729,U_11728,U_11727) != U_11725
& hBOOL(hAPP(hAPP(c_member(U_11728),U_11725),U_11729)) )
& hBOOL(hAPP(hAPP(c_member(U_11728),sK271(U_11732,U_11731,U_11730,U_11729,U_11728,U_11727)),U_11729)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11728),U_11729))
| ~ class_Groups_Ocomm__monoid__add(U_11727) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK271]),skolemize(U_11726,sK271(U_11732,U_11731,U_11730,U_11729,U_11728,U_11727))],[f_3089_2]) ).
fof(f_3089_4,plain,
! [U_11732,U_11731,U_11730,U_11729,U_11728,U_11727] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11732,U_11727),U_11731),hAPP(c_Set_Oimage(U_11728,U_11732,U_11730),U_11729)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11728,U_11727),hAPP(c_Fun_Ocomp(U_11732,U_11727,U_11728,U_11731),U_11730)),U_11729)
| ( hAPP(U_11731,hAPP(U_11730,sK271(U_11732,U_11731,U_11730,U_11729,U_11728,U_11727))) != c_Groups_Ozero__class_Ozero(U_11727)
& hAPP(U_11730,sK271(U_11732,U_11731,U_11730,U_11729,U_11728,U_11727)) = hAPP(U_11730,sK272(U_11732,U_11731,U_11730,U_11729,U_11728,U_11727))
& sK271(U_11732,U_11731,U_11730,U_11729,U_11728,U_11727) != sK272(U_11732,U_11731,U_11730,U_11729,U_11728,U_11727)
& hBOOL(hAPP(hAPP(c_member(U_11728),sK272(U_11732,U_11731,U_11730,U_11729,U_11728,U_11727)),U_11729))
& hBOOL(hAPP(hAPP(c_member(U_11728),sK271(U_11732,U_11731,U_11730,U_11729,U_11728,U_11727)),U_11729)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11728),U_11729))
| ~ class_Groups_Ocomm__monoid__add(U_11727) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK272]),skolemize(U_11725,sK272(U_11732,U_11731,U_11730,U_11729,U_11728,U_11727))],[f_3089_3]) ).
cnf(f_3089_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_11728),sK271(U_11732,U_11731,U_11730,U_11729,U_11728,U_11727)),U_11729))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11732,U_11727),U_11731),hAPP(c_Set_Oimage(U_11728,U_11732,U_11730),U_11729)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11728,U_11727),hAPP(c_Fun_Ocomp(U_11732,U_11727,U_11728,U_11731),U_11730)),U_11729)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11728),U_11729))
| ~ class_Groups_Ocomm__monoid__add(U_11727) ),
inference(clausify,[status(thm)],[f_3089_4]) ).
cnf(f_3089_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_11728),sK272(U_11732,U_11731,U_11730,U_11729,U_11728,U_11727)),U_11729))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11732,U_11727),U_11731),hAPP(c_Set_Oimage(U_11728,U_11732,U_11730),U_11729)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11728,U_11727),hAPP(c_Fun_Ocomp(U_11732,U_11727,U_11728,U_11731),U_11730)),U_11729)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11728),U_11729))
| ~ class_Groups_Ocomm__monoid__add(U_11727) ),
inference(clausify,[status(thm)],[f_3089_4]) ).
cnf(f_3089_7,plain,
( sK271(U_11732,U_11731,U_11730,U_11729,U_11728,U_11727) != sK272(U_11732,U_11731,U_11730,U_11729,U_11728,U_11727)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11732,U_11727),U_11731),hAPP(c_Set_Oimage(U_11728,U_11732,U_11730),U_11729)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11728,U_11727),hAPP(c_Fun_Ocomp(U_11732,U_11727,U_11728,U_11731),U_11730)),U_11729)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11728),U_11729))
| ~ class_Groups_Ocomm__monoid__add(U_11727) ),
inference(clausify,[status(thm)],[f_3089_4]) ).
cnf(f_3089_8,plain,
( hAPP(U_11730,sK271(U_11732,U_11731,U_11730,U_11729,U_11728,U_11727)) = hAPP(U_11730,sK272(U_11732,U_11731,U_11730,U_11729,U_11728,U_11727))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11732,U_11727),U_11731),hAPP(c_Set_Oimage(U_11728,U_11732,U_11730),U_11729)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11728,U_11727),hAPP(c_Fun_Ocomp(U_11732,U_11727,U_11728,U_11731),U_11730)),U_11729)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11728),U_11729))
| ~ class_Groups_Ocomm__monoid__add(U_11727) ),
inference(clausify,[status(thm)],[f_3089_4]) ).
cnf(f_3089_9,plain,
( hAPP(U_11731,hAPP(U_11730,sK271(U_11732,U_11731,U_11730,U_11729,U_11728,U_11727))) != c_Groups_Ozero__class_Ozero(U_11727)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11732,U_11727),U_11731),hAPP(c_Set_Oimage(U_11728,U_11732,U_11730),U_11729)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11728,U_11727),hAPP(c_Fun_Ocomp(U_11732,U_11727,U_11728,U_11731),U_11730)),U_11729)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11728),U_11729))
| ~ class_Groups_Ocomm__monoid__add(U_11727) ),
inference(clausify,[status(thm)],[f_3089_4]) ).
fof(f_3090_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_3090_2,plain,
! [U_11737,U_11736,U_11735,U_11734] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11734,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11735) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11734,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11737)
| ? [U_11733] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11734,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11733)),U_11735) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11734,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_11733),U_11736))),U_11737) ),
inference(variable_rename,[status(thm)],[f_3090_1]) ).
fof(f_3090_3,plain,
! [U_11737,U_11736,U_11735,U_11734] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11734,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11735) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11734,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11737)
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11734,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK273(U_11737,U_11736,U_11735,U_11734))),U_11735) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11734,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),sK273(U_11737,U_11736,U_11735,U_11734)),U_11736))),U_11737) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK273]),skolemize(U_11733,sK273(U_11737,U_11736,U_11735,U_11734))],[f_3090_2]) ).
cnf(f_3090_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11734,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11735) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11734,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11737)
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11734,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK273(U_11737,U_11736,U_11735,U_11734))),U_11735) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11734,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),sK273(U_11737,U_11736,U_11735,U_11734)),U_11736))),U_11737) ),
inference(clausify,[status(thm)],[f_3090_3]) ).
fof(f_3091_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_3091_2,plain,
! [U_11741,U_11740,U_11739] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11739,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11739,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11740)),U_11741))
| ? [U_11738] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11739,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11739,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11738)),U_11740)),U_11741)) ),
inference(variable_rename,[status(thm)],[f_3091_1]) ).
fof(f_3091_3,plain,
! [U_11741,U_11740,U_11739] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11739,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11739,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11740)),U_11741))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11739,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11739,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK274(U_11741,U_11740,U_11739))),U_11740)),U_11741)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK274]),skolemize(U_11738,sK274(U_11741,U_11740,U_11739))],[f_3091_2]) ).
cnf(f_3091_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11739,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11739,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11740)),U_11741))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11739,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11739,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK274(U_11741,U_11740,U_11739))),U_11740)),U_11741)) ),
inference(clausify,[status(thm)],[f_3091_3]) ).
fof(f_3092_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_3092_2,plain,
! [U_11750,U_11749,U_11748,U_11747,U_11746,U_11745,U_11744,U_11743] :
( hAPP(c_Set_Oimage(U_11743,U_11744,U_11745),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11747,tc_fun(U_11743,tc_HOL_Obool)),U_11748),U_11749)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11747,tc_fun(U_11744,tc_HOL_Obool)),U_11748),hAPP(hAPP(c_COMBB(tc_fun(U_11743,tc_HOL_Obool),tc_fun(U_11744,tc_HOL_Obool),U_11747),c_Set_Oimage(U_11743,U_11744,U_11745)),U_11749))
| ~ hBOOL(hAPP(hAPP(c_member(U_11747),U_11750),U_11748))
| ? [U_11742] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11743,tc_HOL_Obool)),hAPP(U_11749,U_11742)),U_11746))
& hBOOL(hAPP(hAPP(c_member(U_11747),U_11742),U_11748)) )
| ~ c_Fun_Oinj__on(U_11743,U_11744,U_11745,U_11746) ),
inference(variable_rename,[status(thm)],[f_3092_1]) ).
fof(f_3092_3,plain,
! [U_11750,U_11749,U_11748,U_11747,U_11746,U_11745,U_11744,U_11743] :
( hAPP(c_Set_Oimage(U_11743,U_11744,U_11745),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11747,tc_fun(U_11743,tc_HOL_Obool)),U_11748),U_11749)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11747,tc_fun(U_11744,tc_HOL_Obool)),U_11748),hAPP(hAPP(c_COMBB(tc_fun(U_11743,tc_HOL_Obool),tc_fun(U_11744,tc_HOL_Obool),U_11747),c_Set_Oimage(U_11743,U_11744,U_11745)),U_11749))
| ~ hBOOL(hAPP(hAPP(c_member(U_11747),U_11750),U_11748))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11743,tc_HOL_Obool)),hAPP(U_11749,sK275(U_11750,U_11749,U_11748,U_11747,U_11746,U_11745,U_11744,U_11743))),U_11746))
& hBOOL(hAPP(hAPP(c_member(U_11747),sK275(U_11750,U_11749,U_11748,U_11747,U_11746,U_11745,U_11744,U_11743)),U_11748)) )
| ~ c_Fun_Oinj__on(U_11743,U_11744,U_11745,U_11746) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK275]),skolemize(U_11742,sK275(U_11750,U_11749,U_11748,U_11747,U_11746,U_11745,U_11744,U_11743))],[f_3092_2]) ).
cnf(f_3092_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11747),sK275(U_11750,U_11749,U_11748,U_11747,U_11746,U_11745,U_11744,U_11743)),U_11748))
| hAPP(c_Set_Oimage(U_11743,U_11744,U_11745),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11747,tc_fun(U_11743,tc_HOL_Obool)),U_11748),U_11749)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11747,tc_fun(U_11744,tc_HOL_Obool)),U_11748),hAPP(hAPP(c_COMBB(tc_fun(U_11743,tc_HOL_Obool),tc_fun(U_11744,tc_HOL_Obool),U_11747),c_Set_Oimage(U_11743,U_11744,U_11745)),U_11749))
| ~ hBOOL(hAPP(hAPP(c_member(U_11747),U_11750),U_11748))
| ~ c_Fun_Oinj__on(U_11743,U_11744,U_11745,U_11746) ),
inference(clausify,[status(thm)],[f_3092_3]) ).
cnf(f_3092_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11743,tc_HOL_Obool)),hAPP(U_11749,sK275(U_11750,U_11749,U_11748,U_11747,U_11746,U_11745,U_11744,U_11743))),U_11746))
| hAPP(c_Set_Oimage(U_11743,U_11744,U_11745),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11747,tc_fun(U_11743,tc_HOL_Obool)),U_11748),U_11749)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11747,tc_fun(U_11744,tc_HOL_Obool)),U_11748),hAPP(hAPP(c_COMBB(tc_fun(U_11743,tc_HOL_Obool),tc_fun(U_11744,tc_HOL_Obool),U_11747),c_Set_Oimage(U_11743,U_11744,U_11745)),U_11749))
| ~ hBOOL(hAPP(hAPP(c_member(U_11747),U_11750),U_11748))
| ~ c_Fun_Oinj__on(U_11743,U_11744,U_11745,U_11746) ),
inference(clausify,[status(thm)],[f_3092_3]) ).
fof(f_3093_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_3093_2,plain,
! [U_11758,U_11757,U_11756,U_11755,U_11754,U_11753,U_11752,U_11751] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11751,U_11752),tc_prod(U_11751,U_11752))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11751,U_11752),tc_prod(U_11751,U_11752)),hAPP(hAPP(c_Product__Type_OPair(U_11751,U_11752),U_11753),U_11754)),hAPP(hAPP(c_Product__Type_OPair(U_11751,U_11752),U_11755),U_11756))),c_Wellfounded_Olex__prod(U_11751,U_11752,U_11757,U_11758)))
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11752,U_11752)),hAPP(hAPP(c_Product__Type_OPair(U_11752,U_11752),U_11754),U_11756)),U_11758))
| U_11753 != U_11755 )
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11751,U_11751)),hAPP(hAPP(c_Product__Type_OPair(U_11751,U_11751),U_11753),U_11755)),U_11757)) ) )
& ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11752,U_11752)),hAPP(hAPP(c_Product__Type_OPair(U_11752,U_11752),U_11754),U_11756)),U_11758))
& U_11753 = U_11755 )
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_11751,U_11751)),hAPP(hAPP(c_Product__Type_OPair(U_11751,U_11751),U_11753),U_11755)),U_11757))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11751,U_11752),tc_prod(U_11751,U_11752))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11751,U_11752),tc_prod(U_11751,U_11752)),hAPP(hAPP(c_Product__Type_OPair(U_11751,U_11752),U_11753),U_11754)),hAPP(hAPP(c_Product__Type_OPair(U_11751,U_11752),U_11755),U_11756))),c_Wellfounded_Olex__prod(U_11751,U_11752,U_11757,U_11758))) ) ),
inference(variable_rename,[status(thm)],[f_3093_1]) ).
fof(f_3093_3,plain,
( ! [U_11774,U_11772,U_11770,U_11768,U_11766,U_11764,U_11762,U_11760] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11760,U_11762),tc_prod(U_11760,U_11762))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11760,U_11762),tc_prod(U_11760,U_11762)),hAPP(hAPP(c_Product__Type_OPair(U_11760,U_11762),U_11764),U_11766)),hAPP(hAPP(c_Product__Type_OPair(U_11760,U_11762),U_11768),U_11770))),c_Wellfounded_Olex__prod(U_11760,U_11762,U_11772,U_11774)))
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11762,U_11762)),hAPP(hAPP(c_Product__Type_OPair(U_11762,U_11762),U_11766),U_11770)),U_11774))
| U_11764 != U_11768 )
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11760,U_11760)),hAPP(hAPP(c_Product__Type_OPair(U_11760,U_11760),U_11764),U_11768)),U_11772)) ) )
& ! [U_11773,U_11771,U_11769,U_11767,U_11765,U_11763,U_11761,U_11759] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11761,U_11761)),hAPP(hAPP(c_Product__Type_OPair(U_11761,U_11761),U_11765),U_11769)),U_11773))
& U_11763 = U_11767 )
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_11759,U_11759)),hAPP(hAPP(c_Product__Type_OPair(U_11759,U_11759),U_11763),U_11767)),U_11771))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11759,U_11761),tc_prod(U_11759,U_11761))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11759,U_11761),tc_prod(U_11759,U_11761)),hAPP(hAPP(c_Product__Type_OPair(U_11759,U_11761),U_11763),U_11765)),hAPP(hAPP(c_Product__Type_OPair(U_11759,U_11761),U_11767),U_11769))),c_Wellfounded_Olex__prod(U_11759,U_11761,U_11771,U_11773))) ) ),
inference(miniscope,[status(thm)],[f_3093_2]) ).
cnf(f_3093_4,plain,
( U_11763 = U_11767
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_11759,U_11759)),hAPP(hAPP(c_Product__Type_OPair(U_11759,U_11759),U_11763),U_11767)),U_11771))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11759,U_11761),tc_prod(U_11759,U_11761))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11759,U_11761),tc_prod(U_11759,U_11761)),hAPP(hAPP(c_Product__Type_OPair(U_11759,U_11761),U_11763),U_11765)),hAPP(hAPP(c_Product__Type_OPair(U_11759,U_11761),U_11767),U_11769))),c_Wellfounded_Olex__prod(U_11759,U_11761,U_11771,U_11773))) ),
inference(clausify,[status(thm)],[f_3093_3]) ).
cnf(f_3093_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11761,U_11761)),hAPP(hAPP(c_Product__Type_OPair(U_11761,U_11761),U_11765),U_11769)),U_11773))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_11759,U_11759)),hAPP(hAPP(c_Product__Type_OPair(U_11759,U_11759),U_11763),U_11767)),U_11771))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11759,U_11761),tc_prod(U_11759,U_11761))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11759,U_11761),tc_prod(U_11759,U_11761)),hAPP(hAPP(c_Product__Type_OPair(U_11759,U_11761),U_11763),U_11765)),hAPP(hAPP(c_Product__Type_OPair(U_11759,U_11761),U_11767),U_11769))),c_Wellfounded_Olex__prod(U_11759,U_11761,U_11771,U_11773))) ),
inference(clausify,[status(thm)],[f_3093_3]) ).
cnf(f_3093_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11760,U_11760)),hAPP(hAPP(c_Product__Type_OPair(U_11760,U_11760),U_11764),U_11768)),U_11772))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11760,U_11762),tc_prod(U_11760,U_11762))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11760,U_11762),tc_prod(U_11760,U_11762)),hAPP(hAPP(c_Product__Type_OPair(U_11760,U_11762),U_11764),U_11766)),hAPP(hAPP(c_Product__Type_OPair(U_11760,U_11762),U_11768),U_11770))),c_Wellfounded_Olex__prod(U_11760,U_11762,U_11772,U_11774))) ),
inference(clausify,[status(thm)],[f_3093_3]) ).
cnf(f_3093_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11762,U_11762)),hAPP(hAPP(c_Product__Type_OPair(U_11762,U_11762),U_11766),U_11770)),U_11774))
| U_11764 != U_11768
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11760,U_11762),tc_prod(U_11760,U_11762))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11760,U_11762),tc_prod(U_11760,U_11762)),hAPP(hAPP(c_Product__Type_OPair(U_11760,U_11762),U_11764),U_11766)),hAPP(hAPP(c_Product__Type_OPair(U_11760,U_11762),U_11768),U_11770))),c_Wellfounded_Olex__prod(U_11760,U_11762,U_11772,U_11774))) ),
inference(clausify,[status(thm)],[f_3093_3]) ).
fof(f_3094_1,plain,
! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_P_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2)))
| ~ hBOOL(hAPP(V_P_2,V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_same__fstI]) ).
fof(f_3094_2,plain,
! [U_11781,U_11780,U_11779,U_11778,U_11777,U_11776,U_11775] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11781,U_11777),tc_prod(U_11781,U_11777))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11781,U_11777),tc_prod(U_11781,U_11777)),hAPP(hAPP(c_Product__Type_OPair(U_11781,U_11777),U_11776),U_11778)),hAPP(hAPP(c_Product__Type_OPair(U_11781,U_11777),U_11776),U_11779))),c_Recdef_Osame__fst(U_11781,U_11777,U_11775,U_11780)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11777,U_11777)),hAPP(hAPP(c_Product__Type_OPair(U_11777,U_11777),U_11778),U_11779)),hAPP(U_11780,U_11776)))
| ~ hBOOL(hAPP(U_11775,U_11776)) ),
inference(variable_rename,[status(thm)],[f_3094_1]) ).
cnf(f_3094_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11781,U_11777),tc_prod(U_11781,U_11777))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11781,U_11777),tc_prod(U_11781,U_11777)),hAPP(hAPP(c_Product__Type_OPair(U_11781,U_11777),U_11776),U_11778)),hAPP(hAPP(c_Product__Type_OPair(U_11781,U_11777),U_11776),U_11779))),c_Recdef_Osame__fst(U_11781,U_11777,U_11775,U_11780)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11777,U_11777)),hAPP(hAPP(c_Product__Type_OPair(U_11777,U_11777),U_11778),U_11779)),hAPP(U_11780,U_11776)))
| ~ hBOOL(hAPP(U_11775,U_11776)) ),
inference(clausify,[status(thm)],[f_3094_2]) ).
fof(f_3095_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_3095_2,plain,
! [U_11784,U_11783,U_11782] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11782,tc_HOL_Obool),tc_fun(U_11782,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11782,tc_HOL_Obool),tc_fun(U_11782,tc_HOL_Obool)),U_11783),U_11784)),c_Wellfounded_Ofinite__psubset(U_11782)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11782),U_11784))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11782,tc_HOL_Obool)),U_11783),U_11784)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11782),U_11784))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11782,tc_HOL_Obool)),U_11783),U_11784)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11782,tc_HOL_Obool),tc_fun(U_11782,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11782,tc_HOL_Obool),tc_fun(U_11782,tc_HOL_Obool)),U_11783),U_11784)),c_Wellfounded_Ofinite__psubset(U_11782))) ) ),
inference(variable_rename,[status(thm)],[f_3095_1]) ).
fof(f_3095_3,plain,
( ! [U_11790,U_11788,U_11786] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11786,tc_HOL_Obool),tc_fun(U_11786,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11786,tc_HOL_Obool),tc_fun(U_11786,tc_HOL_Obool)),U_11788),U_11790)),c_Wellfounded_Ofinite__psubset(U_11786)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11786),U_11790))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11786,tc_HOL_Obool)),U_11788),U_11790)) )
& ! [U_11789,U_11787,U_11785] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11785),U_11789))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11785,tc_HOL_Obool)),U_11787),U_11789)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11785,tc_HOL_Obool),tc_fun(U_11785,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11785,tc_HOL_Obool),tc_fun(U_11785,tc_HOL_Obool)),U_11787),U_11789)),c_Wellfounded_Ofinite__psubset(U_11785))) ) ),
inference(miniscope,[status(thm)],[f_3095_2]) ).
cnf(f_3095_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11785,tc_HOL_Obool)),U_11787),U_11789))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11785,tc_HOL_Obool),tc_fun(U_11785,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11785,tc_HOL_Obool),tc_fun(U_11785,tc_HOL_Obool)),U_11787),U_11789)),c_Wellfounded_Ofinite__psubset(U_11785))) ),
inference(clausify,[status(thm)],[f_3095_3]) ).
cnf(f_3095_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11785),U_11789))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11785,tc_HOL_Obool),tc_fun(U_11785,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11785,tc_HOL_Obool),tc_fun(U_11785,tc_HOL_Obool)),U_11787),U_11789)),c_Wellfounded_Ofinite__psubset(U_11785))) ),
inference(clausify,[status(thm)],[f_3095_3]) ).
cnf(f_3095_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11786,tc_HOL_Obool),tc_fun(U_11786,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11786,tc_HOL_Obool),tc_fun(U_11786,tc_HOL_Obool)),U_11788),U_11790)),c_Wellfounded_Ofinite__psubset(U_11786)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11786),U_11790))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11786,tc_HOL_Obool)),U_11788),U_11790)) ),
inference(clausify,[status(thm)],[f_3095_3]) ).
fof(f_3096_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_3096_2,plain,
! [U_11796,U_11795,U_11794,U_11793,U_11792,U_11791] :
( hAPP(U_11794,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11791,tc_HOL_Obool)),U_11795),U_11796)) = hAPP(c_Fun_Ocomp(U_11792,U_11792,U_11792,hAPP(U_11794,U_11795)),hAPP(U_11794,U_11796))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11791),U_11796))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11791),U_11795))
| ~ c_Finite__Set_Ofolding__idem(U_11791,U_11792,U_11793,U_11794) ),
inference(variable_rename,[status(thm)],[f_3096_1]) ).
cnf(f_3096_3,plain,
( hAPP(U_11794,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11791,tc_HOL_Obool)),U_11795),U_11796)) = hAPP(c_Fun_Ocomp(U_11792,U_11792,U_11792,hAPP(U_11794,U_11795)),hAPP(U_11794,U_11796))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11791),U_11796))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11791),U_11795))
| ~ c_Finite__Set_Ofolding__idem(U_11791,U_11792,U_11793,U_11794) ),
inference(clausify,[status(thm)],[f_3096_2]) ).
fof(f_3097_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_3097_2,plain,
! [U_11803,U_11802,U_11801,U_11800,U_11799,U_11798,U_11797] :
( hAPP(c_Fun_Ocomp(U_11798,U_11798,U_11801,hAPP(U_11799,U_11802)),hAPP(c_Fun_Ocomp(U_11798,U_11798,U_11801,hAPP(U_11799,U_11802)),U_11803)) = hAPP(c_Fun_Ocomp(U_11798,U_11798,U_11801,hAPP(U_11799,U_11802)),U_11803)
| ~ c_Finite__Set_Ofolding__idem(U_11797,U_11798,U_11799,U_11800) ),
inference(variable_rename,[status(thm)],[f_3097_1]) ).
fof(f_3097_3,plain,
! [U_11803,U_11802,U_11801,U_11800,U_11799,U_11798] :
( ! [U_11797] : ~ c_Finite__Set_Ofolding__idem(U_11797,U_11798,U_11799,U_11800)
| hAPP(c_Fun_Ocomp(U_11798,U_11798,U_11801,hAPP(U_11799,U_11802)),hAPP(c_Fun_Ocomp(U_11798,U_11798,U_11801,hAPP(U_11799,U_11802)),U_11803)) = hAPP(c_Fun_Ocomp(U_11798,U_11798,U_11801,hAPP(U_11799,U_11802)),U_11803) ),
inference(miniscope,[status(thm)],[f_3097_2]) ).
cnf(f_3097_4,plain,
( ~ c_Finite__Set_Ofolding__idem(U_11797,U_11798,U_11799,U_11800)
| hAPP(c_Fun_Ocomp(U_11798,U_11798,U_11801,hAPP(U_11799,U_11802)),hAPP(c_Fun_Ocomp(U_11798,U_11798,U_11801,hAPP(U_11799,U_11802)),U_11803)) = hAPP(c_Fun_Ocomp(U_11798,U_11798,U_11801,hAPP(U_11799,U_11802)),U_11803) ),
inference(clausify,[status(thm)],[f_3097_3]) ).
fof(f_3098_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_3098_2,plain,
! [U_11808,U_11807,U_11806,U_11805,U_11804] :
( hAPP(c_Fun_Ocomp(U_11805,U_11805,U_11805,hAPP(U_11806,U_11808)),hAPP(U_11806,U_11808)) = hAPP(U_11806,U_11808)
| ~ c_Finite__Set_Ofolding__idem(U_11804,U_11805,U_11806,U_11807) ),
inference(variable_rename,[status(thm)],[f_3098_1]) ).
fof(f_3098_3,plain,
! [U_11808,U_11807,U_11806,U_11805] :
( ! [U_11804] : ~ c_Finite__Set_Ofolding__idem(U_11804,U_11805,U_11806,U_11807)
| hAPP(c_Fun_Ocomp(U_11805,U_11805,U_11805,hAPP(U_11806,U_11808)),hAPP(U_11806,U_11808)) = hAPP(U_11806,U_11808) ),
inference(miniscope,[status(thm)],[f_3098_2]) ).
cnf(f_3098_4,plain,
( ~ c_Finite__Set_Ofolding__idem(U_11804,U_11805,U_11806,U_11807)
| hAPP(c_Fun_Ocomp(U_11805,U_11805,U_11805,hAPP(U_11806,U_11808)),hAPP(U_11806,U_11808)) = hAPP(U_11806,U_11808) ),
inference(clausify,[status(thm)],[f_3098_3]) ).
fof(f_3099_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_3099_2,plain,
! [U_11814,U_11813,U_11812,U_11811,U_11810,U_11809] :
( hAPP(c_Fun_Ocomp(U_11810,U_11810,U_11810,hAPP(U_11812,U_11813)),hAPP(U_11811,U_11814)) = hAPP(U_11812,U_11813)
| ~ hBOOL(hAPP(hAPP(c_member(U_11809),U_11814),U_11813))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11809),U_11813))
| ~ c_Finite__Set_Ofolding__idem(U_11809,U_11810,U_11811,U_11812) ),
inference(variable_rename,[status(thm)],[f_3099_1]) ).
cnf(f_3099_3,plain,
( hAPP(c_Fun_Ocomp(U_11810,U_11810,U_11810,hAPP(U_11812,U_11813)),hAPP(U_11811,U_11814)) = hAPP(U_11812,U_11813)
| ~ hBOOL(hAPP(hAPP(c_member(U_11809),U_11814),U_11813))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11809),U_11813))
| ~ c_Finite__Set_Ofolding__idem(U_11809,U_11810,U_11811,U_11812) ),
inference(clausify,[status(thm)],[f_3099_2]) ).
fof(f_3100_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_3100_2,plain,
! [U_11820,U_11819,U_11818,U_11817,U_11816,U_11815] :
( hAPP(U_11818,hAPP(hAPP(c_Set_Oinsert(U_11815),U_11820),U_11819)) = hAPP(c_Fun_Ocomp(U_11816,U_11816,U_11816,hAPP(U_11818,U_11819)),hAPP(U_11817,U_11820))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11815),U_11819))
| ~ c_Finite__Set_Ofolding__idem(U_11815,U_11816,U_11817,U_11818) ),
inference(variable_rename,[status(thm)],[f_3100_1]) ).
cnf(f_3100_3,plain,
( hAPP(U_11818,hAPP(hAPP(c_Set_Oinsert(U_11815),U_11820),U_11819)) = hAPP(c_Fun_Ocomp(U_11816,U_11816,U_11816,hAPP(U_11818,U_11819)),hAPP(U_11817,U_11820))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11815),U_11819))
| ~ c_Finite__Set_Ofolding__idem(U_11815,U_11816,U_11817,U_11818) ),
inference(clausify,[status(thm)],[f_3100_2]) ).
fof(f_3101_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_3101_2,plain,
! [U_11826,U_11825,U_11824,U_11823,U_11822,U_11821] :
( hAPP(c_Fun_Ocomp(U_11822,U_11822,U_11822,hAPP(U_11824,U_11825)),hAPP(U_11824,U_11826)) = hAPP(U_11824,U_11825)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11821,tc_HOL_Obool)),U_11826),U_11825))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11821),U_11825))
| ~ c_Finite__Set_Ofolding__idem(U_11821,U_11822,U_11823,U_11824) ),
inference(variable_rename,[status(thm)],[f_3101_1]) ).
cnf(f_3101_3,plain,
( hAPP(c_Fun_Ocomp(U_11822,U_11822,U_11822,hAPP(U_11824,U_11825)),hAPP(U_11824,U_11826)) = hAPP(U_11824,U_11825)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11821,tc_HOL_Obool)),U_11826),U_11825))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11821),U_11825))
| ~ c_Finite__Set_Ofolding__idem(U_11821,U_11822,U_11823,U_11824) ),
inference(clausify,[status(thm)],[f_3101_2]) ).
fof(f_3102_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_3102_2,plain,
! [U_11833,U_11832,U_11831,U_11830,U_11829,U_11828] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11828),hAPP(U_11831,U_11833)),U_11832))
| ~ hBOOL(hAPP(hAPP(c_member(U_11829),U_11833),U_11830))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11829,U_11828),U_11831),U_11830) != U_11832
| ? [U_11827] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11828),c_Groups_Ozero__class_Ozero(U_11828)),hAPP(U_11831,U_11827)))
& hBOOL(hAPP(hAPP(c_member(U_11829),U_11827),U_11830)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11829),U_11830))
| ~ class_Groups_Oordered__ab__group__add(U_11828) ),
inference(variable_rename,[status(thm)],[f_3102_1]) ).
fof(f_3102_3,plain,
! [U_11833,U_11832,U_11831,U_11830,U_11829,U_11828] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11828),hAPP(U_11831,U_11833)),U_11832))
| ~ hBOOL(hAPP(hAPP(c_member(U_11829),U_11833),U_11830))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11829,U_11828),U_11831),U_11830) != U_11832
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11828),c_Groups_Ozero__class_Ozero(U_11828)),hAPP(U_11831,sK276(U_11833,U_11832,U_11831,U_11830,U_11829,U_11828))))
& hBOOL(hAPP(hAPP(c_member(U_11829),sK276(U_11833,U_11832,U_11831,U_11830,U_11829,U_11828)),U_11830)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11829),U_11830))
| ~ class_Groups_Oordered__ab__group__add(U_11828) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK276]),skolemize(U_11827,sK276(U_11833,U_11832,U_11831,U_11830,U_11829,U_11828))],[f_3102_2]) ).
cnf(f_3102_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11829),sK276(U_11833,U_11832,U_11831,U_11830,U_11829,U_11828)),U_11830))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11828),hAPP(U_11831,U_11833)),U_11832))
| ~ hBOOL(hAPP(hAPP(c_member(U_11829),U_11833),U_11830))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11829,U_11828),U_11831),U_11830) != U_11832
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11829),U_11830))
| ~ class_Groups_Oordered__ab__group__add(U_11828) ),
inference(clausify,[status(thm)],[f_3102_3]) ).
cnf(f_3102_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11828),c_Groups_Ozero__class_Ozero(U_11828)),hAPP(U_11831,sK276(U_11833,U_11832,U_11831,U_11830,U_11829,U_11828))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11828),hAPP(U_11831,U_11833)),U_11832))
| ~ hBOOL(hAPP(hAPP(c_member(U_11829),U_11833),U_11830))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11829,U_11828),U_11831),U_11830) != U_11832
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11829),U_11830))
| ~ class_Groups_Oordered__ab__group__add(U_11828) ),
inference(clausify,[status(thm)],[f_3102_3]) ).
fof(f_3103_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_3103_2,plain,
! [U_11839,U_11838,U_11837,U_11836,U_11835] :
( hAPP(U_11838,U_11839) = c_Groups_Ozero__class_Ozero(U_11835)
| ~ hBOOL(hAPP(hAPP(c_member(U_11836),U_11839),U_11837))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11836,U_11835),U_11838),U_11837) != c_Groups_Ozero__class_Ozero(U_11835)
| ? [U_11834] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11835),c_Groups_Ozero__class_Ozero(U_11835)),hAPP(U_11838,U_11834)))
& hBOOL(hAPP(hAPP(c_member(U_11836),U_11834),U_11837)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11836),U_11837))
| ~ class_Groups_Oordered__ab__group__add(U_11835) ),
inference(variable_rename,[status(thm)],[f_3103_1]) ).
fof(f_3103_3,plain,
! [U_11839,U_11838,U_11837,U_11836,U_11835] :
( hAPP(U_11838,U_11839) = c_Groups_Ozero__class_Ozero(U_11835)
| ~ hBOOL(hAPP(hAPP(c_member(U_11836),U_11839),U_11837))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11836,U_11835),U_11838),U_11837) != c_Groups_Ozero__class_Ozero(U_11835)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11835),c_Groups_Ozero__class_Ozero(U_11835)),hAPP(U_11838,sK277(U_11839,U_11838,U_11837,U_11836,U_11835))))
& hBOOL(hAPP(hAPP(c_member(U_11836),sK277(U_11839,U_11838,U_11837,U_11836,U_11835)),U_11837)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11836),U_11837))
| ~ class_Groups_Oordered__ab__group__add(U_11835) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK277]),skolemize(U_11834,sK277(U_11839,U_11838,U_11837,U_11836,U_11835))],[f_3103_2]) ).
cnf(f_3103_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11836),sK277(U_11839,U_11838,U_11837,U_11836,U_11835)),U_11837))
| hAPP(U_11838,U_11839) = c_Groups_Ozero__class_Ozero(U_11835)
| ~ hBOOL(hAPP(hAPP(c_member(U_11836),U_11839),U_11837))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11836,U_11835),U_11838),U_11837) != c_Groups_Ozero__class_Ozero(U_11835)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11836),U_11837))
| ~ class_Groups_Oordered__ab__group__add(U_11835) ),
inference(clausify,[status(thm)],[f_3103_3]) ).
cnf(f_3103_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11835),c_Groups_Ozero__class_Ozero(U_11835)),hAPP(U_11838,sK277(U_11839,U_11838,U_11837,U_11836,U_11835))))
| hAPP(U_11838,U_11839) = c_Groups_Ozero__class_Ozero(U_11835)
| ~ hBOOL(hAPP(hAPP(c_member(U_11836),U_11839),U_11837))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11836,U_11835),U_11838),U_11837) != c_Groups_Ozero__class_Ozero(U_11835)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11836),U_11837))
| ~ class_Groups_Oordered__ab__group__add(U_11835) ),
inference(clausify,[status(thm)],[f_3103_3]) ).
fof(f_3104_1,plain,
! [V_n_2,V_P_2,V_Q_2] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_P_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Q_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_P_2)),V_Q_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))
| ? [B_x] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Q_2,B_x)),hAPP(V_P_2,B_x))) ),
inference(fof_nnf,[status(thm)],[fact_sum__diff__distrib]) ).
fof(f_3104_2,plain,
! [U_11843,U_11842,U_11841] :
( 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_11842),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11843))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_11841),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11843))) = 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_11842)),U_11841)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11843))
| ? [U_11840] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_11841,U_11840)),hAPP(U_11842,U_11840))) ),
inference(variable_rename,[status(thm)],[f_3104_1]) ).
fof(f_3104_3,plain,
! [U_11843,U_11842,U_11841] :
( 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_11842),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11843))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_11841),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11843))) = 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_11842)),U_11841)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11843))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_11841,sK278(U_11843,U_11842,U_11841))),hAPP(U_11842,sK278(U_11843,U_11842,U_11841)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK278]),skolemize(U_11840,sK278(U_11843,U_11842,U_11841))],[f_3104_2]) ).
cnf(f_3104_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_11842),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11843))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_11841),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11843))) = 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_11842)),U_11841)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11843))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_11841,sK278(U_11843,U_11842,U_11841))),hAPP(U_11842,sK278(U_11843,U_11842,U_11841)))) ),
inference(clausify,[status(thm)],[f_3104_3]) ).
fof(f_3105_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_3105_2,plain,
! [U_11850,U_11849,U_11848,U_11847,U_11846,U_11845,U_11844] : hAPP(c_Product__Type_Oapsnd(U_11844,U_11845,U_11846,U_11847),hAPP(c_Product__Type_Oapfst(U_11848,U_11846,U_11844,U_11849),U_11850)) = hAPP(hAPP(c_Product__Type_OPair(U_11846,U_11845),hAPP(U_11849,hAPP(c_Product__Type_Ofst(U_11848,U_11844),U_11850))),hAPP(U_11847,hAPP(c_Product__Type_Osnd(U_11848,U_11844),U_11850))),
inference(variable_rename,[status(thm)],[f_3105_1]) ).
cnf(f_3105_3,plain,
hAPP(c_Product__Type_Oapsnd(U_11844,U_11845,U_11846,U_11847),hAPP(c_Product__Type_Oapfst(U_11848,U_11846,U_11844,U_11849),U_11850)) = hAPP(hAPP(c_Product__Type_OPair(U_11846,U_11845),hAPP(U_11849,hAPP(c_Product__Type_Ofst(U_11848,U_11844),U_11850))),hAPP(U_11847,hAPP(c_Product__Type_Osnd(U_11848,U_11844),U_11850))),
inference(clausify,[status(thm)],[f_3105_2]) ).
fof(f_3106_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_3106_2,plain,
! [U_11857,U_11856,U_11855,U_11854,U_11853,U_11852,U_11851] : hAPP(c_Product__Type_Oapfst(U_11851,U_11852,U_11853,U_11854),hAPP(c_Product__Type_Oapsnd(U_11855,U_11853,U_11851,U_11856),U_11857)) = hAPP(hAPP(c_Product__Type_OPair(U_11852,U_11853),hAPP(U_11854,hAPP(c_Product__Type_Ofst(U_11851,U_11855),U_11857))),hAPP(U_11856,hAPP(c_Product__Type_Osnd(U_11851,U_11855),U_11857))),
inference(variable_rename,[status(thm)],[f_3106_1]) ).
cnf(f_3106_3,plain,
hAPP(c_Product__Type_Oapfst(U_11851,U_11852,U_11853,U_11854),hAPP(c_Product__Type_Oapsnd(U_11855,U_11853,U_11851,U_11856),U_11857)) = hAPP(hAPP(c_Product__Type_OPair(U_11852,U_11853),hAPP(U_11854,hAPP(c_Product__Type_Ofst(U_11851,U_11855),U_11857))),hAPP(U_11856,hAPP(c_Product__Type_Osnd(U_11851,U_11855),U_11857))),
inference(clausify,[status(thm)],[f_3106_2]) ).
fof(f_3107_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_3107_2,plain,
! [U_11861,U_11860,U_11859,U_11858] :
( 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_11858),U_11860)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11859),U_11861))),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11860),U_11861))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11858),U_11859)) ),
inference(variable_rename,[status(thm)],[f_3107_1]) ).
cnf(f_3107_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_11858),U_11860)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11859),U_11861))),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11860),U_11861))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11858),U_11859)) ),
inference(clausify,[status(thm)],[f_3107_2]) ).
fof(f_3108_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_3108_2,plain,
! [U_11868,U_11867,U_11866,U_11865,U_11864,U_11863,U_11862] : hAPP(c_Product__Type_Oapfst(U_11862,U_11863,U_11864,U_11865),hAPP(c_Product__Type_Oapfst(U_11866,U_11862,U_11864,U_11867),U_11868)) = hAPP(c_Product__Type_Oapfst(U_11866,U_11863,U_11864,hAPP(c_Fun_Ocomp(U_11862,U_11863,U_11866,U_11865),U_11867)),U_11868),
inference(variable_rename,[status(thm)],[f_3108_1]) ).
cnf(f_3108_3,plain,
hAPP(c_Product__Type_Oapfst(U_11862,U_11863,U_11864,U_11865),hAPP(c_Product__Type_Oapfst(U_11866,U_11862,U_11864,U_11867),U_11868)) = hAPP(c_Product__Type_Oapfst(U_11866,U_11863,U_11864,hAPP(c_Fun_Ocomp(U_11862,U_11863,U_11866,U_11865),U_11867)),U_11868),
inference(clausify,[status(thm)],[f_3108_2]) ).
fof(f_3109_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_3109_2,plain,
! [U_11873,U_11872,U_11871,U_11870,U_11869] : hAPP(c_Product__Type_Osnd(U_11869,U_11870),hAPP(c_Product__Type_Oapfst(U_11871,U_11869,U_11870,U_11872),U_11873)) = hAPP(c_Product__Type_Osnd(U_11871,U_11870),U_11873),
inference(variable_rename,[status(thm)],[f_3109_1]) ).
cnf(f_3109_3,plain,
hAPP(c_Product__Type_Osnd(U_11869,U_11870),hAPP(c_Product__Type_Oapfst(U_11871,U_11869,U_11870,U_11872),U_11873)) = hAPP(c_Product__Type_Osnd(U_11871,U_11870),U_11873),
inference(clausify,[status(thm)],[f_3109_2]) ).
fof(f_3110_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_3110_2,plain,
! [U_11879,U_11878,U_11877,U_11876,U_11875,U_11874] :
( ( hAPP(c_Product__Type_Oapfst(U_11874,U_11875,U_11876,U_11877),U_11878) = hAPP(c_Product__Type_Oapfst(U_11874,U_11875,U_11876,U_11879),U_11878)
| hAPP(U_11877,hAPP(c_Product__Type_Ofst(U_11874,U_11876),U_11878)) != hAPP(U_11879,hAPP(c_Product__Type_Ofst(U_11874,U_11876),U_11878)) )
& ( hAPP(U_11877,hAPP(c_Product__Type_Ofst(U_11874,U_11876),U_11878)) = hAPP(U_11879,hAPP(c_Product__Type_Ofst(U_11874,U_11876),U_11878))
| hAPP(c_Product__Type_Oapfst(U_11874,U_11875,U_11876,U_11877),U_11878) != hAPP(c_Product__Type_Oapfst(U_11874,U_11875,U_11876,U_11879),U_11878) ) ),
inference(variable_rename,[status(thm)],[f_3110_1]) ).
fof(f_3110_3,plain,
( ! [U_11891,U_11889,U_11887,U_11885,U_11883,U_11881] :
( hAPP(c_Product__Type_Oapfst(U_11881,U_11883,U_11885,U_11887),U_11889) = hAPP(c_Product__Type_Oapfst(U_11881,U_11883,U_11885,U_11891),U_11889)
| hAPP(U_11887,hAPP(c_Product__Type_Ofst(U_11881,U_11885),U_11889)) != hAPP(U_11891,hAPP(c_Product__Type_Ofst(U_11881,U_11885),U_11889)) )
& ! [U_11890,U_11888,U_11886,U_11884,U_11882,U_11880] :
( hAPP(U_11886,hAPP(c_Product__Type_Ofst(U_11880,U_11884),U_11888)) = hAPP(U_11890,hAPP(c_Product__Type_Ofst(U_11880,U_11884),U_11888))
| hAPP(c_Product__Type_Oapfst(U_11880,U_11882,U_11884,U_11886),U_11888) != hAPP(c_Product__Type_Oapfst(U_11880,U_11882,U_11884,U_11890),U_11888) ) ),
inference(miniscope,[status(thm)],[f_3110_2]) ).
cnf(f_3110_4,plain,
( hAPP(U_11886,hAPP(c_Product__Type_Ofst(U_11880,U_11884),U_11888)) = hAPP(U_11890,hAPP(c_Product__Type_Ofst(U_11880,U_11884),U_11888))
| hAPP(c_Product__Type_Oapfst(U_11880,U_11882,U_11884,U_11886),U_11888) != hAPP(c_Product__Type_Oapfst(U_11880,U_11882,U_11884,U_11890),U_11888) ),
inference(clausify,[status(thm)],[f_3110_3]) ).
cnf(f_3110_5,plain,
( hAPP(c_Product__Type_Oapfst(U_11881,U_11883,U_11885,U_11887),U_11889) = hAPP(c_Product__Type_Oapfst(U_11881,U_11883,U_11885,U_11891),U_11889)
| hAPP(U_11887,hAPP(c_Product__Type_Ofst(U_11881,U_11885),U_11889)) != hAPP(U_11891,hAPP(c_Product__Type_Ofst(U_11881,U_11885),U_11889)) ),
inference(clausify,[status(thm)],[f_3110_3]) ).
fof(f_3111_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_3111_2,plain,
! [U_11896,U_11895,U_11894,U_11893,U_11892] : hAPP(c_Product__Type_Ofst(U_11892,U_11893),hAPP(c_Product__Type_Oapfst(U_11894,U_11892,U_11893,U_11895),U_11896)) = hAPP(U_11895,hAPP(c_Product__Type_Ofst(U_11894,U_11893),U_11896)),
inference(variable_rename,[status(thm)],[f_3111_1]) ).
cnf(f_3111_3,plain,
hAPP(c_Product__Type_Ofst(U_11892,U_11893),hAPP(c_Product__Type_Oapfst(U_11894,U_11892,U_11893,U_11895),U_11896)) = hAPP(U_11895,hAPP(c_Product__Type_Ofst(U_11894,U_11893),U_11896)),
inference(clausify,[status(thm)],[f_3111_2]) ).
fof(f_3112_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_3112_2,plain,
! [U_11902,U_11901,U_11900,U_11899,U_11898,U_11897] : hAPP(c_Product__Type_Oapfst(U_11897,U_11898,U_11899,U_11900),hAPP(hAPP(c_Product__Type_OPair(U_11897,U_11899),U_11901),U_11902)) = hAPP(hAPP(c_Product__Type_OPair(U_11898,U_11899),hAPP(U_11900,U_11901)),U_11902),
inference(variable_rename,[status(thm)],[f_3112_1]) ).
cnf(f_3112_3,plain,
hAPP(c_Product__Type_Oapfst(U_11897,U_11898,U_11899,U_11900),hAPP(hAPP(c_Product__Type_OPair(U_11897,U_11899),U_11901),U_11902)) = hAPP(hAPP(c_Product__Type_OPair(U_11898,U_11899),hAPP(U_11900,U_11901)),U_11902),
inference(clausify,[status(thm)],[f_3112_2]) ).
fof(f_3113_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_3113_2,plain,
! [U_11909,U_11908,U_11907,U_11906,U_11905,U_11904,U_11903] : hAPP(c_Product__Type_Oapsnd(U_11903,U_11904,U_11905,U_11906),hAPP(c_Product__Type_Oapfst(U_11907,U_11905,U_11903,U_11908),U_11909)) = hAPP(c_Product__Type_Oapfst(U_11907,U_11905,U_11904,U_11908),hAPP(c_Product__Type_Oapsnd(U_11903,U_11904,U_11907,U_11906),U_11909)),
inference(variable_rename,[status(thm)],[f_3113_1]) ).
cnf(f_3113_3,plain,
hAPP(c_Product__Type_Oapsnd(U_11903,U_11904,U_11905,U_11906),hAPP(c_Product__Type_Oapfst(U_11907,U_11905,U_11903,U_11908),U_11909)) = hAPP(c_Product__Type_Oapfst(U_11907,U_11905,U_11904,U_11908),hAPP(c_Product__Type_Oapsnd(U_11903,U_11904,U_11907,U_11906),U_11909)),
inference(clausify,[status(thm)],[f_3113_2]) ).
fof(f_3114_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_3114_2,plain,
! [U_11913,U_11912,U_11911,U_11910] :
( 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_11910),U_11912)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11911),U_11913))),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11910),U_11911)) ),
inference(variable_rename,[status(thm)],[f_3114_1]) ).
cnf(f_3114_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_11910),U_11912)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11911),U_11913))),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11910),U_11911)) ),
inference(clausify,[status(thm)],[f_3114_2]) ).
fof(f_3115_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_3115_2,plain,
! [U_11917,U_11916,U_11915,U_11914] :
( 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_11914),U_11916)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11915),U_11917))),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11916),U_11917))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11914),U_11915)) ),
inference(variable_rename,[status(thm)],[f_3115_1]) ).
cnf(f_3115_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_11914),U_11916)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11915),U_11917))),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11916),U_11917))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11914),U_11915)) ),
inference(clausify,[status(thm)],[f_3115_2]) ).
fof(f_3116_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_3116_2,plain,
! [U_11921,U_11920,U_11919,U_11918] :
( 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_11919),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11920),U_11921))),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_11919),U_11921)),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_11918),U_11920)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11918),U_11919)) ),
inference(variable_rename,[status(thm)],[f_3116_1]) ).
cnf(f_3116_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_11919),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11920),U_11921))),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_11919),U_11921)),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_11918),U_11920)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11918),U_11919)) ),
inference(clausify,[status(thm)],[f_3116_2]) ).
fof(f_3117_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_3117_2,plain,
! [U_11925,U_11924,U_11923,U_11922] :
( 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_11924),U_11925)),U_11923)),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_11925),U_11923)),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_11924),U_11922)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11922),U_11923)) ),
inference(variable_rename,[status(thm)],[f_3117_1]) ).
cnf(f_3117_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_11924),U_11925)),U_11923)),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_11925),U_11923)),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_11924),U_11922)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11922),U_11923)) ),
inference(clausify,[status(thm)],[f_3117_2]) ).
fof(f_3118_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_3118_2,plain,
! [U_11926] :
( 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_11926)),c_FunDef_Omax__strict))
| U_11926 = 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_11926)) ),
inference(variable_rename,[status(thm)],[f_3118_1]) ).
cnf(f_3118_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_11926)),c_FunDef_Omax__strict))
| U_11926 = 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_11926)) ),
inference(clausify,[status(thm)],[f_3118_2]) ).
fof(f_3119_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_3119_2,plain,
! [U_11927] :
( 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_11927),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
| U_11927 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_3119_1]) ).
cnf(f_3119_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_11927),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
| U_11927 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3119_2]) ).
fof(f_3120_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_3120_2,plain,
! [U_11931,U_11930,U_11929,U_11928] :
( 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_11928),U_11930)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11929),U_11931))),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11928),U_11929)) ),
inference(variable_rename,[status(thm)],[f_3120_1]) ).
cnf(f_3120_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_11928),U_11930)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11929),U_11931))),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11928),U_11929)) ),
inference(clausify,[status(thm)],[f_3120_2]) ).
fof(f_3121_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_3121_2,plain,
! [U_11935,U_11934,U_11933,U_11932] :
( 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_11934),U_11935)),U_11933)),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_11935),U_11933)),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_11934),U_11932)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11932),U_11933)) ),
inference(variable_rename,[status(thm)],[f_3121_1]) ).
cnf(f_3121_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_11934),U_11935)),U_11933)),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_11935),U_11933)),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_11934),U_11932)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11932),U_11933)) ),
inference(clausify,[status(thm)],[f_3121_2]) ).
fof(f_3122_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_3122_2,plain,
! [U_11939,U_11938,U_11937,U_11936] :
( 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_11937),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11938),U_11939))),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_11937),U_11939)),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_11936),U_11938)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11936),U_11937)) ),
inference(variable_rename,[status(thm)],[f_3122_1]) ).
cnf(f_3122_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_11937),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11938),U_11939))),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_11937),U_11939)),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_11936),U_11938)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11936),U_11937)) ),
inference(clausify,[status(thm)],[f_3122_2]) ).
fof(f_3123_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_3123_2,plain,
! [U_11940] :
( 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_11940)),c_FunDef_Omax__weak))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11940)) ),
inference(variable_rename,[status(thm)],[f_3123_1]) ).
cnf(f_3123_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_11940)),c_FunDef_Omax__weak))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11940)) ),
inference(clausify,[status(thm)],[f_3123_2]) ).
fof(f_3124_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_3124_2,plain,
! [U_11941] : 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_11941),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_3124_1]) ).
cnf(f_3124_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_11941),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_3124_2]) ).
fof(f_3125_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_3125_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_3125_1]) ).
fof(f_3126_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_3126_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_3126_1]) ).
fof(f_3127_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_3127_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_3127_1]) ).
fof(f_3128_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_3128_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_3128_1]) ).
fof(f_3129_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_3129_2,plain,
! [U_11947,U_11946,U_11945,U_11944,U_11943,U_11942] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11942,tc_HOL_Obool),tc_fun(U_11942,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11942,tc_HOL_Obool),tc_fun(U_11942,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11942,tc_HOL_Obool)),U_11943),U_11946)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11942,tc_HOL_Obool)),U_11944),U_11947))),c_Wellfounded_Omax__ext(U_11942,U_11945)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11942,tc_HOL_Obool),tc_fun(U_11942,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11942,tc_HOL_Obool),tc_fun(U_11942,tc_HOL_Obool)),U_11946),U_11947)),c_Wellfounded_Omax__ext(U_11942,U_11945)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11942,tc_HOL_Obool),tc_fun(U_11942,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11942,tc_HOL_Obool),tc_fun(U_11942,tc_HOL_Obool)),U_11943),U_11944)),c_Wellfounded_Omax__ext(U_11942,U_11945))) ),
inference(variable_rename,[status(thm)],[f_3129_1]) ).
cnf(f_3129_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11942,tc_HOL_Obool),tc_fun(U_11942,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11942,tc_HOL_Obool),tc_fun(U_11942,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11942,tc_HOL_Obool)),U_11943),U_11946)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11942,tc_HOL_Obool)),U_11944),U_11947))),c_Wellfounded_Omax__ext(U_11942,U_11945)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11942,tc_HOL_Obool),tc_fun(U_11942,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11942,tc_HOL_Obool),tc_fun(U_11942,tc_HOL_Obool)),U_11946),U_11947)),c_Wellfounded_Omax__ext(U_11942,U_11945)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11942,tc_HOL_Obool),tc_fun(U_11942,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11942,tc_HOL_Obool),tc_fun(U_11942,tc_HOL_Obool)),U_11943),U_11944)),c_Wellfounded_Omax__ext(U_11942,U_11945))) ),
inference(clausify,[status(thm)],[f_3129_2]) ).
fof(f_3130_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_3130_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_3130_1]) ).
fof(f_3131_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_3131_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_3131_1]) ).
fof(f_3132_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_3132_2,plain,
! [U_11951,U_11950,U_11949,U_11948] :
( ( c_Wellfounded_Omax__extp(U_11948,hAPP(hAPP(c_COMBC(U_11948,tc_fun(tc_prod(U_11948,U_11948),tc_HOL_Obool),tc_fun(U_11948,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11948,tc_fun(tc_fun(tc_prod(U_11948,U_11948),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11948,U_11948),tc_HOL_Obool),tc_fun(U_11948,tc_HOL_Obool)),U_11948),c_COMBC(U_11948,tc_fun(tc_prod(U_11948,U_11948),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11948,tc_prod(U_11948,U_11948)),tc_fun(U_11948,tc_fun(tc_fun(tc_prod(U_11948,U_11948),tc_HOL_Obool),tc_HOL_Obool)),U_11948),hAPP(c_COMBB(tc_prod(U_11948,U_11948),tc_fun(tc_fun(tc_prod(U_11948,U_11948),tc_HOL_Obool),tc_HOL_Obool),U_11948),c_member(tc_prod(U_11948,U_11948)))),c_Product__Type_OPair(U_11948,U_11948)))),U_11949),U_11950,U_11951)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11948,tc_HOL_Obool),tc_fun(U_11948,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11948,tc_HOL_Obool),tc_fun(U_11948,tc_HOL_Obool)),U_11950),U_11951)),c_Wellfounded_Omax__ext(U_11948,U_11949))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11948,tc_HOL_Obool),tc_fun(U_11948,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11948,tc_HOL_Obool),tc_fun(U_11948,tc_HOL_Obool)),U_11950),U_11951)),c_Wellfounded_Omax__ext(U_11948,U_11949)))
| ~ c_Wellfounded_Omax__extp(U_11948,hAPP(hAPP(c_COMBC(U_11948,tc_fun(tc_prod(U_11948,U_11948),tc_HOL_Obool),tc_fun(U_11948,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11948,tc_fun(tc_fun(tc_prod(U_11948,U_11948),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11948,U_11948),tc_HOL_Obool),tc_fun(U_11948,tc_HOL_Obool)),U_11948),c_COMBC(U_11948,tc_fun(tc_prod(U_11948,U_11948),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11948,tc_prod(U_11948,U_11948)),tc_fun(U_11948,tc_fun(tc_fun(tc_prod(U_11948,U_11948),tc_HOL_Obool),tc_HOL_Obool)),U_11948),hAPP(c_COMBB(tc_prod(U_11948,U_11948),tc_fun(tc_fun(tc_prod(U_11948,U_11948),tc_HOL_Obool),tc_HOL_Obool),U_11948),c_member(tc_prod(U_11948,U_11948)))),c_Product__Type_OPair(U_11948,U_11948)))),U_11949),U_11950,U_11951) ) ),
inference(variable_rename,[status(thm)],[f_3132_1]) ).
fof(f_3132_3,plain,
( ! [U_11959,U_11957,U_11955,U_11953] :
( c_Wellfounded_Omax__extp(U_11953,hAPP(hAPP(c_COMBC(U_11953,tc_fun(tc_prod(U_11953,U_11953),tc_HOL_Obool),tc_fun(U_11953,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11953,tc_fun(tc_fun(tc_prod(U_11953,U_11953),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11953,U_11953),tc_HOL_Obool),tc_fun(U_11953,tc_HOL_Obool)),U_11953),c_COMBC(U_11953,tc_fun(tc_prod(U_11953,U_11953),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11953,tc_prod(U_11953,U_11953)),tc_fun(U_11953,tc_fun(tc_fun(tc_prod(U_11953,U_11953),tc_HOL_Obool),tc_HOL_Obool)),U_11953),hAPP(c_COMBB(tc_prod(U_11953,U_11953),tc_fun(tc_fun(tc_prod(U_11953,U_11953),tc_HOL_Obool),tc_HOL_Obool),U_11953),c_member(tc_prod(U_11953,U_11953)))),c_Product__Type_OPair(U_11953,U_11953)))),U_11955),U_11957,U_11959)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11953,tc_HOL_Obool),tc_fun(U_11953,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11953,tc_HOL_Obool),tc_fun(U_11953,tc_HOL_Obool)),U_11957),U_11959)),c_Wellfounded_Omax__ext(U_11953,U_11955))) )
& ! [U_11958,U_11956,U_11954,U_11952] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11952,tc_HOL_Obool),tc_fun(U_11952,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11952,tc_HOL_Obool),tc_fun(U_11952,tc_HOL_Obool)),U_11956),U_11958)),c_Wellfounded_Omax__ext(U_11952,U_11954)))
| ~ c_Wellfounded_Omax__extp(U_11952,hAPP(hAPP(c_COMBC(U_11952,tc_fun(tc_prod(U_11952,U_11952),tc_HOL_Obool),tc_fun(U_11952,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11952,tc_fun(tc_fun(tc_prod(U_11952,U_11952),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11952,U_11952),tc_HOL_Obool),tc_fun(U_11952,tc_HOL_Obool)),U_11952),c_COMBC(U_11952,tc_fun(tc_prod(U_11952,U_11952),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11952,tc_prod(U_11952,U_11952)),tc_fun(U_11952,tc_fun(tc_fun(tc_prod(U_11952,U_11952),tc_HOL_Obool),tc_HOL_Obool)),U_11952),hAPP(c_COMBB(tc_prod(U_11952,U_11952),tc_fun(tc_fun(tc_prod(U_11952,U_11952),tc_HOL_Obool),tc_HOL_Obool),U_11952),c_member(tc_prod(U_11952,U_11952)))),c_Product__Type_OPair(U_11952,U_11952)))),U_11954),U_11956,U_11958) ) ),
inference(miniscope,[status(thm)],[f_3132_2]) ).
cnf(f_3132_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11952,tc_HOL_Obool),tc_fun(U_11952,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11952,tc_HOL_Obool),tc_fun(U_11952,tc_HOL_Obool)),U_11956),U_11958)),c_Wellfounded_Omax__ext(U_11952,U_11954)))
| ~ c_Wellfounded_Omax__extp(U_11952,hAPP(hAPP(c_COMBC(U_11952,tc_fun(tc_prod(U_11952,U_11952),tc_HOL_Obool),tc_fun(U_11952,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11952,tc_fun(tc_fun(tc_prod(U_11952,U_11952),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11952,U_11952),tc_HOL_Obool),tc_fun(U_11952,tc_HOL_Obool)),U_11952),c_COMBC(U_11952,tc_fun(tc_prod(U_11952,U_11952),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11952,tc_prod(U_11952,U_11952)),tc_fun(U_11952,tc_fun(tc_fun(tc_prod(U_11952,U_11952),tc_HOL_Obool),tc_HOL_Obool)),U_11952),hAPP(c_COMBB(tc_prod(U_11952,U_11952),tc_fun(tc_fun(tc_prod(U_11952,U_11952),tc_HOL_Obool),tc_HOL_Obool),U_11952),c_member(tc_prod(U_11952,U_11952)))),c_Product__Type_OPair(U_11952,U_11952)))),U_11954),U_11956,U_11958) ),
inference(clausify,[status(thm)],[f_3132_3]) ).
cnf(f_3132_5,plain,
( c_Wellfounded_Omax__extp(U_11953,hAPP(hAPP(c_COMBC(U_11953,tc_fun(tc_prod(U_11953,U_11953),tc_HOL_Obool),tc_fun(U_11953,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11953,tc_fun(tc_fun(tc_prod(U_11953,U_11953),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11953,U_11953),tc_HOL_Obool),tc_fun(U_11953,tc_HOL_Obool)),U_11953),c_COMBC(U_11953,tc_fun(tc_prod(U_11953,U_11953),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11953,tc_prod(U_11953,U_11953)),tc_fun(U_11953,tc_fun(tc_fun(tc_prod(U_11953,U_11953),tc_HOL_Obool),tc_HOL_Obool)),U_11953),hAPP(c_COMBB(tc_prod(U_11953,U_11953),tc_fun(tc_fun(tc_prod(U_11953,U_11953),tc_HOL_Obool),tc_HOL_Obool),U_11953),c_member(tc_prod(U_11953,U_11953)))),c_Product__Type_OPair(U_11953,U_11953)))),U_11955),U_11957,U_11959)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11953,tc_HOL_Obool),tc_fun(U_11953,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11953,tc_HOL_Obool),tc_fun(U_11953,tc_HOL_Obool)),U_11957),U_11959)),c_Wellfounded_Omax__ext(U_11953,U_11955))) ),
inference(clausify,[status(thm)],[f_3132_3]) ).
fof(f_3133_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_3133_2,plain,
! [U_11961,U_11960] :
( ( 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_11960),U_11961)),c_Wellfounded_Oless__than))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11960),U_11961)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11960),U_11961))
| ~ 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_11960),U_11961)),c_Wellfounded_Oless__than)) ) ),
inference(variable_rename,[status(thm)],[f_3133_1]) ).
fof(f_3133_3,plain,
( ! [U_11965,U_11963] :
( 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_11963),U_11965)),c_Wellfounded_Oless__than))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11963),U_11965)) )
& ! [U_11964,U_11962] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11962),U_11964))
| ~ 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_11962),U_11964)),c_Wellfounded_Oless__than)) ) ),
inference(miniscope,[status(thm)],[f_3133_2]) ).
cnf(f_3133_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11962),U_11964))
| ~ 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_11962),U_11964)),c_Wellfounded_Oless__than)) ),
inference(clausify,[status(thm)],[f_3133_3]) ).
cnf(f_3133_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_11963),U_11965)),c_Wellfounded_Oless__than))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11963),U_11965)) ),
inference(clausify,[status(thm)],[f_3133_3]) ).
fof(f_3134_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_3134_2,plain,
! [U_11969,U_11968,U_11967,U_11966] :
( ( 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_11966),U_11967)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11968),U_11969))),c_Int_Ointrel))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11966),U_11969) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11968),U_11967) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11966),U_11969) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11968),U_11967)
| ~ 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_11966),U_11967)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11968),U_11969))),c_Int_Ointrel)) ) ),
inference(variable_rename,[status(thm)],[f_3134_1]) ).
fof(f_3134_3,plain,
( ! [U_11977,U_11975,U_11973,U_11971] :
( 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_11971),U_11973)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11975),U_11977))),c_Int_Ointrel))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11971),U_11977) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11975),U_11973) )
& ! [U_11976,U_11974,U_11972,U_11970] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11970),U_11976) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11974),U_11972)
| ~ 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_11970),U_11972)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11974),U_11976))),c_Int_Ointrel)) ) ),
inference(miniscope,[status(thm)],[f_3134_2]) ).
cnf(f_3134_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11970),U_11976) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11974),U_11972)
| ~ 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_11970),U_11972)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11974),U_11976))),c_Int_Ointrel)) ),
inference(clausify,[status(thm)],[f_3134_3]) ).
cnf(f_3134_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_11971),U_11973)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11975),U_11977))),c_Int_Ointrel))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11971),U_11977) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11975),U_11973) ),
inference(clausify,[status(thm)],[f_3134_3]) ).
fof(f_3135_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_3135_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_3135_1]) ).
fof(f_3136_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_3136_2,plain,
! [U_11980,U_11979,U_11978] : c_Wellfounded_Omlex__prod(U_11978,U_11979,U_11980) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_11978),U_11978),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_11978,c_Wellfounded_Oless__than,U_11980)),hAPP(hAPP(c_COMBS(U_11978,U_11978,tc_prod(tc_Nat_Onat,U_11978)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_11978,tc_prod(tc_Nat_Onat,U_11978)),U_11978),c_Product__Type_OPair(tc_Nat_Onat,U_11978)),U_11979)),c_COMBI(U_11978))),
inference(variable_rename,[status(thm)],[f_3136_1]) ).
cnf(f_3136_3,plain,
c_Wellfounded_Omlex__prod(U_11978,U_11979,U_11980) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_11978),U_11978),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_11978,c_Wellfounded_Oless__than,U_11980)),hAPP(hAPP(c_COMBS(U_11978,U_11978,tc_prod(tc_Nat_Onat,U_11978)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_11978,tc_prod(tc_Nat_Onat,U_11978)),U_11978),c_Product__Type_OPair(tc_Nat_Onat,U_11978)),U_11979)),c_COMBI(U_11978))),
inference(clausify,[status(thm)],[f_3136_2]) ).
fof(f_3137_1,plain,
! [V_f_2,T_c,V_P_2,T_b] :
( c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_P_2),V_f_2))
| ~ c_FunDef_Oreduction__pair(T_b,V_P_2) ),
inference(fof_nnf,[status(thm)],[fact_rp__inv__image__rp]) ).
fof(f_3137_2,plain,
! [U_11984,U_11983,U_11982,U_11981] :
( c_FunDef_Oreduction__pair(U_11983,hAPP(hAPP(c_FunDef_Orp__inv__image(U_11981,U_11983),U_11982),U_11984))
| ~ c_FunDef_Oreduction__pair(U_11981,U_11982) ),
inference(variable_rename,[status(thm)],[f_3137_1]) ).
cnf(f_3137_3,plain,
( c_FunDef_Oreduction__pair(U_11983,hAPP(hAPP(c_FunDef_Orp__inv__image(U_11981,U_11983),U_11982),U_11984))
| ~ c_FunDef_Oreduction__pair(U_11981,U_11982) ),
inference(clausify,[status(thm)],[f_3137_2]) ).
fof(f_3138_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_3138_2,plain,
! [U_11993,U_11992,U_11991,U_11990,U_11989,U_11988,U_11987,U_11986] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11988,U_11986),U_11993),U_11991) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11987,U_11986),U_11992),U_11990)
| ? [U_11985] :
( hAPP(U_11992,U_11985) != hAPP(hAPP(c_Fun_Ocomp(U_11988,U_11986,U_11987,U_11993),U_11989),U_11985)
& hBOOL(hAPP(hAPP(c_member(U_11987),U_11985),U_11990)) )
| U_11991 != hAPP(c_Set_Oimage(U_11987,U_11988,U_11989),U_11990)
| ~ c_Fun_Oinj__on(U_11987,U_11988,U_11989,U_11990)
| ~ class_Groups_Ocomm__monoid__mult(U_11986) ),
inference(variable_rename,[status(thm)],[f_3138_1]) ).
fof(f_3138_3,plain,
! [U_11993,U_11992,U_11991,U_11990,U_11989,U_11988,U_11987,U_11986] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11988,U_11986),U_11993),U_11991) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11987,U_11986),U_11992),U_11990)
| ( hAPP(U_11992,sK279(U_11993,U_11992,U_11991,U_11990,U_11989,U_11988,U_11987,U_11986)) != hAPP(hAPP(c_Fun_Ocomp(U_11988,U_11986,U_11987,U_11993),U_11989),sK279(U_11993,U_11992,U_11991,U_11990,U_11989,U_11988,U_11987,U_11986))
& hBOOL(hAPP(hAPP(c_member(U_11987),sK279(U_11993,U_11992,U_11991,U_11990,U_11989,U_11988,U_11987,U_11986)),U_11990)) )
| U_11991 != hAPP(c_Set_Oimage(U_11987,U_11988,U_11989),U_11990)
| ~ c_Fun_Oinj__on(U_11987,U_11988,U_11989,U_11990)
| ~ class_Groups_Ocomm__monoid__mult(U_11986) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK279]),skolemize(U_11985,sK279(U_11993,U_11992,U_11991,U_11990,U_11989,U_11988,U_11987,U_11986))],[f_3138_2]) ).
cnf(f_3138_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11987),sK279(U_11993,U_11992,U_11991,U_11990,U_11989,U_11988,U_11987,U_11986)),U_11990))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11988,U_11986),U_11993),U_11991) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11987,U_11986),U_11992),U_11990)
| U_11991 != hAPP(c_Set_Oimage(U_11987,U_11988,U_11989),U_11990)
| ~ c_Fun_Oinj__on(U_11987,U_11988,U_11989,U_11990)
| ~ class_Groups_Ocomm__monoid__mult(U_11986) ),
inference(clausify,[status(thm)],[f_3138_3]) ).
cnf(f_3138_5,plain,
( hAPP(U_11992,sK279(U_11993,U_11992,U_11991,U_11990,U_11989,U_11988,U_11987,U_11986)) != hAPP(hAPP(c_Fun_Ocomp(U_11988,U_11986,U_11987,U_11993),U_11989),sK279(U_11993,U_11992,U_11991,U_11990,U_11989,U_11988,U_11987,U_11986))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11988,U_11986),U_11993),U_11991) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11987,U_11986),U_11992),U_11990)
| U_11991 != hAPP(c_Set_Oimage(U_11987,U_11988,U_11989),U_11990)
| ~ c_Fun_Oinj__on(U_11987,U_11988,U_11989,U_11990)
| ~ class_Groups_Ocomm__monoid__mult(U_11986) ),
inference(clausify,[status(thm)],[f_3138_3]) ).
fof(f_3139_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_3139_2,plain,
! [U_11995,U_11994] : c_FunDef_Orp__inv__image(U_11994,U_11995) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_11994,U_11994),tc_HOL_Obool),tc_fun(tc_prod(U_11994,U_11994),tc_HOL_Obool),tc_fun(tc_fun(U_11995,U_11994),tc_prod(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_11994,U_11994),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11994,U_11994),tc_HOL_Obool),tc_fun(tc_fun(U_11995,U_11994),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_11994,U_11994),tc_HOL_Obool),tc_fun(tc_fun(U_11995,U_11994),tc_prod(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_11995,U_11994),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool)),tc_fun(tc_fun(U_11995,U_11994),tc_prod(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_11994,U_11994),tc_HOL_Obool),tc_fun(tc_fun(U_11995,U_11994),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_11994,U_11994),tc_HOL_Obool),tc_fun(tc_fun(U_11995,U_11994),tc_prod(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool))))),tc_fun(tc_prod(U_11994,U_11994),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_11995,U_11994),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool)),tc_fun(tc_fun(U_11995,U_11994),tc_prod(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool))),tc_fun(tc_prod(U_11994,U_11994),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11995,U_11994),tc_fun(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_11995,U_11994),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool)),tc_fun(tc_fun(U_11995,U_11994),tc_prod(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool)))),tc_fun(tc_prod(U_11994,U_11994),tc_HOL_Obool)),c_COMBS(tc_fun(U_11995,U_11994),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11995,U_11994),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool)),tc_fun(tc_fun(U_11995,U_11994),tc_fun(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool)))),tc_fun(tc_prod(U_11994,U_11994),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool))),tc_fun(U_11995,U_11994)),c_Product__Type_OPair(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool)))),c_Relation_Oinv__image(U_11994,U_11995))))),c_Relation_Oinv__image(U_11994,U_11995))),
inference(variable_rename,[status(thm)],[f_3139_1]) ).
cnf(f_3139_3,plain,
c_FunDef_Orp__inv__image(U_11994,U_11995) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_11994,U_11994),tc_HOL_Obool),tc_fun(tc_prod(U_11994,U_11994),tc_HOL_Obool),tc_fun(tc_fun(U_11995,U_11994),tc_prod(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_11994,U_11994),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11994,U_11994),tc_HOL_Obool),tc_fun(tc_fun(U_11995,U_11994),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_11994,U_11994),tc_HOL_Obool),tc_fun(tc_fun(U_11995,U_11994),tc_prod(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_11995,U_11994),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool)),tc_fun(tc_fun(U_11995,U_11994),tc_prod(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_11994,U_11994),tc_HOL_Obool),tc_fun(tc_fun(U_11995,U_11994),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_11994,U_11994),tc_HOL_Obool),tc_fun(tc_fun(U_11995,U_11994),tc_prod(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool))))),tc_fun(tc_prod(U_11994,U_11994),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_11995,U_11994),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool)),tc_fun(tc_fun(U_11995,U_11994),tc_prod(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool))),tc_fun(tc_prod(U_11994,U_11994),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11995,U_11994),tc_fun(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_11995,U_11994),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool)),tc_fun(tc_fun(U_11995,U_11994),tc_prod(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool)))),tc_fun(tc_prod(U_11994,U_11994),tc_HOL_Obool)),c_COMBS(tc_fun(U_11995,U_11994),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11995,U_11994),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool)),tc_fun(tc_fun(U_11995,U_11994),tc_fun(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool)))),tc_fun(tc_prod(U_11994,U_11994),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool))),tc_fun(U_11995,U_11994)),c_Product__Type_OPair(tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool),tc_fun(tc_prod(U_11995,U_11995),tc_HOL_Obool)))),c_Relation_Oinv__image(U_11994,U_11995))))),c_Relation_Oinv__image(U_11994,U_11995))),
inference(clausify,[status(thm)],[f_3139_2]) ).
fof(f_3140_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_3140_2,plain,
! [U_12001,U_12000,U_11999,U_11998,U_11997,U_11996] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11996,U_11996)),hAPP(hAPP(c_Product__Type_OPair(U_11996,U_11996),U_11997),U_11998)),hAPP(hAPP(c_Relation_Oinv__image(U_11999,U_11996),U_12000),U_12001)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11999,U_11999)),hAPP(hAPP(c_Product__Type_OPair(U_11999,U_11999),hAPP(U_12001,U_11997)),hAPP(U_12001,U_11998))),U_12000)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11999,U_11999)),hAPP(hAPP(c_Product__Type_OPair(U_11999,U_11999),hAPP(U_12001,U_11997)),hAPP(U_12001,U_11998))),U_12000))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11996,U_11996)),hAPP(hAPP(c_Product__Type_OPair(U_11996,U_11996),U_11997),U_11998)),hAPP(hAPP(c_Relation_Oinv__image(U_11999,U_11996),U_12000),U_12001))) ) ),
inference(variable_rename,[status(thm)],[f_3140_1]) ).
fof(f_3140_3,plain,
( ! [U_12013,U_12011,U_12009,U_12007,U_12005] :
( ! [U_12003] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_12003,U_12003)),hAPP(hAPP(c_Product__Type_OPair(U_12003,U_12003),U_12005),U_12007)),hAPP(hAPP(c_Relation_Oinv__image(U_12009,U_12003),U_12011),U_12013)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12009,U_12009)),hAPP(hAPP(c_Product__Type_OPair(U_12009,U_12009),hAPP(U_12013,U_12005)),hAPP(U_12013,U_12007))),U_12011)) )
& ! [U_12012,U_12010,U_12008,U_12006,U_12004] :
( ! [U_12002] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12002,U_12002)),hAPP(hAPP(c_Product__Type_OPair(U_12002,U_12002),U_12004),U_12006)),hAPP(hAPP(c_Relation_Oinv__image(U_12008,U_12002),U_12010),U_12012)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_12008,U_12008)),hAPP(hAPP(c_Product__Type_OPair(U_12008,U_12008),hAPP(U_12012,U_12004)),hAPP(U_12012,U_12006))),U_12010)) ) ),
inference(miniscope,[status(thm)],[f_3140_2]) ).
cnf(f_3140_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12002,U_12002)),hAPP(hAPP(c_Product__Type_OPair(U_12002,U_12002),U_12004),U_12006)),hAPP(hAPP(c_Relation_Oinv__image(U_12008,U_12002),U_12010),U_12012)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_12008,U_12008)),hAPP(hAPP(c_Product__Type_OPair(U_12008,U_12008),hAPP(U_12012,U_12004)),hAPP(U_12012,U_12006))),U_12010)) ),
inference(clausify,[status(thm)],[f_3140_3]) ).
cnf(f_3140_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12003,U_12003)),hAPP(hAPP(c_Product__Type_OPair(U_12003,U_12003),U_12005),U_12007)),hAPP(hAPP(c_Relation_Oinv__image(U_12009,U_12003),U_12011),U_12013)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12009,U_12009)),hAPP(hAPP(c_Product__Type_OPair(U_12009,U_12009),hAPP(U_12013,U_12005)),hAPP(U_12013,U_12007))),U_12011)) ),
inference(clausify,[status(thm)],[f_3140_3]) ).
fof(f_3141_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_3141_2,plain,
! [U_12015,U_12014] :
( ( 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_12014),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_12015),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_12014),U_12015)),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_12014),U_12015)),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_12014),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_12015),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[f_3141_1]) ).
fof(f_3141_3,plain,
( ! [U_12019,U_12017] :
( 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_12017),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_12019),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_12017),U_12019)),c_Int_Ointrel)) )
& ! [U_12018,U_12016] :
( 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_12016),U_12018)),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_12016),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_12018),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
inference(miniscope,[status(thm)],[f_3141_2]) ).
cnf(f_3141_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_12016),U_12018)),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_12016),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_12018),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_3141_3]) ).
cnf(f_3141_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_12017),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_12019),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_12017),U_12019)),c_Int_Ointrel)) ),
inference(clausify,[status(thm)],[f_3141_3]) ).
fof(f_3142_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_3142_2,plain,
! [U_12025,U_12024,U_12023,U_12022,U_12021] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12021),U_12024),U_12022) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12021),U_12025),U_12023)
| ? [U_12020] :
( hAPP(U_12024,U_12020) != hAPP(U_12025,U_12020)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12020)) )
| ~ c_Nat__Transfer_Onat__set(U_12023)
| U_12022 != U_12023
| ~ class_Groups_Ocomm__monoid__mult(U_12021)
| ~ class_Groups_Ocomm__monoid__add(U_12021) ),
inference(variable_rename,[status(thm)],[f_3142_1]) ).
fof(f_3142_3,plain,
! [U_12025,U_12024,U_12023,U_12022,U_12021] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12021),U_12024),U_12022) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12021),U_12025),U_12023)
| ( hAPP(U_12024,sK280(U_12025,U_12024,U_12023,U_12022,U_12021)) != hAPP(U_12025,sK280(U_12025,U_12024,U_12023,U_12022,U_12021))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK280(U_12025,U_12024,U_12023,U_12022,U_12021))) )
| ~ c_Nat__Transfer_Onat__set(U_12023)
| U_12022 != U_12023
| ~ class_Groups_Ocomm__monoid__mult(U_12021)
| ~ class_Groups_Ocomm__monoid__add(U_12021) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK280]),skolemize(U_12020,sK280(U_12025,U_12024,U_12023,U_12022,U_12021))],[f_3142_2]) ).
cnf(f_3142_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK280(U_12025,U_12024,U_12023,U_12022,U_12021)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12021),U_12024),U_12022) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12021),U_12025),U_12023)
| ~ c_Nat__Transfer_Onat__set(U_12023)
| U_12022 != U_12023
| ~ class_Groups_Ocomm__monoid__mult(U_12021)
| ~ class_Groups_Ocomm__monoid__add(U_12021) ),
inference(clausify,[status(thm)],[f_3142_3]) ).
cnf(f_3142_5,plain,
( hAPP(U_12024,sK280(U_12025,U_12024,U_12023,U_12022,U_12021)) != hAPP(U_12025,sK280(U_12025,U_12024,U_12023,U_12022,U_12021))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12021),U_12024),U_12022) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12021),U_12025),U_12023)
| ~ c_Nat__Transfer_Onat__set(U_12023)
| U_12022 != U_12023
| ~ class_Groups_Ocomm__monoid__mult(U_12021)
| ~ class_Groups_Ocomm__monoid__add(U_12021) ),
inference(clausify,[status(thm)],[f_3142_3]) ).
fof(f_3143_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_3143_2,plain,
! [U_12028,U_12027,U_12026] : hAPP(c_Relation_OImage(U_12026,U_12027,U_12028),c_Orderings_Obot__class_Obot(tc_fun(U_12026,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_12027,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3143_1]) ).
cnf(f_3143_3,plain,
hAPP(c_Relation_OImage(U_12026,U_12027,U_12028),c_Orderings_Obot__class_Obot(tc_fun(U_12026,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_12027,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3143_2]) ).
fof(f_3144_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_3144_2,plain,
! [U_12033,U_12032,U_12031,U_12030,U_12029] : hAPP(c_Relation_OImage(U_12029,U_12030,U_12031),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12029,tc_HOL_Obool)),U_12032),U_12033)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12030,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12029,U_12030,U_12031),U_12032)),hAPP(c_Relation_OImage(U_12029,U_12030,U_12031),U_12033)),
inference(variable_rename,[status(thm)],[f_3144_1]) ).
cnf(f_3144_3,plain,
hAPP(c_Relation_OImage(U_12029,U_12030,U_12031),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12029,tc_HOL_Obool)),U_12032),U_12033)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12030,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12029,U_12030,U_12031),U_12032)),hAPP(c_Relation_OImage(U_12029,U_12030,U_12031),U_12033)),
inference(clausify,[status(thm)],[f_3144_2]) ).
fof(f_3145_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_3145_2,plain,
! [U_12038,U_12037,U_12036,U_12035,U_12034] : hAPP(c_Relation_OImage(U_12034,U_12035,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12034,U_12035),tc_HOL_Obool)),U_12036),U_12037)),U_12038) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12035,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12034,U_12035,U_12036),U_12038)),hAPP(c_Relation_OImage(U_12034,U_12035,U_12037),U_12038)),
inference(variable_rename,[status(thm)],[f_3145_1]) ).
cnf(f_3145_3,plain,
hAPP(c_Relation_OImage(U_12034,U_12035,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12034,U_12035),tc_HOL_Obool)),U_12036),U_12037)),U_12038) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12035,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12034,U_12035,U_12036),U_12038)),hAPP(c_Relation_OImage(U_12034,U_12035,U_12037),U_12038)),
inference(clausify,[status(thm)],[f_3145_2]) ).
fof(f_3146_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_3146_2,plain,
! [U_12044,U_12043,U_12042,U_12041,U_12040,U_12039] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12040,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12039,U_12040,U_12041),U_12043)),hAPP(c_Relation_OImage(U_12039,U_12040,U_12042),U_12044)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12039,tc_HOL_Obool)),U_12043),U_12044))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12039,U_12040),tc_HOL_Obool)),U_12041),U_12042)) ),
inference(variable_rename,[status(thm)],[f_3146_1]) ).
cnf(f_3146_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12040,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12039,U_12040,U_12041),U_12043)),hAPP(c_Relation_OImage(U_12039,U_12040,U_12042),U_12044)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12039,tc_HOL_Obool)),U_12043),U_12044))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12039,U_12040),tc_HOL_Obool)),U_12041),U_12042)) ),
inference(clausify,[status(thm)],[f_3146_2]) ).
fof(f_3147_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_3147_2,plain,
! [U_12049,U_12048,U_12047,U_12046,U_12045] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12045,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12046,U_12045,U_12047),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12046,tc_HOL_Obool)),U_12048),U_12049))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12045,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12046,U_12045,U_12047),U_12048)),hAPP(c_Relation_OImage(U_12046,U_12045,U_12047),U_12049)))),
inference(variable_rename,[status(thm)],[f_3147_1]) ).
cnf(f_3147_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12045,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12046,U_12045,U_12047),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12046,tc_HOL_Obool)),U_12048),U_12049))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12045,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12046,U_12045,U_12047),U_12048)),hAPP(c_Relation_OImage(U_12046,U_12045,U_12047),U_12049)))),
inference(clausify,[status(thm)],[f_3147_2]) ).
fof(f_3148_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_3148_2,plain,
! [U_12055,U_12054,U_12053,U_12052,U_12051,U_12050] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12050,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12051,U_12050,U_12052),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12053,tc_fun(U_12051,tc_HOL_Obool)),U_12054),U_12055))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12053,tc_fun(U_12050,tc_HOL_Obool)),U_12054),hAPP(hAPP(c_COMBB(tc_fun(U_12051,tc_HOL_Obool),tc_fun(U_12050,tc_HOL_Obool),U_12053),c_Relation_OImage(U_12051,U_12050,U_12052)),U_12055)))),
inference(variable_rename,[status(thm)],[f_3148_1]) ).
cnf(f_3148_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12050,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12051,U_12050,U_12052),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12053,tc_fun(U_12051,tc_HOL_Obool)),U_12054),U_12055))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12053,tc_fun(U_12050,tc_HOL_Obool)),U_12054),hAPP(hAPP(c_COMBB(tc_fun(U_12051,tc_HOL_Obool),tc_fun(U_12050,tc_HOL_Obool),U_12053),c_Relation_OImage(U_12051,U_12050,U_12052)),U_12055)))),
inference(clausify,[status(thm)],[f_3148_2]) ).
fof(f_3149_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_3149_2,plain,
! [U_12061,U_12060,U_12059,U_12058,U_12057,U_12056] : hAPP(c_Relation_OImage(U_12056,U_12057,U_12058),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12059,tc_fun(U_12056,tc_HOL_Obool)),U_12060),U_12061)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12059,tc_fun(U_12057,tc_HOL_Obool)),U_12060),hAPP(hAPP(c_COMBB(tc_fun(U_12056,tc_HOL_Obool),tc_fun(U_12057,tc_HOL_Obool),U_12059),c_Relation_OImage(U_12056,U_12057,U_12058)),U_12061)),
inference(variable_rename,[status(thm)],[f_3149_1]) ).
cnf(f_3149_3,plain,
hAPP(c_Relation_OImage(U_12056,U_12057,U_12058),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12059,tc_fun(U_12056,tc_HOL_Obool)),U_12060),U_12061)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12059,tc_fun(U_12057,tc_HOL_Obool)),U_12060),hAPP(hAPP(c_COMBB(tc_fun(U_12056,tc_HOL_Obool),tc_fun(U_12057,tc_HOL_Obool),U_12059),c_Relation_OImage(U_12056,U_12057,U_12058)),U_12061)),
inference(clausify,[status(thm)],[f_3149_2]) ).
fof(f_3150_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_3150_2,plain,
! [U_12067,U_12066,U_12065,U_12064,U_12063,U_12062] :
( hBOOL(hAPP(hAPP(c_member(U_12065),U_12066),hAPP(c_Relation_OImage(U_12062,U_12065,U_12067),U_12064)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12062,U_12065)),hAPP(hAPP(c_Product__Type_OPair(U_12062,U_12065),U_12063),U_12066)),U_12067))
| ~ hBOOL(hAPP(hAPP(c_member(U_12062),U_12063),U_12064)) ),
inference(variable_rename,[status(thm)],[f_3150_1]) ).
cnf(f_3150_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_12065),U_12066),hAPP(c_Relation_OImage(U_12062,U_12065,U_12067),U_12064)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12062,U_12065)),hAPP(hAPP(c_Product__Type_OPair(U_12062,U_12065),U_12063),U_12066)),U_12067))
| ~ hBOOL(hAPP(hAPP(c_member(U_12062),U_12063),U_12064)) ),
inference(clausify,[status(thm)],[f_3150_2]) ).
fof(f_3151_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_3151_2,plain,
! [U_12074,U_12073,U_12072,U_12071,U_12070] :
( ( hBOOL(hAPP(hAPP(c_member(U_12070),U_12071),hAPP(c_Relation_OImage(U_12072,U_12070,U_12073),U_12074)))
| ! [U_12069] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12072,U_12070)),hAPP(hAPP(c_Product__Type_OPair(U_12072,U_12070),U_12069),U_12071)),U_12073))
| ~ hBOOL(hAPP(hAPP(c_member(U_12072),U_12069),U_12074)) ) )
& ( ? [U_12068] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12072,U_12070)),hAPP(hAPP(c_Product__Type_OPair(U_12072,U_12070),U_12068),U_12071)),U_12073))
& hBOOL(hAPP(hAPP(c_member(U_12072),U_12068),U_12074)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12070),U_12071),hAPP(c_Relation_OImage(U_12072,U_12070,U_12073),U_12074))) ) ),
inference(variable_rename,[status(thm)],[f_3151_1]) ).
fof(f_3151_3,plain,
( ! [U_12084,U_12082,U_12080,U_12078,U_12076] :
( hBOOL(hAPP(hAPP(c_member(U_12076),U_12078),hAPP(c_Relation_OImage(U_12080,U_12076,U_12082),U_12084)))
| ! [U_12069] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12080,U_12076)),hAPP(hAPP(c_Product__Type_OPair(U_12080,U_12076),U_12069),U_12078)),U_12082))
| ~ hBOOL(hAPP(hAPP(c_member(U_12080),U_12069),U_12084)) ) )
& ! [U_12083,U_12081,U_12079,U_12077,U_12075] :
( ? [U_12068] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12079,U_12075)),hAPP(hAPP(c_Product__Type_OPair(U_12079,U_12075),U_12068),U_12077)),U_12081))
& hBOOL(hAPP(hAPP(c_member(U_12079),U_12068),U_12083)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12075),U_12077),hAPP(c_Relation_OImage(U_12079,U_12075,U_12081),U_12083))) ) ),
inference(miniscope,[status(thm)],[f_3151_2]) ).
fof(f_3151_4,plain,
( ! [U_12084,U_12082,U_12080,U_12078,U_12076] :
( hBOOL(hAPP(hAPP(c_member(U_12076),U_12078),hAPP(c_Relation_OImage(U_12080,U_12076,U_12082),U_12084)))
| ! [U_12069] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12080,U_12076)),hAPP(hAPP(c_Product__Type_OPair(U_12080,U_12076),U_12069),U_12078)),U_12082))
| ~ hBOOL(hAPP(hAPP(c_member(U_12080),U_12069),U_12084)) ) )
& ! [U_12083,U_12081,U_12079,U_12077,U_12075] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12079,U_12075)),hAPP(hAPP(c_Product__Type_OPair(U_12079,U_12075),sK281(U_12083,U_12081,U_12079,U_12077,U_12075)),U_12077)),U_12081))
& hBOOL(hAPP(hAPP(c_member(U_12079),sK281(U_12083,U_12081,U_12079,U_12077,U_12075)),U_12083)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12075),U_12077),hAPP(c_Relation_OImage(U_12079,U_12075,U_12081),U_12083))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK281]),skolemize(U_12068,sK281(U_12083,U_12081,U_12079,U_12077,U_12075))],[f_3151_3]) ).
cnf(f_3151_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_12079),sK281(U_12083,U_12081,U_12079,U_12077,U_12075)),U_12083))
| ~ hBOOL(hAPP(hAPP(c_member(U_12075),U_12077),hAPP(c_Relation_OImage(U_12079,U_12075,U_12081),U_12083))) ),
inference(clausify,[status(thm)],[f_3151_4]) ).
cnf(f_3151_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12079,U_12075)),hAPP(hAPP(c_Product__Type_OPair(U_12079,U_12075),sK281(U_12083,U_12081,U_12079,U_12077,U_12075)),U_12077)),U_12081))
| ~ hBOOL(hAPP(hAPP(c_member(U_12075),U_12077),hAPP(c_Relation_OImage(U_12079,U_12075,U_12081),U_12083))) ),
inference(clausify,[status(thm)],[f_3151_4]) ).
cnf(f_3151_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_12076),U_12078),hAPP(c_Relation_OImage(U_12080,U_12076,U_12082),U_12084)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12080,U_12076)),hAPP(hAPP(c_Product__Type_OPair(U_12080,U_12076),U_12069),U_12078)),U_12082))
| ~ hBOOL(hAPP(hAPP(c_member(U_12080),U_12069),U_12084)) ),
inference(clausify,[status(thm)],[f_3151_4]) ).
fof(f_3152_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_3152_2,plain,
! [U_12088,U_12087,U_12086,U_12085] : hAPP(c_Relation_OImage(U_12085,U_12086,U_12087),U_12088) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12085,tc_fun(U_12086,tc_HOL_Obool)),U_12088),hAPP(hAPP(c_COMBB(tc_fun(U_12085,tc_HOL_Obool),tc_fun(U_12086,tc_HOL_Obool),U_12085),c_Relation_OImage(U_12085,U_12086,U_12087)),hAPP(hAPP(c_COMBC(U_12085,tc_fun(U_12085,tc_HOL_Obool),tc_fun(U_12085,tc_HOL_Obool)),c_Set_Oinsert(U_12085)),c_Orderings_Obot__class_Obot(tc_fun(U_12085,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_3152_1]) ).
cnf(f_3152_3,plain,
hAPP(c_Relation_OImage(U_12085,U_12086,U_12087),U_12088) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12085,tc_fun(U_12086,tc_HOL_Obool)),U_12088),hAPP(hAPP(c_COMBB(tc_fun(U_12085,tc_HOL_Obool),tc_fun(U_12086,tc_HOL_Obool),U_12085),c_Relation_OImage(U_12085,U_12086,U_12087)),hAPP(hAPP(c_COMBC(U_12085,tc_fun(U_12085,tc_HOL_Obool),tc_fun(U_12085,tc_HOL_Obool)),c_Set_Oinsert(U_12085)),c_Orderings_Obot__class_Obot(tc_fun(U_12085,tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_3152_2]) ).
fof(f_3153_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_3153_2,plain,
! [U_12093,U_12092,U_12091,U_12090,U_12089] :
( ( hBOOL(hAPP(hAPP(c_member(U_12089),U_12090),hAPP(c_Relation_OImage(U_12091,U_12089,U_12092),hAPP(hAPP(c_Set_Oinsert(U_12091),U_12093),c_Orderings_Obot__class_Obot(tc_fun(U_12091,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12091,U_12089)),hAPP(hAPP(c_Product__Type_OPair(U_12091,U_12089),U_12093),U_12090)),U_12092)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12091,U_12089)),hAPP(hAPP(c_Product__Type_OPair(U_12091,U_12089),U_12093),U_12090)),U_12092))
| ~ hBOOL(hAPP(hAPP(c_member(U_12089),U_12090),hAPP(c_Relation_OImage(U_12091,U_12089,U_12092),hAPP(hAPP(c_Set_Oinsert(U_12091),U_12093),c_Orderings_Obot__class_Obot(tc_fun(U_12091,tc_HOL_Obool)))))) ) ),
inference(variable_rename,[status(thm)],[f_3153_1]) ).
fof(f_3153_3,plain,
( ! [U_12103,U_12101,U_12099,U_12097,U_12095] :
( hBOOL(hAPP(hAPP(c_member(U_12095),U_12097),hAPP(c_Relation_OImage(U_12099,U_12095,U_12101),hAPP(hAPP(c_Set_Oinsert(U_12099),U_12103),c_Orderings_Obot__class_Obot(tc_fun(U_12099,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12099,U_12095)),hAPP(hAPP(c_Product__Type_OPair(U_12099,U_12095),U_12103),U_12097)),U_12101)) )
& ! [U_12102,U_12100,U_12098,U_12096,U_12094] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12098,U_12094)),hAPP(hAPP(c_Product__Type_OPair(U_12098,U_12094),U_12102),U_12096)),U_12100))
| ~ hBOOL(hAPP(hAPP(c_member(U_12094),U_12096),hAPP(c_Relation_OImage(U_12098,U_12094,U_12100),hAPP(hAPP(c_Set_Oinsert(U_12098),U_12102),c_Orderings_Obot__class_Obot(tc_fun(U_12098,tc_HOL_Obool)))))) ) ),
inference(miniscope,[status(thm)],[f_3153_2]) ).
cnf(f_3153_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12098,U_12094)),hAPP(hAPP(c_Product__Type_OPair(U_12098,U_12094),U_12102),U_12096)),U_12100))
| ~ hBOOL(hAPP(hAPP(c_member(U_12094),U_12096),hAPP(c_Relation_OImage(U_12098,U_12094,U_12100),hAPP(hAPP(c_Set_Oinsert(U_12098),U_12102),c_Orderings_Obot__class_Obot(tc_fun(U_12098,tc_HOL_Obool)))))) ),
inference(clausify,[status(thm)],[f_3153_3]) ).
cnf(f_3153_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_12095),U_12097),hAPP(c_Relation_OImage(U_12099,U_12095,U_12101),hAPP(hAPP(c_Set_Oinsert(U_12099),U_12103),c_Orderings_Obot__class_Obot(tc_fun(U_12099,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12099,U_12095)),hAPP(hAPP(c_Product__Type_OPair(U_12099,U_12095),U_12103),U_12097)),U_12101)) ),
inference(clausify,[status(thm)],[f_3153_3]) ).
fof(f_3154_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_3154_2,plain,
! [U_12104] : c_Wellfounded_Omeasure(U_12104) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_12104),c_Wellfounded_Oless__than),
inference(variable_rename,[status(thm)],[f_3154_1]) ).
cnf(f_3154_3,plain,
c_Wellfounded_Omeasure(U_12104) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_12104),c_Wellfounded_Oless__than),
inference(clausify,[status(thm)],[f_3154_2]) ).
fof(f_3155_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_3155_2,plain,
! [U_12107,U_12106,U_12105] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_12105),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_12106),U_12107)),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_12105),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12105),U_12106)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12105),U_12107))
| ~ class_Rings_Oring__1(U_12105) ),
inference(variable_rename,[status(thm)],[f_3155_1]) ).
cnf(f_3155_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_12105),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_12106),U_12107)),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_12105),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12105),U_12106)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12105),U_12107))
| ~ class_Rings_Oring__1(U_12105) ),
inference(clausify,[status(thm)],[f_3155_2]) ).
fof(f_3156_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_3156_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_3156_1]) ).
fof(f_3157_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_3157_2,plain,
! [U_12111,U_12110,U_12109,U_12108] : 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_12108),U_12109)),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_12110),U_12111)),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_12108),U_12110)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12109),U_12111))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12108),U_12111)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12109),U_12110)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_3157_1]) ).
cnf(f_3157_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_12108),U_12109)),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_12110),U_12111)),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_12108),U_12110)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12109),U_12111))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12108),U_12111)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12109),U_12110)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_3157_2]) ).
fof(f_3158_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_3158_2,plain,
! [U_12112] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,U_12112)) = U_12112,
inference(variable_rename,[status(thm)],[f_3158_1]) ).
cnf(f_3158_3,plain,
hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,U_12112)) = U_12112,
inference(clausify,[status(thm)],[f_3158_2]) ).
fof(f_3159_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_3159_2,plain,
! [U_12114,U_12113] : 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_12113),U_12114)),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_12114),U_12113)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_3159_1]) ).
cnf(f_3159_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_12113),U_12114)),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_12114),U_12113)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_3159_2]) ).
fof(f_3160_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_3160_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_3160_1]) ).
fof(f_3161_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_3161_2,plain,
! [U_12115] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_12115) = 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_12115),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_3161_1]) ).
cnf(f_3161_3,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_12115) = 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_12115),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_3161_2]) ).
fof(f_3162_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_3162_2,plain,
! [U_12119,U_12118,U_12117,U_12116] : 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_12116),U_12117)),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_12118),U_12119)),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_12116),U_12118)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12117),U_12119))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_3162_1]) ).
cnf(f_3162_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_12116),U_12117)),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_12118),U_12119)),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_12116),U_12118)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12117),U_12119))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_3162_2]) ).
fof(f_3163_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_3163_2,plain,
! [U_12121,U_12120] : 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_12120),U_12121)),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_12120),U_12121),
inference(variable_rename,[status(thm)],[f_3163_1]) ).
cnf(f_3163_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_12120),U_12121)),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_12120),U_12121),
inference(clausify,[status(thm)],[f_3163_2]) ).
fof(f_3164_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_3164_2,plain,
! [U_12122] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12122) = 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_12122)),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_3164_1]) ).
cnf(f_3164_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_12122) = 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_12122)),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_3164_2]) ).
fof(f_3165_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_3165_2,plain,
! [U_12126,U_12125,U_12124,U_12123] :
( ( 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_12123),U_12124)),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_12125),U_12126)),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_12123),U_12126)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12125),U_12124))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12123),U_12126)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12125),U_12124)))
| ~ 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_12123),U_12124)),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_12125),U_12126)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
inference(variable_rename,[status(thm)],[f_3165_1]) ).
fof(f_3165_3,plain,
( ! [U_12134,U_12132,U_12130,U_12128] :
( 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_12128),U_12130)),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_12132),U_12134)),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_12128),U_12134)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12132),U_12130))) )
& ! [U_12133,U_12131,U_12129,U_12127] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12127),U_12133)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12131),U_12129)))
| ~ 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_12127),U_12129)),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_12131),U_12133)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
inference(miniscope,[status(thm)],[f_3165_2]) ).
cnf(f_3165_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12127),U_12133)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12131),U_12129)))
| ~ 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_12127),U_12129)),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_12131),U_12133)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ),
inference(clausify,[status(thm)],[f_3165_3]) ).
cnf(f_3165_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_12128),U_12130)),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_12132),U_12134)),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_12128),U_12134)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12132),U_12130))) ),
inference(clausify,[status(thm)],[f_3165_3]) ).
fof(f_3166_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_3166_2,plain,
! [U_12138,U_12137,U_12136,U_12135] :
( ( 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_12135),U_12136)),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_12137),U_12138)),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_12135),U_12138)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12137),U_12136))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12135),U_12138)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12137),U_12136)))
| ~ 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_12135),U_12136)),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_12137),U_12138)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
inference(variable_rename,[status(thm)],[f_3166_1]) ).
fof(f_3166_3,plain,
( ! [U_12146,U_12144,U_12142,U_12140] :
( 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_12140),U_12142)),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_12144),U_12146)),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_12140),U_12146)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12144),U_12142))) )
& ! [U_12145,U_12143,U_12141,U_12139] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12139),U_12145)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12143),U_12141)))
| ~ 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_12139),U_12141)),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_12143),U_12145)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
inference(miniscope,[status(thm)],[f_3166_2]) ).
cnf(f_3166_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_12139),U_12145)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12143),U_12141)))
| ~ 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_12139),U_12141)),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_12143),U_12145)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ),
inference(clausify,[status(thm)],[f_3166_3]) ).
cnf(f_3166_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_12140),U_12142)),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_12144),U_12146)),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_12140),U_12146)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12144),U_12142))) ),
inference(clausify,[status(thm)],[f_3166_3]) ).
fof(f_3167_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_3167_2,plain,
! [U_12150,U_12149] :
( ( c_Relation_Oirrefl(U_12149,U_12150)
| ? [U_12148] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_12149,U_12149)),hAPP(hAPP(c_Product__Type_OPair(U_12149,U_12149),U_12148),U_12148)),U_12150)) )
& ( ! [U_12147] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12149,U_12149)),hAPP(hAPP(c_Product__Type_OPair(U_12149,U_12149),U_12147),U_12147)),U_12150))
| ~ c_Relation_Oirrefl(U_12149,U_12150) ) ),
inference(variable_rename,[status(thm)],[f_3167_1]) ).
fof(f_3167_3,plain,
( ! [U_12154,U_12152] :
( c_Relation_Oirrefl(U_12152,U_12154)
| ? [U_12148] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_12152,U_12152)),hAPP(hAPP(c_Product__Type_OPair(U_12152,U_12152),U_12148),U_12148)),U_12154)) )
& ! [U_12153,U_12151] :
( ! [U_12147] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12151,U_12151)),hAPP(hAPP(c_Product__Type_OPair(U_12151,U_12151),U_12147),U_12147)),U_12153))
| ~ c_Relation_Oirrefl(U_12151,U_12153) ) ),
inference(miniscope,[status(thm)],[f_3167_2]) ).
fof(f_3167_4,plain,
( ! [U_12154,U_12152] :
( c_Relation_Oirrefl(U_12152,U_12154)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_12152,U_12152)),hAPP(hAPP(c_Product__Type_OPair(U_12152,U_12152),sK282(U_12154,U_12152)),sK282(U_12154,U_12152))),U_12154)) )
& ! [U_12153,U_12151] :
( ! [U_12147] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12151,U_12151)),hAPP(hAPP(c_Product__Type_OPair(U_12151,U_12151),U_12147),U_12147)),U_12153))
| ~ c_Relation_Oirrefl(U_12151,U_12153) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK282]),skolemize(U_12148,sK282(U_12154,U_12152))],[f_3167_3]) ).
cnf(f_3167_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12151,U_12151)),hAPP(hAPP(c_Product__Type_OPair(U_12151,U_12151),U_12147),U_12147)),U_12153))
| ~ c_Relation_Oirrefl(U_12151,U_12153) ),
inference(clausify,[status(thm)],[f_3167_4]) ).
cnf(f_3167_6,plain,
( c_Relation_Oirrefl(U_12152,U_12154)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_12152,U_12152)),hAPP(hAPP(c_Product__Type_OPair(U_12152,U_12152),sK282(U_12154,U_12152)),sK282(U_12154,U_12152))),U_12154)) ),
inference(clausify,[status(thm)],[f_3167_4]) ).
fof(f_3168_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_3168_2,plain,
! [U_12157] :
? [U_12156,U_12155] : U_12157 = 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_12156),U_12155)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_3168_1]) ).
fof(f_3168_3,plain,
! [U_12157] :
? [U_12155] : U_12157 = 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),sK283(U_12157)),U_12155)),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,[sK283]),skolemize(U_12156,sK283(U_12157))],[f_3168_2]) ).
fof(f_3168_4,plain,
! [U_12157] : U_12157 = 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),sK283(U_12157)),sK284(U_12157))),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,[sK284]),skolemize(U_12155,sK284(U_12157))],[f_3168_3]) ).
cnf(f_3168_5,plain,
U_12157 = 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),sK283(U_12157)),sK284(U_12157))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_3168_4]) ).
fof(f_3169_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_3169_2,plain,
! [U_12161,U_12160,U_12159,U_12158] : hAPP(c_Relation_OField(U_12158),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_12158,U_12158)),hAPP(hAPP(c_Product__Type_OPair(U_12158,U_12158),U_12159),U_12160)),U_12161)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12158,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12158),U_12159),hAPP(hAPP(c_Set_Oinsert(U_12158),U_12160),c_Orderings_Obot__class_Obot(tc_fun(U_12158,tc_HOL_Obool))))),hAPP(c_Relation_OField(U_12158),U_12161)),
inference(variable_rename,[status(thm)],[f_3169_1]) ).
cnf(f_3169_3,plain,
hAPP(c_Relation_OField(U_12158),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_12158,U_12158)),hAPP(hAPP(c_Product__Type_OPair(U_12158,U_12158),U_12159),U_12160)),U_12161)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12158,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12158),U_12159),hAPP(hAPP(c_Set_Oinsert(U_12158),U_12160),c_Orderings_Obot__class_Obot(tc_fun(U_12158,tc_HOL_Obool))))),hAPP(c_Relation_OField(U_12158),U_12161)),
inference(clausify,[status(thm)],[f_3169_2]) ).
fof(f_3170_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_3170_2,plain,
! [U_12163,U_12162] : hAPP(c_Relation_OField(U_12162),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_12162,U_12162),tc_HOL_Obool),U_12163)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_12162,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(U_12162,U_12162),tc_HOL_Obool),tc_fun(U_12162,tc_HOL_Obool),c_Relation_OField(U_12162)),U_12163)),
inference(variable_rename,[status(thm)],[f_3170_1]) ).
cnf(f_3170_3,plain,
hAPP(c_Relation_OField(U_12162),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_12162,U_12162),tc_HOL_Obool),U_12163)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_12162,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(U_12162,U_12162),tc_HOL_Obool),tc_fun(U_12162,tc_HOL_Obool),c_Relation_OField(U_12162)),U_12163)),
inference(clausify,[status(thm)],[f_3170_2]) ).
fof(f_3171_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_3171_2,plain,
! [U_12164] : hAPP(c_Relation_OField(U_12164),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12164,U_12164),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_12164,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3171_1]) ).
cnf(f_3171_3,plain,
hAPP(c_Relation_OField(U_12164),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12164,U_12164),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_12164,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3171_2]) ).
fof(f_3172_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_3172_2,plain,
! [U_12167,U_12166,U_12165] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12165,tc_HOL_Obool)),hAPP(c_Relation_OField(U_12165),U_12166)),hAPP(c_Relation_OField(U_12165),U_12167)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12165,U_12165),tc_HOL_Obool)),U_12166),U_12167)) ),
inference(variable_rename,[status(thm)],[f_3172_1]) ).
cnf(f_3172_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12165,tc_HOL_Obool)),hAPP(c_Relation_OField(U_12165),U_12166)),hAPP(c_Relation_OField(U_12165),U_12167)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12165,U_12165),tc_HOL_Obool)),U_12166),U_12167)) ),
inference(clausify,[status(thm)],[f_3172_2]) ).
fof(f_3173_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_3173_2,plain,
! [U_12170,U_12169,U_12168] : hAPP(c_Relation_OField(U_12168),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12168,U_12168),tc_HOL_Obool)),U_12169),U_12170)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12168,tc_HOL_Obool)),hAPP(c_Relation_OField(U_12168),U_12169)),hAPP(c_Relation_OField(U_12168),U_12170)),
inference(variable_rename,[status(thm)],[f_3173_1]) ).
cnf(f_3173_3,plain,
hAPP(c_Relation_OField(U_12168),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12168,U_12168),tc_HOL_Obool)),U_12169),U_12170)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12168,tc_HOL_Obool)),hAPP(c_Relation_OField(U_12168),U_12169)),hAPP(c_Relation_OField(U_12168),U_12170)),
inference(clausify,[status(thm)],[f_3173_2]) ).
fof(f_3174_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_3174_2,plain,
! [U_12172,U_12171] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12171),hAPP(c_Relation_OField(U_12171),U_12172)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12171,U_12171)),U_12172)) ),
inference(variable_rename,[status(thm)],[f_3174_1]) ).
cnf(f_3174_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12171),hAPP(c_Relation_OField(U_12171),U_12172)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12171,U_12171)),U_12172)) ),
inference(clausify,[status(thm)],[f_3174_2]) ).
fof(f_3175_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_3175_2,plain,
! [U_12174,U_12173] : c_Relation_OId__on(U_12173,U_12174) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12173,tc_fun(tc_prod(U_12173,U_12173),tc_HOL_Obool)),U_12174),hAPP(hAPP(c_COMBC(U_12173,tc_fun(tc_prod(U_12173,U_12173),tc_HOL_Obool),tc_fun(tc_prod(U_12173,U_12173),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(U_12173,U_12173),tc_fun(tc_fun(tc_prod(U_12173,U_12173),tc_HOL_Obool),tc_fun(tc_prod(U_12173,U_12173),tc_HOL_Obool)),U_12173),c_Set_Oinsert(tc_prod(U_12173,U_12173))),hAPP(hAPP(c_COMBS(U_12173,U_12173,tc_prod(U_12173,U_12173)),c_Product__Type_OPair(U_12173,U_12173)),c_COMBI(U_12173)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12173,U_12173),tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_3175_1]) ).
cnf(f_3175_3,plain,
c_Relation_OId__on(U_12173,U_12174) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12173,tc_fun(tc_prod(U_12173,U_12173),tc_HOL_Obool)),U_12174),hAPP(hAPP(c_COMBC(U_12173,tc_fun(tc_prod(U_12173,U_12173),tc_HOL_Obool),tc_fun(tc_prod(U_12173,U_12173),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(U_12173,U_12173),tc_fun(tc_fun(tc_prod(U_12173,U_12173),tc_HOL_Obool),tc_fun(tc_prod(U_12173,U_12173),tc_HOL_Obool)),U_12173),c_Set_Oinsert(tc_prod(U_12173,U_12173))),hAPP(hAPP(c_COMBS(U_12173,U_12173,tc_prod(U_12173,U_12173)),c_Product__Type_OPair(U_12173,U_12173)),c_COMBI(U_12173)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12173,U_12173),tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_3175_2]) ).
fof(f_3176_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_3176_2,plain,
! [U_12177,U_12176,U_12175] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12175),U_12176),U_12177) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12175,tc_fun(tc_fun(U_12175,tc_HOL_Obool),tc_HOL_Obool)),U_12176),hAPP(hAPP(c_COMBC(U_12175,tc_fun(tc_fun(U_12175,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_12175,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12175,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_12175,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_12175,tc_HOL_Obool),tc_HOL_Obool)),U_12175),c_Set_Oinsert(tc_fun(U_12175,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12175,tc_HOL_Obool),tc_fun(U_12175,tc_HOL_Obool),U_12175),c_Relation_OImage(U_12175,U_12175,U_12177)),hAPP(hAPP(c_COMBC(U_12175,tc_fun(U_12175,tc_HOL_Obool),tc_fun(U_12175,tc_HOL_Obool)),c_Set_Oinsert(U_12175)),c_Orderings_Obot__class_Obot(tc_fun(U_12175,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_12175,tc_HOL_Obool),tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_3176_1]) ).
cnf(f_3176_3,plain,
hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12175),U_12176),U_12177) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12175,tc_fun(tc_fun(U_12175,tc_HOL_Obool),tc_HOL_Obool)),U_12176),hAPP(hAPP(c_COMBC(U_12175,tc_fun(tc_fun(U_12175,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_12175,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12175,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_12175,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_12175,tc_HOL_Obool),tc_HOL_Obool)),U_12175),c_Set_Oinsert(tc_fun(U_12175,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12175,tc_HOL_Obool),tc_fun(U_12175,tc_HOL_Obool),U_12175),c_Relation_OImage(U_12175,U_12175,U_12177)),hAPP(hAPP(c_COMBC(U_12175,tc_fun(U_12175,tc_HOL_Obool),tc_fun(U_12175,tc_HOL_Obool)),c_Set_Oinsert(U_12175)),c_Orderings_Obot__class_Obot(tc_fun(U_12175,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_12175,tc_HOL_Obool),tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_3176_2]) ).
fof(f_3177_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_3177_2,plain,
! [U_12183,U_12182,U_12181,U_12180,U_12179] :
( ? [U_12178] :
( hBOOL(hAPP(hAPP(c_member(U_12181),U_12178),U_12183))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_12181,U_12179)),hAPP(hAPP(c_Product__Type_OPair(U_12181,U_12179),U_12178),U_12180)),U_12182)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12179),U_12180),hAPP(c_Relation_OImage(U_12181,U_12179,U_12182),U_12183))) ),
inference(variable_rename,[status(thm)],[f_3177_1]) ).
fof(f_3177_3,plain,
! [U_12183,U_12182,U_12181,U_12180,U_12179] :
( ( hBOOL(hAPP(hAPP(c_member(U_12181),sK285(U_12183,U_12182,U_12181,U_12180,U_12179)),U_12183))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_12181,U_12179)),hAPP(hAPP(c_Product__Type_OPair(U_12181,U_12179),sK285(U_12183,U_12182,U_12181,U_12180,U_12179)),U_12180)),U_12182)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12179),U_12180),hAPP(c_Relation_OImage(U_12181,U_12179,U_12182),U_12183))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK285]),skolemize(U_12178,sK285(U_12183,U_12182,U_12181,U_12180,U_12179))],[f_3177_2]) ).
cnf(f_3177_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12181,U_12179)),hAPP(hAPP(c_Product__Type_OPair(U_12181,U_12179),sK285(U_12183,U_12182,U_12181,U_12180,U_12179)),U_12180)),U_12182))
| ~ hBOOL(hAPP(hAPP(c_member(U_12179),U_12180),hAPP(c_Relation_OImage(U_12181,U_12179,U_12182),U_12183))) ),
inference(clausify,[status(thm)],[f_3177_3]) ).
cnf(f_3177_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_12181),sK285(U_12183,U_12182,U_12181,U_12180,U_12179)),U_12183))
| ~ hBOOL(hAPP(hAPP(c_member(U_12179),U_12180),hAPP(c_Relation_OImage(U_12181,U_12179,U_12182),U_12183))) ),
inference(clausify,[status(thm)],[f_3177_3]) ).
fof(f_3178_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_3178_2,plain,
! [U_12185,U_12184] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12184),c_Orderings_Obot__class_Obot(tc_fun(U_12184,tc_HOL_Obool))),U_12185) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_12184,tc_HOL_Obool),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3178_1]) ).
cnf(f_3178_3,plain,
hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12184),c_Orderings_Obot__class_Obot(tc_fun(U_12184,tc_HOL_Obool))),U_12185) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_12184,tc_HOL_Obool),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3178_2]) ).
fof(f_3179_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_3179_2,plain,
! [U_12188,U_12187,U_12186] :
( ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_12186,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12186),U_12187),U_12188)
| U_12187 != c_Orderings_Obot__class_Obot(tc_fun(U_12186,tc_HOL_Obool)) )
& ( U_12187 = c_Orderings_Obot__class_Obot(tc_fun(U_12186,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_12186,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12186),U_12187),U_12188) ) ),
inference(variable_rename,[status(thm)],[f_3179_1]) ).
fof(f_3179_3,plain,
( ! [U_12194,U_12192,U_12190] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_12190,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12190),U_12192),U_12194)
| U_12192 != c_Orderings_Obot__class_Obot(tc_fun(U_12190,tc_HOL_Obool)) )
& ! [U_12193,U_12191,U_12189] :
( U_12191 = c_Orderings_Obot__class_Obot(tc_fun(U_12189,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_12189,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12189),U_12191),U_12193) ) ),
inference(miniscope,[status(thm)],[f_3179_2]) ).
cnf(f_3179_4,plain,
( U_12191 = c_Orderings_Obot__class_Obot(tc_fun(U_12189,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_12189,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12189),U_12191),U_12193) ),
inference(clausify,[status(thm)],[f_3179_3]) ).
cnf(f_3179_5,plain,
( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_12190,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12190),U_12192),U_12194)
| U_12192 != c_Orderings_Obot__class_Obot(tc_fun(U_12190,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3179_3]) ).
fof(f_3180_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_3180_2,plain,
! [U_12197,U_12196,U_12195] :
( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12195),U_12196),U_12197) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_12195,tc_HOL_Obool),tc_HOL_Obool))
| U_12196 != c_Orderings_Obot__class_Obot(tc_fun(U_12195,tc_HOL_Obool)) )
& ( U_12196 = c_Orderings_Obot__class_Obot(tc_fun(U_12195,tc_HOL_Obool))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12195),U_12196),U_12197) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_12195,tc_HOL_Obool),tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_3180_1]) ).
fof(f_3180_3,plain,
( ! [U_12203,U_12201,U_12199] :
( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12199),U_12201),U_12203) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_12199,tc_HOL_Obool),tc_HOL_Obool))
| U_12201 != c_Orderings_Obot__class_Obot(tc_fun(U_12199,tc_HOL_Obool)) )
& ! [U_12202,U_12200,U_12198] :
( U_12200 = c_Orderings_Obot__class_Obot(tc_fun(U_12198,tc_HOL_Obool))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12198),U_12200),U_12202) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_12198,tc_HOL_Obool),tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_3180_2]) ).
cnf(f_3180_4,plain,
( U_12200 = c_Orderings_Obot__class_Obot(tc_fun(U_12198,tc_HOL_Obool))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12198),U_12200),U_12202) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_12198,tc_HOL_Obool),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3180_3]) ).
cnf(f_3180_5,plain,
( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12199),U_12201),U_12203) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_12199,tc_HOL_Obool),tc_HOL_Obool))
| U_12201 != c_Orderings_Obot__class_Obot(tc_fun(U_12199,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3180_3]) ).
fof(f_3181_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_3181_2,plain,
! [U_12205,U_12204] : c_Relation_OId__on(U_12204,U_12205) = hAPP(c_Product__Type_Oprod_Oprod__case(U_12204,U_12204,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_12204,tc_HOL_Obool,tc_fun(U_12204,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12204,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(U_12204,tc_HOL_Obool)),U_12204),c_COMBC(U_12204,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12204,tc_HOL_Obool),tc_fun(U_12204,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12204),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12204),c_fconj)),c_fequal))),U_12205)),
inference(variable_rename,[status(thm)],[f_3181_1]) ).
cnf(f_3181_3,plain,
c_Relation_OId__on(U_12204,U_12205) = hAPP(c_Product__Type_Oprod_Oprod__case(U_12204,U_12204,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_12204,tc_HOL_Obool,tc_fun(U_12204,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12204,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(U_12204,tc_HOL_Obool)),U_12204),c_COMBC(U_12204,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12204,tc_HOL_Obool),tc_fun(U_12204,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_12204),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12204),c_fconj)),c_fequal))),U_12205)),
inference(clausify,[status(thm)],[f_3181_2]) ).
fof(f_3182_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_3182_2,plain,
! [U_12206] : c_Relation_OId__on(U_12206,c_Orderings_Obot__class_Obot(tc_fun(U_12206,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12206,U_12206),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3182_1]) ).
cnf(f_3182_3,plain,
c_Relation_OId__on(U_12206,c_Orderings_Obot__class_Obot(tc_fun(U_12206,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12206,U_12206),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3182_2]) ).
fof(f_3183_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_3183_2,plain,
! [U_12209,U_12208,U_12207] : hAPP(c_Relation_OImage(U_12207,U_12207,c_Relation_OId__on(U_12207,U_12208)),U_12209) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12207,tc_HOL_Obool)),U_12208),U_12209),
inference(variable_rename,[status(thm)],[f_3183_1]) ).
cnf(f_3183_3,plain,
hAPP(c_Relation_OImage(U_12207,U_12207,c_Relation_OId__on(U_12207,U_12208)),U_12209) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12207,tc_HOL_Obool)),U_12208),U_12209),
inference(clausify,[status(thm)],[f_3183_2]) ).
fof(f_3184_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_3184_2,plain,
! [U_12213,U_12212,U_12211,U_12210] :
( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12210),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12210,tc_HOL_Obool)),U_12212),hAPP(hAPP(c_Set_Oinsert(U_12210),U_12213),c_Orderings_Obot__class_Obot(tc_fun(U_12210,tc_HOL_Obool))))),U_12211) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(U_12210,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12210),U_12212),U_12211)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12210),hAPP(hAPP(c_Set_Oinsert(U_12210),U_12213),c_Orderings_Obot__class_Obot(tc_fun(U_12210,tc_HOL_Obool)))),U_12211))
| ~ hBOOL(hAPP(hAPP(c_member(U_12210),U_12213),U_12212))
| ~ c_Fun_Oinj__on(U_12210,tc_fun(tc_fun(U_12210,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12210,tc_fun(tc_prod(U_12210,U_12210),tc_HOL_Obool),tc_fun(tc_fun(U_12210,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12210,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_12210,U_12210),tc_HOL_Obool),tc_fun(tc_fun(U_12210,tc_HOL_Obool),tc_HOL_Obool)),U_12210),c_Equiv__Relations_Oquotient(U_12210)),hAPP(hAPP(c_COMBC(U_12210,tc_fun(U_12210,tc_HOL_Obool),tc_fun(U_12210,tc_HOL_Obool)),c_Set_Oinsert(U_12210)),c_Orderings_Obot__class_Obot(tc_fun(U_12210,tc_HOL_Obool))))),U_12211),U_12212) ),
inference(variable_rename,[status(thm)],[f_3184_1]) ).
cnf(f_3184_3,plain,
( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12210),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12210,tc_HOL_Obool)),U_12212),hAPP(hAPP(c_Set_Oinsert(U_12210),U_12213),c_Orderings_Obot__class_Obot(tc_fun(U_12210,tc_HOL_Obool))))),U_12211) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(U_12210,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12210),U_12212),U_12211)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12210),hAPP(hAPP(c_Set_Oinsert(U_12210),U_12213),c_Orderings_Obot__class_Obot(tc_fun(U_12210,tc_HOL_Obool)))),U_12211))
| ~ hBOOL(hAPP(hAPP(c_member(U_12210),U_12213),U_12212))
| ~ c_Fun_Oinj__on(U_12210,tc_fun(tc_fun(U_12210,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12210,tc_fun(tc_prod(U_12210,U_12210),tc_HOL_Obool),tc_fun(tc_fun(U_12210,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12210,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_12210,U_12210),tc_HOL_Obool),tc_fun(tc_fun(U_12210,tc_HOL_Obool),tc_HOL_Obool)),U_12210),c_Equiv__Relations_Oquotient(U_12210)),hAPP(hAPP(c_COMBC(U_12210,tc_fun(U_12210,tc_HOL_Obool),tc_fun(U_12210,tc_HOL_Obool)),c_Set_Oinsert(U_12210)),c_Orderings_Obot__class_Obot(tc_fun(U_12210,tc_HOL_Obool))))),U_12211),U_12212) ),
inference(clausify,[status(thm)],[f_3184_2]) ).
fof(f_3185_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_3185_2,plain,
! [U_12217,U_12216,U_12215,U_12214] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_12214,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12214,U_12214,U_12217),hAPP(hAPP(c_Set_Oinsert(U_12214),U_12215),c_Orderings_Obot__class_Obot(tc_fun(U_12214,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12214),U_12216),U_12217)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12214),U_12215),U_12216)) ),
inference(variable_rename,[status(thm)],[f_3185_1]) ).
cnf(f_3185_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_12214,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12214,U_12214,U_12217),hAPP(hAPP(c_Set_Oinsert(U_12214),U_12215),c_Orderings_Obot__class_Obot(tc_fun(U_12214,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12214),U_12216),U_12217)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12214),U_12215),U_12216)) ),
inference(clausify,[status(thm)],[f_3185_2]) ).
fof(f_3186_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_3186_2,plain,
! [U_12221,U_12220,U_12219,U_12218] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12220,U_12220)),hAPP(hAPP(c_Product__Type_OPair(U_12220,U_12220),U_12218),U_12219)),c_Relation_OId__on(U_12220,U_12221)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12220),U_12218),U_12221))
| U_12218 != U_12219 ),
inference(variable_rename,[status(thm)],[f_3186_1]) ).
cnf(f_3186_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12220,U_12220)),hAPP(hAPP(c_Product__Type_OPair(U_12220,U_12220),U_12218),U_12219)),c_Relation_OId__on(U_12220,U_12221)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12220),U_12218),U_12221))
| U_12218 != U_12219 ),
inference(clausify,[status(thm)],[f_3186_2]) ).
fof(f_3187_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_3187_2,plain,
! [U_12225,U_12224,U_12223,U_12222] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12222,U_12222)),hAPP(hAPP(c_Product__Type_OPair(U_12222,U_12222),U_12223),U_12224)),c_Relation_OId__on(U_12222,U_12225)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12222),U_12223),U_12225))
| U_12223 != U_12224 )
& ( ( hBOOL(hAPP(hAPP(c_member(U_12222),U_12223),U_12225))
& U_12223 = U_12224 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12222,U_12222)),hAPP(hAPP(c_Product__Type_OPair(U_12222,U_12222),U_12223),U_12224)),c_Relation_OId__on(U_12222,U_12225))) ) ),
inference(variable_rename,[status(thm)],[f_3187_1]) ).
fof(f_3187_3,plain,
( ! [U_12233,U_12231,U_12229,U_12227] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12227,U_12227)),hAPP(hAPP(c_Product__Type_OPair(U_12227,U_12227),U_12229),U_12231)),c_Relation_OId__on(U_12227,U_12233)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12227),U_12229),U_12233))
| U_12229 != U_12231 )
& ! [U_12232,U_12230,U_12228,U_12226] :
( ( hBOOL(hAPP(hAPP(c_member(U_12226),U_12228),U_12232))
& U_12228 = U_12230 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12226,U_12226)),hAPP(hAPP(c_Product__Type_OPair(U_12226,U_12226),U_12228),U_12230)),c_Relation_OId__on(U_12226,U_12232))) ) ),
inference(miniscope,[status(thm)],[f_3187_2]) ).
cnf(f_3187_4,plain,
( U_12228 = U_12230
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12226,U_12226)),hAPP(hAPP(c_Product__Type_OPair(U_12226,U_12226),U_12228),U_12230)),c_Relation_OId__on(U_12226,U_12232))) ),
inference(clausify,[status(thm)],[f_3187_3]) ).
cnf(f_3187_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_12226),U_12228),U_12232))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12226,U_12226)),hAPP(hAPP(c_Product__Type_OPair(U_12226,U_12226),U_12228),U_12230)),c_Relation_OId__on(U_12226,U_12232))) ),
inference(clausify,[status(thm)],[f_3187_3]) ).
cnf(f_3187_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12227,U_12227)),hAPP(hAPP(c_Product__Type_OPair(U_12227,U_12227),U_12229),U_12231)),c_Relation_OId__on(U_12227,U_12233)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12227),U_12229),U_12233))
| U_12229 != U_12231 ),
inference(clausify,[status(thm)],[f_3187_3]) ).
fof(f_3188_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_3188_2,plain,
! [U_12236,U_12235,U_12234] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12234),hAPP(hAPP(c_Set_Oinsert(U_12234),U_12235),c_Orderings_Obot__class_Obot(tc_fun(U_12234,tc_HOL_Obool)))),U_12236) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_12234,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12234,U_12234,U_12236),hAPP(hAPP(c_Set_Oinsert(U_12234),U_12235),c_Orderings_Obot__class_Obot(tc_fun(U_12234,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_12234,tc_HOL_Obool),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_3188_1]) ).
cnf(f_3188_3,plain,
hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12234),hAPP(hAPP(c_Set_Oinsert(U_12234),U_12235),c_Orderings_Obot__class_Obot(tc_fun(U_12234,tc_HOL_Obool)))),U_12236) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_12234,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12234,U_12234,U_12236),hAPP(hAPP(c_Set_Oinsert(U_12234),U_12235),c_Orderings_Obot__class_Obot(tc_fun(U_12234,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_12234,tc_HOL_Obool),tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_3188_2]) ).
fof(f_3189_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_3189_2,plain,
! [U_12239,U_12238,U_12237] :
( hAPP(c_Finite__Set_Ocard(tc_fun(U_12237,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12237),U_12238),U_12239)) = hAPP(c_Finite__Set_Ocard(U_12237),U_12238)
| ~ c_Fun_Oinj__on(U_12237,tc_fun(tc_fun(U_12237,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12237,tc_fun(tc_prod(U_12237,U_12237),tc_HOL_Obool),tc_fun(tc_fun(U_12237,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12237,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_12237,U_12237),tc_HOL_Obool),tc_fun(tc_fun(U_12237,tc_HOL_Obool),tc_HOL_Obool)),U_12237),c_Equiv__Relations_Oquotient(U_12237)),hAPP(hAPP(c_COMBC(U_12237,tc_fun(U_12237,tc_HOL_Obool),tc_fun(U_12237,tc_HOL_Obool)),c_Set_Oinsert(U_12237)),c_Orderings_Obot__class_Obot(tc_fun(U_12237,tc_HOL_Obool))))),U_12239),U_12238)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12237),U_12238)) ),
inference(variable_rename,[status(thm)],[f_3189_1]) ).
cnf(f_3189_3,plain,
( hAPP(c_Finite__Set_Ocard(tc_fun(U_12237,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12237),U_12238),U_12239)) = hAPP(c_Finite__Set_Ocard(U_12237),U_12238)
| ~ c_Fun_Oinj__on(U_12237,tc_fun(tc_fun(U_12237,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12237,tc_fun(tc_prod(U_12237,U_12237),tc_HOL_Obool),tc_fun(tc_fun(U_12237,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12237,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_12237,U_12237),tc_HOL_Obool),tc_fun(tc_fun(U_12237,tc_HOL_Obool),tc_HOL_Obool)),U_12237),c_Equiv__Relations_Oquotient(U_12237)),hAPP(hAPP(c_COMBC(U_12237,tc_fun(U_12237,tc_HOL_Obool),tc_fun(U_12237,tc_HOL_Obool)),c_Set_Oinsert(U_12237)),c_Orderings_Obot__class_Obot(tc_fun(U_12237,tc_HOL_Obool))))),U_12239),U_12238)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12237),U_12238)) ),
inference(clausify,[status(thm)],[f_3189_2]) ).
fof(f_3190_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_3190_2,plain,
! [U_12245,U_12244,U_12243,U_12242,U_12241,U_12240] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12240,U_12240)),hAPP(hAPP(c_Product__Type_OPair(U_12240,U_12240),U_12244),U_12245)),U_12242))
| ~ hBOOL(hAPP(hAPP(c_member(U_12240),U_12243),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12240,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12240,U_12240,U_12242),hAPP(hAPP(c_Set_Oinsert(U_12240),U_12244),c_Orderings_Obot__class_Obot(tc_fun(U_12240,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_12240,U_12240,U_12242),hAPP(hAPP(c_Set_Oinsert(U_12240),U_12245),c_Orderings_Obot__class_Obot(tc_fun(U_12240,tc_HOL_Obool)))))))
| ~ c_Equiv__Relations_Oequiv(U_12240,U_12241,U_12242) ),
inference(variable_rename,[status(thm)],[f_3190_1]) ).
cnf(f_3190_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12240,U_12240)),hAPP(hAPP(c_Product__Type_OPair(U_12240,U_12240),U_12244),U_12245)),U_12242))
| ~ hBOOL(hAPP(hAPP(c_member(U_12240),U_12243),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12240,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12240,U_12240,U_12242),hAPP(hAPP(c_Set_Oinsert(U_12240),U_12244),c_Orderings_Obot__class_Obot(tc_fun(U_12240,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_12240,U_12240,U_12242),hAPP(hAPP(c_Set_Oinsert(U_12240),U_12245),c_Orderings_Obot__class_Obot(tc_fun(U_12240,tc_HOL_Obool)))))))
| ~ c_Equiv__Relations_Oequiv(U_12240,U_12241,U_12242) ),
inference(clausify,[status(thm)],[f_3190_2]) ).
fof(f_3191_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_3191_2,plain,
! [U_12250,U_12249,U_12248,U_12247,U_12246] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12246,U_12246)),hAPP(hAPP(c_Product__Type_OPair(U_12246,U_12246),U_12250),U_12249)),U_12248))
| ~ hBOOL(hAPP(hAPP(c_member(U_12246),U_12249),U_12247))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12246,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12246,U_12246,U_12248),hAPP(hAPP(c_Set_Oinsert(U_12246),U_12249),c_Orderings_Obot__class_Obot(tc_fun(U_12246,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_12246,U_12246,U_12248),hAPP(hAPP(c_Set_Oinsert(U_12246),U_12250),c_Orderings_Obot__class_Obot(tc_fun(U_12246,tc_HOL_Obool))))))
| ~ c_Equiv__Relations_Oequiv(U_12246,U_12247,U_12248) ),
inference(variable_rename,[status(thm)],[f_3191_1]) ).
cnf(f_3191_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12246,U_12246)),hAPP(hAPP(c_Product__Type_OPair(U_12246,U_12246),U_12250),U_12249)),U_12248))
| ~ hBOOL(hAPP(hAPP(c_member(U_12246),U_12249),U_12247))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12246,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12246,U_12246,U_12248),hAPP(hAPP(c_Set_Oinsert(U_12246),U_12249),c_Orderings_Obot__class_Obot(tc_fun(U_12246,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_12246,U_12246,U_12248),hAPP(hAPP(c_Set_Oinsert(U_12246),U_12250),c_Orderings_Obot__class_Obot(tc_fun(U_12246,tc_HOL_Obool))))))
| ~ c_Equiv__Relations_Oequiv(U_12246,U_12247,U_12248) ),
inference(clausify,[status(thm)],[f_3191_2]) ).
fof(f_3192_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_3192_2,plain,
! [U_12255,U_12254,U_12253,U_12252] :
( ? [U_12251] :
( hBOOL(hAPP(hAPP(c_member(U_12252),U_12251),U_12254))
& U_12253 = hAPP(c_Relation_OImage(U_12252,U_12252,U_12255),hAPP(hAPP(c_Set_Oinsert(U_12252),U_12251),c_Orderings_Obot__class_Obot(tc_fun(U_12252,tc_HOL_Obool)))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12252,tc_HOL_Obool)),U_12253),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12252),U_12254),U_12255))) ),
inference(variable_rename,[status(thm)],[f_3192_1]) ).
fof(f_3192_3,plain,
! [U_12255,U_12254,U_12253,U_12252] :
( ( hBOOL(hAPP(hAPP(c_member(U_12252),sK286(U_12255,U_12254,U_12253,U_12252)),U_12254))
& U_12253 = hAPP(c_Relation_OImage(U_12252,U_12252,U_12255),hAPP(hAPP(c_Set_Oinsert(U_12252),sK286(U_12255,U_12254,U_12253,U_12252)),c_Orderings_Obot__class_Obot(tc_fun(U_12252,tc_HOL_Obool)))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12252,tc_HOL_Obool)),U_12253),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12252),U_12254),U_12255))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK286]),skolemize(U_12251,sK286(U_12255,U_12254,U_12253,U_12252))],[f_3192_2]) ).
cnf(f_3192_4,plain,
( U_12253 = hAPP(c_Relation_OImage(U_12252,U_12252,U_12255),hAPP(hAPP(c_Set_Oinsert(U_12252),sK286(U_12255,U_12254,U_12253,U_12252)),c_Orderings_Obot__class_Obot(tc_fun(U_12252,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12252,tc_HOL_Obool)),U_12253),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12252),U_12254),U_12255))) ),
inference(clausify,[status(thm)],[f_3192_3]) ).
cnf(f_3192_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_12252),sK286(U_12255,U_12254,U_12253,U_12252)),U_12254))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12252,tc_HOL_Obool)),U_12253),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12252),U_12254),U_12255))) ),
inference(clausify,[status(thm)],[f_3192_3]) ).
fof(f_3193_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_3193_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_3193_1]) ).
fof(f_3194_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_3194_2,plain,
! [U_12258,U_12257,U_12256] :
( c_Complete__Lattice_OSup__class_OSup(tc_fun(U_12256,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12256),U_12257),U_12258)) = U_12257
| ~ c_Equiv__Relations_Oequiv(U_12256,U_12257,U_12258) ),
inference(variable_rename,[status(thm)],[f_3194_1]) ).
cnf(f_3194_3,plain,
( c_Complete__Lattice_OSup__class_OSup(tc_fun(U_12256,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12256),U_12257),U_12258)) = U_12257
| ~ c_Equiv__Relations_Oequiv(U_12256,U_12257,U_12258) ),
inference(clausify,[status(thm)],[f_3194_2]) ).
fof(f_3195_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_3195_2,plain,
! [U_12262,U_12261,U_12260,U_12259] :
( hBOOL(hAPP(hAPP(c_member(U_12259),U_12262),hAPP(c_Relation_OImage(U_12259,U_12259,U_12261),hAPP(hAPP(c_Set_Oinsert(U_12259),U_12262),c_Orderings_Obot__class_Obot(tc_fun(U_12259,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_12259),U_12262),U_12260))
| ~ c_Equiv__Relations_Oequiv(U_12259,U_12260,U_12261) ),
inference(variable_rename,[status(thm)],[f_3195_1]) ).
cnf(f_3195_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_12259),U_12262),hAPP(c_Relation_OImage(U_12259,U_12259,U_12261),hAPP(hAPP(c_Set_Oinsert(U_12259),U_12262),c_Orderings_Obot__class_Obot(tc_fun(U_12259,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_12259),U_12262),U_12260))
| ~ c_Equiv__Relations_Oequiv(U_12259,U_12260,U_12261) ),
inference(clausify,[status(thm)],[f_3195_2]) ).
fof(f_3196_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_3196_2,plain,
! [U_12267,U_12266,U_12265,U_12264,U_12263] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12263,tc_HOL_Obool)),U_12266),U_12267) = c_Orderings_Obot__class_Obot(tc_fun(U_12263,tc_HOL_Obool))
| U_12266 = U_12267
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12263,tc_HOL_Obool)),U_12267),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12263),U_12264),U_12265)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12263,tc_HOL_Obool)),U_12266),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12263),U_12264),U_12265)))
| ~ c_Equiv__Relations_Oequiv(U_12263,U_12264,U_12265) ),
inference(variable_rename,[status(thm)],[f_3196_1]) ).
cnf(f_3196_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12263,tc_HOL_Obool)),U_12266),U_12267) = c_Orderings_Obot__class_Obot(tc_fun(U_12263,tc_HOL_Obool))
| U_12266 = U_12267
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12263,tc_HOL_Obool)),U_12267),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12263),U_12264),U_12265)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12263,tc_HOL_Obool)),U_12266),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12263),U_12264),U_12265)))
| ~ c_Equiv__Relations_Oequiv(U_12263,U_12264,U_12265) ),
inference(clausify,[status(thm)],[f_3196_2]) ).
fof(f_3197_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_3197_2,plain,
! [U_12272,U_12271,U_12270,U_12269,U_12268] :
( hAPP(c_Relation_OImage(U_12268,U_12268,U_12270),hAPP(hAPP(c_Set_Oinsert(U_12268),U_12271),c_Orderings_Obot__class_Obot(tc_fun(U_12268,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12268,U_12268,U_12270),hAPP(hAPP(c_Set_Oinsert(U_12268),U_12272),c_Orderings_Obot__class_Obot(tc_fun(U_12268,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12268,U_12268)),hAPP(hAPP(c_Product__Type_OPair(U_12268,U_12268),U_12271),U_12272)),U_12270))
| ~ c_Equiv__Relations_Oequiv(U_12268,U_12269,U_12270) ),
inference(variable_rename,[status(thm)],[f_3197_1]) ).
cnf(f_3197_3,plain,
( hAPP(c_Relation_OImage(U_12268,U_12268,U_12270),hAPP(hAPP(c_Set_Oinsert(U_12268),U_12271),c_Orderings_Obot__class_Obot(tc_fun(U_12268,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12268,U_12268,U_12270),hAPP(hAPP(c_Set_Oinsert(U_12268),U_12272),c_Orderings_Obot__class_Obot(tc_fun(U_12268,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12268,U_12268)),hAPP(hAPP(c_Product__Type_OPair(U_12268,U_12268),U_12271),U_12272)),U_12270))
| ~ c_Equiv__Relations_Oequiv(U_12268,U_12269,U_12270) ),
inference(clausify,[status(thm)],[f_3197_2]) ).
fof(f_3198_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_3198_2,plain,
! [U_12279,U_12278,U_12277,U_12276,U_12275,U_12274,U_12273] :
( U_12276 = U_12277
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12273,U_12273)),hAPP(hAPP(c_Product__Type_OPair(U_12273,U_12273),U_12278),U_12279)),U_12275))
| ~ hBOOL(hAPP(hAPP(c_member(U_12273),U_12279),U_12277))
| ~ hBOOL(hAPP(hAPP(c_member(U_12273),U_12278),U_12276))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12273,tc_HOL_Obool)),U_12277),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12273),U_12274),U_12275)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12273,tc_HOL_Obool)),U_12276),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12273),U_12274),U_12275)))
| ~ c_Equiv__Relations_Oequiv(U_12273,U_12274,U_12275) ),
inference(variable_rename,[status(thm)],[f_3198_1]) ).
cnf(f_3198_3,plain,
( U_12276 = U_12277
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12273,U_12273)),hAPP(hAPP(c_Product__Type_OPair(U_12273,U_12273),U_12278),U_12279)),U_12275))
| ~ hBOOL(hAPP(hAPP(c_member(U_12273),U_12279),U_12277))
| ~ hBOOL(hAPP(hAPP(c_member(U_12273),U_12278),U_12276))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12273,tc_HOL_Obool)),U_12277),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12273),U_12274),U_12275)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12273,tc_HOL_Obool)),U_12276),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12273),U_12274),U_12275)))
| ~ c_Equiv__Relations_Oequiv(U_12273,U_12274,U_12275) ),
inference(clausify,[status(thm)],[f_3198_2]) ).
fof(f_3199_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_3199_2,plain,
! [U_12286,U_12285,U_12284,U_12283,U_12282,U_12281,U_12280] :
( ( ( U_12283 = U_12284
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12280,U_12280)),hAPP(hAPP(c_Product__Type_OPair(U_12280,U_12280),U_12285),U_12286)),U_12282)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12280,U_12280)),hAPP(hAPP(c_Product__Type_OPair(U_12280,U_12280),U_12285),U_12286)),U_12282))
| U_12283 != U_12284 ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12280),U_12286),U_12284))
| ~ hBOOL(hAPP(hAPP(c_member(U_12280),U_12285),U_12283))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12280,tc_HOL_Obool)),U_12284),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12280),U_12281),U_12282)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12280,tc_HOL_Obool)),U_12283),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12280),U_12281),U_12282)))
| ~ c_Equiv__Relations_Oequiv(U_12280,U_12281,U_12282) ),
inference(variable_rename,[status(thm)],[f_3199_1]) ).
cnf(f_3199_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12280,U_12280)),hAPP(hAPP(c_Product__Type_OPair(U_12280,U_12280),U_12285),U_12286)),U_12282))
| U_12283 != U_12284
| ~ hBOOL(hAPP(hAPP(c_member(U_12280),U_12286),U_12284))
| ~ hBOOL(hAPP(hAPP(c_member(U_12280),U_12285),U_12283))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12280,tc_HOL_Obool)),U_12284),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12280),U_12281),U_12282)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12280,tc_HOL_Obool)),U_12283),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12280),U_12281),U_12282)))
| ~ c_Equiv__Relations_Oequiv(U_12280,U_12281,U_12282) ),
inference(clausify,[status(thm)],[f_3199_2]) ).
cnf(f_3199_4,plain,
( U_12283 = U_12284
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12280,U_12280)),hAPP(hAPP(c_Product__Type_OPair(U_12280,U_12280),U_12285),U_12286)),U_12282))
| ~ hBOOL(hAPP(hAPP(c_member(U_12280),U_12286),U_12284))
| ~ hBOOL(hAPP(hAPP(c_member(U_12280),U_12285),U_12283))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12280,tc_HOL_Obool)),U_12284),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12280),U_12281),U_12282)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12280,tc_HOL_Obool)),U_12283),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12280),U_12281),U_12282)))
| ~ c_Equiv__Relations_Oequiv(U_12280,U_12281,U_12282) ),
inference(clausify,[status(thm)],[f_3199_2]) ).
fof(f_3200_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_3200_2,plain,
! [U_12291,U_12290,U_12289,U_12288,U_12287] :
( ( ( hAPP(c_Relation_OImage(U_12287,U_12287,U_12289),hAPP(hAPP(c_Set_Oinsert(U_12287),U_12290),c_Orderings_Obot__class_Obot(tc_fun(U_12287,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12287,U_12287,U_12289),hAPP(hAPP(c_Set_Oinsert(U_12287),U_12291),c_Orderings_Obot__class_Obot(tc_fun(U_12287,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12287,U_12287)),hAPP(hAPP(c_Product__Type_OPair(U_12287,U_12287),U_12290),U_12291)),U_12289)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12287,U_12287)),hAPP(hAPP(c_Product__Type_OPair(U_12287,U_12287),U_12290),U_12291)),U_12289))
| hAPP(c_Relation_OImage(U_12287,U_12287,U_12289),hAPP(hAPP(c_Set_Oinsert(U_12287),U_12290),c_Orderings_Obot__class_Obot(tc_fun(U_12287,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12287,U_12287,U_12289),hAPP(hAPP(c_Set_Oinsert(U_12287),U_12291),c_Orderings_Obot__class_Obot(tc_fun(U_12287,tc_HOL_Obool)))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12287),U_12291),U_12288))
| ~ hBOOL(hAPP(hAPP(c_member(U_12287),U_12290),U_12288))
| ~ c_Equiv__Relations_Oequiv(U_12287,U_12288,U_12289) ),
inference(variable_rename,[status(thm)],[f_3200_1]) ).
cnf(f_3200_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12287,U_12287)),hAPP(hAPP(c_Product__Type_OPair(U_12287,U_12287),U_12290),U_12291)),U_12289))
| hAPP(c_Relation_OImage(U_12287,U_12287,U_12289),hAPP(hAPP(c_Set_Oinsert(U_12287),U_12290),c_Orderings_Obot__class_Obot(tc_fun(U_12287,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12287,U_12287,U_12289),hAPP(hAPP(c_Set_Oinsert(U_12287),U_12291),c_Orderings_Obot__class_Obot(tc_fun(U_12287,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(U_12287),U_12291),U_12288))
| ~ hBOOL(hAPP(hAPP(c_member(U_12287),U_12290),U_12288))
| ~ c_Equiv__Relations_Oequiv(U_12287,U_12288,U_12289) ),
inference(clausify,[status(thm)],[f_3200_2]) ).
cnf(f_3200_4,plain,
( hAPP(c_Relation_OImage(U_12287,U_12287,U_12289),hAPP(hAPP(c_Set_Oinsert(U_12287),U_12290),c_Orderings_Obot__class_Obot(tc_fun(U_12287,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12287,U_12287,U_12289),hAPP(hAPP(c_Set_Oinsert(U_12287),U_12291),c_Orderings_Obot__class_Obot(tc_fun(U_12287,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12287,U_12287)),hAPP(hAPP(c_Product__Type_OPair(U_12287,U_12287),U_12290),U_12291)),U_12289))
| ~ hBOOL(hAPP(hAPP(c_member(U_12287),U_12291),U_12288))
| ~ hBOOL(hAPP(hAPP(c_member(U_12287),U_12290),U_12288))
| ~ c_Equiv__Relations_Oequiv(U_12287,U_12288,U_12289) ),
inference(clausify,[status(thm)],[f_3200_2]) ).
fof(f_3201_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_3201_2,plain,
! [U_12296,U_12295,U_12294,U_12293,U_12292] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12292,U_12292)),hAPP(hAPP(c_Product__Type_OPair(U_12292,U_12292),U_12294),U_12295)),U_12293))
| ~ hBOOL(hAPP(hAPP(c_member(U_12292),U_12295),U_12296))
| ~ c_Equiv__Relations_Oequiv(U_12292,U_12296,U_12293)
| hAPP(c_Relation_OImage(U_12292,U_12292,U_12293),hAPP(hAPP(c_Set_Oinsert(U_12292),U_12294),c_Orderings_Obot__class_Obot(tc_fun(U_12292,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12292,U_12292,U_12293),hAPP(hAPP(c_Set_Oinsert(U_12292),U_12295),c_Orderings_Obot__class_Obot(tc_fun(U_12292,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_3201_1]) ).
cnf(f_3201_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12292,U_12292)),hAPP(hAPP(c_Product__Type_OPair(U_12292,U_12292),U_12294),U_12295)),U_12293))
| ~ hBOOL(hAPP(hAPP(c_member(U_12292),U_12295),U_12296))
| ~ c_Equiv__Relations_Oequiv(U_12292,U_12296,U_12293)
| hAPP(c_Relation_OImage(U_12292,U_12292,U_12293),hAPP(hAPP(c_Set_Oinsert(U_12292),U_12294),c_Orderings_Obot__class_Obot(tc_fun(U_12292,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12292,U_12292,U_12293),hAPP(hAPP(c_Set_Oinsert(U_12292),U_12295),c_Orderings_Obot__class_Obot(tc_fun(U_12292,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_3201_2]) ).
fof(f_3202_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_3202_2,plain,
! [U_12301,U_12300,U_12299,U_12298,U_12297] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12297,U_12297)),hAPP(hAPP(c_Product__Type_OPair(U_12297,U_12297),U_12300),U_12301)),U_12299))
| ~ hBOOL(hAPP(hAPP(c_member(U_12297),U_12301),U_12298))
| ~ hBOOL(hAPP(hAPP(c_member(U_12297),U_12300),U_12298))
| hAPP(c_Relation_OImage(U_12297,U_12297,U_12299),hAPP(hAPP(c_Set_Oinsert(U_12297),U_12300),c_Orderings_Obot__class_Obot(tc_fun(U_12297,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12297,U_12297,U_12299),hAPP(hAPP(c_Set_Oinsert(U_12297),U_12301),c_Orderings_Obot__class_Obot(tc_fun(U_12297,tc_HOL_Obool)))) )
& ( ( hBOOL(hAPP(hAPP(c_member(U_12297),U_12301),U_12298))
& hBOOL(hAPP(hAPP(c_member(U_12297),U_12300),U_12298))
& hAPP(c_Relation_OImage(U_12297,U_12297,U_12299),hAPP(hAPP(c_Set_Oinsert(U_12297),U_12300),c_Orderings_Obot__class_Obot(tc_fun(U_12297,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12297,U_12297,U_12299),hAPP(hAPP(c_Set_Oinsert(U_12297),U_12301),c_Orderings_Obot__class_Obot(tc_fun(U_12297,tc_HOL_Obool)))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12297,U_12297)),hAPP(hAPP(c_Product__Type_OPair(U_12297,U_12297),U_12300),U_12301)),U_12299)) ) )
| ~ c_Equiv__Relations_Oequiv(U_12297,U_12298,U_12299) ),
inference(variable_rename,[status(thm)],[f_3202_1]) ).
cnf(f_3202_3,plain,
( hAPP(c_Relation_OImage(U_12297,U_12297,U_12299),hAPP(hAPP(c_Set_Oinsert(U_12297),U_12300),c_Orderings_Obot__class_Obot(tc_fun(U_12297,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12297,U_12297,U_12299),hAPP(hAPP(c_Set_Oinsert(U_12297),U_12301),c_Orderings_Obot__class_Obot(tc_fun(U_12297,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12297,U_12297)),hAPP(hAPP(c_Product__Type_OPair(U_12297,U_12297),U_12300),U_12301)),U_12299))
| ~ c_Equiv__Relations_Oequiv(U_12297,U_12298,U_12299) ),
inference(clausify,[status(thm)],[f_3202_2]) ).
cnf(f_3202_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12297),U_12300),U_12298))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12297,U_12297)),hAPP(hAPP(c_Product__Type_OPair(U_12297,U_12297),U_12300),U_12301)),U_12299))
| ~ c_Equiv__Relations_Oequiv(U_12297,U_12298,U_12299) ),
inference(clausify,[status(thm)],[f_3202_2]) ).
cnf(f_3202_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_12297),U_12301),U_12298))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12297,U_12297)),hAPP(hAPP(c_Product__Type_OPair(U_12297,U_12297),U_12300),U_12301)),U_12299))
| ~ c_Equiv__Relations_Oequiv(U_12297,U_12298,U_12299) ),
inference(clausify,[status(thm)],[f_3202_2]) ).
cnf(f_3202_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12297,U_12297)),hAPP(hAPP(c_Product__Type_OPair(U_12297,U_12297),U_12300),U_12301)),U_12299))
| ~ hBOOL(hAPP(hAPP(c_member(U_12297),U_12301),U_12298))
| ~ hBOOL(hAPP(hAPP(c_member(U_12297),U_12300),U_12298))
| hAPP(c_Relation_OImage(U_12297,U_12297,U_12299),hAPP(hAPP(c_Set_Oinsert(U_12297),U_12300),c_Orderings_Obot__class_Obot(tc_fun(U_12297,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12297,U_12297,U_12299),hAPP(hAPP(c_Set_Oinsert(U_12297),U_12301),c_Orderings_Obot__class_Obot(tc_fun(U_12297,tc_HOL_Obool))))
| ~ c_Equiv__Relations_Oequiv(U_12297,U_12298,U_12299) ),
inference(clausify,[status(thm)],[f_3202_2]) ).
fof(f_3203_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_3203_2,plain,
! [U_12306,U_12305,U_12304,U_12303,U_12302] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12302,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12302,U_12302,U_12304),hAPP(hAPP(c_Set_Oinsert(U_12302),U_12305),c_Orderings_Obot__class_Obot(tc_fun(U_12302,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_12302,U_12302,U_12304),hAPP(hAPP(c_Set_Oinsert(U_12302),U_12306),c_Orderings_Obot__class_Obot(tc_fun(U_12302,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12302,U_12302)),hAPP(hAPP(c_Product__Type_OPair(U_12302,U_12302),U_12305),U_12306)),U_12304))
| ~ c_Equiv__Relations_Oequiv(U_12302,U_12303,U_12304) ),
inference(variable_rename,[status(thm)],[f_3203_1]) ).
cnf(f_3203_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12302,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12302,U_12302,U_12304),hAPP(hAPP(c_Set_Oinsert(U_12302),U_12305),c_Orderings_Obot__class_Obot(tc_fun(U_12302,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_12302,U_12302,U_12304),hAPP(hAPP(c_Set_Oinsert(U_12302),U_12306),c_Orderings_Obot__class_Obot(tc_fun(U_12302,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12302,U_12302)),hAPP(hAPP(c_Product__Type_OPair(U_12302,U_12302),U_12305),U_12306)),U_12304))
| ~ c_Equiv__Relations_Oequiv(U_12302,U_12303,U_12304) ),
inference(clausify,[status(thm)],[f_3203_2]) ).
fof(f_3204_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_3204_2,plain,
! [U_12311,U_12310,U_12309,U_12308,U_12307] :
( ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12307),hAPP(hAPP(c_Set_Oinsert(U_12307),U_12310),c_Orderings_Obot__class_Obot(tc_fun(U_12307,tc_HOL_Obool)))),U_12309) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12307),hAPP(hAPP(c_Set_Oinsert(U_12307),U_12311),c_Orderings_Obot__class_Obot(tc_fun(U_12307,tc_HOL_Obool)))),U_12309)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12307,U_12307)),hAPP(hAPP(c_Product__Type_OPair(U_12307,U_12307),U_12310),U_12311)),U_12309)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12307,U_12307)),hAPP(hAPP(c_Product__Type_OPair(U_12307,U_12307),U_12310),U_12311)),U_12309))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12307),hAPP(hAPP(c_Set_Oinsert(U_12307),U_12310),c_Orderings_Obot__class_Obot(tc_fun(U_12307,tc_HOL_Obool)))),U_12309) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12307),hAPP(hAPP(c_Set_Oinsert(U_12307),U_12311),c_Orderings_Obot__class_Obot(tc_fun(U_12307,tc_HOL_Obool)))),U_12309) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12307),U_12311),U_12308))
| ~ hBOOL(hAPP(hAPP(c_member(U_12307),U_12310),U_12308))
| ~ c_Equiv__Relations_Oequiv(U_12307,U_12308,U_12309) ),
inference(variable_rename,[status(thm)],[f_3204_1]) ).
cnf(f_3204_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12307,U_12307)),hAPP(hAPP(c_Product__Type_OPair(U_12307,U_12307),U_12310),U_12311)),U_12309))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12307),hAPP(hAPP(c_Set_Oinsert(U_12307),U_12310),c_Orderings_Obot__class_Obot(tc_fun(U_12307,tc_HOL_Obool)))),U_12309) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12307),hAPP(hAPP(c_Set_Oinsert(U_12307),U_12311),c_Orderings_Obot__class_Obot(tc_fun(U_12307,tc_HOL_Obool)))),U_12309)
| ~ hBOOL(hAPP(hAPP(c_member(U_12307),U_12311),U_12308))
| ~ hBOOL(hAPP(hAPP(c_member(U_12307),U_12310),U_12308))
| ~ c_Equiv__Relations_Oequiv(U_12307,U_12308,U_12309) ),
inference(clausify,[status(thm)],[f_3204_2]) ).
cnf(f_3204_4,plain,
( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12307),hAPP(hAPP(c_Set_Oinsert(U_12307),U_12310),c_Orderings_Obot__class_Obot(tc_fun(U_12307,tc_HOL_Obool)))),U_12309) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12307),hAPP(hAPP(c_Set_Oinsert(U_12307),U_12311),c_Orderings_Obot__class_Obot(tc_fun(U_12307,tc_HOL_Obool)))),U_12309)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12307,U_12307)),hAPP(hAPP(c_Product__Type_OPair(U_12307,U_12307),U_12310),U_12311)),U_12309))
| ~ hBOOL(hAPP(hAPP(c_member(U_12307),U_12311),U_12308))
| ~ hBOOL(hAPP(hAPP(c_member(U_12307),U_12310),U_12308))
| ~ c_Equiv__Relations_Oequiv(U_12307,U_12308,U_12309) ),
inference(clausify,[status(thm)],[f_3204_2]) ).
fof(f_3205_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_3205_2,plain,
! [U_12321,U_12320,U_12319,U_12318,U_12317,U_12316,U_12315,U_12314,U_12313,U_12312] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12312,tc_fun(U_12318,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12312,U_12312,U_12314),hAPP(hAPP(c_Set_Oinsert(U_12312),U_12320),c_Orderings_Obot__class_Obot(tc_fun(U_12312,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(U_12315,tc_fun(U_12318,tc_HOL_Obool)),tc_fun(U_12318,tc_HOL_Obool),U_12312),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12315,tc_fun(U_12318,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12315,U_12315,U_12317),hAPP(hAPP(c_Set_Oinsert(U_12315),U_12321),c_Orderings_Obot__class_Obot(tc_fun(U_12315,tc_HOL_Obool)))))),U_12319)) = hAPP(hAPP(U_12319,U_12320),U_12321)
| ~ hBOOL(hAPP(hAPP(c_member(U_12315),U_12321),U_12316))
| ~ hBOOL(hAPP(hAPP(c_member(U_12312),U_12320),U_12313))
| ~ c_Equiv__Relations_Ocongruent2(U_12312,U_12315,tc_fun(U_12318,tc_HOL_Obool),U_12314,U_12317,U_12319)
| ~ c_Equiv__Relations_Oequiv(U_12315,U_12316,U_12317)
| ~ c_Equiv__Relations_Oequiv(U_12312,U_12313,U_12314) ),
inference(variable_rename,[status(thm)],[f_3205_1]) ).
cnf(f_3205_3,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12312,tc_fun(U_12318,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12312,U_12312,U_12314),hAPP(hAPP(c_Set_Oinsert(U_12312),U_12320),c_Orderings_Obot__class_Obot(tc_fun(U_12312,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(U_12315,tc_fun(U_12318,tc_HOL_Obool)),tc_fun(U_12318,tc_HOL_Obool),U_12312),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12315,tc_fun(U_12318,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12315,U_12315,U_12317),hAPP(hAPP(c_Set_Oinsert(U_12315),U_12321),c_Orderings_Obot__class_Obot(tc_fun(U_12315,tc_HOL_Obool)))))),U_12319)) = hAPP(hAPP(U_12319,U_12320),U_12321)
| ~ hBOOL(hAPP(hAPP(c_member(U_12315),U_12321),U_12316))
| ~ hBOOL(hAPP(hAPP(c_member(U_12312),U_12320),U_12313))
| ~ c_Equiv__Relations_Ocongruent2(U_12312,U_12315,tc_fun(U_12318,tc_HOL_Obool),U_12314,U_12317,U_12319)
| ~ c_Equiv__Relations_Oequiv(U_12315,U_12316,U_12317)
| ~ c_Equiv__Relations_Oequiv(U_12312,U_12313,U_12314) ),
inference(clausify,[status(thm)],[f_3205_2]) ).
fof(f_3206_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_3206_2,plain,
! [U_12327,U_12326,U_12325,U_12324,U_12323,U_12322] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12322,tc_fun(U_12325,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12322,U_12322,U_12324),hAPP(hAPP(c_Set_Oinsert(U_12322),U_12327),c_Orderings_Obot__class_Obot(tc_fun(U_12322,tc_HOL_Obool))))),U_12326) = hAPP(U_12326,U_12327)
| ~ hBOOL(hAPP(hAPP(c_member(U_12322),U_12327),U_12323))
| ~ c_Equiv__Relations_Ocongruent(U_12322,tc_fun(U_12325,tc_HOL_Obool),U_12324,U_12326)
| ~ c_Equiv__Relations_Oequiv(U_12322,U_12323,U_12324) ),
inference(variable_rename,[status(thm)],[f_3206_1]) ).
cnf(f_3206_3,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12322,tc_fun(U_12325,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12322,U_12322,U_12324),hAPP(hAPP(c_Set_Oinsert(U_12322),U_12327),c_Orderings_Obot__class_Obot(tc_fun(U_12322,tc_HOL_Obool))))),U_12326) = hAPP(U_12326,U_12327)
| ~ hBOOL(hAPP(hAPP(c_member(U_12322),U_12327),U_12323))
| ~ c_Equiv__Relations_Ocongruent(U_12322,tc_fun(U_12325,tc_HOL_Obool),U_12324,U_12326)
| ~ c_Equiv__Relations_Oequiv(U_12322,U_12323,U_12324) ),
inference(clausify,[status(thm)],[f_3206_2]) ).
fof(f_3207_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_3207_2,plain,
! [U_12329,U_12328] :
( ( c_Equiv__Relations_Oequiv(U_12328,c_Orderings_Otop__class_Otop(tc_fun(U_12328,tc_HOL_Obool)),U_12329)
| ~ c_Equiv__Relations_Oequivp(U_12328,hAPP(hAPP(c_COMBC(U_12328,tc_fun(tc_prod(U_12328,U_12328),tc_HOL_Obool),tc_fun(U_12328,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12328,tc_fun(tc_fun(tc_prod(U_12328,U_12328),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12328,U_12328),tc_HOL_Obool),tc_fun(U_12328,tc_HOL_Obool)),U_12328),c_COMBC(U_12328,tc_fun(tc_prod(U_12328,U_12328),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12328,tc_prod(U_12328,U_12328)),tc_fun(U_12328,tc_fun(tc_fun(tc_prod(U_12328,U_12328),tc_HOL_Obool),tc_HOL_Obool)),U_12328),hAPP(c_COMBB(tc_prod(U_12328,U_12328),tc_fun(tc_fun(tc_prod(U_12328,U_12328),tc_HOL_Obool),tc_HOL_Obool),U_12328),c_member(tc_prod(U_12328,U_12328)))),c_Product__Type_OPair(U_12328,U_12328)))),U_12329)) )
& ( c_Equiv__Relations_Oequivp(U_12328,hAPP(hAPP(c_COMBC(U_12328,tc_fun(tc_prod(U_12328,U_12328),tc_HOL_Obool),tc_fun(U_12328,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12328,tc_fun(tc_fun(tc_prod(U_12328,U_12328),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12328,U_12328),tc_HOL_Obool),tc_fun(U_12328,tc_HOL_Obool)),U_12328),c_COMBC(U_12328,tc_fun(tc_prod(U_12328,U_12328),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12328,tc_prod(U_12328,U_12328)),tc_fun(U_12328,tc_fun(tc_fun(tc_prod(U_12328,U_12328),tc_HOL_Obool),tc_HOL_Obool)),U_12328),hAPP(c_COMBB(tc_prod(U_12328,U_12328),tc_fun(tc_fun(tc_prod(U_12328,U_12328),tc_HOL_Obool),tc_HOL_Obool),U_12328),c_member(tc_prod(U_12328,U_12328)))),c_Product__Type_OPair(U_12328,U_12328)))),U_12329))
| ~ c_Equiv__Relations_Oequiv(U_12328,c_Orderings_Otop__class_Otop(tc_fun(U_12328,tc_HOL_Obool)),U_12329) ) ),
inference(variable_rename,[status(thm)],[f_3207_1]) ).
fof(f_3207_3,plain,
( ! [U_12333,U_12331] :
( c_Equiv__Relations_Oequiv(U_12331,c_Orderings_Otop__class_Otop(tc_fun(U_12331,tc_HOL_Obool)),U_12333)
| ~ c_Equiv__Relations_Oequivp(U_12331,hAPP(hAPP(c_COMBC(U_12331,tc_fun(tc_prod(U_12331,U_12331),tc_HOL_Obool),tc_fun(U_12331,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12331,tc_fun(tc_fun(tc_prod(U_12331,U_12331),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12331,U_12331),tc_HOL_Obool),tc_fun(U_12331,tc_HOL_Obool)),U_12331),c_COMBC(U_12331,tc_fun(tc_prod(U_12331,U_12331),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12331,tc_prod(U_12331,U_12331)),tc_fun(U_12331,tc_fun(tc_fun(tc_prod(U_12331,U_12331),tc_HOL_Obool),tc_HOL_Obool)),U_12331),hAPP(c_COMBB(tc_prod(U_12331,U_12331),tc_fun(tc_fun(tc_prod(U_12331,U_12331),tc_HOL_Obool),tc_HOL_Obool),U_12331),c_member(tc_prod(U_12331,U_12331)))),c_Product__Type_OPair(U_12331,U_12331)))),U_12333)) )
& ! [U_12332,U_12330] :
( c_Equiv__Relations_Oequivp(U_12330,hAPP(hAPP(c_COMBC(U_12330,tc_fun(tc_prod(U_12330,U_12330),tc_HOL_Obool),tc_fun(U_12330,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12330,tc_fun(tc_fun(tc_prod(U_12330,U_12330),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12330,U_12330),tc_HOL_Obool),tc_fun(U_12330,tc_HOL_Obool)),U_12330),c_COMBC(U_12330,tc_fun(tc_prod(U_12330,U_12330),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12330,tc_prod(U_12330,U_12330)),tc_fun(U_12330,tc_fun(tc_fun(tc_prod(U_12330,U_12330),tc_HOL_Obool),tc_HOL_Obool)),U_12330),hAPP(c_COMBB(tc_prod(U_12330,U_12330),tc_fun(tc_fun(tc_prod(U_12330,U_12330),tc_HOL_Obool),tc_HOL_Obool),U_12330),c_member(tc_prod(U_12330,U_12330)))),c_Product__Type_OPair(U_12330,U_12330)))),U_12332))
| ~ c_Equiv__Relations_Oequiv(U_12330,c_Orderings_Otop__class_Otop(tc_fun(U_12330,tc_HOL_Obool)),U_12332) ) ),
inference(miniscope,[status(thm)],[f_3207_2]) ).
cnf(f_3207_4,plain,
( c_Equiv__Relations_Oequivp(U_12330,hAPP(hAPP(c_COMBC(U_12330,tc_fun(tc_prod(U_12330,U_12330),tc_HOL_Obool),tc_fun(U_12330,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12330,tc_fun(tc_fun(tc_prod(U_12330,U_12330),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12330,U_12330),tc_HOL_Obool),tc_fun(U_12330,tc_HOL_Obool)),U_12330),c_COMBC(U_12330,tc_fun(tc_prod(U_12330,U_12330),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12330,tc_prod(U_12330,U_12330)),tc_fun(U_12330,tc_fun(tc_fun(tc_prod(U_12330,U_12330),tc_HOL_Obool),tc_HOL_Obool)),U_12330),hAPP(c_COMBB(tc_prod(U_12330,U_12330),tc_fun(tc_fun(tc_prod(U_12330,U_12330),tc_HOL_Obool),tc_HOL_Obool),U_12330),c_member(tc_prod(U_12330,U_12330)))),c_Product__Type_OPair(U_12330,U_12330)))),U_12332))
| ~ c_Equiv__Relations_Oequiv(U_12330,c_Orderings_Otop__class_Otop(tc_fun(U_12330,tc_HOL_Obool)),U_12332) ),
inference(clausify,[status(thm)],[f_3207_3]) ).
cnf(f_3207_5,plain,
( c_Equiv__Relations_Oequiv(U_12331,c_Orderings_Otop__class_Otop(tc_fun(U_12331,tc_HOL_Obool)),U_12333)
| ~ c_Equiv__Relations_Oequivp(U_12331,hAPP(hAPP(c_COMBC(U_12331,tc_fun(tc_prod(U_12331,U_12331),tc_HOL_Obool),tc_fun(U_12331,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12331,tc_fun(tc_fun(tc_prod(U_12331,U_12331),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12331,U_12331),tc_HOL_Obool),tc_fun(U_12331,tc_HOL_Obool)),U_12331),c_COMBC(U_12331,tc_fun(tc_prod(U_12331,U_12331),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12331,tc_prod(U_12331,U_12331)),tc_fun(U_12331,tc_fun(tc_fun(tc_prod(U_12331,U_12331),tc_HOL_Obool),tc_HOL_Obool)),U_12331),hAPP(c_COMBB(tc_prod(U_12331,U_12331),tc_fun(tc_fun(tc_prod(U_12331,U_12331),tc_HOL_Obool),tc_HOL_Obool),U_12331),c_member(tc_prod(U_12331,U_12331)))),c_Product__Type_OPair(U_12331,U_12331)))),U_12333)) ),
inference(clausify,[status(thm)],[f_3207_3]) ).
fof(f_3208_1,plain,
! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal),
inference(fof_nnf,[status(thm)],[fact_identity__equivp]) ).
fof(f_3208_2,plain,
! [U_12334] : c_Equiv__Relations_Oequivp(U_12334,c_fequal),
inference(variable_rename,[status(thm)],[f_3208_1]) ).
cnf(f_3208_3,plain,
c_Equiv__Relations_Oequivp(U_12334,c_fequal),
inference(clausify,[status(thm)],[f_3208_2]) ).
fof(f_3209_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_3209_2,plain,
! [U_12340,U_12339] :
( ( c_Equiv__Relations_Oequivp(U_12339,U_12340)
| ? [U_12338,U_12337] :
( ( ~ hBOOL(hAPP(hAPP(U_12340,U_12338),U_12337))
& hAPP(U_12340,U_12338) = hAPP(U_12340,U_12337) )
| ( hAPP(U_12340,U_12338) != hAPP(U_12340,U_12337)
& hBOOL(hAPP(hAPP(U_12340,U_12338),U_12337)) ) ) )
& ( ! [U_12336,U_12335] :
( ( hBOOL(hAPP(hAPP(U_12340,U_12336),U_12335))
| hAPP(U_12340,U_12336) != hAPP(U_12340,U_12335) )
& ( hAPP(U_12340,U_12336) = hAPP(U_12340,U_12335)
| ~ hBOOL(hAPP(hAPP(U_12340,U_12336),U_12335)) ) )
| ~ c_Equiv__Relations_Oequivp(U_12339,U_12340) ) ),
inference(variable_rename,[status(thm)],[f_3209_1]) ).
fof(f_3209_3,plain,
( ! [U_12352] :
( ! [U_12350] : c_Equiv__Relations_Oequivp(U_12350,U_12352)
| ? [U_12348,U_12346] :
( ~ hBOOL(hAPP(hAPP(U_12352,U_12348),U_12346))
& hAPP(U_12352,U_12348) = hAPP(U_12352,U_12346) )
| ? [U_12347,U_12345] :
( hAPP(U_12352,U_12347) != hAPP(U_12352,U_12345)
& hBOOL(hAPP(hAPP(U_12352,U_12347),U_12345)) ) )
& ! [U_12351] :
( ! [U_12349] : ~ c_Equiv__Relations_Oequivp(U_12349,U_12351)
| ( ! [U_12344,U_12342] :
( hBOOL(hAPP(hAPP(U_12351,U_12344),U_12342))
| hAPP(U_12351,U_12344) != hAPP(U_12351,U_12342) )
& ! [U_12343,U_12341] :
( hAPP(U_12351,U_12343) = hAPP(U_12351,U_12341)
| ~ hBOOL(hAPP(hAPP(U_12351,U_12343),U_12341)) ) ) ) ),
inference(miniscope,[status(thm)],[f_3209_2]) ).
fof(f_3209_4,plain,
( ! [U_12352] :
( ! [U_12350] : c_Equiv__Relations_Oequivp(U_12350,U_12352)
| ? [U_12348,U_12346] :
( ~ hBOOL(hAPP(hAPP(U_12352,U_12348),U_12346))
& hAPP(U_12352,U_12348) = hAPP(U_12352,U_12346) )
| ? [U_12345] :
( hAPP(U_12352,sK287(U_12352)) != hAPP(U_12352,U_12345)
& hBOOL(hAPP(hAPP(U_12352,sK287(U_12352)),U_12345)) ) )
& ! [U_12351] :
( ! [U_12349] : ~ c_Equiv__Relations_Oequivp(U_12349,U_12351)
| ( ! [U_12344,U_12342] :
( hBOOL(hAPP(hAPP(U_12351,U_12344),U_12342))
| hAPP(U_12351,U_12344) != hAPP(U_12351,U_12342) )
& ! [U_12343,U_12341] :
( hAPP(U_12351,U_12343) = hAPP(U_12351,U_12341)
| ~ hBOOL(hAPP(hAPP(U_12351,U_12343),U_12341)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK287]),skolemize(U_12347,sK287(U_12352))],[f_3209_3]) ).
fof(f_3209_5,plain,
( ! [U_12352] :
( ! [U_12350] : c_Equiv__Relations_Oequivp(U_12350,U_12352)
| ? [U_12348,U_12346] :
( ~ hBOOL(hAPP(hAPP(U_12352,U_12348),U_12346))
& hAPP(U_12352,U_12348) = hAPP(U_12352,U_12346) )
| ( hAPP(U_12352,sK287(U_12352)) != hAPP(U_12352,sK288(U_12352))
& hBOOL(hAPP(hAPP(U_12352,sK287(U_12352)),sK288(U_12352))) ) )
& ! [U_12351] :
( ! [U_12349] : ~ c_Equiv__Relations_Oequivp(U_12349,U_12351)
| ( ! [U_12344,U_12342] :
( hBOOL(hAPP(hAPP(U_12351,U_12344),U_12342))
| hAPP(U_12351,U_12344) != hAPP(U_12351,U_12342) )
& ! [U_12343,U_12341] :
( hAPP(U_12351,U_12343) = hAPP(U_12351,U_12341)
| ~ hBOOL(hAPP(hAPP(U_12351,U_12343),U_12341)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK288]),skolemize(U_12345,sK288(U_12352))],[f_3209_4]) ).
fof(f_3209_6,plain,
( ! [U_12352] :
( ! [U_12350] : c_Equiv__Relations_Oequivp(U_12350,U_12352)
| ? [U_12346] :
( ~ hBOOL(hAPP(hAPP(U_12352,sK289(U_12352)),U_12346))
& hAPP(U_12352,sK289(U_12352)) = hAPP(U_12352,U_12346) )
| ( hAPP(U_12352,sK287(U_12352)) != hAPP(U_12352,sK288(U_12352))
& hBOOL(hAPP(hAPP(U_12352,sK287(U_12352)),sK288(U_12352))) ) )
& ! [U_12351] :
( ! [U_12349] : ~ c_Equiv__Relations_Oequivp(U_12349,U_12351)
| ( ! [U_12344,U_12342] :
( hBOOL(hAPP(hAPP(U_12351,U_12344),U_12342))
| hAPP(U_12351,U_12344) != hAPP(U_12351,U_12342) )
& ! [U_12343,U_12341] :
( hAPP(U_12351,U_12343) = hAPP(U_12351,U_12341)
| ~ hBOOL(hAPP(hAPP(U_12351,U_12343),U_12341)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK289]),skolemize(U_12348,sK289(U_12352))],[f_3209_5]) ).
fof(f_3209_7,plain,
( ! [U_12352] :
( ! [U_12350] : c_Equiv__Relations_Oequivp(U_12350,U_12352)
| ( ~ hBOOL(hAPP(hAPP(U_12352,sK289(U_12352)),sK290(U_12352)))
& hAPP(U_12352,sK289(U_12352)) = hAPP(U_12352,sK290(U_12352)) )
| ( hAPP(U_12352,sK287(U_12352)) != hAPP(U_12352,sK288(U_12352))
& hBOOL(hAPP(hAPP(U_12352,sK287(U_12352)),sK288(U_12352))) ) )
& ! [U_12351] :
( ! [U_12349] : ~ c_Equiv__Relations_Oequivp(U_12349,U_12351)
| ( ! [U_12344,U_12342] :
( hBOOL(hAPP(hAPP(U_12351,U_12344),U_12342))
| hAPP(U_12351,U_12344) != hAPP(U_12351,U_12342) )
& ! [U_12343,U_12341] :
( hAPP(U_12351,U_12343) = hAPP(U_12351,U_12341)
| ~ hBOOL(hAPP(hAPP(U_12351,U_12343),U_12341)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK290]),skolemize(U_12346,sK290(U_12352))],[f_3209_6]) ).
cnf(f_3209_8,plain,
( hAPP(U_12351,U_12343) = hAPP(U_12351,U_12341)
| ~ hBOOL(hAPP(hAPP(U_12351,U_12343),U_12341))
| ~ c_Equiv__Relations_Oequivp(U_12349,U_12351) ),
inference(clausify,[status(thm)],[f_3209_7]) ).
cnf(f_3209_9,plain,
( hBOOL(hAPP(hAPP(U_12351,U_12344),U_12342))
| hAPP(U_12351,U_12344) != hAPP(U_12351,U_12342)
| ~ c_Equiv__Relations_Oequivp(U_12349,U_12351) ),
inference(clausify,[status(thm)],[f_3209_7]) ).
cnf(f_3209_10,plain,
( hAPP(U_12352,sK289(U_12352)) = hAPP(U_12352,sK290(U_12352))
| hBOOL(hAPP(hAPP(U_12352,sK287(U_12352)),sK288(U_12352)))
| c_Equiv__Relations_Oequivp(U_12350,U_12352) ),
inference(clausify,[status(thm)],[f_3209_7]) ).
cnf(f_3209_11,plain,
( ~ hBOOL(hAPP(hAPP(U_12352,sK289(U_12352)),sK290(U_12352)))
| hBOOL(hAPP(hAPP(U_12352,sK287(U_12352)),sK288(U_12352)))
| c_Equiv__Relations_Oequivp(U_12350,U_12352) ),
inference(clausify,[status(thm)],[f_3209_7]) ).
cnf(f_3209_12,plain,
( hAPP(U_12352,sK289(U_12352)) = hAPP(U_12352,sK290(U_12352))
| hAPP(U_12352,sK287(U_12352)) != hAPP(U_12352,sK288(U_12352))
| c_Equiv__Relations_Oequivp(U_12350,U_12352) ),
inference(clausify,[status(thm)],[f_3209_7]) ).
cnf(f_3209_13,plain,
( ~ hBOOL(hAPP(hAPP(U_12352,sK289(U_12352)),sK290(U_12352)))
| hAPP(U_12352,sK287(U_12352)) != hAPP(U_12352,sK288(U_12352))
| c_Equiv__Relations_Oequivp(U_12350,U_12352) ),
inference(clausify,[status(thm)],[f_3209_7]) ).
fof(f_3210_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_3210_2,plain,
! [U_12355,U_12354,U_12353] :
( hBOOL(hAPP(hAPP(U_12354,U_12355),U_12355))
| ~ c_Equiv__Relations_Oequivp(U_12353,U_12354) ),
inference(variable_rename,[status(thm)],[f_3210_1]) ).
fof(f_3210_3,plain,
! [U_12355,U_12354] :
( ! [U_12353] : ~ c_Equiv__Relations_Oequivp(U_12353,U_12354)
| hBOOL(hAPP(hAPP(U_12354,U_12355),U_12355)) ),
inference(miniscope,[status(thm)],[f_3210_2]) ).
cnf(f_3210_4,plain,
( ~ c_Equiv__Relations_Oequivp(U_12353,U_12354)
| hBOOL(hAPP(hAPP(U_12354,U_12355),U_12355)) ),
inference(clausify,[status(thm)],[f_3210_3]) ).
fof(f_3211_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_3211_2,plain,
! [U_12359,U_12358,U_12357,U_12356] :
( hBOOL(hAPP(hAPP(U_12357,U_12359),U_12358))
| ~ hBOOL(hAPP(hAPP(U_12357,U_12358),U_12359))
| ~ c_Equiv__Relations_Oequivp(U_12356,U_12357) ),
inference(variable_rename,[status(thm)],[f_3211_1]) ).
fof(f_3211_3,plain,
! [U_12359,U_12358,U_12357] :
( ! [U_12356] : ~ c_Equiv__Relations_Oequivp(U_12356,U_12357)
| hBOOL(hAPP(hAPP(U_12357,U_12359),U_12358))
| ~ hBOOL(hAPP(hAPP(U_12357,U_12358),U_12359)) ),
inference(miniscope,[status(thm)],[f_3211_2]) ).
cnf(f_3211_4,plain,
( ~ c_Equiv__Relations_Oequivp(U_12356,U_12357)
| hBOOL(hAPP(hAPP(U_12357,U_12359),U_12358))
| ~ hBOOL(hAPP(hAPP(U_12357,U_12358),U_12359)) ),
inference(clausify,[status(thm)],[f_3211_3]) ).
fof(f_3212_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_3212_2,plain,
! [U_12364,U_12363,U_12362,U_12361,U_12360] :
( hBOOL(hAPP(hAPP(U_12361,U_12362),U_12364))
| ~ hBOOL(hAPP(hAPP(U_12361,U_12363),U_12364))
| ~ hBOOL(hAPP(hAPP(U_12361,U_12362),U_12363))
| ~ c_Equiv__Relations_Oequivp(U_12360,U_12361) ),
inference(variable_rename,[status(thm)],[f_3212_1]) ).
fof(f_3212_3,plain,
! [U_12364,U_12363,U_12362,U_12361] :
( ! [U_12360] : ~ c_Equiv__Relations_Oequivp(U_12360,U_12361)
| hBOOL(hAPP(hAPP(U_12361,U_12362),U_12364))
| ~ hBOOL(hAPP(hAPP(U_12361,U_12363),U_12364))
| ~ hBOOL(hAPP(hAPP(U_12361,U_12362),U_12363)) ),
inference(miniscope,[status(thm)],[f_3212_2]) ).
cnf(f_3212_4,plain,
( ~ c_Equiv__Relations_Oequivp(U_12360,U_12361)
| hBOOL(hAPP(hAPP(U_12361,U_12362),U_12364))
| ~ hBOOL(hAPP(hAPP(U_12361,U_12363),U_12364))
| ~ hBOOL(hAPP(hAPP(U_12361,U_12362),U_12363)) ),
inference(clausify,[status(thm)],[f_3212_3]) ).
fof(f_3213_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_3213_2,plain,
! [U_12372,U_12371,U_12370,U_12369,U_12368,U_12367,U_12366,U_12365] :
( c_Equiv__Relations_Ocongruent(U_12368,U_12369,U_12370,hAPP(U_12371,U_12372))
| ~ hBOOL(hAPP(hAPP(c_member(U_12365),U_12372),U_12366))
| ~ c_Equiv__Relations_Ocongruent2(U_12365,U_12368,U_12369,U_12367,U_12370,U_12371)
| ~ c_Equiv__Relations_Oequiv(U_12365,U_12366,U_12367) ),
inference(variable_rename,[status(thm)],[f_3213_1]) ).
cnf(f_3213_3,plain,
( c_Equiv__Relations_Ocongruent(U_12368,U_12369,U_12370,hAPP(U_12371,U_12372))
| ~ hBOOL(hAPP(hAPP(c_member(U_12365),U_12372),U_12366))
| ~ c_Equiv__Relations_Ocongruent2(U_12365,U_12368,U_12369,U_12367,U_12370,U_12371)
| ~ c_Equiv__Relations_Oequiv(U_12365,U_12366,U_12367) ),
inference(clausify,[status(thm)],[f_3213_2]) ).
fof(f_3214_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_3214_2,plain,
! [U_12378,U_12377,U_12376,U_12375] :
( ( c_Equiv__Relations_Ocongruent(U_12375,U_12376,U_12377,U_12378)
| ? [U_12374] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12375,U_12375,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12375,tc_fun(U_12375,U_12376),tc_fun(U_12375,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12376,tc_HOL_Obool),tc_fun(tc_fun(U_12375,U_12376),tc_fun(U_12375,tc_HOL_Obool)),U_12375),c_COMBB(U_12376,tc_HOL_Obool,U_12375)),hAPP(hAPP(c_COMBB(U_12376,tc_fun(U_12376,tc_HOL_Obool),U_12375),c_fequal),U_12378))),U_12378)),U_12374))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_12375,U_12375)),U_12374),U_12377)) ) )
& ( ! [U_12373] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12375,U_12375,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12375,tc_fun(U_12375,U_12376),tc_fun(U_12375,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12376,tc_HOL_Obool),tc_fun(tc_fun(U_12375,U_12376),tc_fun(U_12375,tc_HOL_Obool)),U_12375),c_COMBB(U_12376,tc_HOL_Obool,U_12375)),hAPP(hAPP(c_COMBB(U_12376,tc_fun(U_12376,tc_HOL_Obool),U_12375),c_fequal),U_12378))),U_12378)),U_12373))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12375,U_12375)),U_12373),U_12377)) )
| ~ c_Equiv__Relations_Ocongruent(U_12375,U_12376,U_12377,U_12378) ) ),
inference(variable_rename,[status(thm)],[f_3214_1]) ).
fof(f_3214_3,plain,
( ! [U_12386,U_12384,U_12382,U_12380] :
( c_Equiv__Relations_Ocongruent(U_12380,U_12382,U_12384,U_12386)
| ? [U_12374] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12380,U_12380,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12380,tc_fun(U_12380,U_12382),tc_fun(U_12380,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12382,tc_HOL_Obool),tc_fun(tc_fun(U_12380,U_12382),tc_fun(U_12380,tc_HOL_Obool)),U_12380),c_COMBB(U_12382,tc_HOL_Obool,U_12380)),hAPP(hAPP(c_COMBB(U_12382,tc_fun(U_12382,tc_HOL_Obool),U_12380),c_fequal),U_12386))),U_12386)),U_12374))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_12380,U_12380)),U_12374),U_12384)) ) )
& ! [U_12385,U_12383,U_12381,U_12379] :
( ! [U_12373] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12379,U_12379,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12379,tc_fun(U_12379,U_12381),tc_fun(U_12379,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12381,tc_HOL_Obool),tc_fun(tc_fun(U_12379,U_12381),tc_fun(U_12379,tc_HOL_Obool)),U_12379),c_COMBB(U_12381,tc_HOL_Obool,U_12379)),hAPP(hAPP(c_COMBB(U_12381,tc_fun(U_12381,tc_HOL_Obool),U_12379),c_fequal),U_12385))),U_12385)),U_12373))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12379,U_12379)),U_12373),U_12383)) )
| ~ c_Equiv__Relations_Ocongruent(U_12379,U_12381,U_12383,U_12385) ) ),
inference(miniscope,[status(thm)],[f_3214_2]) ).
fof(f_3214_4,plain,
( ! [U_12386,U_12384,U_12382,U_12380] :
( c_Equiv__Relations_Ocongruent(U_12380,U_12382,U_12384,U_12386)
| ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12380,U_12380,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12380,tc_fun(U_12380,U_12382),tc_fun(U_12380,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12382,tc_HOL_Obool),tc_fun(tc_fun(U_12380,U_12382),tc_fun(U_12380,tc_HOL_Obool)),U_12380),c_COMBB(U_12382,tc_HOL_Obool,U_12380)),hAPP(hAPP(c_COMBB(U_12382,tc_fun(U_12382,tc_HOL_Obool),U_12380),c_fequal),U_12386))),U_12386)),sK291(U_12386,U_12384,U_12382,U_12380)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_12380,U_12380)),sK291(U_12386,U_12384,U_12382,U_12380)),U_12384)) ) )
& ! [U_12385,U_12383,U_12381,U_12379] :
( ! [U_12373] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12379,U_12379,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12379,tc_fun(U_12379,U_12381),tc_fun(U_12379,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12381,tc_HOL_Obool),tc_fun(tc_fun(U_12379,U_12381),tc_fun(U_12379,tc_HOL_Obool)),U_12379),c_COMBB(U_12381,tc_HOL_Obool,U_12379)),hAPP(hAPP(c_COMBB(U_12381,tc_fun(U_12381,tc_HOL_Obool),U_12379),c_fequal),U_12385))),U_12385)),U_12373))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12379,U_12379)),U_12373),U_12383)) )
| ~ c_Equiv__Relations_Ocongruent(U_12379,U_12381,U_12383,U_12385) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK291]),skolemize(U_12374,sK291(U_12386,U_12384,U_12382,U_12380))],[f_3214_3]) ).
cnf(f_3214_5,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12379,U_12379,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12379,tc_fun(U_12379,U_12381),tc_fun(U_12379,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12381,tc_HOL_Obool),tc_fun(tc_fun(U_12379,U_12381),tc_fun(U_12379,tc_HOL_Obool)),U_12379),c_COMBB(U_12381,tc_HOL_Obool,U_12379)),hAPP(hAPP(c_COMBB(U_12381,tc_fun(U_12381,tc_HOL_Obool),U_12379),c_fequal),U_12385))),U_12385)),U_12373))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12379,U_12379)),U_12373),U_12383))
| ~ c_Equiv__Relations_Ocongruent(U_12379,U_12381,U_12383,U_12385) ),
inference(clausify,[status(thm)],[f_3214_4]) ).
cnf(f_3214_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12380,U_12380)),sK291(U_12386,U_12384,U_12382,U_12380)),U_12384))
| c_Equiv__Relations_Ocongruent(U_12380,U_12382,U_12384,U_12386) ),
inference(clausify,[status(thm)],[f_3214_4]) ).
cnf(f_3214_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12380,U_12380,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12380,tc_fun(U_12380,U_12382),tc_fun(U_12380,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12382,tc_HOL_Obool),tc_fun(tc_fun(U_12380,U_12382),tc_fun(U_12380,tc_HOL_Obool)),U_12380),c_COMBB(U_12382,tc_HOL_Obool,U_12380)),hAPP(hAPP(c_COMBB(U_12382,tc_fun(U_12382,tc_HOL_Obool),U_12380),c_fequal),U_12386))),U_12386)),sK291(U_12386,U_12384,U_12382,U_12380)))
| c_Equiv__Relations_Ocongruent(U_12380,U_12382,U_12384,U_12386) ),
inference(clausify,[status(thm)],[f_3214_4]) ).
fof(f_3215_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_3215_2,plain,
! [U_12396,U_12395,U_12394,U_12393,U_12392,U_12391,U_12390,U_12389,U_12388,U_12387] :
( hAPP(hAPP(U_12392,U_12393),U_12395) = hAPP(hAPP(U_12392,U_12394),U_12396)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12388,U_12388)),hAPP(hAPP(c_Product__Type_OPair(U_12388,U_12388),U_12395),U_12396)),U_12391))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12387,U_12387)),hAPP(hAPP(c_Product__Type_OPair(U_12387,U_12387),U_12393),U_12394)),U_12390))
| ~ c_Equiv__Relations_Ocongruent2(U_12387,U_12388,U_12389,U_12390,U_12391,U_12392) ),
inference(variable_rename,[status(thm)],[f_3215_1]) ).
cnf(f_3215_3,plain,
( hAPP(hAPP(U_12392,U_12393),U_12395) = hAPP(hAPP(U_12392,U_12394),U_12396)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12388,U_12388)),hAPP(hAPP(c_Product__Type_OPair(U_12388,U_12388),U_12395),U_12396)),U_12391))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12387,U_12387)),hAPP(hAPP(c_Product__Type_OPair(U_12387,U_12387),U_12393),U_12394)),U_12390))
| ~ c_Equiv__Relations_Ocongruent2(U_12387,U_12388,U_12389,U_12390,U_12391,U_12392) ),
inference(clausify,[status(thm)],[f_3215_2]) ).
fof(f_3216_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_3216_2,plain,
! [U_12402,U_12401,U_12400,U_12399,U_12398,U_12397] :
( hAPP(U_12400,U_12401) = hAPP(U_12400,U_12402)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12397,U_12397)),hAPP(hAPP(c_Product__Type_OPair(U_12397,U_12397),U_12401),U_12402)),U_12399))
| ~ c_Equiv__Relations_Ocongruent(U_12397,U_12398,U_12399,U_12400) ),
inference(variable_rename,[status(thm)],[f_3216_1]) ).
cnf(f_3216_3,plain,
( hAPP(U_12400,U_12401) = hAPP(U_12400,U_12402)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12397,U_12397)),hAPP(hAPP(c_Product__Type_OPair(U_12397,U_12397),U_12401),U_12402)),U_12399))
| ~ c_Equiv__Relations_Ocongruent(U_12397,U_12398,U_12399,U_12400) ),
inference(clausify,[status(thm)],[f_3216_2]) ).
fof(f_3217_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_3217_2,plain,
! [U_12411,U_12410,U_12409,U_12408,U_12407,U_12406,U_12405,U_12404,U_12403] :
( c_Equiv__Relations_Ocongruent(U_12403,tc_fun(U_12409,tc_HOL_Obool),U_12405,hAPP(hAPP(c_COMBB(tc_fun(U_12406,tc_fun(U_12409,tc_HOL_Obool)),tc_fun(U_12409,tc_HOL_Obool),U_12403),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12406,tc_fun(U_12409,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12406,U_12406,U_12408),hAPP(hAPP(c_Set_Oinsert(U_12406),U_12411),c_Orderings_Obot__class_Obot(tc_fun(U_12406,tc_HOL_Obool)))))),U_12410))
| ~ hBOOL(hAPP(hAPP(c_member(U_12406),U_12411),U_12407))
| ~ c_Equiv__Relations_Ocongruent2(U_12403,U_12406,tc_fun(U_12409,tc_HOL_Obool),U_12405,U_12408,U_12410)
| ~ c_Equiv__Relations_Oequiv(U_12406,U_12407,U_12408)
| ~ c_Equiv__Relations_Oequiv(U_12403,U_12404,U_12405) ),
inference(variable_rename,[status(thm)],[f_3217_1]) ).
cnf(f_3217_3,plain,
( c_Equiv__Relations_Ocongruent(U_12403,tc_fun(U_12409,tc_HOL_Obool),U_12405,hAPP(hAPP(c_COMBB(tc_fun(U_12406,tc_fun(U_12409,tc_HOL_Obool)),tc_fun(U_12409,tc_HOL_Obool),U_12403),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12406,tc_fun(U_12409,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12406,U_12406,U_12408),hAPP(hAPP(c_Set_Oinsert(U_12406),U_12411),c_Orderings_Obot__class_Obot(tc_fun(U_12406,tc_HOL_Obool)))))),U_12410))
| ~ hBOOL(hAPP(hAPP(c_member(U_12406),U_12411),U_12407))
| ~ c_Equiv__Relations_Ocongruent2(U_12403,U_12406,tc_fun(U_12409,tc_HOL_Obool),U_12405,U_12408,U_12410)
| ~ c_Equiv__Relations_Oequiv(U_12406,U_12407,U_12408)
| ~ c_Equiv__Relations_Oequiv(U_12403,U_12404,U_12405) ),
inference(clausify,[status(thm)],[f_3217_2]) ).
fof(f_3218_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_3218_2,plain,
! [U_12420,U_12419,U_12418,U_12417,U_12416,U_12415,U_12414] :
( U_12419 = U_12420
| ? [U_12413] :
( ? [U_12412] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12414,U_12414)),hAPP(hAPP(c_Product__Type_OPair(U_12414,U_12414),U_12413),U_12412)),U_12416))
& hAPP(U_12418,U_12413) = hAPP(U_12418,U_12412)
& hBOOL(hAPP(hAPP(c_member(U_12414),U_12412),U_12415)) )
& hBOOL(hAPP(hAPP(c_member(U_12414),U_12413),U_12415)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12414,tc_HOL_Obool)),U_12420),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12414),U_12415),U_12416)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12414,tc_HOL_Obool)),U_12419),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12414),U_12415),U_12416)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12414,tc_fun(U_12417,tc_HOL_Obool)),U_12419),U_12418) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12414,tc_fun(U_12417,tc_HOL_Obool)),U_12420),U_12418)
| ~ c_Equiv__Relations_Ocongruent(U_12414,tc_fun(U_12417,tc_HOL_Obool),U_12416,U_12418)
| ~ c_Equiv__Relations_Oequiv(U_12414,U_12415,U_12416) ),
inference(variable_rename,[status(thm)],[f_3218_1]) ).
fof(f_3218_3,plain,
! [U_12420,U_12419,U_12418,U_12417,U_12416,U_12415,U_12414] :
( U_12419 = U_12420
| ( ? [U_12412] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12414,U_12414)),hAPP(hAPP(c_Product__Type_OPair(U_12414,U_12414),sK292(U_12420,U_12419,U_12418,U_12417,U_12416,U_12415,U_12414)),U_12412)),U_12416))
& hAPP(U_12418,sK292(U_12420,U_12419,U_12418,U_12417,U_12416,U_12415,U_12414)) = hAPP(U_12418,U_12412)
& hBOOL(hAPP(hAPP(c_member(U_12414),U_12412),U_12415)) )
& hBOOL(hAPP(hAPP(c_member(U_12414),sK292(U_12420,U_12419,U_12418,U_12417,U_12416,U_12415,U_12414)),U_12415)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12414,tc_HOL_Obool)),U_12420),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12414),U_12415),U_12416)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12414,tc_HOL_Obool)),U_12419),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12414),U_12415),U_12416)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12414,tc_fun(U_12417,tc_HOL_Obool)),U_12419),U_12418) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12414,tc_fun(U_12417,tc_HOL_Obool)),U_12420),U_12418)
| ~ c_Equiv__Relations_Ocongruent(U_12414,tc_fun(U_12417,tc_HOL_Obool),U_12416,U_12418)
| ~ c_Equiv__Relations_Oequiv(U_12414,U_12415,U_12416) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK292]),skolemize(U_12413,sK292(U_12420,U_12419,U_12418,U_12417,U_12416,U_12415,U_12414))],[f_3218_2]) ).
fof(f_3218_4,plain,
! [U_12420,U_12419,U_12418,U_12417,U_12416,U_12415,U_12414] :
( U_12419 = U_12420
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12414,U_12414)),hAPP(hAPP(c_Product__Type_OPair(U_12414,U_12414),sK292(U_12420,U_12419,U_12418,U_12417,U_12416,U_12415,U_12414)),sK293(U_12420,U_12419,U_12418,U_12417,U_12416,U_12415,U_12414))),U_12416))
& hAPP(U_12418,sK292(U_12420,U_12419,U_12418,U_12417,U_12416,U_12415,U_12414)) = hAPP(U_12418,sK293(U_12420,U_12419,U_12418,U_12417,U_12416,U_12415,U_12414))
& hBOOL(hAPP(hAPP(c_member(U_12414),sK293(U_12420,U_12419,U_12418,U_12417,U_12416,U_12415,U_12414)),U_12415))
& hBOOL(hAPP(hAPP(c_member(U_12414),sK292(U_12420,U_12419,U_12418,U_12417,U_12416,U_12415,U_12414)),U_12415)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12414,tc_HOL_Obool)),U_12420),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12414),U_12415),U_12416)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12414,tc_HOL_Obool)),U_12419),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12414),U_12415),U_12416)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12414,tc_fun(U_12417,tc_HOL_Obool)),U_12419),U_12418) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12414,tc_fun(U_12417,tc_HOL_Obool)),U_12420),U_12418)
| ~ c_Equiv__Relations_Ocongruent(U_12414,tc_fun(U_12417,tc_HOL_Obool),U_12416,U_12418)
| ~ c_Equiv__Relations_Oequiv(U_12414,U_12415,U_12416) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK293]),skolemize(U_12412,sK293(U_12420,U_12419,U_12418,U_12417,U_12416,U_12415,U_12414))],[f_3218_3]) ).
cnf(f_3218_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_12414),sK292(U_12420,U_12419,U_12418,U_12417,U_12416,U_12415,U_12414)),U_12415))
| U_12419 = U_12420
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12414,tc_HOL_Obool)),U_12420),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12414),U_12415),U_12416)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12414,tc_HOL_Obool)),U_12419),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12414),U_12415),U_12416)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12414,tc_fun(U_12417,tc_HOL_Obool)),U_12419),U_12418) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12414,tc_fun(U_12417,tc_HOL_Obool)),U_12420),U_12418)
| ~ c_Equiv__Relations_Ocongruent(U_12414,tc_fun(U_12417,tc_HOL_Obool),U_12416,U_12418)
| ~ c_Equiv__Relations_Oequiv(U_12414,U_12415,U_12416) ),
inference(clausify,[status(thm)],[f_3218_4]) ).
cnf(f_3218_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_12414),sK293(U_12420,U_12419,U_12418,U_12417,U_12416,U_12415,U_12414)),U_12415))
| U_12419 = U_12420
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12414,tc_HOL_Obool)),U_12420),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12414),U_12415),U_12416)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12414,tc_HOL_Obool)),U_12419),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12414),U_12415),U_12416)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12414,tc_fun(U_12417,tc_HOL_Obool)),U_12419),U_12418) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12414,tc_fun(U_12417,tc_HOL_Obool)),U_12420),U_12418)
| ~ c_Equiv__Relations_Ocongruent(U_12414,tc_fun(U_12417,tc_HOL_Obool),U_12416,U_12418)
| ~ c_Equiv__Relations_Oequiv(U_12414,U_12415,U_12416) ),
inference(clausify,[status(thm)],[f_3218_4]) ).
cnf(f_3218_7,plain,
( hAPP(U_12418,sK292(U_12420,U_12419,U_12418,U_12417,U_12416,U_12415,U_12414)) = hAPP(U_12418,sK293(U_12420,U_12419,U_12418,U_12417,U_12416,U_12415,U_12414))
| U_12419 = U_12420
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12414,tc_HOL_Obool)),U_12420),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12414),U_12415),U_12416)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12414,tc_HOL_Obool)),U_12419),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12414),U_12415),U_12416)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12414,tc_fun(U_12417,tc_HOL_Obool)),U_12419),U_12418) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12414,tc_fun(U_12417,tc_HOL_Obool)),U_12420),U_12418)
| ~ c_Equiv__Relations_Ocongruent(U_12414,tc_fun(U_12417,tc_HOL_Obool),U_12416,U_12418)
| ~ c_Equiv__Relations_Oequiv(U_12414,U_12415,U_12416) ),
inference(clausify,[status(thm)],[f_3218_4]) ).
cnf(f_3218_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12414,U_12414)),hAPP(hAPP(c_Product__Type_OPair(U_12414,U_12414),sK292(U_12420,U_12419,U_12418,U_12417,U_12416,U_12415,U_12414)),sK293(U_12420,U_12419,U_12418,U_12417,U_12416,U_12415,U_12414))),U_12416))
| U_12419 = U_12420
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12414,tc_HOL_Obool)),U_12420),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12414),U_12415),U_12416)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12414,tc_HOL_Obool)),U_12419),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12414),U_12415),U_12416)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12414,tc_fun(U_12417,tc_HOL_Obool)),U_12419),U_12418) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12414,tc_fun(U_12417,tc_HOL_Obool)),U_12420),U_12418)
| ~ c_Equiv__Relations_Ocongruent(U_12414,tc_fun(U_12417,tc_HOL_Obool),U_12416,U_12418)
| ~ c_Equiv__Relations_Oequiv(U_12414,U_12415,U_12416) ),
inference(clausify,[status(thm)],[f_3218_4]) ).
fof(f_3219_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_3219_2,plain,
! [U_12433,U_12432,U_12431,U_12430,U_12429,U_12428,U_12427,U_12426,U_12425,U_12424,U_12423] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_12429,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12423,tc_fun(U_12429,tc_HOL_Obool)),U_12431),hAPP(hAPP(c_COMBB(tc_fun(U_12426,tc_fun(U_12429,tc_HOL_Obool)),tc_fun(U_12429,tc_HOL_Obool),U_12423),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12426,tc_fun(U_12429,tc_HOL_Obool)),U_12432)),U_12430))),U_12433))
| ? [U_12422] :
( ? [U_12421] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12429,tc_HOL_Obool)),hAPP(hAPP(U_12430,U_12422),U_12421)),U_12433))
& hBOOL(hAPP(hAPP(c_member(U_12426),U_12421),U_12427)) )
& hBOOL(hAPP(hAPP(c_member(U_12423),U_12422),U_12424)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12426,tc_HOL_Obool)),U_12432),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12426),U_12427),U_12428)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12423,tc_HOL_Obool)),U_12431),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12423),U_12424),U_12425)))
| ~ c_Equiv__Relations_Ocongruent2(U_12423,U_12426,tc_fun(U_12429,tc_HOL_Obool),U_12425,U_12428,U_12430)
| ~ c_Equiv__Relations_Oequiv(U_12426,U_12427,U_12428)
| ~ c_Equiv__Relations_Oequiv(U_12423,U_12424,U_12425) ),
inference(variable_rename,[status(thm)],[f_3219_1]) ).
fof(f_3219_3,plain,
! [U_12433,U_12432,U_12431,U_12430,U_12429,U_12428,U_12427,U_12426,U_12425,U_12424,U_12423] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_12429,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12423,tc_fun(U_12429,tc_HOL_Obool)),U_12431),hAPP(hAPP(c_COMBB(tc_fun(U_12426,tc_fun(U_12429,tc_HOL_Obool)),tc_fun(U_12429,tc_HOL_Obool),U_12423),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12426,tc_fun(U_12429,tc_HOL_Obool)),U_12432)),U_12430))),U_12433))
| ( ? [U_12421] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12429,tc_HOL_Obool)),hAPP(hAPP(U_12430,sK294(U_12433,U_12432,U_12431,U_12430,U_12429,U_12428,U_12427,U_12426,U_12425,U_12424,U_12423)),U_12421)),U_12433))
& hBOOL(hAPP(hAPP(c_member(U_12426),U_12421),U_12427)) )
& hBOOL(hAPP(hAPP(c_member(U_12423),sK294(U_12433,U_12432,U_12431,U_12430,U_12429,U_12428,U_12427,U_12426,U_12425,U_12424,U_12423)),U_12424)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12426,tc_HOL_Obool)),U_12432),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12426),U_12427),U_12428)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12423,tc_HOL_Obool)),U_12431),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12423),U_12424),U_12425)))
| ~ c_Equiv__Relations_Ocongruent2(U_12423,U_12426,tc_fun(U_12429,tc_HOL_Obool),U_12425,U_12428,U_12430)
| ~ c_Equiv__Relations_Oequiv(U_12426,U_12427,U_12428)
| ~ c_Equiv__Relations_Oequiv(U_12423,U_12424,U_12425) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK294]),skolemize(U_12422,sK294(U_12433,U_12432,U_12431,U_12430,U_12429,U_12428,U_12427,U_12426,U_12425,U_12424,U_12423))],[f_3219_2]) ).
fof(f_3219_4,plain,
! [U_12433,U_12432,U_12431,U_12430,U_12429,U_12428,U_12427,U_12426,U_12425,U_12424,U_12423] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_12429,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12423,tc_fun(U_12429,tc_HOL_Obool)),U_12431),hAPP(hAPP(c_COMBB(tc_fun(U_12426,tc_fun(U_12429,tc_HOL_Obool)),tc_fun(U_12429,tc_HOL_Obool),U_12423),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12426,tc_fun(U_12429,tc_HOL_Obool)),U_12432)),U_12430))),U_12433))
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12429,tc_HOL_Obool)),hAPP(hAPP(U_12430,sK294(U_12433,U_12432,U_12431,U_12430,U_12429,U_12428,U_12427,U_12426,U_12425,U_12424,U_12423)),sK295(U_12433,U_12432,U_12431,U_12430,U_12429,U_12428,U_12427,U_12426,U_12425,U_12424,U_12423))),U_12433))
& hBOOL(hAPP(hAPP(c_member(U_12426),sK295(U_12433,U_12432,U_12431,U_12430,U_12429,U_12428,U_12427,U_12426,U_12425,U_12424,U_12423)),U_12427))
& hBOOL(hAPP(hAPP(c_member(U_12423),sK294(U_12433,U_12432,U_12431,U_12430,U_12429,U_12428,U_12427,U_12426,U_12425,U_12424,U_12423)),U_12424)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12426,tc_HOL_Obool)),U_12432),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12426),U_12427),U_12428)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12423,tc_HOL_Obool)),U_12431),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12423),U_12424),U_12425)))
| ~ c_Equiv__Relations_Ocongruent2(U_12423,U_12426,tc_fun(U_12429,tc_HOL_Obool),U_12425,U_12428,U_12430)
| ~ c_Equiv__Relations_Oequiv(U_12426,U_12427,U_12428)
| ~ c_Equiv__Relations_Oequiv(U_12423,U_12424,U_12425) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK295]),skolemize(U_12421,sK295(U_12433,U_12432,U_12431,U_12430,U_12429,U_12428,U_12427,U_12426,U_12425,U_12424,U_12423))],[f_3219_3]) ).
cnf(f_3219_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_12423),sK294(U_12433,U_12432,U_12431,U_12430,U_12429,U_12428,U_12427,U_12426,U_12425,U_12424,U_12423)),U_12424))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_12429,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12423,tc_fun(U_12429,tc_HOL_Obool)),U_12431),hAPP(hAPP(c_COMBB(tc_fun(U_12426,tc_fun(U_12429,tc_HOL_Obool)),tc_fun(U_12429,tc_HOL_Obool),U_12423),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12426,tc_fun(U_12429,tc_HOL_Obool)),U_12432)),U_12430))),U_12433))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12426,tc_HOL_Obool)),U_12432),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12426),U_12427),U_12428)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12423,tc_HOL_Obool)),U_12431),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12423),U_12424),U_12425)))
| ~ c_Equiv__Relations_Ocongruent2(U_12423,U_12426,tc_fun(U_12429,tc_HOL_Obool),U_12425,U_12428,U_12430)
| ~ c_Equiv__Relations_Oequiv(U_12426,U_12427,U_12428)
| ~ c_Equiv__Relations_Oequiv(U_12423,U_12424,U_12425) ),
inference(clausify,[status(thm)],[f_3219_4]) ).
cnf(f_3219_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_12426),sK295(U_12433,U_12432,U_12431,U_12430,U_12429,U_12428,U_12427,U_12426,U_12425,U_12424,U_12423)),U_12427))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_12429,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12423,tc_fun(U_12429,tc_HOL_Obool)),U_12431),hAPP(hAPP(c_COMBB(tc_fun(U_12426,tc_fun(U_12429,tc_HOL_Obool)),tc_fun(U_12429,tc_HOL_Obool),U_12423),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12426,tc_fun(U_12429,tc_HOL_Obool)),U_12432)),U_12430))),U_12433))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12426,tc_HOL_Obool)),U_12432),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12426),U_12427),U_12428)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12423,tc_HOL_Obool)),U_12431),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12423),U_12424),U_12425)))
| ~ c_Equiv__Relations_Ocongruent2(U_12423,U_12426,tc_fun(U_12429,tc_HOL_Obool),U_12425,U_12428,U_12430)
| ~ c_Equiv__Relations_Oequiv(U_12426,U_12427,U_12428)
| ~ c_Equiv__Relations_Oequiv(U_12423,U_12424,U_12425) ),
inference(clausify,[status(thm)],[f_3219_4]) ).
cnf(f_3219_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12429,tc_HOL_Obool)),hAPP(hAPP(U_12430,sK294(U_12433,U_12432,U_12431,U_12430,U_12429,U_12428,U_12427,U_12426,U_12425,U_12424,U_12423)),sK295(U_12433,U_12432,U_12431,U_12430,U_12429,U_12428,U_12427,U_12426,U_12425,U_12424,U_12423))),U_12433))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_12429,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12423,tc_fun(U_12429,tc_HOL_Obool)),U_12431),hAPP(hAPP(c_COMBB(tc_fun(U_12426,tc_fun(U_12429,tc_HOL_Obool)),tc_fun(U_12429,tc_HOL_Obool),U_12423),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12426,tc_fun(U_12429,tc_HOL_Obool)),U_12432)),U_12430))),U_12433))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12426,tc_HOL_Obool)),U_12432),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12426),U_12427),U_12428)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12423,tc_HOL_Obool)),U_12431),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12423),U_12424),U_12425)))
| ~ c_Equiv__Relations_Ocongruent2(U_12423,U_12426,tc_fun(U_12429,tc_HOL_Obool),U_12425,U_12428,U_12430)
| ~ c_Equiv__Relations_Oequiv(U_12426,U_12427,U_12428)
| ~ c_Equiv__Relations_Oequiv(U_12423,U_12424,U_12425) ),
inference(clausify,[status(thm)],[f_3219_4]) ).
fof(f_3220_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_3220_2,plain,
! [U_12441,U_12440,U_12439,U_12438,U_12437,U_12436,U_12435] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_12438,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12435,tc_fun(U_12438,tc_HOL_Obool)),U_12440),U_12439)),U_12441))
| ? [U_12434] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12438,tc_HOL_Obool)),hAPP(U_12439,U_12434)),U_12441))
& hBOOL(hAPP(hAPP(c_member(U_12435),U_12434),U_12436)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12435,tc_HOL_Obool)),U_12440),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12435),U_12436),U_12437)))
| ~ c_Equiv__Relations_Ocongruent(U_12435,tc_fun(U_12438,tc_HOL_Obool),U_12437,U_12439)
| ~ c_Equiv__Relations_Oequiv(U_12435,U_12436,U_12437) ),
inference(variable_rename,[status(thm)],[f_3220_1]) ).
fof(f_3220_3,plain,
! [U_12441,U_12440,U_12439,U_12438,U_12437,U_12436,U_12435] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_12438,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12435,tc_fun(U_12438,tc_HOL_Obool)),U_12440),U_12439)),U_12441))
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12438,tc_HOL_Obool)),hAPP(U_12439,sK296(U_12441,U_12440,U_12439,U_12438,U_12437,U_12436,U_12435))),U_12441))
& hBOOL(hAPP(hAPP(c_member(U_12435),sK296(U_12441,U_12440,U_12439,U_12438,U_12437,U_12436,U_12435)),U_12436)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12435,tc_HOL_Obool)),U_12440),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12435),U_12436),U_12437)))
| ~ c_Equiv__Relations_Ocongruent(U_12435,tc_fun(U_12438,tc_HOL_Obool),U_12437,U_12439)
| ~ c_Equiv__Relations_Oequiv(U_12435,U_12436,U_12437) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK296]),skolemize(U_12434,sK296(U_12441,U_12440,U_12439,U_12438,U_12437,U_12436,U_12435))],[f_3220_2]) ).
cnf(f_3220_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12435),sK296(U_12441,U_12440,U_12439,U_12438,U_12437,U_12436,U_12435)),U_12436))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_12438,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12435,tc_fun(U_12438,tc_HOL_Obool)),U_12440),U_12439)),U_12441))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12435,tc_HOL_Obool)),U_12440),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12435),U_12436),U_12437)))
| ~ c_Equiv__Relations_Ocongruent(U_12435,tc_fun(U_12438,tc_HOL_Obool),U_12437,U_12439)
| ~ c_Equiv__Relations_Oequiv(U_12435,U_12436,U_12437) ),
inference(clausify,[status(thm)],[f_3220_3]) ).
cnf(f_3220_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12438,tc_HOL_Obool)),hAPP(U_12439,sK296(U_12441,U_12440,U_12439,U_12438,U_12437,U_12436,U_12435))),U_12441))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_12438,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12435,tc_fun(U_12438,tc_HOL_Obool)),U_12440),U_12439)),U_12441))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12435,tc_HOL_Obool)),U_12440),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12435),U_12436),U_12437)))
| ~ c_Equiv__Relations_Ocongruent(U_12435,tc_fun(U_12438,tc_HOL_Obool),U_12437,U_12439)
| ~ c_Equiv__Relations_Oequiv(U_12435,U_12436,U_12437) ),
inference(clausify,[status(thm)],[f_3220_3]) ).
fof(f_3221_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_3221_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_3221_1]) ).
fof(f_3222_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_3222_2,plain,
! [U_12448,U_12447,U_12446] :
( ( c_Relation_Orefl__on(U_12446,U_12447,U_12448)
| ? [U_12445] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12446,U_12446)),hAPP(hAPP(c_Product__Type_OPair(U_12446,U_12446),U_12445),U_12445)),U_12448))
& hBOOL(hAPP(hAPP(c_member(U_12446),U_12445),U_12447)) )
| ? [U_12444] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12446,U_12446,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12446,tc_fun(U_12446,tc_HOL_Obool),tc_fun(U_12446,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12446,tc_HOL_Obool),tc_fun(U_12446,tc_HOL_Obool)),U_12446),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12446)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12446),c_fconj),hAPP(hAPP(c_COMBC(U_12446,tc_fun(U_12446,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12446)),U_12447)))),hAPP(hAPP(c_COMBC(U_12446,tc_fun(U_12446,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12446)),U_12447))),U_12444))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_12446,U_12446)),U_12444),U_12448)) ) )
& ( ( ! [U_12443] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12446,U_12446)),hAPP(hAPP(c_Product__Type_OPair(U_12446,U_12446),U_12443),U_12443)),U_12448))
| ~ hBOOL(hAPP(hAPP(c_member(U_12446),U_12443),U_12447)) )
& ! [U_12442] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12446,U_12446,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12446,tc_fun(U_12446,tc_HOL_Obool),tc_fun(U_12446,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12446,tc_HOL_Obool),tc_fun(U_12446,tc_HOL_Obool)),U_12446),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12446)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12446),c_fconj),hAPP(hAPP(c_COMBC(U_12446,tc_fun(U_12446,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12446)),U_12447)))),hAPP(hAPP(c_COMBC(U_12446,tc_fun(U_12446,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12446)),U_12447))),U_12442))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12446,U_12446)),U_12442),U_12448)) ) )
| ~ c_Relation_Orefl__on(U_12446,U_12447,U_12448) ) ),
inference(variable_rename,[status(thm)],[f_3222_1]) ).
fof(f_3222_3,plain,
( ! [U_12454,U_12452,U_12450] :
( c_Relation_Orefl__on(U_12450,U_12452,U_12454)
| ? [U_12445] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12450,U_12450)),hAPP(hAPP(c_Product__Type_OPair(U_12450,U_12450),U_12445),U_12445)),U_12454))
& hBOOL(hAPP(hAPP(c_member(U_12450),U_12445),U_12452)) )
| ? [U_12444] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12450,U_12450,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12450,tc_fun(U_12450,tc_HOL_Obool),tc_fun(U_12450,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12450,tc_HOL_Obool),tc_fun(U_12450,tc_HOL_Obool)),U_12450),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12450)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12450),c_fconj),hAPP(hAPP(c_COMBC(U_12450,tc_fun(U_12450,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12450)),U_12452)))),hAPP(hAPP(c_COMBC(U_12450,tc_fun(U_12450,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12450)),U_12452))),U_12444))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_12450,U_12450)),U_12444),U_12454)) ) )
& ! [U_12453,U_12451,U_12449] :
( ( ! [U_12443] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12449,U_12449)),hAPP(hAPP(c_Product__Type_OPair(U_12449,U_12449),U_12443),U_12443)),U_12453))
| ~ hBOOL(hAPP(hAPP(c_member(U_12449),U_12443),U_12451)) )
& ! [U_12442] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12449,U_12449,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12449,tc_fun(U_12449,tc_HOL_Obool),tc_fun(U_12449,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12449,tc_HOL_Obool),tc_fun(U_12449,tc_HOL_Obool)),U_12449),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12449)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12449),c_fconj),hAPP(hAPP(c_COMBC(U_12449,tc_fun(U_12449,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12449)),U_12451)))),hAPP(hAPP(c_COMBC(U_12449,tc_fun(U_12449,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12449)),U_12451))),U_12442))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12449,U_12449)),U_12442),U_12453)) ) )
| ~ c_Relation_Orefl__on(U_12449,U_12451,U_12453) ) ),
inference(miniscope,[status(thm)],[f_3222_2]) ).
fof(f_3222_4,plain,
( ! [U_12454,U_12452,U_12450] :
( c_Relation_Orefl__on(U_12450,U_12452,U_12454)
| ? [U_12445] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12450,U_12450)),hAPP(hAPP(c_Product__Type_OPair(U_12450,U_12450),U_12445),U_12445)),U_12454))
& hBOOL(hAPP(hAPP(c_member(U_12450),U_12445),U_12452)) )
| ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12450,U_12450,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12450,tc_fun(U_12450,tc_HOL_Obool),tc_fun(U_12450,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12450,tc_HOL_Obool),tc_fun(U_12450,tc_HOL_Obool)),U_12450),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12450)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12450),c_fconj),hAPP(hAPP(c_COMBC(U_12450,tc_fun(U_12450,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12450)),U_12452)))),hAPP(hAPP(c_COMBC(U_12450,tc_fun(U_12450,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12450)),U_12452))),sK297(U_12454,U_12452,U_12450)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_12450,U_12450)),sK297(U_12454,U_12452,U_12450)),U_12454)) ) )
& ! [U_12453,U_12451,U_12449] :
( ( ! [U_12443] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12449,U_12449)),hAPP(hAPP(c_Product__Type_OPair(U_12449,U_12449),U_12443),U_12443)),U_12453))
| ~ hBOOL(hAPP(hAPP(c_member(U_12449),U_12443),U_12451)) )
& ! [U_12442] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12449,U_12449,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12449,tc_fun(U_12449,tc_HOL_Obool),tc_fun(U_12449,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12449,tc_HOL_Obool),tc_fun(U_12449,tc_HOL_Obool)),U_12449),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12449)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12449),c_fconj),hAPP(hAPP(c_COMBC(U_12449,tc_fun(U_12449,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12449)),U_12451)))),hAPP(hAPP(c_COMBC(U_12449,tc_fun(U_12449,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12449)),U_12451))),U_12442))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12449,U_12449)),U_12442),U_12453)) ) )
| ~ c_Relation_Orefl__on(U_12449,U_12451,U_12453) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK297]),skolemize(U_12444,sK297(U_12454,U_12452,U_12450))],[f_3222_3]) ).
fof(f_3222_5,plain,
( ! [U_12454,U_12452,U_12450] :
( c_Relation_Orefl__on(U_12450,U_12452,U_12454)
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12450,U_12450)),hAPP(hAPP(c_Product__Type_OPair(U_12450,U_12450),sK298(U_12454,U_12452,U_12450)),sK298(U_12454,U_12452,U_12450))),U_12454))
& hBOOL(hAPP(hAPP(c_member(U_12450),sK298(U_12454,U_12452,U_12450)),U_12452)) )
| ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12450,U_12450,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12450,tc_fun(U_12450,tc_HOL_Obool),tc_fun(U_12450,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12450,tc_HOL_Obool),tc_fun(U_12450,tc_HOL_Obool)),U_12450),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12450)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12450),c_fconj),hAPP(hAPP(c_COMBC(U_12450,tc_fun(U_12450,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12450)),U_12452)))),hAPP(hAPP(c_COMBC(U_12450,tc_fun(U_12450,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12450)),U_12452))),sK297(U_12454,U_12452,U_12450)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_12450,U_12450)),sK297(U_12454,U_12452,U_12450)),U_12454)) ) )
& ! [U_12453,U_12451,U_12449] :
( ( ! [U_12443] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12449,U_12449)),hAPP(hAPP(c_Product__Type_OPair(U_12449,U_12449),U_12443),U_12443)),U_12453))
| ~ hBOOL(hAPP(hAPP(c_member(U_12449),U_12443),U_12451)) )
& ! [U_12442] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12449,U_12449,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12449,tc_fun(U_12449,tc_HOL_Obool),tc_fun(U_12449,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12449,tc_HOL_Obool),tc_fun(U_12449,tc_HOL_Obool)),U_12449),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12449)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12449),c_fconj),hAPP(hAPP(c_COMBC(U_12449,tc_fun(U_12449,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12449)),U_12451)))),hAPP(hAPP(c_COMBC(U_12449,tc_fun(U_12449,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12449)),U_12451))),U_12442))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12449,U_12449)),U_12442),U_12453)) ) )
| ~ c_Relation_Orefl__on(U_12449,U_12451,U_12453) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK298]),skolemize(U_12445,sK298(U_12454,U_12452,U_12450))],[f_3222_4]) ).
cnf(f_3222_6,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12449,U_12449,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12449,tc_fun(U_12449,tc_HOL_Obool),tc_fun(U_12449,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12449,tc_HOL_Obool),tc_fun(U_12449,tc_HOL_Obool)),U_12449),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12449)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12449),c_fconj),hAPP(hAPP(c_COMBC(U_12449,tc_fun(U_12449,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12449)),U_12451)))),hAPP(hAPP(c_COMBC(U_12449,tc_fun(U_12449,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12449)),U_12451))),U_12442))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12449,U_12449)),U_12442),U_12453))
| ~ c_Relation_Orefl__on(U_12449,U_12451,U_12453) ),
inference(clausify,[status(thm)],[f_3222_5]) ).
cnf(f_3222_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12449,U_12449)),hAPP(hAPP(c_Product__Type_OPair(U_12449,U_12449),U_12443),U_12443)),U_12453))
| ~ hBOOL(hAPP(hAPP(c_member(U_12449),U_12443),U_12451))
| ~ c_Relation_Orefl__on(U_12449,U_12451,U_12453) ),
inference(clausify,[status(thm)],[f_3222_5]) ).
cnf(f_3222_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_12450),sK298(U_12454,U_12452,U_12450)),U_12452))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_12450,U_12450)),sK297(U_12454,U_12452,U_12450)),U_12454))
| c_Relation_Orefl__on(U_12450,U_12452,U_12454) ),
inference(clausify,[status(thm)],[f_3222_5]) ).
cnf(f_3222_9,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12450,U_12450)),hAPP(hAPP(c_Product__Type_OPair(U_12450,U_12450),sK298(U_12454,U_12452,U_12450)),sK298(U_12454,U_12452,U_12450))),U_12454))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_12450,U_12450)),sK297(U_12454,U_12452,U_12450)),U_12454))
| c_Relation_Orefl__on(U_12450,U_12452,U_12454) ),
inference(clausify,[status(thm)],[f_3222_5]) ).
cnf(f_3222_10,plain,
( hBOOL(hAPP(hAPP(c_member(U_12450),sK298(U_12454,U_12452,U_12450)),U_12452))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12450,U_12450,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12450,tc_fun(U_12450,tc_HOL_Obool),tc_fun(U_12450,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12450,tc_HOL_Obool),tc_fun(U_12450,tc_HOL_Obool)),U_12450),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12450)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12450),c_fconj),hAPP(hAPP(c_COMBC(U_12450,tc_fun(U_12450,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12450)),U_12452)))),hAPP(hAPP(c_COMBC(U_12450,tc_fun(U_12450,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12450)),U_12452))),sK297(U_12454,U_12452,U_12450)))
| c_Relation_Orefl__on(U_12450,U_12452,U_12454) ),
inference(clausify,[status(thm)],[f_3222_5]) ).
cnf(f_3222_11,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12450,U_12450)),hAPP(hAPP(c_Product__Type_OPair(U_12450,U_12450),sK298(U_12454,U_12452,U_12450)),sK298(U_12454,U_12452,U_12450))),U_12454))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_12450,U_12450,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12450,tc_fun(U_12450,tc_HOL_Obool),tc_fun(U_12450,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12450,tc_HOL_Obool),tc_fun(U_12450,tc_HOL_Obool)),U_12450),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12450)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12450),c_fconj),hAPP(hAPP(c_COMBC(U_12450,tc_fun(U_12450,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12450)),U_12452)))),hAPP(hAPP(c_COMBC(U_12450,tc_fun(U_12450,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12450)),U_12452))),sK297(U_12454,U_12452,U_12450)))
| c_Relation_Orefl__on(U_12450,U_12452,U_12454) ),
inference(clausify,[status(thm)],[f_3222_5]) ).
fof(f_3223_1,plain,
! [V_A_2,V_c_2,T_b] :
( ? [B_x] :
( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_c_2),c_Relation_OId__on(T_b,V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_Id__onE]) ).
fof(f_3223_2,plain,
! [U_12458,U_12457,U_12456] :
( ? [U_12455] :
( U_12457 = hAPP(hAPP(c_Product__Type_OPair(U_12456,U_12456),U_12455),U_12455)
& hBOOL(hAPP(hAPP(c_member(U_12456),U_12455),U_12458)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12456,U_12456)),U_12457),c_Relation_OId__on(U_12456,U_12458))) ),
inference(variable_rename,[status(thm)],[f_3223_1]) ).
fof(f_3223_3,plain,
! [U_12458,U_12457,U_12456] :
( ( U_12457 = hAPP(hAPP(c_Product__Type_OPair(U_12456,U_12456),sK299(U_12458,U_12457,U_12456)),sK299(U_12458,U_12457,U_12456))
& hBOOL(hAPP(hAPP(c_member(U_12456),sK299(U_12458,U_12457,U_12456)),U_12458)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12456,U_12456)),U_12457),c_Relation_OId__on(U_12456,U_12458))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK299]),skolemize(U_12455,sK299(U_12458,U_12457,U_12456))],[f_3223_2]) ).
cnf(f_3223_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12456),sK299(U_12458,U_12457,U_12456)),U_12458))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12456,U_12456)),U_12457),c_Relation_OId__on(U_12456,U_12458))) ),
inference(clausify,[status(thm)],[f_3223_3]) ).
cnf(f_3223_5,plain,
( U_12457 = hAPP(hAPP(c_Product__Type_OPair(U_12456,U_12456),sK299(U_12458,U_12457,U_12456)),sK299(U_12458,U_12457,U_12456))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12456,U_12456)),U_12457),c_Relation_OId__on(U_12456,U_12458))) ),
inference(clausify,[status(thm)],[f_3223_3]) ).
fof(f_3224_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_3224_2,plain,
! [U_12460,U_12459] : c_Relation_Orefl__on(U_12459,U_12460,c_Relation_OId__on(U_12459,U_12460)),
inference(variable_rename,[status(thm)],[f_3224_1]) ).
cnf(f_3224_3,plain,
c_Relation_Orefl__on(U_12459,U_12460,c_Relation_OId__on(U_12459,U_12460)),
inference(clausify,[status(thm)],[f_3224_2]) ).
fof(f_3225_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_3225_2,plain,
! [U_12461] : c_Relation_Orefl__on(U_12461,c_Orderings_Obot__class_Obot(tc_fun(U_12461,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12461,U_12461),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_3225_1]) ).
cnf(f_3225_3,plain,
c_Relation_Orefl__on(U_12461,c_Orderings_Obot__class_Obot(tc_fun(U_12461,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12461,U_12461),tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_3225_2]) ).
fof(f_3226_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_3226_2,plain,
! [U_12466,U_12465,U_12464,U_12463,U_12462] :
( c_Relation_Orefl__on(U_12462,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12462,tc_HOL_Obool)),U_12463),U_12465),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12462,U_12462),tc_HOL_Obool)),U_12464),U_12466))
| ~ c_Relation_Orefl__on(U_12462,U_12465,U_12466)
| ~ c_Relation_Orefl__on(U_12462,U_12463,U_12464) ),
inference(variable_rename,[status(thm)],[f_3226_1]) ).
cnf(f_3226_3,plain,
( c_Relation_Orefl__on(U_12462,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12462,tc_HOL_Obool)),U_12463),U_12465),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12462,U_12462),tc_HOL_Obool)),U_12464),U_12466))
| ~ c_Relation_Orefl__on(U_12462,U_12465,U_12466)
| ~ c_Relation_Orefl__on(U_12462,U_12463,U_12464) ),
inference(clausify,[status(thm)],[f_3226_2]) ).
fof(f_3227_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_3227_2,plain,
! [U_12471,U_12470,U_12469,U_12468,U_12467] :
( c_Relation_Orefl__on(U_12467,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12467,tc_HOL_Obool)),U_12468),U_12470),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12467,U_12467),tc_HOL_Obool)),U_12469),U_12471))
| ~ c_Relation_Orefl__on(U_12467,U_12470,U_12471)
| ~ c_Relation_Orefl__on(U_12467,U_12468,U_12469) ),
inference(variable_rename,[status(thm)],[f_3227_1]) ).
cnf(f_3227_3,plain,
( c_Relation_Orefl__on(U_12467,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12467,tc_HOL_Obool)),U_12468),U_12470),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12467,U_12467),tc_HOL_Obool)),U_12469),U_12471))
| ~ c_Relation_Orefl__on(U_12467,U_12470,U_12471)
| ~ c_Relation_Orefl__on(U_12467,U_12468,U_12469) ),
inference(clausify,[status(thm)],[f_3227_2]) ).
fof(f_3228_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_3228_2,plain,
! [U_12472] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_12472)),c_Int_OInteg)),
inference(variable_rename,[status(thm)],[f_3228_1]) ).
cnf(f_3228_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_12472)),c_Int_OInteg)),
inference(clausify,[status(thm)],[f_3228_2]) ).
fof(f_3229_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_3229_2,plain,
! [U_12476,U_12475,U_12474,U_12473] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12473,U_12473)),hAPP(hAPP(c_Product__Type_OPair(U_12473,U_12473),U_12476),U_12476)),U_12475))
| ~ hBOOL(hAPP(hAPP(c_member(U_12473),U_12476),U_12474))
| ~ c_Relation_Orefl__on(U_12473,U_12474,U_12475) ),
inference(variable_rename,[status(thm)],[f_3229_1]) ).
cnf(f_3229_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12473,U_12473)),hAPP(hAPP(c_Product__Type_OPair(U_12473,U_12473),U_12476),U_12476)),U_12475))
| ~ hBOOL(hAPP(hAPP(c_member(U_12473),U_12476),U_12474))
| ~ c_Relation_Orefl__on(U_12473,U_12474,U_12475) ),
inference(clausify,[status(thm)],[f_3229_2]) ).
fof(f_3230_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_3230_2,plain,
! [U_12481,U_12480,U_12479,U_12478,U_12477] :
( hBOOL(hAPP(hAPP(c_member(U_12477),U_12480),U_12478))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12477,U_12477)),hAPP(hAPP(c_Product__Type_OPair(U_12477,U_12477),U_12480),U_12481)),U_12479))
| ~ c_Relation_Orefl__on(U_12477,U_12478,U_12479) ),
inference(variable_rename,[status(thm)],[f_3230_1]) ).
cnf(f_3230_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_12477),U_12480),U_12478))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12477,U_12477)),hAPP(hAPP(c_Product__Type_OPair(U_12477,U_12477),U_12480),U_12481)),U_12479))
| ~ c_Relation_Orefl__on(U_12477,U_12478,U_12479) ),
inference(clausify,[status(thm)],[f_3230_2]) ).
fof(f_3231_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_3231_2,plain,
! [U_12486,U_12485,U_12484,U_12483,U_12482] :
( hBOOL(hAPP(hAPP(c_member(U_12482),U_12486),U_12483))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12482,U_12482)),hAPP(hAPP(c_Product__Type_OPair(U_12482,U_12482),U_12485),U_12486)),U_12484))
| ~ c_Relation_Orefl__on(U_12482,U_12483,U_12484) ),
inference(variable_rename,[status(thm)],[f_3231_1]) ).
cnf(f_3231_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_12482),U_12486),U_12483))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12482,U_12482)),hAPP(hAPP(c_Product__Type_OPair(U_12482,U_12482),U_12485),U_12486)),U_12484))
| ~ c_Relation_Orefl__on(U_12482,U_12483,U_12484) ),
inference(clausify,[status(thm)],[f_3231_2]) ).
fof(f_3232_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_3232_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_3232_1]) ).
fof(f_3233_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_3233_2,plain,
! [U_12492,U_12491,U_12490,U_12489,U_12488] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12488),U_12491),U_12489) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12488),U_12492),U_12490)
| ? [U_12487] :
( hAPP(U_12491,U_12487) != hAPP(U_12492,U_12487)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12487)) )
| ~ c_Nat__Transfer_Onat__set(U_12490)
| U_12489 != U_12490
| ~ class_Groups_Ocomm__monoid__mult(U_12488)
| ~ class_Groups_Ocomm__monoid__add(U_12488) ),
inference(variable_rename,[status(thm)],[f_3233_1]) ).
fof(f_3233_3,plain,
! [U_12492,U_12491,U_12490,U_12489,U_12488] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12488),U_12491),U_12489) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12488),U_12492),U_12490)
| ( hAPP(U_12491,sK300(U_12492,U_12491,U_12490,U_12489,U_12488)) != hAPP(U_12492,sK300(U_12492,U_12491,U_12490,U_12489,U_12488))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK300(U_12492,U_12491,U_12490,U_12489,U_12488))) )
| ~ c_Nat__Transfer_Onat__set(U_12490)
| U_12489 != U_12490
| ~ class_Groups_Ocomm__monoid__mult(U_12488)
| ~ class_Groups_Ocomm__monoid__add(U_12488) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK300]),skolemize(U_12487,sK300(U_12492,U_12491,U_12490,U_12489,U_12488))],[f_3233_2]) ).
cnf(f_3233_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK300(U_12492,U_12491,U_12490,U_12489,U_12488)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12488),U_12491),U_12489) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12488),U_12492),U_12490)
| ~ c_Nat__Transfer_Onat__set(U_12490)
| U_12489 != U_12490
| ~ class_Groups_Ocomm__monoid__mult(U_12488)
| ~ class_Groups_Ocomm__monoid__add(U_12488) ),
inference(clausify,[status(thm)],[f_3233_3]) ).
cnf(f_3233_5,plain,
( hAPP(U_12491,sK300(U_12492,U_12491,U_12490,U_12489,U_12488)) != hAPP(U_12492,sK300(U_12492,U_12491,U_12490,U_12489,U_12488))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12488),U_12491),U_12489) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12488),U_12492),U_12490)
| ~ c_Nat__Transfer_Onat__set(U_12490)
| U_12489 != U_12490
| ~ class_Groups_Ocomm__monoid__mult(U_12488)
| ~ class_Groups_Ocomm__monoid__add(U_12488) ),
inference(clausify,[status(thm)],[f_3233_3]) ).
fof(f_3234_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_3234_2,plain,
! [U_12495,U_12494,U_12493] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_12493,hAPP(hAPP(c_COMBC(U_12493,tc_fun(tc_prod(U_12493,U_12493),tc_HOL_Obool),tc_fun(U_12493,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12493,tc_fun(tc_fun(tc_prod(U_12493,U_12493),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12493,U_12493),tc_HOL_Obool),tc_fun(U_12493,tc_HOL_Obool)),U_12493),c_COMBC(U_12493,tc_fun(tc_prod(U_12493,U_12493),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12493,tc_prod(U_12493,U_12493)),tc_fun(U_12493,tc_fun(tc_fun(tc_prod(U_12493,U_12493),tc_HOL_Obool),tc_HOL_Obool)),U_12493),hAPP(c_COMBB(tc_prod(U_12493,U_12493),tc_fun(tc_fun(tc_prod(U_12493,U_12493),tc_HOL_Obool),tc_HOL_Obool),U_12493),c_member(tc_prod(U_12493,U_12493)))),c_Product__Type_OPair(U_12493,U_12493)))),U_12494)),U_12495))
| ~ hBOOL(hAPP(hAPP(c_member(U_12493),U_12495),c_Wellfounded_Oacc(U_12493,U_12494))) )
& ( hBOOL(hAPP(hAPP(c_member(U_12493),U_12495),c_Wellfounded_Oacc(U_12493,U_12494)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_12493,hAPP(hAPP(c_COMBC(U_12493,tc_fun(tc_prod(U_12493,U_12493),tc_HOL_Obool),tc_fun(U_12493,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12493,tc_fun(tc_fun(tc_prod(U_12493,U_12493),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12493,U_12493),tc_HOL_Obool),tc_fun(U_12493,tc_HOL_Obool)),U_12493),c_COMBC(U_12493,tc_fun(tc_prod(U_12493,U_12493),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12493,tc_prod(U_12493,U_12493)),tc_fun(U_12493,tc_fun(tc_fun(tc_prod(U_12493,U_12493),tc_HOL_Obool),tc_HOL_Obool)),U_12493),hAPP(c_COMBB(tc_prod(U_12493,U_12493),tc_fun(tc_fun(tc_prod(U_12493,U_12493),tc_HOL_Obool),tc_HOL_Obool),U_12493),c_member(tc_prod(U_12493,U_12493)))),c_Product__Type_OPair(U_12493,U_12493)))),U_12494)),U_12495)) ) ),
inference(variable_rename,[status(thm)],[f_3234_1]) ).
fof(f_3234_3,plain,
( ! [U_12501,U_12499,U_12497] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_12497,hAPP(hAPP(c_COMBC(U_12497,tc_fun(tc_prod(U_12497,U_12497),tc_HOL_Obool),tc_fun(U_12497,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12497,tc_fun(tc_fun(tc_prod(U_12497,U_12497),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12497,U_12497),tc_HOL_Obool),tc_fun(U_12497,tc_HOL_Obool)),U_12497),c_COMBC(U_12497,tc_fun(tc_prod(U_12497,U_12497),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12497,tc_prod(U_12497,U_12497)),tc_fun(U_12497,tc_fun(tc_fun(tc_prod(U_12497,U_12497),tc_HOL_Obool),tc_HOL_Obool)),U_12497),hAPP(c_COMBB(tc_prod(U_12497,U_12497),tc_fun(tc_fun(tc_prod(U_12497,U_12497),tc_HOL_Obool),tc_HOL_Obool),U_12497),c_member(tc_prod(U_12497,U_12497)))),c_Product__Type_OPair(U_12497,U_12497)))),U_12499)),U_12501))
| ~ hBOOL(hAPP(hAPP(c_member(U_12497),U_12501),c_Wellfounded_Oacc(U_12497,U_12499))) )
& ! [U_12500,U_12498,U_12496] :
( hBOOL(hAPP(hAPP(c_member(U_12496),U_12500),c_Wellfounded_Oacc(U_12496,U_12498)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_12496,hAPP(hAPP(c_COMBC(U_12496,tc_fun(tc_prod(U_12496,U_12496),tc_HOL_Obool),tc_fun(U_12496,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12496,tc_fun(tc_fun(tc_prod(U_12496,U_12496),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12496,U_12496),tc_HOL_Obool),tc_fun(U_12496,tc_HOL_Obool)),U_12496),c_COMBC(U_12496,tc_fun(tc_prod(U_12496,U_12496),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12496,tc_prod(U_12496,U_12496)),tc_fun(U_12496,tc_fun(tc_fun(tc_prod(U_12496,U_12496),tc_HOL_Obool),tc_HOL_Obool)),U_12496),hAPP(c_COMBB(tc_prod(U_12496,U_12496),tc_fun(tc_fun(tc_prod(U_12496,U_12496),tc_HOL_Obool),tc_HOL_Obool),U_12496),c_member(tc_prod(U_12496,U_12496)))),c_Product__Type_OPair(U_12496,U_12496)))),U_12498)),U_12500)) ) ),
inference(miniscope,[status(thm)],[f_3234_2]) ).
cnf(f_3234_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12496),U_12500),c_Wellfounded_Oacc(U_12496,U_12498)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_12496,hAPP(hAPP(c_COMBC(U_12496,tc_fun(tc_prod(U_12496,U_12496),tc_HOL_Obool),tc_fun(U_12496,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12496,tc_fun(tc_fun(tc_prod(U_12496,U_12496),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12496,U_12496),tc_HOL_Obool),tc_fun(U_12496,tc_HOL_Obool)),U_12496),c_COMBC(U_12496,tc_fun(tc_prod(U_12496,U_12496),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12496,tc_prod(U_12496,U_12496)),tc_fun(U_12496,tc_fun(tc_fun(tc_prod(U_12496,U_12496),tc_HOL_Obool),tc_HOL_Obool)),U_12496),hAPP(c_COMBB(tc_prod(U_12496,U_12496),tc_fun(tc_fun(tc_prod(U_12496,U_12496),tc_HOL_Obool),tc_HOL_Obool),U_12496),c_member(tc_prod(U_12496,U_12496)))),c_Product__Type_OPair(U_12496,U_12496)))),U_12498)),U_12500)) ),
inference(clausify,[status(thm)],[f_3234_3]) ).
cnf(f_3234_5,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_12497,hAPP(hAPP(c_COMBC(U_12497,tc_fun(tc_prod(U_12497,U_12497),tc_HOL_Obool),tc_fun(U_12497,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12497,tc_fun(tc_fun(tc_prod(U_12497,U_12497),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12497,U_12497),tc_HOL_Obool),tc_fun(U_12497,tc_HOL_Obool)),U_12497),c_COMBC(U_12497,tc_fun(tc_prod(U_12497,U_12497),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12497,tc_prod(U_12497,U_12497)),tc_fun(U_12497,tc_fun(tc_fun(tc_prod(U_12497,U_12497),tc_HOL_Obool),tc_HOL_Obool)),U_12497),hAPP(c_COMBB(tc_prod(U_12497,U_12497),tc_fun(tc_fun(tc_prod(U_12497,U_12497),tc_HOL_Obool),tc_HOL_Obool),U_12497),c_member(tc_prod(U_12497,U_12497)))),c_Product__Type_OPair(U_12497,U_12497)))),U_12499)),U_12501))
| ~ hBOOL(hAPP(hAPP(c_member(U_12497),U_12501),c_Wellfounded_Oacc(U_12497,U_12499))) ),
inference(clausify,[status(thm)],[f_3234_3]) ).
fof(f_3235_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_3235_2,plain,
! [U_12504,U_12503,U_12502] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12502,tc_HOL_Obool)),c_Wellfounded_Oacc(U_12502,U_12504)),c_Wellfounded_Oacc(U_12502,U_12503)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12502,U_12502),tc_HOL_Obool)),U_12503),U_12504)) ),
inference(variable_rename,[status(thm)],[f_3235_1]) ).
cnf(f_3235_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12502,tc_HOL_Obool)),c_Wellfounded_Oacc(U_12502,U_12504)),c_Wellfounded_Oacc(U_12502,U_12503)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12502,U_12502),tc_HOL_Obool)),U_12503),U_12504)) ),
inference(clausify,[status(thm)],[f_3235_2]) ).
fof(f_3236_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_3236_2,plain,
! [U_12509,U_12508,U_12507] :
( ( hBOOL(hAPP(hAPP(c_member(U_12507),U_12508),c_Wellfounded_Oacc(U_12507,U_12509)))
| ? [U_12506] :
( ~ hBOOL(hAPP(hAPP(c_member(U_12507),U_12506),c_Wellfounded_Oacc(U_12507,U_12509)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_12507,U_12507)),hAPP(hAPP(c_Product__Type_OPair(U_12507,U_12507),U_12506),U_12508)),U_12509)) ) )
& ( ! [U_12505] :
( hBOOL(hAPP(hAPP(c_member(U_12507),U_12505),c_Wellfounded_Oacc(U_12507,U_12509)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12507,U_12507)),hAPP(hAPP(c_Product__Type_OPair(U_12507,U_12507),U_12505),U_12508)),U_12509)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12507),U_12508),c_Wellfounded_Oacc(U_12507,U_12509))) ) ),
inference(variable_rename,[status(thm)],[f_3236_1]) ).
fof(f_3236_3,plain,
( ! [U_12515,U_12513,U_12511] :
( hBOOL(hAPP(hAPP(c_member(U_12511),U_12513),c_Wellfounded_Oacc(U_12511,U_12515)))
| ? [U_12506] :
( ~ hBOOL(hAPP(hAPP(c_member(U_12511),U_12506),c_Wellfounded_Oacc(U_12511,U_12515)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_12511,U_12511)),hAPP(hAPP(c_Product__Type_OPair(U_12511,U_12511),U_12506),U_12513)),U_12515)) ) )
& ! [U_12514,U_12512,U_12510] :
( ! [U_12505] :
( hBOOL(hAPP(hAPP(c_member(U_12510),U_12505),c_Wellfounded_Oacc(U_12510,U_12514)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12510,U_12510)),hAPP(hAPP(c_Product__Type_OPair(U_12510,U_12510),U_12505),U_12512)),U_12514)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12510),U_12512),c_Wellfounded_Oacc(U_12510,U_12514))) ) ),
inference(miniscope,[status(thm)],[f_3236_2]) ).
fof(f_3236_4,plain,
( ! [U_12515,U_12513,U_12511] :
( hBOOL(hAPP(hAPP(c_member(U_12511),U_12513),c_Wellfounded_Oacc(U_12511,U_12515)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_12511),sK301(U_12515,U_12513,U_12511)),c_Wellfounded_Oacc(U_12511,U_12515)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_12511,U_12511)),hAPP(hAPP(c_Product__Type_OPair(U_12511,U_12511),sK301(U_12515,U_12513,U_12511)),U_12513)),U_12515)) ) )
& ! [U_12514,U_12512,U_12510] :
( ! [U_12505] :
( hBOOL(hAPP(hAPP(c_member(U_12510),U_12505),c_Wellfounded_Oacc(U_12510,U_12514)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12510,U_12510)),hAPP(hAPP(c_Product__Type_OPair(U_12510,U_12510),U_12505),U_12512)),U_12514)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12510),U_12512),c_Wellfounded_Oacc(U_12510,U_12514))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK301]),skolemize(U_12506,sK301(U_12515,U_12513,U_12511))],[f_3236_3]) ).
cnf(f_3236_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_12510),U_12505),c_Wellfounded_Oacc(U_12510,U_12514)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12510,U_12510)),hAPP(hAPP(c_Product__Type_OPair(U_12510,U_12510),U_12505),U_12512)),U_12514))
| ~ hBOOL(hAPP(hAPP(c_member(U_12510),U_12512),c_Wellfounded_Oacc(U_12510,U_12514))) ),
inference(clausify,[status(thm)],[f_3236_4]) ).
cnf(f_3236_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12511,U_12511)),hAPP(hAPP(c_Product__Type_OPair(U_12511,U_12511),sK301(U_12515,U_12513,U_12511)),U_12513)),U_12515))
| hBOOL(hAPP(hAPP(c_member(U_12511),U_12513),c_Wellfounded_Oacc(U_12511,U_12515))) ),
inference(clausify,[status(thm)],[f_3236_4]) ).
cnf(f_3236_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_12511),sK301(U_12515,U_12513,U_12511)),c_Wellfounded_Oacc(U_12511,U_12515)))
| hBOOL(hAPP(hAPP(c_member(U_12511),U_12513),c_Wellfounded_Oacc(U_12511,U_12515))) ),
inference(clausify,[status(thm)],[f_3236_4]) ).
fof(f_3237_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_3237_2,plain,
! [U_12519,U_12518,U_12517,U_12516] :
( hBOOL(hAPP(hAPP(c_member(U_12516),U_12519),c_Wellfounded_Oacc(U_12516,U_12518)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12516,U_12516)),hAPP(hAPP(c_Product__Type_OPair(U_12516,U_12516),U_12519),U_12517)),U_12518))
| ~ hBOOL(hAPP(hAPP(c_member(U_12516),U_12517),c_Wellfounded_Oacc(U_12516,U_12518))) ),
inference(variable_rename,[status(thm)],[f_3237_1]) ).
cnf(f_3237_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_12516),U_12519),c_Wellfounded_Oacc(U_12516,U_12518)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12516,U_12516)),hAPP(hAPP(c_Product__Type_OPair(U_12516,U_12516),U_12519),U_12517)),U_12518))
| ~ hBOOL(hAPP(hAPP(c_member(U_12516),U_12517),c_Wellfounded_Oacc(U_12516,U_12518))) ),
inference(clausify,[status(thm)],[f_3237_2]) ).
fof(f_3238_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_3238_2,plain,
! [U_12524,U_12523,U_12522,U_12521,U_12520] :
( hAPP(c_Set_Oimage(U_12520,U_12521,U_12522),c_Orderings_Otop__class_Otop(tc_fun(U_12520,tc_HOL_Obool))) = U_12524
| ~ c_Typedef_Otype__definition(U_12520,U_12521,U_12522,U_12523,U_12524) ),
inference(variable_rename,[status(thm)],[f_3238_1]) ).
cnf(f_3238_3,plain,
( hAPP(c_Set_Oimage(U_12520,U_12521,U_12522),c_Orderings_Otop__class_Otop(tc_fun(U_12520,tc_HOL_Obool))) = U_12524
| ~ c_Typedef_Otype__definition(U_12520,U_12521,U_12522,U_12523,U_12524) ),
inference(clausify,[status(thm)],[f_3238_2]) ).
fof(f_3239_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_3239_2,plain,
! [U_12529,U_12528,U_12527,U_12526,U_12525] :
( hAPP(c_Set_Oimage(U_12526,U_12525,U_12528),U_12529) = c_Orderings_Otop__class_Otop(tc_fun(U_12525,tc_HOL_Obool))
| ~ c_Typedef_Otype__definition(U_12525,U_12526,U_12527,U_12528,U_12529) ),
inference(variable_rename,[status(thm)],[f_3239_1]) ).
cnf(f_3239_3,plain,
( hAPP(c_Set_Oimage(U_12526,U_12525,U_12528),U_12529) = c_Orderings_Otop__class_Otop(tc_fun(U_12525,tc_HOL_Obool))
| ~ c_Typedef_Otype__definition(U_12525,U_12526,U_12527,U_12528,U_12529) ),
inference(clausify,[status(thm)],[f_3239_2]) ).
fof(f_3240_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_3240_2,plain,
! [U_12536,U_12535,U_12534,U_12533,U_12532,U_12531,U_12530] :
( ( ( hAPP(U_12533,U_12535) = hAPP(U_12533,U_12536)
| U_12535 != U_12536 )
& ( U_12535 = U_12536
| hAPP(U_12533,U_12535) != hAPP(U_12533,U_12536) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12531),U_12536),U_12534))
| ~ hBOOL(hAPP(hAPP(c_member(U_12531),U_12535),U_12534))
| ~ c_Typedef_Otype__definition(U_12530,U_12531,U_12532,U_12533,U_12534) ),
inference(variable_rename,[status(thm)],[f_3240_1]) ).
fof(f_3240_3,plain,
! [U_12536,U_12535,U_12534,U_12533,U_12532,U_12531] :
( ! [U_12530] : ~ c_Typedef_Otype__definition(U_12530,U_12531,U_12532,U_12533,U_12534)
| ( ( hAPP(U_12533,U_12535) = hAPP(U_12533,U_12536)
| U_12535 != U_12536 )
& ( U_12535 = U_12536
| hAPP(U_12533,U_12535) != hAPP(U_12533,U_12536) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12531),U_12536),U_12534))
| ~ hBOOL(hAPP(hAPP(c_member(U_12531),U_12535),U_12534)) ),
inference(miniscope,[status(thm)],[f_3240_2]) ).
cnf(f_3240_4,plain,
( U_12535 = U_12536
| hAPP(U_12533,U_12535) != hAPP(U_12533,U_12536)
| ~ hBOOL(hAPP(hAPP(c_member(U_12531),U_12536),U_12534))
| ~ hBOOL(hAPP(hAPP(c_member(U_12531),U_12535),U_12534))
| ~ c_Typedef_Otype__definition(U_12530,U_12531,U_12532,U_12533,U_12534) ),
inference(clausify,[status(thm)],[f_3240_3]) ).
cnf(f_3240_5,plain,
( hAPP(U_12533,U_12535) = hAPP(U_12533,U_12536)
| U_12535 != U_12536
| ~ hBOOL(hAPP(hAPP(c_member(U_12531),U_12536),U_12534))
| ~ hBOOL(hAPP(hAPP(c_member(U_12531),U_12535),U_12534))
| ~ c_Typedef_Otype__definition(U_12530,U_12531,U_12532,U_12533,U_12534) ),
inference(clausify,[status(thm)],[f_3240_3]) ).
fof(f_3241_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_3241_2,plain,
! [U_12543,U_12542,U_12541,U_12540,U_12539,U_12538,U_12537] :
( ( ( hAPP(U_12539,U_12542) = hAPP(U_12539,U_12543)
| U_12542 != U_12543 )
& ( U_12542 = U_12543
| hAPP(U_12539,U_12542) != hAPP(U_12539,U_12543) ) )
| ~ c_Typedef_Otype__definition(U_12537,U_12538,U_12539,U_12540,U_12541) ),
inference(variable_rename,[status(thm)],[f_3241_1]) ).
fof(f_3241_3,plain,
! [U_12543,U_12542,U_12541,U_12540,U_12539] :
( ! [U_12538,U_12537] : ~ c_Typedef_Otype__definition(U_12537,U_12538,U_12539,U_12540,U_12541)
| ( ( hAPP(U_12539,U_12542) = hAPP(U_12539,U_12543)
| U_12542 != U_12543 )
& ( U_12542 = U_12543
| hAPP(U_12539,U_12542) != hAPP(U_12539,U_12543) ) ) ),
inference(miniscope,[status(thm)],[f_3241_2]) ).
cnf(f_3241_4,plain,
( U_12542 = U_12543
| hAPP(U_12539,U_12542) != hAPP(U_12539,U_12543)
| ~ c_Typedef_Otype__definition(U_12537,U_12538,U_12539,U_12540,U_12541) ),
inference(clausify,[status(thm)],[f_3241_3]) ).
cnf(f_3241_5,plain,
( hAPP(U_12539,U_12542) = hAPP(U_12539,U_12543)
| U_12542 != U_12543
| ~ c_Typedef_Otype__definition(U_12537,U_12538,U_12539,U_12540,U_12541) ),
inference(clausify,[status(thm)],[f_3241_3]) ).
fof(f_3242_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_3242_2,plain,
! [U_12549,U_12548,U_12547,U_12546,U_12545,U_12544] :
( hAPP(U_12547,hAPP(U_12546,U_12549)) = U_12549
| ~ c_Typedef_Otype__definition(U_12544,U_12545,U_12546,U_12547,U_12548) ),
inference(variable_rename,[status(thm)],[f_3242_1]) ).
fof(f_3242_3,plain,
! [U_12549,U_12548,U_12547,U_12546] :
( ! [U_12545,U_12544] : ~ c_Typedef_Otype__definition(U_12544,U_12545,U_12546,U_12547,U_12548)
| hAPP(U_12547,hAPP(U_12546,U_12549)) = U_12549 ),
inference(miniscope,[status(thm)],[f_3242_2]) ).
cnf(f_3242_4,plain,
( ~ c_Typedef_Otype__definition(U_12544,U_12545,U_12546,U_12547,U_12548)
| hAPP(U_12547,hAPP(U_12546,U_12549)) = U_12549 ),
inference(clausify,[status(thm)],[f_3242_3]) ).
fof(f_3243_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_3243_2,plain,
! [U_12555,U_12554,U_12553,U_12552,U_12551,U_12550] :
( hBOOL(hAPP(hAPP(c_member(U_12551),hAPP(U_12552,U_12555)),U_12554))
| ~ c_Typedef_Otype__definition(U_12550,U_12551,U_12552,U_12553,U_12554) ),
inference(variable_rename,[status(thm)],[f_3243_1]) ).
fof(f_3243_3,plain,
! [U_12555,U_12554,U_12553,U_12552,U_12551] :
( ! [U_12550] : ~ c_Typedef_Otype__definition(U_12550,U_12551,U_12552,U_12553,U_12554)
| hBOOL(hAPP(hAPP(c_member(U_12551),hAPP(U_12552,U_12555)),U_12554)) ),
inference(miniscope,[status(thm)],[f_3243_2]) ).
cnf(f_3243_4,plain,
( ~ c_Typedef_Otype__definition(U_12550,U_12551,U_12552,U_12553,U_12554)
| hBOOL(hAPP(hAPP(c_member(U_12551),hAPP(U_12552,U_12555)),U_12554)) ),
inference(clausify,[status(thm)],[f_3243_3]) ).
fof(f_3244_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_3244_2,plain,
! [U_12561,U_12560,U_12559,U_12558,U_12557,U_12556] :
( hAPP(U_12558,hAPP(U_12559,U_12561)) = U_12561
| ~ hBOOL(hAPP(hAPP(c_member(U_12557),U_12561),U_12560))
| ~ c_Typedef_Otype__definition(U_12556,U_12557,U_12558,U_12559,U_12560) ),
inference(variable_rename,[status(thm)],[f_3244_1]) ).
fof(f_3244_3,plain,
! [U_12561,U_12560,U_12559,U_12558,U_12557] :
( ! [U_12556] : ~ c_Typedef_Otype__definition(U_12556,U_12557,U_12558,U_12559,U_12560)
| hAPP(U_12558,hAPP(U_12559,U_12561)) = U_12561
| ~ hBOOL(hAPP(hAPP(c_member(U_12557),U_12561),U_12560)) ),
inference(miniscope,[status(thm)],[f_3244_2]) ).
cnf(f_3244_4,plain,
( ~ c_Typedef_Otype__definition(U_12556,U_12557,U_12558,U_12559,U_12560)
| hAPP(U_12558,hAPP(U_12559,U_12561)) = U_12561
| ~ hBOOL(hAPP(hAPP(c_member(U_12557),U_12561),U_12560)) ),
inference(clausify,[status(thm)],[f_3244_3]) ).
fof(f_3245_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_3245_2,plain,
! [U_12569,U_12568,U_12567,U_12566] :
( ( c_Wellfounded_Omax__extp(U_12566,U_12567,U_12568,U_12569)
| ? [U_12565] :
( ! [U_12564] :
( ~ hBOOL(hAPP(hAPP(U_12567,U_12565),U_12564))
| ~ hBOOL(hAPP(hAPP(c_member(U_12566),U_12564),U_12569)) )
& hBOOL(hAPP(hAPP(c_member(U_12566),U_12565),U_12568)) )
| U_12569 = c_Orderings_Obot__class_Obot(tc_fun(U_12566,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12566),U_12569))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12566),U_12568)) )
& ( ( ! [U_12563] :
( ? [U_12562] :
( hBOOL(hAPP(hAPP(U_12567,U_12563),U_12562))
& hBOOL(hAPP(hAPP(c_member(U_12566),U_12562),U_12569)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12566),U_12563),U_12568)) )
& U_12569 != c_Orderings_Obot__class_Obot(tc_fun(U_12566,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_12566),U_12569))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_12566),U_12568)) )
| ~ c_Wellfounded_Omax__extp(U_12566,U_12567,U_12568,U_12569) ) ),
inference(variable_rename,[status(thm)],[f_3245_1]) ).
fof(f_3245_3,plain,
( ! [U_12577,U_12575,U_12573,U_12571] :
( c_Wellfounded_Omax__extp(U_12571,U_12573,U_12575,U_12577)
| ? [U_12565] :
( ! [U_12564] :
( ~ hBOOL(hAPP(hAPP(U_12573,U_12565),U_12564))
| ~ hBOOL(hAPP(hAPP(c_member(U_12571),U_12564),U_12577)) )
& hBOOL(hAPP(hAPP(c_member(U_12571),U_12565),U_12575)) )
| U_12577 = c_Orderings_Obot__class_Obot(tc_fun(U_12571,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12571),U_12577))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12571),U_12575)) )
& ! [U_12576,U_12574,U_12572,U_12570] :
( ( ! [U_12563] :
( ? [U_12562] :
( hBOOL(hAPP(hAPP(U_12572,U_12563),U_12562))
& hBOOL(hAPP(hAPP(c_member(U_12570),U_12562),U_12576)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12570),U_12563),U_12574)) )
& U_12576 != c_Orderings_Obot__class_Obot(tc_fun(U_12570,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_12570),U_12576))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_12570),U_12574)) )
| ~ c_Wellfounded_Omax__extp(U_12570,U_12572,U_12574,U_12576) ) ),
inference(miniscope,[status(thm)],[f_3245_2]) ).
fof(f_3245_4,plain,
( ! [U_12577,U_12575,U_12573,U_12571] :
( c_Wellfounded_Omax__extp(U_12571,U_12573,U_12575,U_12577)
| ? [U_12565] :
( ! [U_12564] :
( ~ hBOOL(hAPP(hAPP(U_12573,U_12565),U_12564))
| ~ hBOOL(hAPP(hAPP(c_member(U_12571),U_12564),U_12577)) )
& hBOOL(hAPP(hAPP(c_member(U_12571),U_12565),U_12575)) )
| U_12577 = c_Orderings_Obot__class_Obot(tc_fun(U_12571,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12571),U_12577))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12571),U_12575)) )
& ! [U_12576,U_12574,U_12572,U_12570] :
( ( ! [U_12563] :
( ( hBOOL(hAPP(hAPP(U_12572,U_12563),sK302(U_12576,U_12574,U_12572,U_12570,U_12563)))
& hBOOL(hAPP(hAPP(c_member(U_12570),sK302(U_12576,U_12574,U_12572,U_12570,U_12563)),U_12576)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12570),U_12563),U_12574)) )
& U_12576 != c_Orderings_Obot__class_Obot(tc_fun(U_12570,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_12570),U_12576))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_12570),U_12574)) )
| ~ c_Wellfounded_Omax__extp(U_12570,U_12572,U_12574,U_12576) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK302]),skolemize(U_12562,sK302(U_12576,U_12574,U_12572,U_12570,U_12563))],[f_3245_3]) ).
fof(f_3245_5,plain,
( ! [U_12577,U_12575,U_12573,U_12571] :
( c_Wellfounded_Omax__extp(U_12571,U_12573,U_12575,U_12577)
| ( ! [U_12564] :
( ~ hBOOL(hAPP(hAPP(U_12573,sK303(U_12577,U_12575,U_12573,U_12571)),U_12564))
| ~ hBOOL(hAPP(hAPP(c_member(U_12571),U_12564),U_12577)) )
& hBOOL(hAPP(hAPP(c_member(U_12571),sK303(U_12577,U_12575,U_12573,U_12571)),U_12575)) )
| U_12577 = c_Orderings_Obot__class_Obot(tc_fun(U_12571,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12571),U_12577))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12571),U_12575)) )
& ! [U_12576,U_12574,U_12572,U_12570] :
( ( ! [U_12563] :
( ( hBOOL(hAPP(hAPP(U_12572,U_12563),sK302(U_12576,U_12574,U_12572,U_12570,U_12563)))
& hBOOL(hAPP(hAPP(c_member(U_12570),sK302(U_12576,U_12574,U_12572,U_12570,U_12563)),U_12576)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12570),U_12563),U_12574)) )
& U_12576 != c_Orderings_Obot__class_Obot(tc_fun(U_12570,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_12570),U_12576))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_12570),U_12574)) )
| ~ c_Wellfounded_Omax__extp(U_12570,U_12572,U_12574,U_12576) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK303]),skolemize(U_12565,sK303(U_12577,U_12575,U_12573,U_12571))],[f_3245_4]) ).
cnf(f_3245_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12570),U_12574))
| ~ c_Wellfounded_Omax__extp(U_12570,U_12572,U_12574,U_12576) ),
inference(clausify,[status(thm)],[f_3245_5]) ).
cnf(f_3245_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12570),U_12576))
| ~ c_Wellfounded_Omax__extp(U_12570,U_12572,U_12574,U_12576) ),
inference(clausify,[status(thm)],[f_3245_5]) ).
cnf(f_3245_8,plain,
( U_12576 != c_Orderings_Obot__class_Obot(tc_fun(U_12570,tc_HOL_Obool))
| ~ c_Wellfounded_Omax__extp(U_12570,U_12572,U_12574,U_12576) ),
inference(clausify,[status(thm)],[f_3245_5]) ).
cnf(f_3245_9,plain,
( hBOOL(hAPP(hAPP(c_member(U_12570),sK302(U_12576,U_12574,U_12572,U_12570,U_12563)),U_12576))
| ~ hBOOL(hAPP(hAPP(c_member(U_12570),U_12563),U_12574))
| ~ c_Wellfounded_Omax__extp(U_12570,U_12572,U_12574,U_12576) ),
inference(clausify,[status(thm)],[f_3245_5]) ).
cnf(f_3245_10,plain,
( hBOOL(hAPP(hAPP(U_12572,U_12563),sK302(U_12576,U_12574,U_12572,U_12570,U_12563)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12570),U_12563),U_12574))
| ~ c_Wellfounded_Omax__extp(U_12570,U_12572,U_12574,U_12576) ),
inference(clausify,[status(thm)],[f_3245_5]) ).
cnf(f_3245_11,plain,
( hBOOL(hAPP(hAPP(c_member(U_12571),sK303(U_12577,U_12575,U_12573,U_12571)),U_12575))
| U_12577 = c_Orderings_Obot__class_Obot(tc_fun(U_12571,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12571),U_12577))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12571),U_12575))
| c_Wellfounded_Omax__extp(U_12571,U_12573,U_12575,U_12577) ),
inference(clausify,[status(thm)],[f_3245_5]) ).
cnf(f_3245_12,plain,
( ~ hBOOL(hAPP(hAPP(U_12573,sK303(U_12577,U_12575,U_12573,U_12571)),U_12564))
| ~ hBOOL(hAPP(hAPP(c_member(U_12571),U_12564),U_12577))
| U_12577 = c_Orderings_Obot__class_Obot(tc_fun(U_12571,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12571),U_12577))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12571),U_12575))
| c_Wellfounded_Omax__extp(U_12571,U_12573,U_12575,U_12577) ),
inference(clausify,[status(thm)],[f_3245_5]) ).
fof(f_3246_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_3246_2,plain,
! [U_12583,U_12582,U_12581,U_12580] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_12580,tc_HOL_Obool),tc_fun(U_12580,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_12580,tc_HOL_Obool),tc_fun(U_12580,tc_HOL_Obool)),U_12581),U_12582)),c_Wellfounded_Omax__ext(U_12580,U_12583)))
| ? [U_12579] :
( ! [U_12578] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12580,U_12580)),hAPP(hAPP(c_Product__Type_OPair(U_12580,U_12580),U_12579),U_12578)),U_12583))
| ~ hBOOL(hAPP(hAPP(c_member(U_12580),U_12578),U_12582)) )
& hBOOL(hAPP(hAPP(c_member(U_12580),U_12579),U_12581)) )
| U_12582 = c_Orderings_Obot__class_Obot(tc_fun(U_12580,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12580),U_12582))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12580),U_12581)) ),
inference(variable_rename,[status(thm)],[f_3246_1]) ).
fof(f_3246_3,plain,
! [U_12583,U_12582,U_12581,U_12580] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_12580,tc_HOL_Obool),tc_fun(U_12580,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_12580,tc_HOL_Obool),tc_fun(U_12580,tc_HOL_Obool)),U_12581),U_12582)),c_Wellfounded_Omax__ext(U_12580,U_12583)))
| ( ! [U_12578] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12580,U_12580)),hAPP(hAPP(c_Product__Type_OPair(U_12580,U_12580),sK304(U_12583,U_12582,U_12581,U_12580)),U_12578)),U_12583))
| ~ hBOOL(hAPP(hAPP(c_member(U_12580),U_12578),U_12582)) )
& hBOOL(hAPP(hAPP(c_member(U_12580),sK304(U_12583,U_12582,U_12581,U_12580)),U_12581)) )
| U_12582 = c_Orderings_Obot__class_Obot(tc_fun(U_12580,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12580),U_12582))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12580),U_12581)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK304]),skolemize(U_12579,sK304(U_12583,U_12582,U_12581,U_12580))],[f_3246_2]) ).
cnf(f_3246_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12580),sK304(U_12583,U_12582,U_12581,U_12580)),U_12581))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_12580,tc_HOL_Obool),tc_fun(U_12580,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_12580,tc_HOL_Obool),tc_fun(U_12580,tc_HOL_Obool)),U_12581),U_12582)),c_Wellfounded_Omax__ext(U_12580,U_12583)))
| U_12582 = c_Orderings_Obot__class_Obot(tc_fun(U_12580,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12580),U_12582))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12580),U_12581)) ),
inference(clausify,[status(thm)],[f_3246_3]) ).
cnf(f_3246_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12580,U_12580)),hAPP(hAPP(c_Product__Type_OPair(U_12580,U_12580),sK304(U_12583,U_12582,U_12581,U_12580)),U_12578)),U_12583))
| ~ hBOOL(hAPP(hAPP(c_member(U_12580),U_12578),U_12582))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_12580,tc_HOL_Obool),tc_fun(U_12580,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_12580,tc_HOL_Obool),tc_fun(U_12580,tc_HOL_Obool)),U_12581),U_12582)),c_Wellfounded_Omax__ext(U_12580,U_12583)))
| U_12582 = c_Orderings_Obot__class_Obot(tc_fun(U_12580,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12580),U_12582))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12580),U_12581)) ),
inference(clausify,[status(thm)],[f_3246_3]) ).
fof(f_3247_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_3247_2,plain,
! [U_12584] : c_Nitpick_Ozero__frac(U_12584) = c_Nitpick_OAbs__Frac(U_12584,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_3247_1]) ).
cnf(f_3247_3,plain,
c_Nitpick_Ozero__frac(U_12584) = c_Nitpick_OAbs__Frac(U_12584,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_3247_2]) ).
fof(f_3248_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_3248_2,plain,
! [U_12585] : c_Nitpick_Oone__frac(U_12585) = c_Nitpick_OAbs__Frac(U_12585,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_3248_1]) ).
cnf(f_3248_3,plain,
c_Nitpick_Oone__frac(U_12585) = c_Nitpick_OAbs__Frac(U_12585,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_3248_2]) ).
fof(f_3249_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_3249_2,plain,
! [U_12587,U_12586] : c_Nitpick_Onumber__of__frac(U_12586,U_12587) = c_Nitpick_OAbs__Frac(U_12586,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12587),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[f_3249_1]) ).
cnf(f_3249_3,plain,
c_Nitpick_Onumber__of__frac(U_12586,U_12587) = c_Nitpick_OAbs__Frac(U_12586,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12587),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_3249_2]) ).
fof(f_3250_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_3250_2,plain,
! [U_12590,U_12589,U_12588] : hAPP(hAPP(c_Nitpick_Ofrac(U_12588),U_12589),U_12590) = c_Nitpick_OAbs__Frac(U_12588,c_Nitpick_Onorm__frac(U_12589,U_12590)),
inference(variable_rename,[status(thm)],[f_3250_1]) ).
cnf(f_3250_3,plain,
hAPP(hAPP(c_Nitpick_Ofrac(U_12588),U_12589),U_12590) = c_Nitpick_OAbs__Frac(U_12588,c_Nitpick_Onorm__frac(U_12589,U_12590)),
inference(clausify,[status(thm)],[f_3250_2]) ).
fof(f_3251_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_3251_2,plain,
! [U_12596,U_12595,U_12594,U_12593,U_12592,U_12591] : hAPP(c_Set_Oimage(U_12591,tc_prod(U_12592,U_12593),hAPP(hAPP(c_COMBS(U_12591,U_12593,tc_prod(U_12592,U_12593)),hAPP(hAPP(c_COMBB(U_12592,tc_fun(U_12593,tc_prod(U_12592,U_12593)),U_12591),c_Product__Type_OPair(U_12592,U_12593)),U_12594)),U_12595)),U_12596) = hAPP(hAPP(c_Product__Type_OSigma(U_12592,U_12593),hAPP(c_Set_Oimage(U_12591,U_12592,U_12594),U_12596)),hAPP(hAPP(c_COMBB(tc_fun(U_12591,tc_HOL_Obool),tc_fun(U_12593,tc_HOL_Obool),U_12592),c_Set_Oimage(U_12591,U_12593,U_12595)),hAPP(hAPP(c_COMBC(U_12592,tc_fun(U_12591,tc_HOL_Obool),tc_fun(U_12591,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12591,tc_HOL_Obool),tc_fun(tc_fun(U_12591,tc_HOL_Obool),tc_fun(U_12591,tc_HOL_Obool)),U_12592),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12591,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12592,tc_HOL_Obool),tc_fun(U_12591,tc_HOL_Obool),U_12592),c_Set_Ovimage(U_12591,U_12592,U_12594)),hAPP(hAPP(c_COMBC(U_12592,tc_fun(U_12592,tc_HOL_Obool),tc_fun(U_12592,tc_HOL_Obool)),c_Set_Oinsert(U_12592)),c_Orderings_Obot__class_Obot(tc_fun(U_12592,tc_HOL_Obool)))))),U_12596))),
inference(variable_rename,[status(thm)],[f_3251_1]) ).
cnf(f_3251_3,plain,
hAPP(c_Set_Oimage(U_12591,tc_prod(U_12592,U_12593),hAPP(hAPP(c_COMBS(U_12591,U_12593,tc_prod(U_12592,U_12593)),hAPP(hAPP(c_COMBB(U_12592,tc_fun(U_12593,tc_prod(U_12592,U_12593)),U_12591),c_Product__Type_OPair(U_12592,U_12593)),U_12594)),U_12595)),U_12596) = hAPP(hAPP(c_Product__Type_OSigma(U_12592,U_12593),hAPP(c_Set_Oimage(U_12591,U_12592,U_12594),U_12596)),hAPP(hAPP(c_COMBB(tc_fun(U_12591,tc_HOL_Obool),tc_fun(U_12593,tc_HOL_Obool),U_12592),c_Set_Oimage(U_12591,U_12593,U_12595)),hAPP(hAPP(c_COMBC(U_12592,tc_fun(U_12591,tc_HOL_Obool),tc_fun(U_12591,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12591,tc_HOL_Obool),tc_fun(tc_fun(U_12591,tc_HOL_Obool),tc_fun(U_12591,tc_HOL_Obool)),U_12592),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12591,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12592,tc_HOL_Obool),tc_fun(U_12591,tc_HOL_Obool),U_12592),c_Set_Ovimage(U_12591,U_12592,U_12594)),hAPP(hAPP(c_COMBC(U_12592,tc_fun(U_12592,tc_HOL_Obool),tc_fun(U_12592,tc_HOL_Obool)),c_Set_Oinsert(U_12592)),c_Orderings_Obot__class_Obot(tc_fun(U_12592,tc_HOL_Obool)))))),U_12596))),
inference(clausify,[status(thm)],[f_3251_2]) ).
fof(f_3252_1,plain,
! [V_P_2,V_y_2] :
( hBOOL(hAPP(V_P_2,V_y_2))
| ? [B_x] : ~ hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) ),
inference(fof_nnf,[status(thm)],[fact_Rep__Integ__induct]) ).
fof(f_3252_2,plain,
! [U_12599,U_12598] :
( hBOOL(hAPP(U_12599,U_12598))
| ? [U_12597] : ~ hBOOL(hAPP(U_12599,hAPP(c_Int_ORep__Integ,U_12597)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_12598),c_Int_OInteg)) ),
inference(variable_rename,[status(thm)],[f_3252_1]) ).
fof(f_3252_3,plain,
! [U_12599,U_12598] :
( hBOOL(hAPP(U_12599,U_12598))
| ~ hBOOL(hAPP(U_12599,hAPP(c_Int_ORep__Integ,sK305(U_12599,U_12598))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_12598),c_Int_OInteg)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK305]),skolemize(U_12597,sK305(U_12599,U_12598))],[f_3252_2]) ).
cnf(f_3252_4,plain,
( hBOOL(hAPP(U_12599,U_12598))
| ~ hBOOL(hAPP(U_12599,hAPP(c_Int_ORep__Integ,sK305(U_12599,U_12598))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_12598),c_Int_OInteg)) ),
inference(clausify,[status(thm)],[f_3252_3]) ).
fof(f_3253_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_3253_2,plain,
! [U_12601] :
( ? [U_12600] : U_12601 = hAPP(c_Int_ORep__Integ,U_12600)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_12601),c_Int_OInteg)) ),
inference(variable_rename,[status(thm)],[f_3253_1]) ).
fof(f_3253_3,plain,
! [U_12601] :
( U_12601 = hAPP(c_Int_ORep__Integ,sK306(U_12601))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_12601),c_Int_OInteg)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK306]),skolemize(U_12600,sK306(U_12601))],[f_3253_2]) ).
cnf(f_3253_4,plain,
( U_12601 = hAPP(c_Int_ORep__Integ,sK306(U_12601))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_12601),c_Int_OInteg)) ),
inference(clausify,[status(thm)],[f_3253_3]) ).
fof(f_3254_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_3254_2,plain,
! [U_12607,U_12606,U_12605,U_12604,U_12603,U_12602] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12602,U_12605)),hAPP(hAPP(c_Product__Type_OPair(U_12602,U_12605),U_12603),U_12606)),hAPP(hAPP(c_Product__Type_OSigma(U_12602,U_12605),U_12604),U_12607)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12605),U_12606),hAPP(U_12607,U_12603)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12602),U_12603),U_12604)) ),
inference(variable_rename,[status(thm)],[f_3254_1]) ).
cnf(f_3254_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12602,U_12605)),hAPP(hAPP(c_Product__Type_OPair(U_12602,U_12605),U_12603),U_12606)),hAPP(hAPP(c_Product__Type_OSigma(U_12602,U_12605),U_12604),U_12607)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12605),U_12606),hAPP(U_12607,U_12603)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12602),U_12603),U_12604)) ),
inference(clausify,[status(thm)],[f_3254_2]) ).
fof(f_3255_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_3255_2,plain,
! [U_12611,U_12610,U_12609,U_12608] : hAPP(hAPP(c_Product__Type_OSigma(U_12608,U_12609),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_12608,tc_HOL_Obool),U_12610)),U_12611) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_12608,tc_HOL_Obool),tc_fun(tc_prod(U_12608,U_12609),tc_HOL_Obool)),U_12610),hAPP(hAPP(c_COMBC(tc_fun(U_12608,tc_HOL_Obool),tc_fun(U_12608,tc_fun(U_12609,tc_HOL_Obool)),tc_fun(tc_prod(U_12608,U_12609),tc_HOL_Obool)),c_Product__Type_OSigma(U_12608,U_12609)),U_12611)),
inference(variable_rename,[status(thm)],[f_3255_1]) ).
cnf(f_3255_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12608,U_12609),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_12608,tc_HOL_Obool),U_12610)),U_12611) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_12608,tc_HOL_Obool),tc_fun(tc_prod(U_12608,U_12609),tc_HOL_Obool)),U_12610),hAPP(hAPP(c_COMBC(tc_fun(U_12608,tc_HOL_Obool),tc_fun(U_12608,tc_fun(U_12609,tc_HOL_Obool)),tc_fun(tc_prod(U_12608,U_12609),tc_HOL_Obool)),c_Product__Type_OSigma(U_12608,U_12609)),U_12611)),
inference(clausify,[status(thm)],[f_3255_2]) ).
fof(f_3256_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_3256_2,plain,
! [U_12614,U_12613,U_12612] : hAPP(hAPP(c_Product__Type_OSigma(U_12612,U_12613),c_Orderings_Obot__class_Obot(tc_fun(U_12612,tc_HOL_Obool))),U_12614) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12612,U_12613),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3256_1]) ).
cnf(f_3256_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12612,U_12613),c_Orderings_Obot__class_Obot(tc_fun(U_12612,tc_HOL_Obool))),U_12614) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12612,U_12613),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3256_2]) ).
fof(f_3257_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_3257_2,plain,
! [U_12619,U_12618,U_12617,U_12616,U_12615] : hAPP(hAPP(c_Product__Type_OSigma(U_12615,U_12616),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12615,tc_HOL_Obool)),U_12617),U_12618)),U_12619) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_12615,U_12616),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12615,U_12616),U_12617),U_12619)),hAPP(hAPP(c_Product__Type_OSigma(U_12615,U_12616),U_12618),U_12619)),
inference(variable_rename,[status(thm)],[f_3257_1]) ).
cnf(f_3257_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12615,U_12616),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12615,tc_HOL_Obool)),U_12617),U_12618)),U_12619) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_12615,U_12616),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12615,U_12616),U_12617),U_12619)),hAPP(hAPP(c_Product__Type_OSigma(U_12615,U_12616),U_12618),U_12619)),
inference(clausify,[status(thm)],[f_3257_2]) ).
fof(f_3258_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_3258_2,plain,
! [U_12624,U_12623,U_12622,U_12621,U_12620] : hAPP(hAPP(c_Product__Type_OSigma(U_12620,U_12621),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12620,tc_HOL_Obool)),U_12622),U_12623)),hAPP(c_COMBK(tc_fun(U_12621,tc_HOL_Obool),U_12620),U_12624)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_12620,U_12621),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12620,U_12621),U_12622),hAPP(c_COMBK(tc_fun(U_12621,tc_HOL_Obool),U_12620),U_12624))),hAPP(hAPP(c_Product__Type_OSigma(U_12620,U_12621),U_12623),hAPP(c_COMBK(tc_fun(U_12621,tc_HOL_Obool),U_12620),U_12624))),
inference(variable_rename,[status(thm)],[f_3258_1]) ).
cnf(f_3258_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12620,U_12621),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12620,tc_HOL_Obool)),U_12622),U_12623)),hAPP(c_COMBK(tc_fun(U_12621,tc_HOL_Obool),U_12620),U_12624)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_12620,U_12621),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12620,U_12621),U_12622),hAPP(c_COMBK(tc_fun(U_12621,tc_HOL_Obool),U_12620),U_12624))),hAPP(hAPP(c_Product__Type_OSigma(U_12620,U_12621),U_12623),hAPP(c_COMBK(tc_fun(U_12621,tc_HOL_Obool),U_12620),U_12624))),
inference(clausify,[status(thm)],[f_3258_2]) ).
fof(f_3259_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_3259_2,plain,
! [U_12629,U_12628,U_12627,U_12626,U_12625] : hAPP(hAPP(c_Product__Type_OSigma(U_12625,U_12626),U_12627),hAPP(hAPP(c_COMBS(U_12625,tc_fun(U_12626,tc_HOL_Obool),tc_fun(U_12626,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12626,tc_HOL_Obool),tc_fun(tc_fun(U_12626,tc_HOL_Obool),tc_fun(U_12626,tc_HOL_Obool)),U_12625),c_Groups_Ominus__class_Ominus(tc_fun(U_12626,tc_HOL_Obool))),U_12628)),U_12629)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_12625,U_12626),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12625,U_12626),U_12627),U_12628)),hAPP(hAPP(c_Product__Type_OSigma(U_12625,U_12626),U_12627),U_12629)),
inference(variable_rename,[status(thm)],[f_3259_1]) ).
cnf(f_3259_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12625,U_12626),U_12627),hAPP(hAPP(c_COMBS(U_12625,tc_fun(U_12626,tc_HOL_Obool),tc_fun(U_12626,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12626,tc_HOL_Obool),tc_fun(tc_fun(U_12626,tc_HOL_Obool),tc_fun(U_12626,tc_HOL_Obool)),U_12625),c_Groups_Ominus__class_Ominus(tc_fun(U_12626,tc_HOL_Obool))),U_12628)),U_12629)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_12625,U_12626),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12625,U_12626),U_12627),U_12628)),hAPP(hAPP(c_Product__Type_OSigma(U_12625,U_12626),U_12627),U_12629)),
inference(clausify,[status(thm)],[f_3259_2]) ).
fof(f_3260_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_3260_2,plain,
! [U_12635,U_12634,U_12633,U_12632,U_12631,U_12630] :
( ( ( hAPP(hAPP(c_Product__Type_OSigma(U_12633,U_12630),U_12634),hAPP(c_COMBK(tc_fun(U_12630,tc_HOL_Obool),U_12633),U_12632)) = hAPP(hAPP(c_Product__Type_OSigma(U_12633,U_12630),U_12635),hAPP(c_COMBK(tc_fun(U_12630,tc_HOL_Obool),U_12633),U_12632))
| U_12634 != U_12635 )
& ( U_12634 = U_12635
| hAPP(hAPP(c_Product__Type_OSigma(U_12633,U_12630),U_12634),hAPP(c_COMBK(tc_fun(U_12630,tc_HOL_Obool),U_12633),U_12632)) != hAPP(hAPP(c_Product__Type_OSigma(U_12633,U_12630),U_12635),hAPP(c_COMBK(tc_fun(U_12630,tc_HOL_Obool),U_12633),U_12632)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12630),U_12631),U_12632)) ),
inference(variable_rename,[status(thm)],[f_3260_1]) ).
cnf(f_3260_3,plain,
( U_12634 = U_12635
| hAPP(hAPP(c_Product__Type_OSigma(U_12633,U_12630),U_12634),hAPP(c_COMBK(tc_fun(U_12630,tc_HOL_Obool),U_12633),U_12632)) != hAPP(hAPP(c_Product__Type_OSigma(U_12633,U_12630),U_12635),hAPP(c_COMBK(tc_fun(U_12630,tc_HOL_Obool),U_12633),U_12632))
| ~ hBOOL(hAPP(hAPP(c_member(U_12630),U_12631),U_12632)) ),
inference(clausify,[status(thm)],[f_3260_2]) ).
cnf(f_3260_4,plain,
( hAPP(hAPP(c_Product__Type_OSigma(U_12633,U_12630),U_12634),hAPP(c_COMBK(tc_fun(U_12630,tc_HOL_Obool),U_12633),U_12632)) = hAPP(hAPP(c_Product__Type_OSigma(U_12633,U_12630),U_12635),hAPP(c_COMBK(tc_fun(U_12630,tc_HOL_Obool),U_12633),U_12632))
| U_12634 != U_12635
| ~ hBOOL(hAPP(hAPP(c_member(U_12630),U_12631),U_12632)) ),
inference(clausify,[status(thm)],[f_3260_2]) ).
fof(f_3261_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_3261_2,plain,
! [U_12639,U_12638,U_12637,U_12636] : hAPP(c_Finite__Set_Ocard(tc_prod(U_12636,U_12637)),hAPP(hAPP(c_Product__Type_OSigma(U_12636,U_12637),U_12638),hAPP(c_COMBK(tc_fun(U_12637,tc_HOL_Obool),U_12636),U_12639))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_12636),U_12638)),hAPP(c_Finite__Set_Ocard(U_12637),U_12639)),
inference(variable_rename,[status(thm)],[f_3261_1]) ).
cnf(f_3261_3,plain,
hAPP(c_Finite__Set_Ocard(tc_prod(U_12636,U_12637)),hAPP(hAPP(c_Product__Type_OSigma(U_12636,U_12637),U_12638),hAPP(c_COMBK(tc_fun(U_12637,tc_HOL_Obool),U_12636),U_12639))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_12636),U_12638)),hAPP(c_Finite__Set_Ocard(U_12637),U_12639)),
inference(clausify,[status(thm)],[f_3261_2]) ).
fof(f_3262_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_3262_2,plain,
! [U_12645,U_12644,U_12643,U_12642,U_12641,U_12640] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12641,U_12640),hAPP(hAPP(c_COMBC(U_12641,tc_fun(U_12642,tc_HOL_Obool),U_12640),hAPP(hAPP(c_COMBB(tc_fun(U_12642,U_12640),tc_fun(tc_fun(U_12642,tc_HOL_Obool),U_12640),U_12641),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12642,U_12640)),U_12643)),U_12644)),U_12645) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_12641,U_12642),U_12640),hAPP(c_Product__Type_Oprod_Oprod__case(U_12641,U_12642,U_12640),U_12643)),hAPP(hAPP(c_Product__Type_OSigma(U_12641,U_12642),U_12645),hAPP(c_COMBK(tc_fun(U_12642,tc_HOL_Obool),U_12641),U_12644)))
| ~ class_Groups_Ocomm__monoid__add(U_12640) ),
inference(variable_rename,[status(thm)],[f_3262_1]) ).
cnf(f_3262_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12641,U_12640),hAPP(hAPP(c_COMBC(U_12641,tc_fun(U_12642,tc_HOL_Obool),U_12640),hAPP(hAPP(c_COMBB(tc_fun(U_12642,U_12640),tc_fun(tc_fun(U_12642,tc_HOL_Obool),U_12640),U_12641),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12642,U_12640)),U_12643)),U_12644)),U_12645) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_12641,U_12642),U_12640),hAPP(c_Product__Type_Oprod_Oprod__case(U_12641,U_12642,U_12640),U_12643)),hAPP(hAPP(c_Product__Type_OSigma(U_12641,U_12642),U_12645),hAPP(c_COMBK(tc_fun(U_12642,tc_HOL_Obool),U_12641),U_12644)))
| ~ class_Groups_Ocomm__monoid__add(U_12640) ),
inference(clausify,[status(thm)],[f_3262_2]) ).
fof(f_3263_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_3263_2,plain,
! [U_12648,U_12647,U_12646] : hAPP(hAPP(c_Product__Type_OSigma(U_12646,U_12647),U_12648),hAPP(c_COMBK(tc_fun(U_12647,tc_HOL_Obool),U_12646),c_Orderings_Obot__class_Obot(tc_fun(U_12647,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12646,U_12647),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3263_1]) ).
cnf(f_3263_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12646,U_12647),U_12648),hAPP(c_COMBK(tc_fun(U_12647,tc_HOL_Obool),U_12646),c_Orderings_Obot__class_Obot(tc_fun(U_12647,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12646,U_12647),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3263_2]) ).
fof(f_3264_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_3264_2,plain,
! [U_12652,U_12651,U_12650,U_12649] :
( ( hAPP(hAPP(c_Product__Type_OSigma(U_12649,U_12650),U_12651),hAPP(c_COMBK(tc_fun(U_12650,tc_HOL_Obool),U_12649),U_12652)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12649,U_12650),tc_HOL_Obool))
| ( U_12652 != c_Orderings_Obot__class_Obot(tc_fun(U_12650,tc_HOL_Obool))
& U_12651 != c_Orderings_Obot__class_Obot(tc_fun(U_12649,tc_HOL_Obool)) ) )
& ( U_12652 = c_Orderings_Obot__class_Obot(tc_fun(U_12650,tc_HOL_Obool))
| U_12651 = c_Orderings_Obot__class_Obot(tc_fun(U_12649,tc_HOL_Obool))
| hAPP(hAPP(c_Product__Type_OSigma(U_12649,U_12650),U_12651),hAPP(c_COMBK(tc_fun(U_12650,tc_HOL_Obool),U_12649),U_12652)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12649,U_12650),tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_3264_1]) ).
fof(f_3264_3,plain,
( ! [U_12660,U_12658,U_12656,U_12654] :
( hAPP(hAPP(c_Product__Type_OSigma(U_12654,U_12656),U_12658),hAPP(c_COMBK(tc_fun(U_12656,tc_HOL_Obool),U_12654),U_12660)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12654,U_12656),tc_HOL_Obool))
| ( U_12660 != c_Orderings_Obot__class_Obot(tc_fun(U_12656,tc_HOL_Obool))
& U_12658 != c_Orderings_Obot__class_Obot(tc_fun(U_12654,tc_HOL_Obool)) ) )
& ! [U_12659,U_12657,U_12655,U_12653] :
( U_12659 = c_Orderings_Obot__class_Obot(tc_fun(U_12655,tc_HOL_Obool))
| U_12657 = c_Orderings_Obot__class_Obot(tc_fun(U_12653,tc_HOL_Obool))
| hAPP(hAPP(c_Product__Type_OSigma(U_12653,U_12655),U_12657),hAPP(c_COMBK(tc_fun(U_12655,tc_HOL_Obool),U_12653),U_12659)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12653,U_12655),tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_3264_2]) ).
cnf(f_3264_4,plain,
( U_12659 = c_Orderings_Obot__class_Obot(tc_fun(U_12655,tc_HOL_Obool))
| U_12657 = c_Orderings_Obot__class_Obot(tc_fun(U_12653,tc_HOL_Obool))
| hAPP(hAPP(c_Product__Type_OSigma(U_12653,U_12655),U_12657),hAPP(c_COMBK(tc_fun(U_12655,tc_HOL_Obool),U_12653),U_12659)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12653,U_12655),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3264_3]) ).
cnf(f_3264_5,plain,
( U_12658 != c_Orderings_Obot__class_Obot(tc_fun(U_12654,tc_HOL_Obool))
| hAPP(hAPP(c_Product__Type_OSigma(U_12654,U_12656),U_12658),hAPP(c_COMBK(tc_fun(U_12656,tc_HOL_Obool),U_12654),U_12660)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12654,U_12656),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3264_3]) ).
cnf(f_3264_6,plain,
( U_12660 != c_Orderings_Obot__class_Obot(tc_fun(U_12656,tc_HOL_Obool))
| hAPP(hAPP(c_Product__Type_OSigma(U_12654,U_12656),U_12658),hAPP(c_COMBK(tc_fun(U_12656,tc_HOL_Obool),U_12654),U_12660)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12654,U_12656),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3264_3]) ).
fof(f_3265_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_3265_2,plain,
! [U_12663,U_12662,U_12661] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_12661,U_12662),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12661,U_12662),U_12663),hAPP(c_COMBK(tc_fun(U_12662,tc_HOL_Obool),U_12661),c_Orderings_Otop__class_Otop(tc_fun(U_12662,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(U_12661,U_12662),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12661,tc_HOL_Obool)),U_12663)),hAPP(c_COMBK(tc_fun(U_12662,tc_HOL_Obool),U_12661),c_Orderings_Otop__class_Otop(tc_fun(U_12662,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_3265_1]) ).
cnf(f_3265_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_12661,U_12662),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12661,U_12662),U_12663),hAPP(c_COMBK(tc_fun(U_12662,tc_HOL_Obool),U_12661),c_Orderings_Otop__class_Otop(tc_fun(U_12662,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(U_12661,U_12662),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12661,tc_HOL_Obool)),U_12663)),hAPP(c_COMBK(tc_fun(U_12662,tc_HOL_Obool),U_12661),c_Orderings_Otop__class_Otop(tc_fun(U_12662,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_3265_2]) ).
fof(f_3266_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_3266_2,plain,
! [U_12666,U_12665,U_12664] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_12664,U_12665),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12664,U_12665),c_Orderings_Otop__class_Otop(tc_fun(U_12664,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_12665,tc_HOL_Obool),U_12664),U_12666))) = hAPP(hAPP(c_Product__Type_OSigma(U_12664,U_12665),c_Orderings_Otop__class_Otop(tc_fun(U_12664,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_12665,tc_HOL_Obool),U_12664),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12665,tc_HOL_Obool)),U_12666))),
inference(variable_rename,[status(thm)],[f_3266_1]) ).
cnf(f_3266_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_12664,U_12665),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12664,U_12665),c_Orderings_Otop__class_Otop(tc_fun(U_12664,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_12665,tc_HOL_Obool),U_12664),U_12666))) = hAPP(hAPP(c_Product__Type_OSigma(U_12664,U_12665),c_Orderings_Otop__class_Otop(tc_fun(U_12664,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_12665,tc_HOL_Obool),U_12664),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12665,tc_HOL_Obool)),U_12666))),
inference(clausify,[status(thm)],[f_3266_2]) ).
fof(f_3267_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_3267_2,plain,
! [U_12672,U_12671,U_12670,U_12669,U_12668,U_12667] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12668,U_12667),hAPP(hAPP(c_COMBC(U_12668,tc_fun(U_12669,tc_HOL_Obool),U_12667),hAPP(hAPP(c_COMBB(tc_fun(U_12669,U_12667),tc_fun(tc_fun(U_12669,tc_HOL_Obool),U_12667),U_12668),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12669,U_12667)),U_12670)),U_12671)),U_12672) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_12668,U_12669),U_12667),hAPP(c_Product__Type_Oprod_Oprod__case(U_12668,U_12669,U_12667),U_12670)),hAPP(hAPP(c_Product__Type_OSigma(U_12668,U_12669),U_12672),hAPP(c_COMBK(tc_fun(U_12669,tc_HOL_Obool),U_12668),U_12671)))
| ~ class_Groups_Ocomm__monoid__mult(U_12667) ),
inference(variable_rename,[status(thm)],[f_3267_1]) ).
cnf(f_3267_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12668,U_12667),hAPP(hAPP(c_COMBC(U_12668,tc_fun(U_12669,tc_HOL_Obool),U_12667),hAPP(hAPP(c_COMBB(tc_fun(U_12669,U_12667),tc_fun(tc_fun(U_12669,tc_HOL_Obool),U_12667),U_12668),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12669,U_12667)),U_12670)),U_12671)),U_12672) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_12668,U_12669),U_12667),hAPP(c_Product__Type_Oprod_Oprod__case(U_12668,U_12669,U_12667),U_12670)),hAPP(hAPP(c_Product__Type_OSigma(U_12668,U_12669),U_12672),hAPP(c_COMBK(tc_fun(U_12669,tc_HOL_Obool),U_12668),U_12671)))
| ~ class_Groups_Ocomm__monoid__mult(U_12667) ),
inference(clausify,[status(thm)],[f_3267_2]) ).
fof(f_3268_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_3268_2,plain,
! [U_12677,U_12676,U_12675,U_12674,U_12673] : hAPP(hAPP(c_Product__Type_OSigma(U_12673,U_12674),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12673,tc_HOL_Obool)),U_12675),U_12676)),U_12677) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12673,U_12674),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12673,U_12674),U_12675),U_12677)),hAPP(hAPP(c_Product__Type_OSigma(U_12673,U_12674),U_12676),U_12677)),
inference(variable_rename,[status(thm)],[f_3268_1]) ).
cnf(f_3268_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12673,U_12674),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12673,tc_HOL_Obool)),U_12675),U_12676)),U_12677) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12673,U_12674),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12673,U_12674),U_12675),U_12677)),hAPP(hAPP(c_Product__Type_OSigma(U_12673,U_12674),U_12676),U_12677)),
inference(clausify,[status(thm)],[f_3268_2]) ).
fof(f_3269_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_3269_2,plain,
! [U_12682,U_12681,U_12680,U_12679,U_12678] : hAPP(hAPP(c_Product__Type_OSigma(U_12678,U_12679),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12678,tc_HOL_Obool)),U_12680),U_12681)),hAPP(c_COMBK(tc_fun(U_12679,tc_HOL_Obool),U_12678),U_12682)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12678,U_12679),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12678,U_12679),U_12680),hAPP(c_COMBK(tc_fun(U_12679,tc_HOL_Obool),U_12678),U_12682))),hAPP(hAPP(c_Product__Type_OSigma(U_12678,U_12679),U_12681),hAPP(c_COMBK(tc_fun(U_12679,tc_HOL_Obool),U_12678),U_12682))),
inference(variable_rename,[status(thm)],[f_3269_1]) ).
cnf(f_3269_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12678,U_12679),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12678,tc_HOL_Obool)),U_12680),U_12681)),hAPP(c_COMBK(tc_fun(U_12679,tc_HOL_Obool),U_12678),U_12682)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12678,U_12679),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12678,U_12679),U_12680),hAPP(c_COMBK(tc_fun(U_12679,tc_HOL_Obool),U_12678),U_12682))),hAPP(hAPP(c_Product__Type_OSigma(U_12678,U_12679),U_12681),hAPP(c_COMBK(tc_fun(U_12679,tc_HOL_Obool),U_12678),U_12682))),
inference(clausify,[status(thm)],[f_3269_2]) ).
fof(f_3270_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_3270_2,plain,
! [U_12687,U_12686,U_12685,U_12684,U_12683] : hAPP(hAPP(c_Product__Type_OSigma(U_12683,U_12684),U_12685),hAPP(hAPP(c_COMBS(U_12683,tc_fun(U_12684,tc_HOL_Obool),tc_fun(U_12684,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12684,tc_HOL_Obool),tc_fun(tc_fun(U_12684,tc_HOL_Obool),tc_fun(U_12684,tc_HOL_Obool)),U_12683),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12684,tc_HOL_Obool))),U_12686)),U_12687)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12683,U_12684),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12683,U_12684),U_12685),U_12686)),hAPP(hAPP(c_Product__Type_OSigma(U_12683,U_12684),U_12685),U_12687)),
inference(variable_rename,[status(thm)],[f_3270_1]) ).
cnf(f_3270_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12683,U_12684),U_12685),hAPP(hAPP(c_COMBS(U_12683,tc_fun(U_12684,tc_HOL_Obool),tc_fun(U_12684,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12684,tc_HOL_Obool),tc_fun(tc_fun(U_12684,tc_HOL_Obool),tc_fun(U_12684,tc_HOL_Obool)),U_12683),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12684,tc_HOL_Obool))),U_12686)),U_12687)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12683,U_12684),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12683,U_12684),U_12685),U_12686)),hAPP(hAPP(c_Product__Type_OSigma(U_12683,U_12684),U_12685),U_12687)),
inference(clausify,[status(thm)],[f_3270_2]) ).
fof(f_3271_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_3271_2,plain,
! [U_12691,U_12690,U_12689,U_12688] : hAPP(c_Set_Oimage(tc_prod(U_12688,U_12689),tc_prod(U_12689,U_12688),hAPP(c_Product__Type_Oprod_Oprod__case(U_12688,U_12689,tc_prod(U_12689,U_12688)),hAPP(c_COMBC(U_12689,U_12688,tc_prod(U_12689,U_12688)),c_Product__Type_OPair(U_12689,U_12688)))),hAPP(hAPP(c_Product__Type_OSigma(U_12688,U_12689),U_12690),hAPP(c_COMBK(tc_fun(U_12689,tc_HOL_Obool),U_12688),U_12691))) = hAPP(hAPP(c_Product__Type_OSigma(U_12689,U_12688),U_12691),hAPP(c_COMBK(tc_fun(U_12688,tc_HOL_Obool),U_12689),U_12690)),
inference(variable_rename,[status(thm)],[f_3271_1]) ).
cnf(f_3271_3,plain,
hAPP(c_Set_Oimage(tc_prod(U_12688,U_12689),tc_prod(U_12689,U_12688),hAPP(c_Product__Type_Oprod_Oprod__case(U_12688,U_12689,tc_prod(U_12689,U_12688)),hAPP(c_COMBC(U_12689,U_12688,tc_prod(U_12689,U_12688)),c_Product__Type_OPair(U_12689,U_12688)))),hAPP(hAPP(c_Product__Type_OSigma(U_12688,U_12689),U_12690),hAPP(c_COMBK(tc_fun(U_12689,tc_HOL_Obool),U_12688),U_12691))) = hAPP(hAPP(c_Product__Type_OSigma(U_12689,U_12688),U_12691),hAPP(c_COMBK(tc_fun(U_12688,tc_HOL_Obool),U_12689),U_12690)),
inference(clausify,[status(thm)],[f_3271_2]) ).
fof(f_3272_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_3272_2,plain,
! [U_12695,U_12694,U_12693,U_12692] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12692,U_12694)),hAPP(hAPP(c_Product__Type_OSigma(U_12692,U_12694),U_12693),hAPP(c_COMBK(tc_fun(U_12694,tc_HOL_Obool),U_12692),U_12695))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12694),U_12695))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12692),U_12693)) ),
inference(variable_rename,[status(thm)],[f_3272_1]) ).
cnf(f_3272_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12692,U_12694)),hAPP(hAPP(c_Product__Type_OSigma(U_12692,U_12694),U_12693),hAPP(c_COMBK(tc_fun(U_12694,tc_HOL_Obool),U_12692),U_12695))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12694),U_12695))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12692),U_12693)) ),
inference(clausify,[status(thm)],[f_3272_2]) ).
fof(f_3273_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_3273_2,plain,
! [U_12698,U_12697,U_12696] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12696,U_12696),tc_HOL_Obool)),U_12698),hAPP(hAPP(c_Product__Type_OSigma(U_12696,U_12696),U_12697),hAPP(c_COMBK(tc_fun(U_12696,tc_HOL_Obool),U_12696),U_12697))))
| ~ c_Equiv__Relations_Oequiv(U_12696,U_12697,U_12698) ),
inference(variable_rename,[status(thm)],[f_3273_1]) ).
cnf(f_3273_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12696,U_12696),tc_HOL_Obool)),U_12698),hAPP(hAPP(c_Product__Type_OSigma(U_12696,U_12696),U_12697),hAPP(c_COMBK(tc_fun(U_12696,tc_HOL_Obool),U_12696),U_12697))))
| ~ c_Equiv__Relations_Oequiv(U_12696,U_12697,U_12698) ),
inference(clausify,[status(thm)],[f_3273_2]) ).
fof(f_3274_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_3274_2,plain,
! [U_12703,U_12702,U_12701,U_12700,U_12699] : hAPP(hAPP(c_Product__Type_OSigma(U_12699,U_12700),U_12701),hAPP(hAPP(c_COMBS(U_12699,tc_fun(U_12700,tc_HOL_Obool),tc_fun(U_12700,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12700,tc_HOL_Obool),tc_fun(tc_fun(U_12700,tc_HOL_Obool),tc_fun(U_12700,tc_HOL_Obool)),U_12699),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12700,tc_HOL_Obool))),U_12702)),U_12703)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12699,U_12700),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12699,U_12700),U_12701),U_12702)),hAPP(hAPP(c_Product__Type_OSigma(U_12699,U_12700),U_12701),U_12703)),
inference(variable_rename,[status(thm)],[f_3274_1]) ).
cnf(f_3274_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12699,U_12700),U_12701),hAPP(hAPP(c_COMBS(U_12699,tc_fun(U_12700,tc_HOL_Obool),tc_fun(U_12700,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12700,tc_HOL_Obool),tc_fun(tc_fun(U_12700,tc_HOL_Obool),tc_fun(U_12700,tc_HOL_Obool)),U_12699),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12700,tc_HOL_Obool))),U_12702)),U_12703)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12699,U_12700),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12699,U_12700),U_12701),U_12702)),hAPP(hAPP(c_Product__Type_OSigma(U_12699,U_12700),U_12701),U_12703)),
inference(clausify,[status(thm)],[f_3274_2]) ).
fof(f_3275_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_3275_2,plain,
! [U_12708,U_12707,U_12706,U_12705,U_12704] : hAPP(hAPP(c_Product__Type_OSigma(U_12704,U_12705),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12704,tc_HOL_Obool)),U_12706),U_12707)),hAPP(c_COMBK(tc_fun(U_12705,tc_HOL_Obool),U_12704),U_12708)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12704,U_12705),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12704,U_12705),U_12706),hAPP(c_COMBK(tc_fun(U_12705,tc_HOL_Obool),U_12704),U_12708))),hAPP(hAPP(c_Product__Type_OSigma(U_12704,U_12705),U_12707),hAPP(c_COMBK(tc_fun(U_12705,tc_HOL_Obool),U_12704),U_12708))),
inference(variable_rename,[status(thm)],[f_3275_1]) ).
cnf(f_3275_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12704,U_12705),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12704,tc_HOL_Obool)),U_12706),U_12707)),hAPP(c_COMBK(tc_fun(U_12705,tc_HOL_Obool),U_12704),U_12708)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12704,U_12705),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12704,U_12705),U_12706),hAPP(c_COMBK(tc_fun(U_12705,tc_HOL_Obool),U_12704),U_12708))),hAPP(hAPP(c_Product__Type_OSigma(U_12704,U_12705),U_12707),hAPP(c_COMBK(tc_fun(U_12705,tc_HOL_Obool),U_12704),U_12708))),
inference(clausify,[status(thm)],[f_3275_2]) ).
fof(f_3276_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_3276_2,plain,
! [U_12713,U_12712,U_12711,U_12710,U_12709] : hAPP(hAPP(c_Product__Type_OSigma(U_12709,U_12710),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12709,tc_HOL_Obool)),U_12711),U_12712)),U_12713) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12709,U_12710),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12709,U_12710),U_12711),U_12713)),hAPP(hAPP(c_Product__Type_OSigma(U_12709,U_12710),U_12712),U_12713)),
inference(variable_rename,[status(thm)],[f_3276_1]) ).
cnf(f_3276_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12709,U_12710),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12709,tc_HOL_Obool)),U_12711),U_12712)),U_12713) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12709,U_12710),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12709,U_12710),U_12711),U_12713)),hAPP(hAPP(c_Product__Type_OSigma(U_12709,U_12710),U_12712),U_12713)),
inference(clausify,[status(thm)],[f_3276_2]) ).
fof(f_3277_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_3277_2,plain,
! [U_12715,U_12714] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12714,U_12714),tc_HOL_Obool)),c_Relation_OId__on(U_12714,U_12715)),hAPP(hAPP(c_Product__Type_OSigma(U_12714,U_12714),U_12715),hAPP(c_COMBK(tc_fun(U_12714,tc_HOL_Obool),U_12714),U_12715)))),
inference(variable_rename,[status(thm)],[f_3277_1]) ).
cnf(f_3277_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12714,U_12714),tc_HOL_Obool)),c_Relation_OId__on(U_12714,U_12715)),hAPP(hAPP(c_Product__Type_OSigma(U_12714,U_12714),U_12715),hAPP(c_COMBK(tc_fun(U_12714,tc_HOL_Obool),U_12714),U_12715)))),
inference(clausify,[status(thm)],[f_3277_2]) ).
fof(f_3278_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_3278_2,plain,
! [U_12717,U_12716] : hAPP(hAPP(c_Product__Type_OSigma(U_12716,U_12717),c_Orderings_Otop__class_Otop(tc_fun(U_12716,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_12717,tc_HOL_Obool),U_12716),c_Orderings_Otop__class_Otop(tc_fun(U_12717,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12716,U_12717),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3278_1]) ).
cnf(f_3278_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12716,U_12717),c_Orderings_Otop__class_Otop(tc_fun(U_12716,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_12717,tc_HOL_Obool),U_12716),c_Orderings_Otop__class_Otop(tc_fun(U_12717,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12716,U_12717),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3278_2]) ).
fof(f_3279_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_3279_2,plain,
! [U_12723,U_12722,U_12721,U_12720,U_12719,U_12718] :
( ( hBOOL(hAPP(hAPP(c_member(U_12719),U_12721),hAPP(U_12723,U_12720)))
& hBOOL(hAPP(hAPP(c_member(U_12718),U_12720),U_12722)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12718,U_12719)),hAPP(hAPP(c_Product__Type_OPair(U_12718,U_12719),U_12720),U_12721)),hAPP(hAPP(c_Product__Type_OSigma(U_12718,U_12719),U_12722),U_12723))) ),
inference(variable_rename,[status(thm)],[f_3279_1]) ).
cnf(f_3279_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_12718),U_12720),U_12722))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12718,U_12719)),hAPP(hAPP(c_Product__Type_OPair(U_12718,U_12719),U_12720),U_12721)),hAPP(hAPP(c_Product__Type_OSigma(U_12718,U_12719),U_12722),U_12723))) ),
inference(clausify,[status(thm)],[f_3279_2]) ).
cnf(f_3279_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12719),U_12721),hAPP(U_12723,U_12720)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12718,U_12719)),hAPP(hAPP(c_Product__Type_OPair(U_12718,U_12719),U_12720),U_12721)),hAPP(hAPP(c_Product__Type_OSigma(U_12718,U_12719),U_12722),U_12723))) ),
inference(clausify,[status(thm)],[f_3279_2]) ).
fof(f_3280_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_3280_2,plain,
! [U_12729,U_12728,U_12727,U_12726,U_12725,U_12724] :
( hBOOL(hAPP(hAPP(c_member(U_12725),U_12727),hAPP(U_12729,U_12726)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12724,U_12725)),hAPP(hAPP(c_Product__Type_OPair(U_12724,U_12725),U_12726),U_12727)),hAPP(hAPP(c_Product__Type_OSigma(U_12724,U_12725),U_12728),U_12729))) ),
inference(variable_rename,[status(thm)],[f_3280_1]) ).
fof(f_3280_3,plain,
! [U_12729,U_12728,U_12727,U_12726,U_12725] :
( ! [U_12724] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12724,U_12725)),hAPP(hAPP(c_Product__Type_OPair(U_12724,U_12725),U_12726),U_12727)),hAPP(hAPP(c_Product__Type_OSigma(U_12724,U_12725),U_12728),U_12729)))
| hBOOL(hAPP(hAPP(c_member(U_12725),U_12727),hAPP(U_12729,U_12726))) ),
inference(miniscope,[status(thm)],[f_3280_2]) ).
cnf(f_3280_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12724,U_12725)),hAPP(hAPP(c_Product__Type_OPair(U_12724,U_12725),U_12726),U_12727)),hAPP(hAPP(c_Product__Type_OSigma(U_12724,U_12725),U_12728),U_12729)))
| hBOOL(hAPP(hAPP(c_member(U_12725),U_12727),hAPP(U_12729,U_12726))) ),
inference(clausify,[status(thm)],[f_3280_3]) ).
fof(f_3281_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_3281_2,plain,
! [U_12735,U_12734,U_12733,U_12732,U_12731,U_12730] :
( hBOOL(hAPP(hAPP(c_member(U_12730),U_12732),U_12734))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12730,U_12731)),hAPP(hAPP(c_Product__Type_OPair(U_12730,U_12731),U_12732),U_12733)),hAPP(hAPP(c_Product__Type_OSigma(U_12730,U_12731),U_12734),U_12735))) ),
inference(variable_rename,[status(thm)],[f_3281_1]) ).
cnf(f_3281_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_12730),U_12732),U_12734))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12730,U_12731)),hAPP(hAPP(c_Product__Type_OPair(U_12730,U_12731),U_12732),U_12733)),hAPP(hAPP(c_Product__Type_OSigma(U_12730,U_12731),U_12734),U_12735))) ),
inference(clausify,[status(thm)],[f_3281_2]) ).
fof(f_3282_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_3282_2,plain,
! [U_12741,U_12740,U_12739,U_12738,U_12737,U_12736] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12736,U_12737)),hAPP(hAPP(c_Product__Type_OPair(U_12736,U_12737),U_12738),U_12739)),hAPP(hAPP(c_Product__Type_OSigma(U_12736,U_12737),U_12740),U_12741)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12737),U_12739),hAPP(U_12741,U_12738)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12736),U_12738),U_12740)) )
& ( ( hBOOL(hAPP(hAPP(c_member(U_12737),U_12739),hAPP(U_12741,U_12738)))
& hBOOL(hAPP(hAPP(c_member(U_12736),U_12738),U_12740)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12736,U_12737)),hAPP(hAPP(c_Product__Type_OPair(U_12736,U_12737),U_12738),U_12739)),hAPP(hAPP(c_Product__Type_OSigma(U_12736,U_12737),U_12740),U_12741))) ) ),
inference(variable_rename,[status(thm)],[f_3282_1]) ).
fof(f_3282_3,plain,
( ! [U_12753,U_12751,U_12749,U_12747,U_12745,U_12743] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12743,U_12745)),hAPP(hAPP(c_Product__Type_OPair(U_12743,U_12745),U_12747),U_12749)),hAPP(hAPP(c_Product__Type_OSigma(U_12743,U_12745),U_12751),U_12753)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12745),U_12749),hAPP(U_12753,U_12747)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12743),U_12747),U_12751)) )
& ! [U_12752,U_12750,U_12748,U_12746,U_12744,U_12742] :
( ( hBOOL(hAPP(hAPP(c_member(U_12744),U_12748),hAPP(U_12752,U_12746)))
& hBOOL(hAPP(hAPP(c_member(U_12742),U_12746),U_12750)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12742,U_12744)),hAPP(hAPP(c_Product__Type_OPair(U_12742,U_12744),U_12746),U_12748)),hAPP(hAPP(c_Product__Type_OSigma(U_12742,U_12744),U_12750),U_12752))) ) ),
inference(miniscope,[status(thm)],[f_3282_2]) ).
cnf(f_3282_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12742),U_12746),U_12750))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12742,U_12744)),hAPP(hAPP(c_Product__Type_OPair(U_12742,U_12744),U_12746),U_12748)),hAPP(hAPP(c_Product__Type_OSigma(U_12742,U_12744),U_12750),U_12752))) ),
inference(clausify,[status(thm)],[f_3282_3]) ).
cnf(f_3282_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_12744),U_12748),hAPP(U_12752,U_12746)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12742,U_12744)),hAPP(hAPP(c_Product__Type_OPair(U_12742,U_12744),U_12746),U_12748)),hAPP(hAPP(c_Product__Type_OSigma(U_12742,U_12744),U_12750),U_12752))) ),
inference(clausify,[status(thm)],[f_3282_3]) ).
cnf(f_3282_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12743,U_12745)),hAPP(hAPP(c_Product__Type_OPair(U_12743,U_12745),U_12747),U_12749)),hAPP(hAPP(c_Product__Type_OSigma(U_12743,U_12745),U_12751),U_12753)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12745),U_12749),hAPP(U_12753,U_12747)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12743),U_12747),U_12751)) ),
inference(clausify,[status(thm)],[f_3282_3]) ).
fof(f_3283_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_3283_2,plain,
! [U_12757,U_12756,U_12755,U_12754] : hAPP(c_Finite__Set_Ocard(tc_prod(U_12754,U_12755)),hAPP(hAPP(c_Product__Type_OSigma(U_12754,U_12755),hAPP(hAPP(c_Set_Oinsert(U_12754),U_12756),c_Orderings_Obot__class_Obot(tc_fun(U_12754,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(U_12755,tc_HOL_Obool),U_12754),U_12757))) = hAPP(c_Finite__Set_Ocard(U_12755),U_12757),
inference(variable_rename,[status(thm)],[f_3283_1]) ).
cnf(f_3283_3,plain,
hAPP(c_Finite__Set_Ocard(tc_prod(U_12754,U_12755)),hAPP(hAPP(c_Product__Type_OSigma(U_12754,U_12755),hAPP(hAPP(c_Set_Oinsert(U_12754),U_12756),c_Orderings_Obot__class_Obot(tc_fun(U_12754,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(U_12755,tc_HOL_Obool),U_12754),U_12757))) = hAPP(c_Finite__Set_Ocard(U_12755),U_12757),
inference(clausify,[status(thm)],[f_3283_2]) ).
fof(f_3284_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_3284_2,plain,
! [U_12763,U_12762,U_12761,U_12760,U_12759,U_12758] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12761,U_12758),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12761,U_12758),U_12762),hAPP(c_COMBK(tc_fun(U_12758,tc_HOL_Obool),U_12761),U_12760))),hAPP(hAPP(c_Product__Type_OSigma(U_12761,U_12758),U_12763),hAPP(c_COMBK(tc_fun(U_12758,tc_HOL_Obool),U_12761),U_12760))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12761,tc_HOL_Obool)),U_12762),U_12763)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12761,tc_HOL_Obool)),U_12762),U_12763))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12761,U_12758),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12761,U_12758),U_12762),hAPP(c_COMBK(tc_fun(U_12758,tc_HOL_Obool),U_12761),U_12760))),hAPP(hAPP(c_Product__Type_OSigma(U_12761,U_12758),U_12763),hAPP(c_COMBK(tc_fun(U_12758,tc_HOL_Obool),U_12761),U_12760)))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12758),U_12759),U_12760)) ),
inference(variable_rename,[status(thm)],[f_3284_1]) ).
cnf(f_3284_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12761,tc_HOL_Obool)),U_12762),U_12763))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12761,U_12758),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12761,U_12758),U_12762),hAPP(c_COMBK(tc_fun(U_12758,tc_HOL_Obool),U_12761),U_12760))),hAPP(hAPP(c_Product__Type_OSigma(U_12761,U_12758),U_12763),hAPP(c_COMBK(tc_fun(U_12758,tc_HOL_Obool),U_12761),U_12760))))
| ~ hBOOL(hAPP(hAPP(c_member(U_12758),U_12759),U_12760)) ),
inference(clausify,[status(thm)],[f_3284_2]) ).
cnf(f_3284_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12761,U_12758),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12761,U_12758),U_12762),hAPP(c_COMBK(tc_fun(U_12758,tc_HOL_Obool),U_12761),U_12760))),hAPP(hAPP(c_Product__Type_OSigma(U_12761,U_12758),U_12763),hAPP(c_COMBK(tc_fun(U_12758,tc_HOL_Obool),U_12761),U_12760))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12761,tc_HOL_Obool)),U_12762),U_12763))
| ~ hBOOL(hAPP(hAPP(c_member(U_12758),U_12759),U_12760)) ),
inference(clausify,[status(thm)],[f_3284_2]) ).
fof(f_3285_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_3285_2,plain,
! [U_12769,U_12768,U_12767,U_12766,U_12765,U_12764] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12765,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12764,U_12765,U_12766),U_12769)),U_12768))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12764,U_12765),tc_HOL_Obool)),U_12766),hAPP(hAPP(c_Product__Type_OSigma(U_12764,U_12765),U_12767),hAPP(c_COMBK(tc_fun(U_12765,tc_HOL_Obool),U_12764),U_12768)))) ),
inference(variable_rename,[status(thm)],[f_3285_1]) ).
cnf(f_3285_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12765,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12764,U_12765,U_12766),U_12769)),U_12768))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12764,U_12765),tc_HOL_Obool)),U_12766),hAPP(hAPP(c_Product__Type_OSigma(U_12764,U_12765),U_12767),hAPP(c_COMBK(tc_fun(U_12765,tc_HOL_Obool),U_12764),U_12768)))) ),
inference(clausify,[status(thm)],[f_3285_2]) ).
fof(f_3286_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_3286_2,plain,
! [U_12773,U_12772,U_12771,U_12770] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12770),U_12772))
| U_12773 = c_Orderings_Obot__class_Obot(tc_fun(U_12771,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12770,U_12771)),hAPP(hAPP(c_Product__Type_OSigma(U_12770,U_12771),U_12772),hAPP(c_COMBK(tc_fun(U_12771,tc_HOL_Obool),U_12770),U_12773)))) ),
inference(variable_rename,[status(thm)],[f_3286_1]) ).
cnf(f_3286_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12770),U_12772))
| U_12773 = c_Orderings_Obot__class_Obot(tc_fun(U_12771,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12770,U_12771)),hAPP(hAPP(c_Product__Type_OSigma(U_12770,U_12771),U_12772),hAPP(c_COMBK(tc_fun(U_12771,tc_HOL_Obool),U_12770),U_12773)))) ),
inference(clausify,[status(thm)],[f_3286_2]) ).
fof(f_3287_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_3287_2,plain,
! [U_12777,U_12776,U_12775,U_12774] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12775),U_12777))
| U_12776 = c_Orderings_Obot__class_Obot(tc_fun(U_12774,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12774,U_12775)),hAPP(hAPP(c_Product__Type_OSigma(U_12774,U_12775),U_12776),hAPP(c_COMBK(tc_fun(U_12775,tc_HOL_Obool),U_12774),U_12777)))) ),
inference(variable_rename,[status(thm)],[f_3287_1]) ).
cnf(f_3287_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12775),U_12777))
| U_12776 = c_Orderings_Obot__class_Obot(tc_fun(U_12774,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12774,U_12775)),hAPP(hAPP(c_Product__Type_OSigma(U_12774,U_12775),U_12776),hAPP(c_COMBK(tc_fun(U_12775,tc_HOL_Obool),U_12774),U_12777)))) ),
inference(clausify,[status(thm)],[f_3287_2]) ).
fof(f_3288_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_3288_2,plain,
! [U_12781,U_12780,U_12779,U_12778] :
( ( hAPP(c_Set_Oimage(tc_prod(U_12780,U_12779),U_12780,c_Product__Type_Ofst(U_12780,U_12779)),hAPP(hAPP(c_Product__Type_OSigma(U_12780,U_12779),U_12781),hAPP(c_COMBK(tc_fun(U_12779,tc_HOL_Obool),U_12780),U_12778))) = U_12781
| U_12778 = c_Orderings_Obot__class_Obot(tc_fun(U_12779,tc_HOL_Obool)) )
& ( hAPP(c_Set_Oimage(tc_prod(U_12780,U_12779),U_12780,c_Product__Type_Ofst(U_12780,U_12779)),hAPP(hAPP(c_Product__Type_OSigma(U_12780,U_12779),U_12781),hAPP(c_COMBK(tc_fun(U_12779,tc_HOL_Obool),U_12780),U_12778))) = c_Orderings_Obot__class_Obot(tc_fun(U_12780,tc_HOL_Obool))
| U_12778 != c_Orderings_Obot__class_Obot(tc_fun(U_12779,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_3288_1]) ).
fof(f_3288_3,plain,
( ! [U_12789,U_12787,U_12785,U_12783] :
( hAPP(c_Set_Oimage(tc_prod(U_12787,U_12785),U_12787,c_Product__Type_Ofst(U_12787,U_12785)),hAPP(hAPP(c_Product__Type_OSigma(U_12787,U_12785),U_12789),hAPP(c_COMBK(tc_fun(U_12785,tc_HOL_Obool),U_12787),U_12783))) = U_12789
| U_12783 = c_Orderings_Obot__class_Obot(tc_fun(U_12785,tc_HOL_Obool)) )
& ! [U_12788,U_12786,U_12784,U_12782] :
( hAPP(c_Set_Oimage(tc_prod(U_12786,U_12784),U_12786,c_Product__Type_Ofst(U_12786,U_12784)),hAPP(hAPP(c_Product__Type_OSigma(U_12786,U_12784),U_12788),hAPP(c_COMBK(tc_fun(U_12784,tc_HOL_Obool),U_12786),U_12782))) = c_Orderings_Obot__class_Obot(tc_fun(U_12786,tc_HOL_Obool))
| U_12782 != c_Orderings_Obot__class_Obot(tc_fun(U_12784,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_3288_2]) ).
cnf(f_3288_4,plain,
( hAPP(c_Set_Oimage(tc_prod(U_12786,U_12784),U_12786,c_Product__Type_Ofst(U_12786,U_12784)),hAPP(hAPP(c_Product__Type_OSigma(U_12786,U_12784),U_12788),hAPP(c_COMBK(tc_fun(U_12784,tc_HOL_Obool),U_12786),U_12782))) = c_Orderings_Obot__class_Obot(tc_fun(U_12786,tc_HOL_Obool))
| U_12782 != c_Orderings_Obot__class_Obot(tc_fun(U_12784,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3288_3]) ).
cnf(f_3288_5,plain,
( hAPP(c_Set_Oimage(tc_prod(U_12787,U_12785),U_12787,c_Product__Type_Ofst(U_12787,U_12785)),hAPP(hAPP(c_Product__Type_OSigma(U_12787,U_12785),U_12789),hAPP(c_COMBK(tc_fun(U_12785,tc_HOL_Obool),U_12787),U_12783))) = U_12789
| U_12783 = c_Orderings_Obot__class_Obot(tc_fun(U_12785,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3288_3]) ).
fof(f_3289_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_3289_2,plain,
! [U_12793,U_12792,U_12791,U_12790] :
( ( hAPP(c_Set_Oimage(tc_prod(U_12791,U_12792),U_12792,c_Product__Type_Osnd(U_12791,U_12792)),hAPP(hAPP(c_Product__Type_OSigma(U_12791,U_12792),U_12790),hAPP(c_COMBK(tc_fun(U_12792,tc_HOL_Obool),U_12791),U_12793))) = U_12793
| U_12790 = c_Orderings_Obot__class_Obot(tc_fun(U_12791,tc_HOL_Obool)) )
& ( hAPP(c_Set_Oimage(tc_prod(U_12791,U_12792),U_12792,c_Product__Type_Osnd(U_12791,U_12792)),hAPP(hAPP(c_Product__Type_OSigma(U_12791,U_12792),U_12790),hAPP(c_COMBK(tc_fun(U_12792,tc_HOL_Obool),U_12791),U_12793))) = c_Orderings_Obot__class_Obot(tc_fun(U_12792,tc_HOL_Obool))
| U_12790 != c_Orderings_Obot__class_Obot(tc_fun(U_12791,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_3289_1]) ).
fof(f_3289_3,plain,
( ! [U_12801,U_12799,U_12797,U_12795] :
( hAPP(c_Set_Oimage(tc_prod(U_12797,U_12799),U_12799,c_Product__Type_Osnd(U_12797,U_12799)),hAPP(hAPP(c_Product__Type_OSigma(U_12797,U_12799),U_12795),hAPP(c_COMBK(tc_fun(U_12799,tc_HOL_Obool),U_12797),U_12801))) = U_12801
| U_12795 = c_Orderings_Obot__class_Obot(tc_fun(U_12797,tc_HOL_Obool)) )
& ! [U_12800,U_12798,U_12796,U_12794] :
( hAPP(c_Set_Oimage(tc_prod(U_12796,U_12798),U_12798,c_Product__Type_Osnd(U_12796,U_12798)),hAPP(hAPP(c_Product__Type_OSigma(U_12796,U_12798),U_12794),hAPP(c_COMBK(tc_fun(U_12798,tc_HOL_Obool),U_12796),U_12800))) = c_Orderings_Obot__class_Obot(tc_fun(U_12798,tc_HOL_Obool))
| U_12794 != c_Orderings_Obot__class_Obot(tc_fun(U_12796,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_3289_2]) ).
cnf(f_3289_4,plain,
( hAPP(c_Set_Oimage(tc_prod(U_12796,U_12798),U_12798,c_Product__Type_Osnd(U_12796,U_12798)),hAPP(hAPP(c_Product__Type_OSigma(U_12796,U_12798),U_12794),hAPP(c_COMBK(tc_fun(U_12798,tc_HOL_Obool),U_12796),U_12800))) = c_Orderings_Obot__class_Obot(tc_fun(U_12798,tc_HOL_Obool))
| U_12794 != c_Orderings_Obot__class_Obot(tc_fun(U_12796,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3289_3]) ).
cnf(f_3289_5,plain,
( hAPP(c_Set_Oimage(tc_prod(U_12797,U_12799),U_12799,c_Product__Type_Osnd(U_12797,U_12799)),hAPP(hAPP(c_Product__Type_OSigma(U_12797,U_12799),U_12795),hAPP(c_COMBK(tc_fun(U_12799,tc_HOL_Obool),U_12797),U_12801))) = U_12801
| U_12795 = c_Orderings_Obot__class_Obot(tc_fun(U_12797,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3289_3]) ).
fof(f_3290_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_3290_2,plain,
! [U_12806,U_12805,U_12804] :
( ( c_Relation_Orefl__on(U_12804,U_12805,U_12806)
| ? [U_12803] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12804,U_12804)),hAPP(hAPP(c_Product__Type_OPair(U_12804,U_12804),U_12803),U_12803)),U_12806))
& hBOOL(hAPP(hAPP(c_member(U_12804),U_12803),U_12805)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12804,U_12804),tc_HOL_Obool)),U_12806),hAPP(hAPP(c_Product__Type_OSigma(U_12804,U_12804),U_12805),hAPP(c_COMBK(tc_fun(U_12804,tc_HOL_Obool),U_12804),U_12805)))) )
& ( ( ! [U_12802] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12804,U_12804)),hAPP(hAPP(c_Product__Type_OPair(U_12804,U_12804),U_12802),U_12802)),U_12806))
| ~ hBOOL(hAPP(hAPP(c_member(U_12804),U_12802),U_12805)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12804,U_12804),tc_HOL_Obool)),U_12806),hAPP(hAPP(c_Product__Type_OSigma(U_12804,U_12804),U_12805),hAPP(c_COMBK(tc_fun(U_12804,tc_HOL_Obool),U_12804),U_12805)))) )
| ~ c_Relation_Orefl__on(U_12804,U_12805,U_12806) ) ),
inference(variable_rename,[status(thm)],[f_3290_1]) ).
fof(f_3290_3,plain,
( ! [U_12812,U_12810,U_12808] :
( c_Relation_Orefl__on(U_12808,U_12810,U_12812)
| ? [U_12803] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12808,U_12808)),hAPP(hAPP(c_Product__Type_OPair(U_12808,U_12808),U_12803),U_12803)),U_12812))
& hBOOL(hAPP(hAPP(c_member(U_12808),U_12803),U_12810)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12808,U_12808),tc_HOL_Obool)),U_12812),hAPP(hAPP(c_Product__Type_OSigma(U_12808,U_12808),U_12810),hAPP(c_COMBK(tc_fun(U_12808,tc_HOL_Obool),U_12808),U_12810)))) )
& ! [U_12811,U_12809,U_12807] :
( ( ! [U_12802] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12807,U_12807)),hAPP(hAPP(c_Product__Type_OPair(U_12807,U_12807),U_12802),U_12802)),U_12811))
| ~ hBOOL(hAPP(hAPP(c_member(U_12807),U_12802),U_12809)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12807,U_12807),tc_HOL_Obool)),U_12811),hAPP(hAPP(c_Product__Type_OSigma(U_12807,U_12807),U_12809),hAPP(c_COMBK(tc_fun(U_12807,tc_HOL_Obool),U_12807),U_12809)))) )
| ~ c_Relation_Orefl__on(U_12807,U_12809,U_12811) ) ),
inference(miniscope,[status(thm)],[f_3290_2]) ).
fof(f_3290_4,plain,
( ! [U_12812,U_12810,U_12808] :
( c_Relation_Orefl__on(U_12808,U_12810,U_12812)
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12808,U_12808)),hAPP(hAPP(c_Product__Type_OPair(U_12808,U_12808),sK307(U_12812,U_12810,U_12808)),sK307(U_12812,U_12810,U_12808))),U_12812))
& hBOOL(hAPP(hAPP(c_member(U_12808),sK307(U_12812,U_12810,U_12808)),U_12810)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12808,U_12808),tc_HOL_Obool)),U_12812),hAPP(hAPP(c_Product__Type_OSigma(U_12808,U_12808),U_12810),hAPP(c_COMBK(tc_fun(U_12808,tc_HOL_Obool),U_12808),U_12810)))) )
& ! [U_12811,U_12809,U_12807] :
( ( ! [U_12802] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12807,U_12807)),hAPP(hAPP(c_Product__Type_OPair(U_12807,U_12807),U_12802),U_12802)),U_12811))
| ~ hBOOL(hAPP(hAPP(c_member(U_12807),U_12802),U_12809)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12807,U_12807),tc_HOL_Obool)),U_12811),hAPP(hAPP(c_Product__Type_OSigma(U_12807,U_12807),U_12809),hAPP(c_COMBK(tc_fun(U_12807,tc_HOL_Obool),U_12807),U_12809)))) )
| ~ c_Relation_Orefl__on(U_12807,U_12809,U_12811) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK307]),skolemize(U_12803,sK307(U_12812,U_12810,U_12808))],[f_3290_3]) ).
cnf(f_3290_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12807,U_12807),tc_HOL_Obool)),U_12811),hAPP(hAPP(c_Product__Type_OSigma(U_12807,U_12807),U_12809),hAPP(c_COMBK(tc_fun(U_12807,tc_HOL_Obool),U_12807),U_12809))))
| ~ c_Relation_Orefl__on(U_12807,U_12809,U_12811) ),
inference(clausify,[status(thm)],[f_3290_4]) ).
cnf(f_3290_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12807,U_12807)),hAPP(hAPP(c_Product__Type_OPair(U_12807,U_12807),U_12802),U_12802)),U_12811))
| ~ hBOOL(hAPP(hAPP(c_member(U_12807),U_12802),U_12809))
| ~ c_Relation_Orefl__on(U_12807,U_12809,U_12811) ),
inference(clausify,[status(thm)],[f_3290_4]) ).
cnf(f_3290_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_12808),sK307(U_12812,U_12810,U_12808)),U_12810))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12808,U_12808),tc_HOL_Obool)),U_12812),hAPP(hAPP(c_Product__Type_OSigma(U_12808,U_12808),U_12810),hAPP(c_COMBK(tc_fun(U_12808,tc_HOL_Obool),U_12808),U_12810))))
| c_Relation_Orefl__on(U_12808,U_12810,U_12812) ),
inference(clausify,[status(thm)],[f_3290_4]) ).
cnf(f_3290_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12808,U_12808)),hAPP(hAPP(c_Product__Type_OPair(U_12808,U_12808),sK307(U_12812,U_12810,U_12808)),sK307(U_12812,U_12810,U_12808))),U_12812))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12808,U_12808),tc_HOL_Obool)),U_12812),hAPP(hAPP(c_Product__Type_OSigma(U_12808,U_12808),U_12810),hAPP(c_COMBK(tc_fun(U_12808,tc_HOL_Obool),U_12808),U_12810))))
| c_Relation_Orefl__on(U_12808,U_12810,U_12812) ),
inference(clausify,[status(thm)],[f_3290_4]) ).
fof(f_3291_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_3291_2,plain,
! [U_12818,U_12817,U_12816,U_12815,U_12814,U_12813] : hAPP(hAPP(c_Product__Type_OSigma(U_12813,U_12814),hAPP(hAPP(c_Set_Oinsert(U_12813),U_12815),U_12816)),hAPP(c_COMBK(tc_fun(U_12814,tc_HOL_Obool),U_12813),hAPP(hAPP(c_Set_Oinsert(U_12814),U_12817),U_12818))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(U_12813,U_12814)),hAPP(hAPP(c_Product__Type_OPair(U_12813,U_12814),U_12815),U_12817)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12813,U_12814),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12813,U_12814),U_12816),hAPP(c_COMBK(tc_fun(U_12814,tc_HOL_Obool),U_12813),hAPP(hAPP(c_Set_Oinsert(U_12814),U_12817),U_12818)))),hAPP(hAPP(c_Product__Type_OSigma(U_12813,U_12814),hAPP(hAPP(c_Set_Oinsert(U_12813),U_12815),U_12816)),hAPP(c_COMBK(tc_fun(U_12814,tc_HOL_Obool),U_12813),U_12818)))),
inference(variable_rename,[status(thm)],[f_3291_1]) ).
cnf(f_3291_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12813,U_12814),hAPP(hAPP(c_Set_Oinsert(U_12813),U_12815),U_12816)),hAPP(c_COMBK(tc_fun(U_12814,tc_HOL_Obool),U_12813),hAPP(hAPP(c_Set_Oinsert(U_12814),U_12817),U_12818))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(U_12813,U_12814)),hAPP(hAPP(c_Product__Type_OPair(U_12813,U_12814),U_12815),U_12817)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12813,U_12814),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12813,U_12814),U_12816),hAPP(c_COMBK(tc_fun(U_12814,tc_HOL_Obool),U_12813),hAPP(hAPP(c_Set_Oinsert(U_12814),U_12817),U_12818)))),hAPP(hAPP(c_Product__Type_OSigma(U_12813,U_12814),hAPP(hAPP(c_Set_Oinsert(U_12813),U_12815),U_12816)),hAPP(c_COMBK(tc_fun(U_12814,tc_HOL_Obool),U_12813),U_12818)))),
inference(clausify,[status(thm)],[f_3291_2]) ).
fof(f_3292_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_3292_2,plain,
! [U_12822,U_12821,U_12820,U_12819] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12819),U_12822))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12819,tc_HOL_Obool)),U_12822),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12819),U_12820),U_12821)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12819,U_12819),tc_HOL_Obool)),U_12821),hAPP(hAPP(c_Product__Type_OSigma(U_12819,U_12819),U_12820),hAPP(c_COMBK(tc_fun(U_12819,tc_HOL_Obool),U_12819),U_12820))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12819),U_12820)) ),
inference(variable_rename,[status(thm)],[f_3292_1]) ).
cnf(f_3292_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12819),U_12822))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12819,tc_HOL_Obool)),U_12822),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12819),U_12820),U_12821)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12819,U_12819),tc_HOL_Obool)),U_12821),hAPP(hAPP(c_Product__Type_OSigma(U_12819,U_12819),U_12820),hAPP(c_COMBK(tc_fun(U_12819,tc_HOL_Obool),U_12819),U_12820))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12819),U_12820)) ),
inference(clausify,[status(thm)],[f_3292_2]) ).
fof(f_3293_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_3293_2,plain,
! [U_12828,U_12827,U_12826,U_12825,U_12824,U_12823] : hAPP(c_Set_Ovimage(U_12823,tc_prod(U_12824,U_12825),U_12826),hAPP(hAPP(c_Product__Type_OSigma(U_12824,U_12825),U_12827),hAPP(c_COMBK(tc_fun(U_12825,tc_HOL_Obool),U_12824),U_12828))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12823,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12823,U_12824,hAPP(c_Fun_Ocomp(tc_prod(U_12824,U_12825),U_12824,U_12823,c_Product__Type_Ofst(U_12824,U_12825)),U_12826)),U_12827)),hAPP(c_Set_Ovimage(U_12823,U_12825,hAPP(c_Fun_Ocomp(tc_prod(U_12824,U_12825),U_12825,U_12823,c_Product__Type_Osnd(U_12824,U_12825)),U_12826)),U_12828)),
inference(variable_rename,[status(thm)],[f_3293_1]) ).
cnf(f_3293_3,plain,
hAPP(c_Set_Ovimage(U_12823,tc_prod(U_12824,U_12825),U_12826),hAPP(hAPP(c_Product__Type_OSigma(U_12824,U_12825),U_12827),hAPP(c_COMBK(tc_fun(U_12825,tc_HOL_Obool),U_12824),U_12828))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12823,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12823,U_12824,hAPP(c_Fun_Ocomp(tc_prod(U_12824,U_12825),U_12824,U_12823,c_Product__Type_Ofst(U_12824,U_12825)),U_12826)),U_12827)),hAPP(c_Set_Ovimage(U_12823,U_12825,hAPP(c_Fun_Ocomp(tc_prod(U_12824,U_12825),U_12825,U_12823,c_Product__Type_Osnd(U_12824,U_12825)),U_12826)),U_12828)),
inference(clausify,[status(thm)],[f_3293_2]) ).
fof(f_3294_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_3294_2,plain,
! [U_12836,U_12835,U_12834,U_12833,U_12832,U_12831,U_12830,U_12829] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(U_12829,U_12830),tc_fun(tc_prod(U_12831,U_12832),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12829,U_12830),U_12833),hAPP(c_COMBK(tc_fun(U_12830,tc_HOL_Obool),U_12829),U_12834))),hAPP(c_Product__Type_Oprod_Oprod__case(U_12829,U_12830,tc_fun(tc_prod(U_12831,U_12832),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_12829,tc_fun(U_12830,tc_fun(U_12831,tc_fun(U_12832,tc_HOL_Obool))),tc_fun(U_12830,tc_fun(tc_prod(U_12831,U_12832),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12831,tc_fun(U_12832,tc_HOL_Obool)),tc_fun(tc_prod(U_12831,U_12832),tc_HOL_Obool)),tc_fun(tc_fun(U_12830,tc_fun(U_12831,tc_fun(U_12832,tc_HOL_Obool))),tc_fun(U_12830,tc_fun(tc_prod(U_12831,U_12832),tc_HOL_Obool))),U_12829),c_COMBB(tc_fun(U_12831,tc_fun(U_12832,tc_HOL_Obool)),tc_fun(tc_prod(U_12831,U_12832),tc_HOL_Obool),U_12830)),hAPP(hAPP(c_COMBB(tc_fun(U_12831,tc_HOL_Obool),tc_fun(tc_fun(U_12831,tc_fun(U_12832,tc_HOL_Obool)),tc_fun(tc_prod(U_12831,U_12832),tc_HOL_Obool)),U_12829),c_Product__Type_OSigma(U_12831,U_12832)),U_12835))),hAPP(hAPP(c_COMBB(tc_fun(U_12832,tc_HOL_Obool),tc_fun(U_12831,tc_fun(U_12832,tc_HOL_Obool)),U_12830),c_COMBK(tc_fun(U_12832,tc_HOL_Obool),U_12831)),U_12836)))) = hAPP(hAPP(c_Product__Type_OSigma(U_12831,U_12832),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12829,tc_fun(U_12831,tc_HOL_Obool)),U_12833),U_12835)),hAPP(c_COMBK(tc_fun(U_12832,tc_HOL_Obool),U_12831),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12830,tc_fun(U_12832,tc_HOL_Obool)),U_12834),U_12836))),
inference(variable_rename,[status(thm)],[f_3294_1]) ).
cnf(f_3294_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(U_12829,U_12830),tc_fun(tc_prod(U_12831,U_12832),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12829,U_12830),U_12833),hAPP(c_COMBK(tc_fun(U_12830,tc_HOL_Obool),U_12829),U_12834))),hAPP(c_Product__Type_Oprod_Oprod__case(U_12829,U_12830,tc_fun(tc_prod(U_12831,U_12832),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_12829,tc_fun(U_12830,tc_fun(U_12831,tc_fun(U_12832,tc_HOL_Obool))),tc_fun(U_12830,tc_fun(tc_prod(U_12831,U_12832),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12831,tc_fun(U_12832,tc_HOL_Obool)),tc_fun(tc_prod(U_12831,U_12832),tc_HOL_Obool)),tc_fun(tc_fun(U_12830,tc_fun(U_12831,tc_fun(U_12832,tc_HOL_Obool))),tc_fun(U_12830,tc_fun(tc_prod(U_12831,U_12832),tc_HOL_Obool))),U_12829),c_COMBB(tc_fun(U_12831,tc_fun(U_12832,tc_HOL_Obool)),tc_fun(tc_prod(U_12831,U_12832),tc_HOL_Obool),U_12830)),hAPP(hAPP(c_COMBB(tc_fun(U_12831,tc_HOL_Obool),tc_fun(tc_fun(U_12831,tc_fun(U_12832,tc_HOL_Obool)),tc_fun(tc_prod(U_12831,U_12832),tc_HOL_Obool)),U_12829),c_Product__Type_OSigma(U_12831,U_12832)),U_12835))),hAPP(hAPP(c_COMBB(tc_fun(U_12832,tc_HOL_Obool),tc_fun(U_12831,tc_fun(U_12832,tc_HOL_Obool)),U_12830),c_COMBK(tc_fun(U_12832,tc_HOL_Obool),U_12831)),U_12836)))) = hAPP(hAPP(c_Product__Type_OSigma(U_12831,U_12832),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12829,tc_fun(U_12831,tc_HOL_Obool)),U_12833),U_12835)),hAPP(c_COMBK(tc_fun(U_12832,tc_HOL_Obool),U_12831),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12830,tc_fun(U_12832,tc_HOL_Obool)),U_12834),U_12836))),
inference(clausify,[status(thm)],[f_3294_2]) ).
fof(f_3295_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_3295_2,plain,
! [U_12840,U_12839,U_12838,U_12837] : hAPP(hAPP(c_Product__Type_OSigma(U_12837,U_12838),U_12839),U_12840) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12837,tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool)),U_12839),hAPP(hAPP(c_COMBS(U_12837,tc_fun(U_12838,tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool)),tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12838,tc_HOL_Obool),tc_fun(tc_fun(U_12838,tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool)),tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool)),U_12837),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12838,tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool))),U_12840)),hAPP(hAPP(c_COMBC(U_12837,tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool),tc_fun(U_12838,tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12838,tc_fun(tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool),tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool),tc_fun(U_12838,tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool))),U_12837),c_COMBC(U_12838,tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool),tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12838,tc_prod(U_12837,U_12838)),tc_fun(U_12838,tc_fun(tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool),tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool))),U_12837),hAPP(c_COMBB(tc_prod(U_12837,U_12838),tc_fun(tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool),tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool)),U_12838),c_Set_Oinsert(tc_prod(U_12837,U_12838)))),c_Product__Type_OPair(U_12837,U_12838)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_3295_1]) ).
cnf(f_3295_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12837,U_12838),U_12839),U_12840) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12837,tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool)),U_12839),hAPP(hAPP(c_COMBS(U_12837,tc_fun(U_12838,tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool)),tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12838,tc_HOL_Obool),tc_fun(tc_fun(U_12838,tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool)),tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool)),U_12837),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12838,tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool))),U_12840)),hAPP(hAPP(c_COMBC(U_12837,tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool),tc_fun(U_12838,tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12838,tc_fun(tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool),tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool),tc_fun(U_12838,tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool))),U_12837),c_COMBC(U_12838,tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool),tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12838,tc_prod(U_12837,U_12838)),tc_fun(U_12838,tc_fun(tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool),tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool))),U_12837),hAPP(c_COMBB(tc_prod(U_12837,U_12838),tc_fun(tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool),tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool)),U_12838),c_Set_Oinsert(tc_prod(U_12837,U_12838)))),c_Product__Type_OPair(U_12837,U_12838)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12837,U_12838),tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_3295_2]) ).
fof(f_3296_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_3296_2,plain,
! [U_12843,U_12842,U_12841] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_12841,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12841),U_12842),U_12843)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12841,U_12841),tc_HOL_Obool)),U_12843),hAPP(hAPP(c_Product__Type_OSigma(U_12841,U_12841),U_12842),hAPP(c_COMBK(tc_fun(U_12841,tc_HOL_Obool),U_12841),U_12842))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12841),U_12842)) ),
inference(variable_rename,[status(thm)],[f_3296_1]) ).
cnf(f_3296_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_12841,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12841),U_12842),U_12843)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12841,U_12841),tc_HOL_Obool)),U_12843),hAPP(hAPP(c_Product__Type_OSigma(U_12841,U_12841),U_12842),hAPP(c_COMBK(tc_fun(U_12841,tc_HOL_Obool),U_12841),U_12842))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12841),U_12842)) ),
inference(clausify,[status(thm)],[f_3296_2]) ).
fof(f_3297_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_3297_2,plain,
! [U_12848,U_12847,U_12846,U_12845] :
? [U_12844] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12846,U_12845),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12845,tc_prod(U_12846,U_12845),U_12844),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12846,tc_fun(U_12845,tc_HOL_Obool)),U_12847),U_12848))),hAPP(hAPP(c_Product__Type_OSigma(U_12846,U_12845),U_12847),U_12848)))
& c_Fun_Oinj__on(U_12845,tc_prod(U_12846,U_12845),U_12844,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12846,tc_fun(U_12845,tc_HOL_Obool)),U_12847),U_12848)) ),
inference(variable_rename,[status(thm)],[f_3297_1]) ).
fof(f_3297_3,plain,
! [U_12848,U_12847,U_12846,U_12845] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12846,U_12845),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12845,tc_prod(U_12846,U_12845),sK308(U_12848,U_12847,U_12846,U_12845)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12846,tc_fun(U_12845,tc_HOL_Obool)),U_12847),U_12848))),hAPP(hAPP(c_Product__Type_OSigma(U_12846,U_12845),U_12847),U_12848)))
& c_Fun_Oinj__on(U_12845,tc_prod(U_12846,U_12845),sK308(U_12848,U_12847,U_12846,U_12845),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12846,tc_fun(U_12845,tc_HOL_Obool)),U_12847),U_12848)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK308]),skolemize(U_12844,sK308(U_12848,U_12847,U_12846,U_12845))],[f_3297_2]) ).
cnf(f_3297_4,plain,
c_Fun_Oinj__on(U_12845,tc_prod(U_12846,U_12845),sK308(U_12848,U_12847,U_12846,U_12845),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12846,tc_fun(U_12845,tc_HOL_Obool)),U_12847),U_12848)),
inference(clausify,[status(thm)],[f_3297_3]) ).
cnf(f_3297_5,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12846,U_12845),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12845,tc_prod(U_12846,U_12845),sK308(U_12848,U_12847,U_12846,U_12845)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12846,tc_fun(U_12845,tc_HOL_Obool)),U_12847),U_12848))),hAPP(hAPP(c_Product__Type_OSigma(U_12846,U_12845),U_12847),U_12848))),
inference(clausify,[status(thm)],[f_3297_3]) ).
fof(f_3298_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_3298_2,plain,
! [U_12852,U_12851,U_12850] :
( c_Relation_Orefl__on(U_12850,U_12852,U_12851)
| ? [U_12849] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12850,U_12850)),hAPP(hAPP(c_Product__Type_OPair(U_12850,U_12850),U_12849),U_12849)),U_12851))
& hBOOL(hAPP(hAPP(c_member(U_12850),U_12849),U_12852)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12850,U_12850),tc_HOL_Obool)),U_12851),hAPP(hAPP(c_Product__Type_OSigma(U_12850,U_12850),U_12852),hAPP(c_COMBK(tc_fun(U_12850,tc_HOL_Obool),U_12850),U_12852)))) ),
inference(variable_rename,[status(thm)],[f_3298_1]) ).
fof(f_3298_3,plain,
! [U_12852,U_12851,U_12850] :
( c_Relation_Orefl__on(U_12850,U_12852,U_12851)
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12850,U_12850)),hAPP(hAPP(c_Product__Type_OPair(U_12850,U_12850),sK309(U_12852,U_12851,U_12850)),sK309(U_12852,U_12851,U_12850))),U_12851))
& hBOOL(hAPP(hAPP(c_member(U_12850),sK309(U_12852,U_12851,U_12850)),U_12852)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12850,U_12850),tc_HOL_Obool)),U_12851),hAPP(hAPP(c_Product__Type_OSigma(U_12850,U_12850),U_12852),hAPP(c_COMBK(tc_fun(U_12850,tc_HOL_Obool),U_12850),U_12852)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK309]),skolemize(U_12849,sK309(U_12852,U_12851,U_12850))],[f_3298_2]) ).
cnf(f_3298_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12850),sK309(U_12852,U_12851,U_12850)),U_12852))
| c_Relation_Orefl__on(U_12850,U_12852,U_12851)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12850,U_12850),tc_HOL_Obool)),U_12851),hAPP(hAPP(c_Product__Type_OSigma(U_12850,U_12850),U_12852),hAPP(c_COMBK(tc_fun(U_12850,tc_HOL_Obool),U_12850),U_12852)))) ),
inference(clausify,[status(thm)],[f_3298_3]) ).
cnf(f_3298_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12850,U_12850)),hAPP(hAPP(c_Product__Type_OPair(U_12850,U_12850),sK309(U_12852,U_12851,U_12850)),sK309(U_12852,U_12851,U_12850))),U_12851))
| c_Relation_Orefl__on(U_12850,U_12852,U_12851)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12850,U_12850),tc_HOL_Obool)),U_12851),hAPP(hAPP(c_Product__Type_OSigma(U_12850,U_12850),U_12852),hAPP(c_COMBK(tc_fun(U_12850,tc_HOL_Obool),U_12850),U_12852)))) ),
inference(clausify,[status(thm)],[f_3298_3]) ).
fof(f_3299_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_3299_2,plain,
! [U_12859,U_12858,U_12857,U_12856,U_12855,U_12854] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12854,U_12855,c_Groups_Otimes__class_Otimes(U_12854)),hAPP(hAPP(c_COMBS(U_12855,tc_fun(U_12857,tc_HOL_Obool),U_12854),hAPP(hAPP(c_COMBC(U_12855,U_12854,tc_fun(tc_fun(U_12857,tc_HOL_Obool),U_12854)),hAPP(hAPP(c_COMBB(tc_fun(U_12857,U_12854),tc_fun(U_12854,tc_fun(tc_fun(U_12857,tc_HOL_Obool),U_12854)),U_12855),c_Finite__Set_Ofold__image(U_12854,U_12857,c_Groups_Otimes__class_Otimes(U_12854))),U_12859)),c_Groups_Oone__class_Oone(U_12854))),U_12858)),c_Groups_Oone__class_Oone(U_12854)),U_12856) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12854,tc_prod(U_12855,U_12857),c_Groups_Otimes__class_Otimes(U_12854)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12855,U_12857,U_12854),U_12859)),c_Groups_Oone__class_Oone(U_12854)),hAPP(hAPP(c_Product__Type_OSigma(U_12855,U_12857),U_12856),U_12858))
| ? [U_12853] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12857),hAPP(U_12858,U_12853)))
& hBOOL(hAPP(hAPP(c_member(U_12855),U_12853),U_12856)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12855),U_12856))
| ~ class_Groups_Ocomm__monoid__mult(U_12854) ),
inference(variable_rename,[status(thm)],[f_3299_1]) ).
fof(f_3299_3,plain,
! [U_12859,U_12858,U_12857,U_12856,U_12855,U_12854] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12854,U_12855,c_Groups_Otimes__class_Otimes(U_12854)),hAPP(hAPP(c_COMBS(U_12855,tc_fun(U_12857,tc_HOL_Obool),U_12854),hAPP(hAPP(c_COMBC(U_12855,U_12854,tc_fun(tc_fun(U_12857,tc_HOL_Obool),U_12854)),hAPP(hAPP(c_COMBB(tc_fun(U_12857,U_12854),tc_fun(U_12854,tc_fun(tc_fun(U_12857,tc_HOL_Obool),U_12854)),U_12855),c_Finite__Set_Ofold__image(U_12854,U_12857,c_Groups_Otimes__class_Otimes(U_12854))),U_12859)),c_Groups_Oone__class_Oone(U_12854))),U_12858)),c_Groups_Oone__class_Oone(U_12854)),U_12856) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12854,tc_prod(U_12855,U_12857),c_Groups_Otimes__class_Otimes(U_12854)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12855,U_12857,U_12854),U_12859)),c_Groups_Oone__class_Oone(U_12854)),hAPP(hAPP(c_Product__Type_OSigma(U_12855,U_12857),U_12856),U_12858))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12857),hAPP(U_12858,sK310(U_12859,U_12858,U_12857,U_12856,U_12855,U_12854))))
& hBOOL(hAPP(hAPP(c_member(U_12855),sK310(U_12859,U_12858,U_12857,U_12856,U_12855,U_12854)),U_12856)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12855),U_12856))
| ~ class_Groups_Ocomm__monoid__mult(U_12854) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK310]),skolemize(U_12853,sK310(U_12859,U_12858,U_12857,U_12856,U_12855,U_12854))],[f_3299_2]) ).
cnf(f_3299_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12855),sK310(U_12859,U_12858,U_12857,U_12856,U_12855,U_12854)),U_12856))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12854,U_12855,c_Groups_Otimes__class_Otimes(U_12854)),hAPP(hAPP(c_COMBS(U_12855,tc_fun(U_12857,tc_HOL_Obool),U_12854),hAPP(hAPP(c_COMBC(U_12855,U_12854,tc_fun(tc_fun(U_12857,tc_HOL_Obool),U_12854)),hAPP(hAPP(c_COMBB(tc_fun(U_12857,U_12854),tc_fun(U_12854,tc_fun(tc_fun(U_12857,tc_HOL_Obool),U_12854)),U_12855),c_Finite__Set_Ofold__image(U_12854,U_12857,c_Groups_Otimes__class_Otimes(U_12854))),U_12859)),c_Groups_Oone__class_Oone(U_12854))),U_12858)),c_Groups_Oone__class_Oone(U_12854)),U_12856) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12854,tc_prod(U_12855,U_12857),c_Groups_Otimes__class_Otimes(U_12854)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12855,U_12857,U_12854),U_12859)),c_Groups_Oone__class_Oone(U_12854)),hAPP(hAPP(c_Product__Type_OSigma(U_12855,U_12857),U_12856),U_12858))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12855),U_12856))
| ~ class_Groups_Ocomm__monoid__mult(U_12854) ),
inference(clausify,[status(thm)],[f_3299_3]) ).
cnf(f_3299_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12857),hAPP(U_12858,sK310(U_12859,U_12858,U_12857,U_12856,U_12855,U_12854))))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12854,U_12855,c_Groups_Otimes__class_Otimes(U_12854)),hAPP(hAPP(c_COMBS(U_12855,tc_fun(U_12857,tc_HOL_Obool),U_12854),hAPP(hAPP(c_COMBC(U_12855,U_12854,tc_fun(tc_fun(U_12857,tc_HOL_Obool),U_12854)),hAPP(hAPP(c_COMBB(tc_fun(U_12857,U_12854),tc_fun(U_12854,tc_fun(tc_fun(U_12857,tc_HOL_Obool),U_12854)),U_12855),c_Finite__Set_Ofold__image(U_12854,U_12857,c_Groups_Otimes__class_Otimes(U_12854))),U_12859)),c_Groups_Oone__class_Oone(U_12854))),U_12858)),c_Groups_Oone__class_Oone(U_12854)),U_12856) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12854,tc_prod(U_12855,U_12857),c_Groups_Otimes__class_Otimes(U_12854)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12855,U_12857,U_12854),U_12859)),c_Groups_Oone__class_Oone(U_12854)),hAPP(hAPP(c_Product__Type_OSigma(U_12855,U_12857),U_12856),U_12858))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12855),U_12856))
| ~ class_Groups_Ocomm__monoid__mult(U_12854) ),
inference(clausify,[status(thm)],[f_3299_3]) ).
fof(f_3300_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_3300_2,plain,
! [U_12866,U_12865,U_12864,U_12863,U_12862,U_12861] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12862,U_12861),hAPP(hAPP(c_COMBS(U_12862,tc_fun(U_12864,tc_HOL_Obool),U_12861),hAPP(hAPP(c_COMBB(tc_fun(U_12864,U_12861),tc_fun(tc_fun(U_12864,tc_HOL_Obool),U_12861),U_12862),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12864,U_12861)),U_12866)),U_12865)),U_12863) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_12862,U_12864),U_12861),hAPP(c_Product__Type_Oprod_Oprod__case(U_12862,U_12864,U_12861),U_12866)),hAPP(hAPP(c_Product__Type_OSigma(U_12862,U_12864),U_12863),U_12865))
| ? [U_12860] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12864),hAPP(U_12865,U_12860)))
& hBOOL(hAPP(hAPP(c_member(U_12862),U_12860),U_12863)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12862),U_12863))
| ~ class_Groups_Ocomm__monoid__mult(U_12861) ),
inference(variable_rename,[status(thm)],[f_3300_1]) ).
fof(f_3300_3,plain,
! [U_12866,U_12865,U_12864,U_12863,U_12862,U_12861] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12862,U_12861),hAPP(hAPP(c_COMBS(U_12862,tc_fun(U_12864,tc_HOL_Obool),U_12861),hAPP(hAPP(c_COMBB(tc_fun(U_12864,U_12861),tc_fun(tc_fun(U_12864,tc_HOL_Obool),U_12861),U_12862),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12864,U_12861)),U_12866)),U_12865)),U_12863) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_12862,U_12864),U_12861),hAPP(c_Product__Type_Oprod_Oprod__case(U_12862,U_12864,U_12861),U_12866)),hAPP(hAPP(c_Product__Type_OSigma(U_12862,U_12864),U_12863),U_12865))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12864),hAPP(U_12865,sK311(U_12866,U_12865,U_12864,U_12863,U_12862,U_12861))))
& hBOOL(hAPP(hAPP(c_member(U_12862),sK311(U_12866,U_12865,U_12864,U_12863,U_12862,U_12861)),U_12863)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12862),U_12863))
| ~ class_Groups_Ocomm__monoid__mult(U_12861) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK311]),skolemize(U_12860,sK311(U_12866,U_12865,U_12864,U_12863,U_12862,U_12861))],[f_3300_2]) ).
cnf(f_3300_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12862),sK311(U_12866,U_12865,U_12864,U_12863,U_12862,U_12861)),U_12863))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12862,U_12861),hAPP(hAPP(c_COMBS(U_12862,tc_fun(U_12864,tc_HOL_Obool),U_12861),hAPP(hAPP(c_COMBB(tc_fun(U_12864,U_12861),tc_fun(tc_fun(U_12864,tc_HOL_Obool),U_12861),U_12862),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12864,U_12861)),U_12866)),U_12865)),U_12863) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_12862,U_12864),U_12861),hAPP(c_Product__Type_Oprod_Oprod__case(U_12862,U_12864,U_12861),U_12866)),hAPP(hAPP(c_Product__Type_OSigma(U_12862,U_12864),U_12863),U_12865))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12862),U_12863))
| ~ class_Groups_Ocomm__monoid__mult(U_12861) ),
inference(clausify,[status(thm)],[f_3300_3]) ).
cnf(f_3300_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12864),hAPP(U_12865,sK311(U_12866,U_12865,U_12864,U_12863,U_12862,U_12861))))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12862,U_12861),hAPP(hAPP(c_COMBS(U_12862,tc_fun(U_12864,tc_HOL_Obool),U_12861),hAPP(hAPP(c_COMBB(tc_fun(U_12864,U_12861),tc_fun(tc_fun(U_12864,tc_HOL_Obool),U_12861),U_12862),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12864,U_12861)),U_12866)),U_12865)),U_12863) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_12862,U_12864),U_12861),hAPP(c_Product__Type_Oprod_Oprod__case(U_12862,U_12864,U_12861),U_12866)),hAPP(hAPP(c_Product__Type_OSigma(U_12862,U_12864),U_12863),U_12865))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12862),U_12863))
| ~ class_Groups_Ocomm__monoid__mult(U_12861) ),
inference(clausify,[status(thm)],[f_3300_3]) ).
fof(f_3301_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_3301_2,plain,
! [U_12873,U_12872,U_12871,U_12870,U_12869,U_12868] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12869,U_12868),hAPP(hAPP(c_COMBS(U_12869,tc_fun(U_12871,tc_HOL_Obool),U_12868),hAPP(hAPP(c_COMBB(tc_fun(U_12871,U_12868),tc_fun(tc_fun(U_12871,tc_HOL_Obool),U_12868),U_12869),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12871,U_12868)),U_12873)),U_12872)),U_12870) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_12869,U_12871),U_12868),hAPP(c_Product__Type_Oprod_Oprod__case(U_12869,U_12871,U_12868),U_12873)),hAPP(hAPP(c_Product__Type_OSigma(U_12869,U_12871),U_12870),U_12872))
| ? [U_12867] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12871),hAPP(U_12872,U_12867)))
& hBOOL(hAPP(hAPP(c_member(U_12869),U_12867),U_12870)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12869),U_12870))
| ~ class_Groups_Ocomm__monoid__add(U_12868) ),
inference(variable_rename,[status(thm)],[f_3301_1]) ).
fof(f_3301_3,plain,
! [U_12873,U_12872,U_12871,U_12870,U_12869,U_12868] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12869,U_12868),hAPP(hAPP(c_COMBS(U_12869,tc_fun(U_12871,tc_HOL_Obool),U_12868),hAPP(hAPP(c_COMBB(tc_fun(U_12871,U_12868),tc_fun(tc_fun(U_12871,tc_HOL_Obool),U_12868),U_12869),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12871,U_12868)),U_12873)),U_12872)),U_12870) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_12869,U_12871),U_12868),hAPP(c_Product__Type_Oprod_Oprod__case(U_12869,U_12871,U_12868),U_12873)),hAPP(hAPP(c_Product__Type_OSigma(U_12869,U_12871),U_12870),U_12872))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12871),hAPP(U_12872,sK312(U_12873,U_12872,U_12871,U_12870,U_12869,U_12868))))
& hBOOL(hAPP(hAPP(c_member(U_12869),sK312(U_12873,U_12872,U_12871,U_12870,U_12869,U_12868)),U_12870)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12869),U_12870))
| ~ class_Groups_Ocomm__monoid__add(U_12868) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK312]),skolemize(U_12867,sK312(U_12873,U_12872,U_12871,U_12870,U_12869,U_12868))],[f_3301_2]) ).
cnf(f_3301_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12869),sK312(U_12873,U_12872,U_12871,U_12870,U_12869,U_12868)),U_12870))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12869,U_12868),hAPP(hAPP(c_COMBS(U_12869,tc_fun(U_12871,tc_HOL_Obool),U_12868),hAPP(hAPP(c_COMBB(tc_fun(U_12871,U_12868),tc_fun(tc_fun(U_12871,tc_HOL_Obool),U_12868),U_12869),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12871,U_12868)),U_12873)),U_12872)),U_12870) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_12869,U_12871),U_12868),hAPP(c_Product__Type_Oprod_Oprod__case(U_12869,U_12871,U_12868),U_12873)),hAPP(hAPP(c_Product__Type_OSigma(U_12869,U_12871),U_12870),U_12872))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12869),U_12870))
| ~ class_Groups_Ocomm__monoid__add(U_12868) ),
inference(clausify,[status(thm)],[f_3301_3]) ).
cnf(f_3301_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12871),hAPP(U_12872,sK312(U_12873,U_12872,U_12871,U_12870,U_12869,U_12868))))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12869,U_12868),hAPP(hAPP(c_COMBS(U_12869,tc_fun(U_12871,tc_HOL_Obool),U_12868),hAPP(hAPP(c_COMBB(tc_fun(U_12871,U_12868),tc_fun(tc_fun(U_12871,tc_HOL_Obool),U_12868),U_12869),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12871,U_12868)),U_12873)),U_12872)),U_12870) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_12869,U_12871),U_12868),hAPP(c_Product__Type_Oprod_Oprod__case(U_12869,U_12871,U_12868),U_12873)),hAPP(hAPP(c_Product__Type_OSigma(U_12869,U_12871),U_12870),U_12872))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12869),U_12870))
| ~ class_Groups_Ocomm__monoid__add(U_12868) ),
inference(clausify,[status(thm)],[f_3301_3]) ).
fof(f_3302_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_3302_2,plain,
! [U_12878,U_12877,U_12876,U_12875] :
( hAPP(c_Finite__Set_Ocard(tc_prod(U_12875,U_12877)),hAPP(hAPP(c_Product__Type_OSigma(U_12875,U_12877),U_12876),U_12878)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12875,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12877,tc_HOL_Obool),tc_Nat_Onat,U_12875),c_Finite__Set_Ocard(U_12877)),U_12878)),U_12876)
| ? [U_12874] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12877),hAPP(U_12878,U_12874)))
& hBOOL(hAPP(hAPP(c_member(U_12875),U_12874),U_12876)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12875),U_12876)) ),
inference(variable_rename,[status(thm)],[f_3302_1]) ).
fof(f_3302_3,plain,
! [U_12878,U_12877,U_12876,U_12875] :
( hAPP(c_Finite__Set_Ocard(tc_prod(U_12875,U_12877)),hAPP(hAPP(c_Product__Type_OSigma(U_12875,U_12877),U_12876),U_12878)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12875,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12877,tc_HOL_Obool),tc_Nat_Onat,U_12875),c_Finite__Set_Ocard(U_12877)),U_12878)),U_12876)
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12877),hAPP(U_12878,sK313(U_12878,U_12877,U_12876,U_12875))))
& hBOOL(hAPP(hAPP(c_member(U_12875),sK313(U_12878,U_12877,U_12876,U_12875)),U_12876)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12875),U_12876)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK313]),skolemize(U_12874,sK313(U_12878,U_12877,U_12876,U_12875))],[f_3302_2]) ).
cnf(f_3302_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12875),sK313(U_12878,U_12877,U_12876,U_12875)),U_12876))
| hAPP(c_Finite__Set_Ocard(tc_prod(U_12875,U_12877)),hAPP(hAPP(c_Product__Type_OSigma(U_12875,U_12877),U_12876),U_12878)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12875,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12877,tc_HOL_Obool),tc_Nat_Onat,U_12875),c_Finite__Set_Ocard(U_12877)),U_12878)),U_12876)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12875),U_12876)) ),
inference(clausify,[status(thm)],[f_3302_3]) ).
cnf(f_3302_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12877),hAPP(U_12878,sK313(U_12878,U_12877,U_12876,U_12875))))
| hAPP(c_Finite__Set_Ocard(tc_prod(U_12875,U_12877)),hAPP(hAPP(c_Product__Type_OSigma(U_12875,U_12877),U_12876),U_12878)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12875,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12877,tc_HOL_Obool),tc_Nat_Onat,U_12875),c_Finite__Set_Ocard(U_12877)),U_12878)),U_12876)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12875),U_12876)) ),
inference(clausify,[status(thm)],[f_3302_3]) ).
fof(f_3303_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_3303_2,plain,
! [U_12883,U_12882,U_12881,U_12880] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12880,U_12882)),hAPP(hAPP(c_Product__Type_OSigma(U_12880,U_12882),U_12881),U_12883)))
| ? [U_12879] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12882),hAPP(U_12883,U_12879)))
& hBOOL(hAPP(hAPP(c_member(U_12880),U_12879),U_12881)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12880),U_12881)) ),
inference(variable_rename,[status(thm)],[f_3303_1]) ).
fof(f_3303_3,plain,
! [U_12883,U_12882,U_12881,U_12880] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12880,U_12882)),hAPP(hAPP(c_Product__Type_OSigma(U_12880,U_12882),U_12881),U_12883)))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12882),hAPP(U_12883,sK314(U_12883,U_12882,U_12881,U_12880))))
& hBOOL(hAPP(hAPP(c_member(U_12880),sK314(U_12883,U_12882,U_12881,U_12880)),U_12881)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12880),U_12881)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK314]),skolemize(U_12879,sK314(U_12883,U_12882,U_12881,U_12880))],[f_3303_2]) ).
cnf(f_3303_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12880),sK314(U_12883,U_12882,U_12881,U_12880)),U_12881))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12880,U_12882)),hAPP(hAPP(c_Product__Type_OSigma(U_12880,U_12882),U_12881),U_12883)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12880),U_12881)) ),
inference(clausify,[status(thm)],[f_3303_3]) ).
cnf(f_3303_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12882),hAPP(U_12883,sK314(U_12883,U_12882,U_12881,U_12880))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12880,U_12882)),hAPP(hAPP(c_Product__Type_OSigma(U_12880,U_12882),U_12881),U_12883)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12880),U_12881)) ),
inference(clausify,[status(thm)],[f_3303_3]) ).
fof(f_3304_1,plain,
! [V_B_2,V_A_2,V_c_2,T_c,T_b] :
( ? [B_x] :
( ? [B_y] :
( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)
& hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x))) )
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_SigmaE]) ).
fof(f_3304_2,plain,
! [U_12890,U_12889,U_12888,U_12887,U_12886] :
( ? [U_12885] :
( ? [U_12884] :
( U_12888 = hAPP(hAPP(c_Product__Type_OPair(U_12886,U_12887),U_12885),U_12884)
& hBOOL(hAPP(hAPP(c_member(U_12887),U_12884),hAPP(U_12890,U_12885))) )
& hBOOL(hAPP(hAPP(c_member(U_12886),U_12885),U_12889)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12886,U_12887)),U_12888),hAPP(hAPP(c_Product__Type_OSigma(U_12886,U_12887),U_12889),U_12890))) ),
inference(variable_rename,[status(thm)],[f_3304_1]) ).
fof(f_3304_3,plain,
! [U_12890,U_12889,U_12888,U_12887,U_12886] :
( ( ? [U_12884] :
( U_12888 = hAPP(hAPP(c_Product__Type_OPair(U_12886,U_12887),sK315(U_12890,U_12889,U_12888,U_12887,U_12886)),U_12884)
& hBOOL(hAPP(hAPP(c_member(U_12887),U_12884),hAPP(U_12890,sK315(U_12890,U_12889,U_12888,U_12887,U_12886)))) )
& hBOOL(hAPP(hAPP(c_member(U_12886),sK315(U_12890,U_12889,U_12888,U_12887,U_12886)),U_12889)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12886,U_12887)),U_12888),hAPP(hAPP(c_Product__Type_OSigma(U_12886,U_12887),U_12889),U_12890))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK315]),skolemize(U_12885,sK315(U_12890,U_12889,U_12888,U_12887,U_12886))],[f_3304_2]) ).
fof(f_3304_4,plain,
! [U_12890,U_12889,U_12888,U_12887,U_12886] :
( ( U_12888 = hAPP(hAPP(c_Product__Type_OPair(U_12886,U_12887),sK315(U_12890,U_12889,U_12888,U_12887,U_12886)),sK316(U_12890,U_12889,U_12888,U_12887,U_12886))
& hBOOL(hAPP(hAPP(c_member(U_12887),sK316(U_12890,U_12889,U_12888,U_12887,U_12886)),hAPP(U_12890,sK315(U_12890,U_12889,U_12888,U_12887,U_12886))))
& hBOOL(hAPP(hAPP(c_member(U_12886),sK315(U_12890,U_12889,U_12888,U_12887,U_12886)),U_12889)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12886,U_12887)),U_12888),hAPP(hAPP(c_Product__Type_OSigma(U_12886,U_12887),U_12889),U_12890))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK316]),skolemize(U_12884,sK316(U_12890,U_12889,U_12888,U_12887,U_12886))],[f_3304_3]) ).
cnf(f_3304_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_12886),sK315(U_12890,U_12889,U_12888,U_12887,U_12886)),U_12889))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12886,U_12887)),U_12888),hAPP(hAPP(c_Product__Type_OSigma(U_12886,U_12887),U_12889),U_12890))) ),
inference(clausify,[status(thm)],[f_3304_4]) ).
cnf(f_3304_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_12887),sK316(U_12890,U_12889,U_12888,U_12887,U_12886)),hAPP(U_12890,sK315(U_12890,U_12889,U_12888,U_12887,U_12886))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12886,U_12887)),U_12888),hAPP(hAPP(c_Product__Type_OSigma(U_12886,U_12887),U_12889),U_12890))) ),
inference(clausify,[status(thm)],[f_3304_4]) ).
cnf(f_3304_7,plain,
( U_12888 = hAPP(hAPP(c_Product__Type_OPair(U_12886,U_12887),sK315(U_12890,U_12889,U_12888,U_12887,U_12886)),sK316(U_12890,U_12889,U_12888,U_12887,U_12886))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12886,U_12887)),U_12888),hAPP(hAPP(c_Product__Type_OSigma(U_12886,U_12887),U_12889),U_12890))) ),
inference(clausify,[status(thm)],[f_3304_4]) ).
fof(f_3305_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_3305_2,plain,
! [U_12896,U_12895,U_12894,U_12893,U_12892,U_12891] :
( hAPP(c_Set_Oimage(tc_prod(U_12891,U_12894),tc_prod(U_12892,U_12895),c_Product__Type_Omap__pair(U_12891,U_12892,U_12894,U_12895,U_12893,U_12896)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12891,U_12894),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12892,U_12895),tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_12894,U_12895,U_12896),c_Orderings_Otop__class_Otop(tc_fun(U_12894,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12895,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_12891,U_12892,U_12893),c_Orderings_Otop__class_Otop(tc_fun(U_12891,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12892,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_3305_1]) ).
cnf(f_3305_3,plain,
( hAPP(c_Set_Oimage(tc_prod(U_12891,U_12894),tc_prod(U_12892,U_12895),c_Product__Type_Omap__pair(U_12891,U_12892,U_12894,U_12895,U_12893,U_12896)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12891,U_12894),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12892,U_12895),tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_12894,U_12895,U_12896),c_Orderings_Otop__class_Otop(tc_fun(U_12894,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12895,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_12891,U_12892,U_12893),c_Orderings_Otop__class_Otop(tc_fun(U_12891,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12892,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3305_2]) ).
fof(f_3306_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_3306_2,plain,
! [U_12905,U_12904,U_12903,U_12902,U_12901,U_12900,U_12899,U_12898,U_12897] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12902,U_12903)),hAPP(hAPP(c_Product__Type_OPair(U_12902,U_12903),hAPP(U_12904,U_12899)),hAPP(U_12905,U_12900))),hAPP(c_Set_Oimage(tc_prod(U_12897,U_12898),tc_prod(U_12902,U_12903),c_Product__Type_Omap__pair(U_12897,U_12902,U_12898,U_12903,U_12904,U_12905)),U_12901)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12897,U_12898)),hAPP(hAPP(c_Product__Type_OPair(U_12897,U_12898),U_12899),U_12900)),U_12901)) ),
inference(variable_rename,[status(thm)],[f_3306_1]) ).
cnf(f_3306_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12902,U_12903)),hAPP(hAPP(c_Product__Type_OPair(U_12902,U_12903),hAPP(U_12904,U_12899)),hAPP(U_12905,U_12900))),hAPP(c_Set_Oimage(tc_prod(U_12897,U_12898),tc_prod(U_12902,U_12903),c_Product__Type_Omap__pair(U_12897,U_12902,U_12898,U_12903,U_12904,U_12905)),U_12901)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12897,U_12898)),hAPP(hAPP(c_Product__Type_OPair(U_12897,U_12898),U_12899),U_12900)),U_12901)) ),
inference(clausify,[status(thm)],[f_3306_2]) ).
fof(f_3307_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_3307_2,plain,
! [U_12913,U_12912,U_12911,U_12910,U_12909,U_12908,U_12907,U_12906] : hAPP(c_Product__Type_Omap__pair(U_12906,U_12907,U_12908,U_12909,U_12910,U_12911),hAPP(hAPP(c_Product__Type_OPair(U_12906,U_12908),U_12912),U_12913)) = hAPP(hAPP(c_Product__Type_OPair(U_12907,U_12909),hAPP(U_12910,U_12912)),hAPP(U_12911,U_12913)),
inference(variable_rename,[status(thm)],[f_3307_1]) ).
cnf(f_3307_3,plain,
hAPP(c_Product__Type_Omap__pair(U_12906,U_12907,U_12908,U_12909,U_12910,U_12911),hAPP(hAPP(c_Product__Type_OPair(U_12906,U_12908),U_12912),U_12913)) = hAPP(hAPP(c_Product__Type_OPair(U_12907,U_12909),hAPP(U_12910,U_12912)),hAPP(U_12911,U_12913)),
inference(clausify,[status(thm)],[f_3307_2]) ).
fof(f_3308_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_3308_2,plain,
! [U_12920,U_12919,U_12918,U_12917,U_12916,U_12915,U_12914] : hAPP(c_Product__Type_Ofst(U_12914,U_12915),hAPP(c_Product__Type_Omap__pair(U_12916,U_12914,U_12917,U_12915,U_12918,U_12919),U_12920)) = hAPP(U_12918,hAPP(c_Product__Type_Ofst(U_12916,U_12917),U_12920)),
inference(variable_rename,[status(thm)],[f_3308_1]) ).
cnf(f_3308_3,plain,
hAPP(c_Product__Type_Ofst(U_12914,U_12915),hAPP(c_Product__Type_Omap__pair(U_12916,U_12914,U_12917,U_12915,U_12918,U_12919),U_12920)) = hAPP(U_12918,hAPP(c_Product__Type_Ofst(U_12916,U_12917),U_12920)),
inference(clausify,[status(thm)],[f_3308_2]) ).
fof(f_3309_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_3309_2,plain,
! [U_12923,U_12922,U_12921] : hAPP(c_Product__Type_Omap__pair(U_12921,U_12921,U_12922,U_12922,c_COMBI(U_12921),c_COMBI(U_12922)),U_12923) = U_12923,
inference(variable_rename,[status(thm)],[f_3309_1]) ).
cnf(f_3309_3,plain,
hAPP(c_Product__Type_Omap__pair(U_12921,U_12921,U_12922,U_12922,c_COMBI(U_12921),c_COMBI(U_12922)),U_12923) = U_12923,
inference(clausify,[status(thm)],[f_3309_2]) ).
fof(f_3310_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_3310_2,plain,
! [U_12930,U_12929,U_12928,U_12927,U_12926,U_12925,U_12924] : hAPP(c_Product__Type_Osnd(U_12924,U_12925),hAPP(c_Product__Type_Omap__pair(U_12926,U_12924,U_12927,U_12925,U_12928,U_12929),U_12930)) = hAPP(U_12929,hAPP(c_Product__Type_Osnd(U_12926,U_12927),U_12930)),
inference(variable_rename,[status(thm)],[f_3310_1]) ).
cnf(f_3310_3,plain,
hAPP(c_Product__Type_Osnd(U_12924,U_12925),hAPP(c_Product__Type_Omap__pair(U_12926,U_12924,U_12927,U_12925,U_12928,U_12929),U_12930)) = hAPP(U_12929,hAPP(c_Product__Type_Osnd(U_12926,U_12927),U_12930)),
inference(clausify,[status(thm)],[f_3310_2]) ).
fof(f_3311_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_3311_2,plain,
! [U_12940,U_12939,U_12938,U_12937,U_12936,U_12935,U_12934,U_12933,U_12932,U_12931] : hAPP(c_Fun_Ocomp(tc_prod(U_12931,U_12932),tc_prod(U_12933,U_12934),tc_prod(U_12935,U_12936),c_Product__Type_Omap__pair(U_12931,U_12933,U_12932,U_12934,U_12937,U_12938)),c_Product__Type_Omap__pair(U_12935,U_12931,U_12936,U_12932,U_12939,U_12940)) = c_Product__Type_Omap__pair(U_12935,U_12933,U_12936,U_12934,hAPP(c_Fun_Ocomp(U_12931,U_12933,U_12935,U_12937),U_12939),hAPP(c_Fun_Ocomp(U_12932,U_12934,U_12936,U_12938),U_12940)),
inference(variable_rename,[status(thm)],[f_3311_1]) ).
cnf(f_3311_3,plain,
hAPP(c_Fun_Ocomp(tc_prod(U_12931,U_12932),tc_prod(U_12933,U_12934),tc_prod(U_12935,U_12936),c_Product__Type_Omap__pair(U_12931,U_12933,U_12932,U_12934,U_12937,U_12938)),c_Product__Type_Omap__pair(U_12935,U_12931,U_12936,U_12932,U_12939,U_12940)) = c_Product__Type_Omap__pair(U_12935,U_12933,U_12936,U_12934,hAPP(c_Fun_Ocomp(U_12931,U_12933,U_12935,U_12937),U_12939),hAPP(c_Fun_Ocomp(U_12932,U_12934,U_12936,U_12938),U_12940)),
inference(clausify,[status(thm)],[f_3311_2]) ).
fof(f_3312_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_3312_2,plain,
! [U_12950,U_12949,U_12948,U_12947,U_12946,U_12945,U_12944,U_12943,U_12942,U_12941] : c_Product__Type_Omap__pair(U_12941,U_12942,U_12943,U_12944,hAPP(c_Fun_Ocomp(U_12945,U_12942,U_12941,U_12946),U_12947),hAPP(c_Fun_Ocomp(U_12948,U_12944,U_12943,U_12949),U_12950)) = hAPP(c_Fun_Ocomp(tc_prod(U_12945,U_12948),tc_prod(U_12942,U_12944),tc_prod(U_12941,U_12943),c_Product__Type_Omap__pair(U_12945,U_12942,U_12948,U_12944,U_12946,U_12949)),c_Product__Type_Omap__pair(U_12941,U_12945,U_12943,U_12948,U_12947,U_12950)),
inference(variable_rename,[status(thm)],[f_3312_1]) ).
cnf(f_3312_3,plain,
c_Product__Type_Omap__pair(U_12941,U_12942,U_12943,U_12944,hAPP(c_Fun_Ocomp(U_12945,U_12942,U_12941,U_12946),U_12947),hAPP(c_Fun_Ocomp(U_12948,U_12944,U_12943,U_12949),U_12950)) = hAPP(c_Fun_Ocomp(tc_prod(U_12945,U_12948),tc_prod(U_12942,U_12944),tc_prod(U_12941,U_12943),c_Product__Type_Omap__pair(U_12945,U_12942,U_12948,U_12944,U_12946,U_12949)),c_Product__Type_Omap__pair(U_12941,U_12945,U_12943,U_12948,U_12947,U_12950)),
inference(clausify,[status(thm)],[f_3312_2]) ).
fof(f_3313_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_3313_2,plain,
! [U_12961,U_12960,U_12959,U_12958,U_12957,U_12956,U_12955,U_12954,U_12953,U_12952,U_12951] : hAPP(c_Product__Type_Omap__pair(U_12951,U_12952,U_12953,U_12954,U_12955,U_12956),hAPP(c_Product__Type_Omap__pair(U_12957,U_12951,U_12958,U_12953,U_12959,U_12960),U_12961)) = hAPP(c_Product__Type_Omap__pair(U_12957,U_12952,U_12958,U_12954,hAPP(c_Fun_Ocomp(U_12951,U_12952,U_12957,U_12955),U_12959),hAPP(c_Fun_Ocomp(U_12953,U_12954,U_12958,U_12956),U_12960)),U_12961),
inference(variable_rename,[status(thm)],[f_3313_1]) ).
cnf(f_3313_3,plain,
hAPP(c_Product__Type_Omap__pair(U_12951,U_12952,U_12953,U_12954,U_12955,U_12956),hAPP(c_Product__Type_Omap__pair(U_12957,U_12951,U_12958,U_12953,U_12959,U_12960),U_12961)) = hAPP(c_Product__Type_Omap__pair(U_12957,U_12952,U_12958,U_12954,hAPP(c_Fun_Ocomp(U_12951,U_12952,U_12957,U_12955),U_12959),hAPP(c_Fun_Ocomp(U_12953,U_12954,U_12958,U_12956),U_12960)),U_12961),
inference(clausify,[status(thm)],[f_3313_2]) ).
fof(f_3314_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_3314_2,plain,
! [U_12967,U_12966,U_12965,U_12964,U_12963,U_12962] : hAPP(c_Fun_Ocomp(tc_prod(U_12962,U_12963),U_12963,tc_prod(U_12964,U_12965),c_Product__Type_Osnd(U_12962,U_12963)),c_Product__Type_Omap__pair(U_12964,U_12962,U_12965,U_12963,U_12966,U_12967)) = hAPP(c_Fun_Ocomp(U_12965,U_12963,tc_prod(U_12964,U_12965),U_12967),c_Product__Type_Osnd(U_12964,U_12965)),
inference(variable_rename,[status(thm)],[f_3314_1]) ).
cnf(f_3314_3,plain,
hAPP(c_Fun_Ocomp(tc_prod(U_12962,U_12963),U_12963,tc_prod(U_12964,U_12965),c_Product__Type_Osnd(U_12962,U_12963)),c_Product__Type_Omap__pair(U_12964,U_12962,U_12965,U_12963,U_12966,U_12967)) = hAPP(c_Fun_Ocomp(U_12965,U_12963,tc_prod(U_12964,U_12965),U_12967),c_Product__Type_Osnd(U_12964,U_12965)),
inference(clausify,[status(thm)],[f_3314_2]) ).
fof(f_3315_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_3315_2,plain,
! [U_12973,U_12972,U_12971,U_12970,U_12969,U_12968] : hAPP(c_Fun_Ocomp(tc_prod(U_12968,U_12969),U_12968,tc_prod(U_12970,U_12971),c_Product__Type_Ofst(U_12968,U_12969)),c_Product__Type_Omap__pair(U_12970,U_12968,U_12971,U_12969,U_12972,U_12973)) = hAPP(c_Fun_Ocomp(U_12970,U_12968,tc_prod(U_12970,U_12971),U_12972),c_Product__Type_Ofst(U_12970,U_12971)),
inference(variable_rename,[status(thm)],[f_3315_1]) ).
cnf(f_3315_3,plain,
hAPP(c_Fun_Ocomp(tc_prod(U_12968,U_12969),U_12968,tc_prod(U_12970,U_12971),c_Product__Type_Ofst(U_12968,U_12969)),c_Product__Type_Omap__pair(U_12970,U_12968,U_12971,U_12969,U_12972,U_12973)) = hAPP(c_Fun_Ocomp(U_12970,U_12968,tc_prod(U_12970,U_12971),U_12972),c_Product__Type_Ofst(U_12970,U_12971)),
inference(clausify,[status(thm)],[f_3315_2]) ).
fof(f_3316_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_3316_2,plain,
! [U_12979,U_12978,U_12977,U_12976,U_12975,U_12974] : c_Product__Type_Omap__pair(U_12974,U_12975,U_12976,U_12977,U_12978,U_12979) = hAPP(c_Product__Type_Oprod_Oprod__case(U_12974,U_12976,tc_prod(U_12975,U_12977)),hAPP(hAPP(c_COMBC(U_12974,tc_fun(U_12976,U_12977),tc_fun(U_12976,tc_prod(U_12975,U_12977))),hAPP(hAPP(c_COMBB(tc_fun(U_12977,tc_prod(U_12975,U_12977)),tc_fun(tc_fun(U_12976,U_12977),tc_fun(U_12976,tc_prod(U_12975,U_12977))),U_12974),c_COMBB(U_12977,tc_prod(U_12975,U_12977),U_12976)),hAPP(hAPP(c_COMBB(U_12975,tc_fun(U_12977,tc_prod(U_12975,U_12977)),U_12974),c_Product__Type_OPair(U_12975,U_12977)),U_12978))),U_12979)),
inference(variable_rename,[status(thm)],[f_3316_1]) ).
cnf(f_3316_3,plain,
c_Product__Type_Omap__pair(U_12974,U_12975,U_12976,U_12977,U_12978,U_12979) = hAPP(c_Product__Type_Oprod_Oprod__case(U_12974,U_12976,tc_prod(U_12975,U_12977)),hAPP(hAPP(c_COMBC(U_12974,tc_fun(U_12976,U_12977),tc_fun(U_12976,tc_prod(U_12975,U_12977))),hAPP(hAPP(c_COMBB(tc_fun(U_12977,tc_prod(U_12975,U_12977)),tc_fun(tc_fun(U_12976,U_12977),tc_fun(U_12976,tc_prod(U_12975,U_12977))),U_12974),c_COMBB(U_12977,tc_prod(U_12975,U_12977),U_12976)),hAPP(hAPP(c_COMBB(U_12975,tc_fun(U_12977,tc_prod(U_12975,U_12977)),U_12974),c_Product__Type_OPair(U_12975,U_12977)),U_12978))),U_12979)),
inference(clausify,[status(thm)],[f_3316_2]) ).
fof(f_3317_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_3317_2,plain,
! [U_12989,U_12988,U_12987,U_12986,U_12985,U_12984,U_12983,U_12982,U_12981,U_12980] :
( hAPP(c_Set_Oimage(tc_prod(U_12980,U_12985),tc_prod(U_12981,U_12986),c_Product__Type_Omap__pair(U_12980,U_12981,U_12985,U_12986,U_12982,U_12987)),hAPP(hAPP(c_Product__Type_OSigma(U_12980,U_12985),U_12983),hAPP(c_COMBK(tc_fun(U_12985,tc_HOL_Obool),U_12980),U_12988))) = hAPP(hAPP(c_Product__Type_OSigma(U_12981,U_12986),U_12984),hAPP(c_COMBK(tc_fun(U_12986,tc_HOL_Obool),U_12981),U_12989))
| hAPP(c_Set_Oimage(U_12985,U_12986,U_12987),U_12988) != U_12989
| hAPP(c_Set_Oimage(U_12980,U_12981,U_12982),U_12983) != U_12984 ),
inference(variable_rename,[status(thm)],[f_3317_1]) ).
cnf(f_3317_3,plain,
( hAPP(c_Set_Oimage(tc_prod(U_12980,U_12985),tc_prod(U_12981,U_12986),c_Product__Type_Omap__pair(U_12980,U_12981,U_12985,U_12986,U_12982,U_12987)),hAPP(hAPP(c_Product__Type_OSigma(U_12980,U_12985),U_12983),hAPP(c_COMBK(tc_fun(U_12985,tc_HOL_Obool),U_12980),U_12988))) = hAPP(hAPP(c_Product__Type_OSigma(U_12981,U_12986),U_12984),hAPP(c_COMBK(tc_fun(U_12986,tc_HOL_Obool),U_12981),U_12989))
| hAPP(c_Set_Oimage(U_12985,U_12986,U_12987),U_12988) != U_12989
| hAPP(c_Set_Oimage(U_12980,U_12981,U_12982),U_12983) != U_12984 ),
inference(clausify,[status(thm)],[f_3317_2]) ).
fof(f_3318_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_3318_2,plain,
! [U_12997,U_12996,U_12995,U_12994,U_12993,U_12992,U_12991,U_12990] :
( c_Fun_Oinj__on(tc_prod(U_12990,U_12994),tc_prod(U_12991,U_12995),c_Product__Type_Omap__pair(U_12990,U_12991,U_12994,U_12995,U_12992,U_12996),hAPP(hAPP(c_Product__Type_OSigma(U_12990,U_12994),U_12993),hAPP(c_COMBK(tc_fun(U_12994,tc_HOL_Obool),U_12990),U_12997)))
| ~ c_Fun_Oinj__on(U_12994,U_12995,U_12996,U_12997)
| ~ c_Fun_Oinj__on(U_12990,U_12991,U_12992,U_12993) ),
inference(variable_rename,[status(thm)],[f_3318_1]) ).
cnf(f_3318_3,plain,
( c_Fun_Oinj__on(tc_prod(U_12990,U_12994),tc_prod(U_12991,U_12995),c_Product__Type_Omap__pair(U_12990,U_12991,U_12994,U_12995,U_12992,U_12996),hAPP(hAPP(c_Product__Type_OSigma(U_12990,U_12994),U_12993),hAPP(c_COMBK(tc_fun(U_12994,tc_HOL_Obool),U_12990),U_12997)))
| ~ c_Fun_Oinj__on(U_12994,U_12995,U_12996,U_12997)
| ~ c_Fun_Oinj__on(U_12990,U_12991,U_12992,U_12993) ),
inference(clausify,[status(thm)],[f_3318_2]) ).
fof(f_3319_1,plain,
! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_c_2,T_c,T_b] :
( ? [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),B_x),B_y)),V_R_2))
& V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(c_Set_Oimage(tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2)),V_R_2))) ),
inference(fof_nnf,[status(thm)],[fact_prod__fun__imageE]) ).
fof(f_3319_2,plain,
! [U_13007,U_13006,U_13005,U_13004,U_13003,U_13002,U_13001,U_13000] :
( ? [U_12999,U_12998] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13003,U_13004)),hAPP(hAPP(c_Product__Type_OPair(U_13003,U_13004),U_12999),U_12998)),U_13007))
& U_13002 = hAPP(hAPP(c_Product__Type_OPair(U_13000,U_13001),hAPP(U_13005,U_12999)),hAPP(U_13006,U_12998)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13000,U_13001)),U_13002),hAPP(c_Set_Oimage(tc_prod(U_13003,U_13004),tc_prod(U_13000,U_13001),c_Product__Type_Omap__pair(U_13003,U_13000,U_13004,U_13001,U_13005,U_13006)),U_13007))) ),
inference(variable_rename,[status(thm)],[f_3319_1]) ).
fof(f_3319_3,plain,
! [U_13007,U_13006,U_13005,U_13004,U_13003,U_13002,U_13001,U_13000] :
( ? [U_12998] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13003,U_13004)),hAPP(hAPP(c_Product__Type_OPair(U_13003,U_13004),sK317(U_13007,U_13006,U_13005,U_13004,U_13003,U_13002,U_13001,U_13000)),U_12998)),U_13007))
& U_13002 = hAPP(hAPP(c_Product__Type_OPair(U_13000,U_13001),hAPP(U_13005,sK317(U_13007,U_13006,U_13005,U_13004,U_13003,U_13002,U_13001,U_13000))),hAPP(U_13006,U_12998)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13000,U_13001)),U_13002),hAPP(c_Set_Oimage(tc_prod(U_13003,U_13004),tc_prod(U_13000,U_13001),c_Product__Type_Omap__pair(U_13003,U_13000,U_13004,U_13001,U_13005,U_13006)),U_13007))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK317]),skolemize(U_12999,sK317(U_13007,U_13006,U_13005,U_13004,U_13003,U_13002,U_13001,U_13000))],[f_3319_2]) ).
fof(f_3319_4,plain,
! [U_13007,U_13006,U_13005,U_13004,U_13003,U_13002,U_13001,U_13000] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13003,U_13004)),hAPP(hAPP(c_Product__Type_OPair(U_13003,U_13004),sK317(U_13007,U_13006,U_13005,U_13004,U_13003,U_13002,U_13001,U_13000)),sK318(U_13007,U_13006,U_13005,U_13004,U_13003,U_13002,U_13001,U_13000))),U_13007))
& U_13002 = hAPP(hAPP(c_Product__Type_OPair(U_13000,U_13001),hAPP(U_13005,sK317(U_13007,U_13006,U_13005,U_13004,U_13003,U_13002,U_13001,U_13000))),hAPP(U_13006,sK318(U_13007,U_13006,U_13005,U_13004,U_13003,U_13002,U_13001,U_13000))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13000,U_13001)),U_13002),hAPP(c_Set_Oimage(tc_prod(U_13003,U_13004),tc_prod(U_13000,U_13001),c_Product__Type_Omap__pair(U_13003,U_13000,U_13004,U_13001,U_13005,U_13006)),U_13007))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK318]),skolemize(U_12998,sK318(U_13007,U_13006,U_13005,U_13004,U_13003,U_13002,U_13001,U_13000))],[f_3319_3]) ).
cnf(f_3319_5,plain,
( U_13002 = hAPP(hAPP(c_Product__Type_OPair(U_13000,U_13001),hAPP(U_13005,sK317(U_13007,U_13006,U_13005,U_13004,U_13003,U_13002,U_13001,U_13000))),hAPP(U_13006,sK318(U_13007,U_13006,U_13005,U_13004,U_13003,U_13002,U_13001,U_13000)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13000,U_13001)),U_13002),hAPP(c_Set_Oimage(tc_prod(U_13003,U_13004),tc_prod(U_13000,U_13001),c_Product__Type_Omap__pair(U_13003,U_13000,U_13004,U_13001,U_13005,U_13006)),U_13007))) ),
inference(clausify,[status(thm)],[f_3319_4]) ).
cnf(f_3319_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13003,U_13004)),hAPP(hAPP(c_Product__Type_OPair(U_13003,U_13004),sK317(U_13007,U_13006,U_13005,U_13004,U_13003,U_13002,U_13001,U_13000)),sK318(U_13007,U_13006,U_13005,U_13004,U_13003,U_13002,U_13001,U_13000))),U_13007))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13000,U_13001)),U_13002),hAPP(c_Set_Oimage(tc_prod(U_13003,U_13004),tc_prod(U_13000,U_13001),c_Product__Type_Omap__pair(U_13003,U_13000,U_13004,U_13001,U_13005,U_13006)),U_13007))) ),
inference(clausify,[status(thm)],[f_3319_4]) ).
fof(f_3320_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_3320_2,plain,
! [U_13014,U_13013,U_13012,U_13011,U_13010,U_13009] :
( c_Fun_Oinj__on(U_13011,U_13012,U_13013,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13010,tc_fun(U_13011,tc_HOL_Obool)),U_13009),U_13014))
| ? [U_13008] :
( ~ c_Fun_Oinj__on(U_13011,U_13012,U_13013,hAPP(U_13014,U_13008))
& hBOOL(hAPP(hAPP(c_member(U_13010),U_13008),U_13009)) )
| U_13009 = c_Orderings_Obot__class_Obot(tc_fun(U_13010,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_3320_1]) ).
fof(f_3320_3,plain,
! [U_13014,U_13013,U_13012,U_13011,U_13010,U_13009] :
( c_Fun_Oinj__on(U_13011,U_13012,U_13013,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13010,tc_fun(U_13011,tc_HOL_Obool)),U_13009),U_13014))
| ( ~ c_Fun_Oinj__on(U_13011,U_13012,U_13013,hAPP(U_13014,sK319(U_13014,U_13013,U_13012,U_13011,U_13010,U_13009)))
& hBOOL(hAPP(hAPP(c_member(U_13010),sK319(U_13014,U_13013,U_13012,U_13011,U_13010,U_13009)),U_13009)) )
| U_13009 = c_Orderings_Obot__class_Obot(tc_fun(U_13010,tc_HOL_Obool)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK319]),skolemize(U_13008,sK319(U_13014,U_13013,U_13012,U_13011,U_13010,U_13009))],[f_3320_2]) ).
cnf(f_3320_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_13010),sK319(U_13014,U_13013,U_13012,U_13011,U_13010,U_13009)),U_13009))
| c_Fun_Oinj__on(U_13011,U_13012,U_13013,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13010,tc_fun(U_13011,tc_HOL_Obool)),U_13009),U_13014))
| U_13009 = c_Orderings_Obot__class_Obot(tc_fun(U_13010,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3320_3]) ).
cnf(f_3320_5,plain,
( ~ c_Fun_Oinj__on(U_13011,U_13012,U_13013,hAPP(U_13014,sK319(U_13014,U_13013,U_13012,U_13011,U_13010,U_13009)))
| c_Fun_Oinj__on(U_13011,U_13012,U_13013,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13010,tc_fun(U_13011,tc_HOL_Obool)),U_13009),U_13014))
| U_13009 = c_Orderings_Obot__class_Obot(tc_fun(U_13010,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3320_3]) ).
fof(f_3321_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_3321_2,plain,
! [U_13016,U_13015] :
( 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_13015))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13016))))) = 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_13015))),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_13016)))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_13015)) ),
inference(variable_rename,[status(thm)],[f_3321_1]) ).
cnf(f_3321_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_13015))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13016))))) = 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_13015))),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_13016)))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_13015)) ),
inference(clausify,[status(thm)],[f_3321_2]) ).
fof(f_3322_1,plain,
! [T_b,V_a_2,V_P_2] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
| ~ hBOOL(hAPP(V_P_2,V_a_2)) ),
inference(fof_nnf,[status(thm)],[fact_CollectI]) ).
fof(f_3322_2,plain,
! [U_13019,U_13018,U_13017] :
( hBOOL(hAPP(hAPP(c_member(U_13019),U_13018),hAPP(c_Set_OCollect(U_13019),U_13017)))
| ~ hBOOL(hAPP(U_13017,U_13018)) ),
inference(variable_rename,[status(thm)],[f_3322_1]) ).
cnf(f_3322_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_13019),U_13018),hAPP(c_Set_OCollect(U_13019),U_13017)))
| ~ hBOOL(hAPP(U_13017,U_13018)) ),
inference(clausify,[status(thm)],[f_3322_2]) ).
fof(f_3323_1,plain,
! [V_Q_2,V_P_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2)),V_Q_2))))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2)))
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Collect__conjI]) ).
fof(f_3323_2,plain,
! [U_13022,U_13021,U_13020] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13020),hAPP(c_Set_OCollect(U_13020),hAPP(hAPP(c_COMBS(U_13020,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13020),c_fconj),U_13021)),U_13022))))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13020),hAPP(c_Set_OCollect(U_13020),U_13022)))
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13020),hAPP(c_Set_OCollect(U_13020),U_13021))) ) ),
inference(variable_rename,[status(thm)],[f_3323_1]) ).
cnf(f_3323_3,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13020),hAPP(c_Set_OCollect(U_13020),U_13021)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_13020),hAPP(c_Set_OCollect(U_13020),hAPP(hAPP(c_COMBS(U_13020,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13020),c_fconj),U_13021)),U_13022)))) ),
inference(clausify,[status(thm)],[f_3323_2]) ).
cnf(f_3323_4,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13020),hAPP(c_Set_OCollect(U_13020),U_13022)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_13020),hAPP(c_Set_OCollect(U_13020),hAPP(hAPP(c_COMBS(U_13020,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13020),c_fconj),U_13021)),U_13022)))) ),
inference(clausify,[status(thm)],[f_3323_2]) ).
fof(f_3324_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_3324_2,plain,
! [U_13023] : 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_13023)))),
inference(variable_rename,[status(thm)],[f_3324_1]) ).
cnf(f_3324_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_13023)))),
inference(clausify,[status(thm)],[f_3324_2]) ).
fof(f_3325_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_3325_2,plain,
! [U_13024] : 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_13024)))),
inference(variable_rename,[status(thm)],[f_3325_1]) ).
cnf(f_3325_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_13024)))),
inference(clausify,[status(thm)],[f_3325_2]) ).
fof(f_3326_1,plain,
! [V_Q_2,V_P_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),V_Q_2)),
inference(fof_nnf,[status(thm)],[fact_SetCompr__Sigma__eq]) ).
fof(f_3326_2,plain,
! [U_13028,U_13027,U_13026,U_13025] : hAPP(c_Set_OCollect(tc_prod(U_13025,U_13026)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13025,U_13026,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_13025,tc_fun(U_13026,tc_HOL_Obool),tc_fun(U_13026,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13026,tc_HOL_Obool),tc_fun(U_13026,tc_HOL_Obool)),U_13025),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13026)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13025),c_fconj),U_13027))),U_13028))) = hAPP(hAPP(c_Product__Type_OSigma(U_13025,U_13026),hAPP(c_Set_OCollect(U_13025),U_13027)),hAPP(hAPP(c_COMBB(tc_fun(U_13026,tc_HOL_Obool),tc_fun(U_13026,tc_HOL_Obool),U_13025),c_Set_OCollect(U_13026)),U_13028)),
inference(variable_rename,[status(thm)],[f_3326_1]) ).
cnf(f_3326_3,plain,
hAPP(c_Set_OCollect(tc_prod(U_13025,U_13026)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13025,U_13026,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_13025,tc_fun(U_13026,tc_HOL_Obool),tc_fun(U_13026,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13026,tc_HOL_Obool),tc_fun(U_13026,tc_HOL_Obool)),U_13025),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13026)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13025),c_fconj),U_13027))),U_13028))) = hAPP(hAPP(c_Product__Type_OSigma(U_13025,U_13026),hAPP(c_Set_OCollect(U_13025),U_13027)),hAPP(hAPP(c_COMBB(tc_fun(U_13026,tc_HOL_Obool),tc_fun(U_13026,tc_HOL_Obool),U_13025),c_Set_OCollect(U_13026)),U_13028)),
inference(clausify,[status(thm)],[f_3326_2]) ).
fof(f_3327_1,plain,
! [V_Q_2,V_P_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Q_2))),
inference(fof_nnf,[status(thm)],[fact_Collect__split]) ).
fof(f_3327_2,plain,
! [U_13032,U_13031,U_13030,U_13029] : hAPP(c_Set_OCollect(tc_prod(U_13029,U_13030)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13029,U_13030,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13029,tc_fun(U_13030,tc_HOL_Obool),tc_fun(U_13030,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13030,tc_HOL_Obool),tc_fun(U_13030,tc_HOL_Obool)),U_13029),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13030)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13029),c_fconj),U_13031))),U_13032))) = hAPP(hAPP(c_Product__Type_OSigma(U_13029,U_13030),hAPP(c_Set_OCollect(U_13029),U_13031)),hAPP(c_COMBK(tc_fun(U_13030,tc_HOL_Obool),U_13029),hAPP(c_Set_OCollect(U_13030),U_13032))),
inference(variable_rename,[status(thm)],[f_3327_1]) ).
cnf(f_3327_3,plain,
hAPP(c_Set_OCollect(tc_prod(U_13029,U_13030)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13029,U_13030,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13029,tc_fun(U_13030,tc_HOL_Obool),tc_fun(U_13030,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13030,tc_HOL_Obool),tc_fun(U_13030,tc_HOL_Obool)),U_13029),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13030)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13029),c_fconj),U_13031))),U_13032))) = hAPP(hAPP(c_Product__Type_OSigma(U_13029,U_13030),hAPP(c_Set_OCollect(U_13029),U_13031)),hAPP(c_COMBK(tc_fun(U_13030,tc_HOL_Obool),U_13029),hAPP(c_Set_OCollect(U_13030),U_13032))),
inference(clausify,[status(thm)],[f_3327_2]) ).
fof(f_3328_1,plain,
! [V_P_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_c),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_P_2),V_f_2)),
inference(fof_nnf,[status(thm)],[fact_vimage__Collect__eq]) ).
fof(f_3328_2,plain,
! [U_13036,U_13035,U_13034,U_13033] : hAPP(c_Set_Ovimage(U_13033,U_13034,U_13035),hAPP(c_Set_OCollect(U_13034),U_13036)) = hAPP(c_Set_OCollect(U_13033),hAPP(hAPP(c_COMBB(U_13034,tc_HOL_Obool,U_13033),U_13036),U_13035)),
inference(variable_rename,[status(thm)],[f_3328_1]) ).
cnf(f_3328_3,plain,
hAPP(c_Set_Ovimage(U_13033,U_13034,U_13035),hAPP(c_Set_OCollect(U_13034),U_13036)) = hAPP(c_Set_OCollect(U_13033),hAPP(hAPP(c_COMBB(U_13034,tc_HOL_Obool,U_13033),U_13036),U_13035)),
inference(clausify,[status(thm)],[f_3328_2]) ).
fof(f_3329_1,plain,
! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),
inference(fof_nnf,[status(thm)],[fact_Collect__neg__eq]) ).
fof(f_3329_2,plain,
! [U_13038,U_13037] : hAPP(c_Set_OCollect(U_13037),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13037),c_fNot),U_13038)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13037,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13037),U_13038)),
inference(variable_rename,[status(thm)],[f_3329_1]) ).
cnf(f_3329_3,plain,
hAPP(c_Set_OCollect(U_13037),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13037),c_fNot),U_13038)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13037,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13037),U_13038)),
inference(clausify,[status(thm)],[f_3329_2]) ).
fof(f_3330_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_3330_2,plain,
! [U_13039] : c_Orderings_Otop__class_Otop(tc_fun(U_13039,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13039),hAPP(c_COMBK(tc_HOL_Obool,U_13039),c_fTrue)),
inference(variable_rename,[status(thm)],[f_3330_1]) ).
cnf(f_3330_3,plain,
c_Orderings_Otop__class_Otop(tc_fun(U_13039,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13039),hAPP(c_COMBK(tc_HOL_Obool,U_13039),c_fTrue)),
inference(clausify,[status(thm)],[f_3330_2]) ).
fof(f_3331_1,plain,
! [V_P_2,T_b] :
( ( hAPP(c_Set_OCollect(T_b),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ? [B_x] : hBOOL(hAPP(V_P_2,B_x)) )
& ( ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x))
| hAPP(c_Set_OCollect(T_b),V_P_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_Collect__empty__eq]) ).
fof(f_3331_2,plain,
! [U_13043,U_13042] :
( ( hAPP(c_Set_OCollect(U_13042),U_13043) = c_Orderings_Obot__class_Obot(tc_fun(U_13042,tc_HOL_Obool))
| ? [U_13041] : hBOOL(hAPP(U_13043,U_13041)) )
& ( ! [U_13040] : ~ hBOOL(hAPP(U_13043,U_13040))
| hAPP(c_Set_OCollect(U_13042),U_13043) != c_Orderings_Obot__class_Obot(tc_fun(U_13042,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_3331_1]) ).
fof(f_3331_3,plain,
( ! [U_13047] :
( ! [U_13045] : hAPP(c_Set_OCollect(U_13045),U_13047) = c_Orderings_Obot__class_Obot(tc_fun(U_13045,tc_HOL_Obool))
| ? [U_13041] : hBOOL(hAPP(U_13047,U_13041)) )
& ! [U_13046] :
( ! [U_13044] : hAPP(c_Set_OCollect(U_13044),U_13046) != c_Orderings_Obot__class_Obot(tc_fun(U_13044,tc_HOL_Obool))
| ! [U_13040] : ~ hBOOL(hAPP(U_13046,U_13040)) ) ),
inference(miniscope,[status(thm)],[f_3331_2]) ).
fof(f_3331_4,plain,
( ! [U_13047] :
( ! [U_13045] : hAPP(c_Set_OCollect(U_13045),U_13047) = c_Orderings_Obot__class_Obot(tc_fun(U_13045,tc_HOL_Obool))
| hBOOL(hAPP(U_13047,sK320(U_13047))) )
& ! [U_13046] :
( ! [U_13044] : hAPP(c_Set_OCollect(U_13044),U_13046) != c_Orderings_Obot__class_Obot(tc_fun(U_13044,tc_HOL_Obool))
| ! [U_13040] : ~ hBOOL(hAPP(U_13046,U_13040)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK320]),skolemize(U_13041,sK320(U_13047))],[f_3331_3]) ).
cnf(f_3331_5,plain,
( hAPP(c_Set_OCollect(U_13044),U_13046) != c_Orderings_Obot__class_Obot(tc_fun(U_13044,tc_HOL_Obool))
| ~ hBOOL(hAPP(U_13046,U_13040)) ),
inference(clausify,[status(thm)],[f_3331_4]) ).
cnf(f_3331_6,plain,
( hAPP(c_Set_OCollect(U_13045),U_13047) = c_Orderings_Obot__class_Obot(tc_fun(U_13045,tc_HOL_Obool))
| hBOOL(hAPP(U_13047,sK320(U_13047))) ),
inference(clausify,[status(thm)],[f_3331_4]) ).
fof(f_3332_1,plain,
! [V_P_2,T_b] :
( ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_P_2)
| ? [B_x] : hBOOL(hAPP(V_P_2,B_x)) )
& ( ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x))
| c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(c_Set_OCollect(T_b),V_P_2) ) ),
inference(fof_nnf,[status(thm)],[fact_empty__Collect__eq]) ).
fof(f_3332_2,plain,
! [U_13051,U_13050] :
( ( c_Orderings_Obot__class_Obot(tc_fun(U_13050,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13050),U_13051)
| ? [U_13049] : hBOOL(hAPP(U_13051,U_13049)) )
& ( ! [U_13048] : ~ hBOOL(hAPP(U_13051,U_13048))
| c_Orderings_Obot__class_Obot(tc_fun(U_13050,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_13050),U_13051) ) ),
inference(variable_rename,[status(thm)],[f_3332_1]) ).
fof(f_3332_3,plain,
( ! [U_13055] :
( ! [U_13053] : c_Orderings_Obot__class_Obot(tc_fun(U_13053,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13053),U_13055)
| ? [U_13049] : hBOOL(hAPP(U_13055,U_13049)) )
& ! [U_13054] :
( ! [U_13052] : c_Orderings_Obot__class_Obot(tc_fun(U_13052,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_13052),U_13054)
| ! [U_13048] : ~ hBOOL(hAPP(U_13054,U_13048)) ) ),
inference(miniscope,[status(thm)],[f_3332_2]) ).
fof(f_3332_4,plain,
( ! [U_13055] :
( ! [U_13053] : c_Orderings_Obot__class_Obot(tc_fun(U_13053,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13053),U_13055)
| hBOOL(hAPP(U_13055,sK321(U_13055))) )
& ! [U_13054] :
( ! [U_13052] : c_Orderings_Obot__class_Obot(tc_fun(U_13052,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_13052),U_13054)
| ! [U_13048] : ~ hBOOL(hAPP(U_13054,U_13048)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK321]),skolemize(U_13049,sK321(U_13055))],[f_3332_3]) ).
cnf(f_3332_5,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_13052,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_13052),U_13054)
| ~ hBOOL(hAPP(U_13054,U_13048)) ),
inference(clausify,[status(thm)],[f_3332_4]) ).
cnf(f_3332_6,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_13053,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13053),U_13055)
| hBOOL(hAPP(U_13055,sK321(U_13055))) ),
inference(clausify,[status(thm)],[f_3332_4]) ).
fof(f_3333_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_3333_2,plain,
! [U_13056] : c_Orderings_Obot__class_Obot(tc_fun(U_13056,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13056),hAPP(c_COMBK(tc_HOL_Obool,U_13056),c_fFalse)),
inference(variable_rename,[status(thm)],[f_3333_1]) ).
cnf(f_3333_3,plain,
c_Orderings_Obot__class_Obot(tc_fun(U_13056,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13056),hAPP(c_COMBK(tc_HOL_Obool,U_13056),c_fFalse)),
inference(clausify,[status(thm)],[f_3333_2]) ).
fof(f_3334_1,plain,
! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)),
inference(fof_nnf,[status(thm)],[fact_Collect__disj__eq]) ).
fof(f_3334_2,plain,
! [U_13059,U_13058,U_13057] : hAPP(c_Set_OCollect(U_13057),hAPP(hAPP(c_COMBS(U_13057,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13057),c_fdisj),U_13058)),U_13059)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13057,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13057),U_13058)),hAPP(c_Set_OCollect(U_13057),U_13059)),
inference(variable_rename,[status(thm)],[f_3334_1]) ).
cnf(f_3334_3,plain,
hAPP(c_Set_OCollect(U_13057),hAPP(hAPP(c_COMBS(U_13057,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13057),c_fdisj),U_13058)),U_13059)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13057,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13057),U_13058)),hAPP(c_Set_OCollect(U_13057),U_13059)),
inference(clausify,[status(thm)],[f_3334_2]) ).
fof(f_3335_1,plain,
! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),V_P_2) = V_P_2,
inference(fof_nnf,[status(thm)],[fact_Collect__def]) ).
fof(f_3335_2,plain,
! [U_13061,U_13060] : hAPP(c_Set_OCollect(U_13060),U_13061) = U_13061,
inference(variable_rename,[status(thm)],[f_3335_1]) ).
cnf(f_3335_3,plain,
hAPP(c_Set_OCollect(U_13060),U_13061) = U_13061,
inference(clausify,[status(thm)],[f_3335_2]) ).
fof(f_3336_1,plain,
! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)),
inference(fof_nnf,[status(thm)],[fact_Collect__conj__eq]) ).
fof(f_3336_2,plain,
! [U_13064,U_13063,U_13062] : hAPP(c_Set_OCollect(U_13062),hAPP(hAPP(c_COMBS(U_13062,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13062),c_fconj),U_13063)),U_13064)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13062,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13062),U_13063)),hAPP(c_Set_OCollect(U_13062),U_13064)),
inference(variable_rename,[status(thm)],[f_3336_1]) ).
cnf(f_3336_3,plain,
hAPP(c_Set_OCollect(U_13062),hAPP(hAPP(c_COMBS(U_13062,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13062),c_fconj),U_13063)),U_13064)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13062,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13062),U_13063)),hAPP(c_Set_OCollect(U_13062),U_13064)),
inference(clausify,[status(thm)],[f_3336_2]) ).
fof(f_3337_1,plain,
! [V_Q_2,V_P_2,T_b] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2)))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Collect__disjI]) ).
fof(f_3337_2,plain,
! [U_13067,U_13066,U_13065] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13065),hAPP(c_Set_OCollect(U_13065),hAPP(hAPP(c_COMBS(U_13065,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13065),c_fdisj),U_13066)),U_13067))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13065),hAPP(c_Set_OCollect(U_13065),U_13067)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13065),hAPP(c_Set_OCollect(U_13065),U_13066))) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13065),hAPP(c_Set_OCollect(U_13065),U_13067)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_13065),hAPP(c_Set_OCollect(U_13065),U_13066))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13065),hAPP(c_Set_OCollect(U_13065),hAPP(hAPP(c_COMBS(U_13065,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13065),c_fdisj),U_13066)),U_13067)))) ) ),
inference(variable_rename,[status(thm)],[f_3337_1]) ).
fof(f_3337_3,plain,
( ! [U_13073,U_13071,U_13069] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13069),hAPP(c_Set_OCollect(U_13069),hAPP(hAPP(c_COMBS(U_13069,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13069),c_fdisj),U_13071)),U_13073))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13069),hAPP(c_Set_OCollect(U_13069),U_13073)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13069),hAPP(c_Set_OCollect(U_13069),U_13071))) )
& ! [U_13072,U_13070,U_13068] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13068),hAPP(c_Set_OCollect(U_13068),U_13072)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_13068),hAPP(c_Set_OCollect(U_13068),U_13070))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13068),hAPP(c_Set_OCollect(U_13068),hAPP(hAPP(c_COMBS(U_13068,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13068),c_fdisj),U_13070)),U_13072)))) ) ),
inference(miniscope,[status(thm)],[f_3337_2]) ).
cnf(f_3337_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13068),hAPP(c_Set_OCollect(U_13068),U_13070)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13068),hAPP(c_Set_OCollect(U_13068),hAPP(hAPP(c_COMBS(U_13068,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13068),c_fdisj),U_13070)),U_13072)))) ),
inference(clausify,[status(thm)],[f_3337_3]) ).
cnf(f_3337_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13068),hAPP(c_Set_OCollect(U_13068),U_13072)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13068),hAPP(c_Set_OCollect(U_13068),hAPP(hAPP(c_COMBS(U_13068,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13068),c_fdisj),U_13070)),U_13072)))) ),
inference(clausify,[status(thm)],[f_3337_3]) ).
cnf(f_3337_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13069),hAPP(c_Set_OCollect(U_13069),hAPP(hAPP(c_COMBS(U_13069,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13069),c_fdisj),U_13071)),U_13073))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13069),hAPP(c_Set_OCollect(U_13069),U_13073)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13069),hAPP(c_Set_OCollect(U_13069),U_13071))) ),
inference(clausify,[status(thm)],[f_3337_3]) ).
fof(f_3338_1,plain,
! [V_P_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)))),V_P_2)),
inference(fof_nnf,[status(thm)],[fact_insert__Collect]) ).
fof(f_3338_2,plain,
! [U_13076,U_13075,U_13074] : hAPP(hAPP(c_Set_Oinsert(U_13074),U_13075),hAPP(c_Set_OCollect(U_13074),U_13076)) = hAPP(c_Set_OCollect(U_13074),hAPP(hAPP(c_COMBS(U_13074,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13074),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13074),c_fNot),hAPP(hAPP(c_COMBC(U_13074,U_13074,tc_HOL_Obool),c_fequal),U_13075)))),U_13076)),
inference(variable_rename,[status(thm)],[f_3338_1]) ).
cnf(f_3338_3,plain,
hAPP(hAPP(c_Set_Oinsert(U_13074),U_13075),hAPP(c_Set_OCollect(U_13074),U_13076)) = hAPP(c_Set_OCollect(U_13074),hAPP(hAPP(c_COMBS(U_13074,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13074),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13074),c_fNot),hAPP(hAPP(c_COMBC(U_13074,U_13074,tc_HOL_Obool),c_fequal),U_13075)))),U_13076)),
inference(clausify,[status(thm)],[f_3338_2]) ).
fof(f_3339_1,plain,
! [V_P_2,V_a_2,T_b] :
( hBOOL(hAPP(V_P_2,V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ),
inference(fof_nnf,[status(thm)],[fact_CollectE]) ).
fof(f_3339_2,plain,
! [U_13079,U_13078,U_13077] :
( hBOOL(hAPP(U_13079,U_13078))
| ~ hBOOL(hAPP(hAPP(c_member(U_13077),U_13078),hAPP(c_Set_OCollect(U_13077),U_13079))) ),
inference(variable_rename,[status(thm)],[f_3339_1]) ).
fof(f_3339_3,plain,
! [U_13079,U_13078] :
( ! [U_13077] : ~ hBOOL(hAPP(hAPP(c_member(U_13077),U_13078),hAPP(c_Set_OCollect(U_13077),U_13079)))
| hBOOL(hAPP(U_13079,U_13078)) ),
inference(miniscope,[status(thm)],[f_3339_2]) ).
cnf(f_3339_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_13077),U_13078),hAPP(c_Set_OCollect(U_13077),U_13079)))
| hBOOL(hAPP(U_13079,U_13078)) ),
inference(clausify,[status(thm)],[f_3339_3]) ).
fof(f_3340_1,plain,
! [V_P_2,V_a_2,T_b] :
( hBOOL(hAPP(V_P_2,V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ),
inference(fof_nnf,[status(thm)],[fact_CollectD]) ).
fof(f_3340_2,plain,
! [U_13082,U_13081,U_13080] :
( hBOOL(hAPP(U_13082,U_13081))
| ~ hBOOL(hAPP(hAPP(c_member(U_13080),U_13081),hAPP(c_Set_OCollect(U_13080),U_13082))) ),
inference(variable_rename,[status(thm)],[f_3340_1]) ).
fof(f_3340_3,plain,
! [U_13082,U_13081] :
( ! [U_13080] : ~ hBOOL(hAPP(hAPP(c_member(U_13080),U_13081),hAPP(c_Set_OCollect(U_13080),U_13082)))
| hBOOL(hAPP(U_13082,U_13081)) ),
inference(miniscope,[status(thm)],[f_3340_2]) ).
cnf(f_3340_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_13080),U_13081),hAPP(c_Set_OCollect(U_13080),U_13082)))
| hBOOL(hAPP(U_13082,U_13081)) ),
inference(clausify,[status(thm)],[f_3340_3]) ).
fof(f_3341_1,plain,
! [V_P_2,V_a_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
| ~ hBOOL(hAPP(V_P_2,V_a_2)) )
& ( hBOOL(hAPP(V_P_2,V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_mem__Collect__eq]) ).
fof(f_3341_2,plain,
! [U_13085,U_13084,U_13083] :
( ( hBOOL(hAPP(hAPP(c_member(U_13083),U_13084),hAPP(c_Set_OCollect(U_13083),U_13085)))
| ~ hBOOL(hAPP(U_13085,U_13084)) )
& ( hBOOL(hAPP(U_13085,U_13084))
| ~ hBOOL(hAPP(hAPP(c_member(U_13083),U_13084),hAPP(c_Set_OCollect(U_13083),U_13085))) ) ),
inference(variable_rename,[status(thm)],[f_3341_1]) ).
fof(f_3341_3,plain,
( ! [U_13091,U_13089] :
( ! [U_13087] : hBOOL(hAPP(hAPP(c_member(U_13087),U_13089),hAPP(c_Set_OCollect(U_13087),U_13091)))
| ~ hBOOL(hAPP(U_13091,U_13089)) )
& ! [U_13090,U_13088] :
( ! [U_13086] : ~ hBOOL(hAPP(hAPP(c_member(U_13086),U_13088),hAPP(c_Set_OCollect(U_13086),U_13090)))
| hBOOL(hAPP(U_13090,U_13088)) ) ),
inference(miniscope,[status(thm)],[f_3341_2]) ).
cnf(f_3341_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_13086),U_13088),hAPP(c_Set_OCollect(U_13086),U_13090)))
| hBOOL(hAPP(U_13090,U_13088)) ),
inference(clausify,[status(thm)],[f_3341_3]) ).
cnf(f_3341_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_13087),U_13089),hAPP(c_Set_OCollect(U_13087),U_13091)))
| ~ hBOOL(hAPP(U_13091,U_13089)) ),
inference(clausify,[status(thm)],[f_3341_3]) ).
fof(f_3342_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_3342_2,plain,
! [U_13093,U_13092] : hAPP(c_Set_OCollect(U_13092),hAPP(hAPP(c_COMBC(U_13092,tc_fun(U_13092,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13092)),U_13093)) = U_13093,
inference(variable_rename,[status(thm)],[f_3342_1]) ).
cnf(f_3342_3,plain,
hAPP(c_Set_OCollect(U_13092),hAPP(hAPP(c_COMBC(U_13092,tc_fun(U_13092,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13092)),U_13093)) = U_13093,
inference(clausify,[status(thm)],[f_3342_2]) ).
fof(f_3343_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_3343_2,plain,
! [U_13096,U_13095,U_13094] : hAPP(hAPP(c_Set_Oinsert(U_13094),U_13095),U_13096) = hAPP(c_Set_OCollect(U_13094),hAPP(hAPP(c_COMBS(U_13094,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13094),c_fdisj),hAPP(hAPP(c_COMBC(U_13094,U_13094,tc_HOL_Obool),c_fequal),U_13095))),hAPP(hAPP(c_COMBC(U_13094,tc_fun(U_13094,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13094)),U_13096))),
inference(variable_rename,[status(thm)],[f_3343_1]) ).
cnf(f_3343_3,plain,
hAPP(hAPP(c_Set_Oinsert(U_13094),U_13095),U_13096) = hAPP(c_Set_OCollect(U_13094),hAPP(hAPP(c_COMBS(U_13094,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13094),c_fdisj),hAPP(hAPP(c_COMBC(U_13094,U_13094,tc_HOL_Obool),c_fequal),U_13095))),hAPP(hAPP(c_COMBC(U_13094,tc_fun(U_13094,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13094)),U_13096))),
inference(clausify,[status(thm)],[f_3343_2]) ).
fof(f_3344_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_3344_2,plain,
! [U_13099,U_13098,U_13097] : hAPP(hAPP(c_Set_Oinsert(U_13097),U_13098),U_13099) = hAPP(c_Set_OCollect(U_13097),hAPP(hAPP(c_COMBS(U_13097,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13097),c_fdisj),hAPP(hAPP(c_COMBC(U_13097,U_13097,tc_HOL_Obool),c_fequal),U_13098))),hAPP(hAPP(c_COMBC(U_13097,tc_fun(U_13097,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13097)),U_13099))),
inference(variable_rename,[status(thm)],[f_3344_1]) ).
cnf(f_3344_3,plain,
hAPP(hAPP(c_Set_Oinsert(U_13097),U_13098),U_13099) = hAPP(c_Set_OCollect(U_13097),hAPP(hAPP(c_COMBS(U_13097,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13097),c_fdisj),hAPP(hAPP(c_COMBC(U_13097,U_13097,tc_HOL_Obool),c_fequal),U_13098))),hAPP(hAPP(c_COMBC(U_13097,tc_fun(U_13097,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13097)),U_13099))),
inference(clausify,[status(thm)],[f_3344_2]) ).
fof(f_3345_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_3345_2,plain,
! [U_13102,U_13101,U_13100] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13100,tc_HOL_Obool)),U_13101),U_13102) = hAPP(c_Set_OCollect(U_13100),hAPP(hAPP(c_COMBS(U_13100,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13100),c_fdisj),hAPP(hAPP(c_COMBC(U_13100,tc_fun(U_13100,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13100)),U_13101))),hAPP(hAPP(c_COMBC(U_13100,tc_fun(U_13100,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13100)),U_13102))),
inference(variable_rename,[status(thm)],[f_3345_1]) ).
cnf(f_3345_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13100,tc_HOL_Obool)),U_13101),U_13102) = hAPP(c_Set_OCollect(U_13100),hAPP(hAPP(c_COMBS(U_13100,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13100),c_fdisj),hAPP(hAPP(c_COMBC(U_13100,tc_fun(U_13100,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13100)),U_13101))),hAPP(hAPP(c_COMBC(U_13100,tc_fun(U_13100,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13100)),U_13102))),
inference(clausify,[status(thm)],[f_3345_2]) ).
fof(f_3346_1,plain,
! [V_P_2,V_A_2,V_x_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))))
| ~ hBOOL(hAPP(V_P_2,V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
& ( ( hBOOL(hAPP(V_P_2,V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2)))) ) ),
inference(fof_nnf,[status(thm)],[fact_Int__Collect]) ).
fof(f_3346_2,plain,
! [U_13106,U_13105,U_13104,U_13103] :
( ( hBOOL(hAPP(hAPP(c_member(U_13103),U_13104),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13103,tc_HOL_Obool)),U_13105),hAPP(c_Set_OCollect(U_13103),U_13106))))
| ~ hBOOL(hAPP(U_13106,U_13104))
| ~ hBOOL(hAPP(hAPP(c_member(U_13103),U_13104),U_13105)) )
& ( ( hBOOL(hAPP(U_13106,U_13104))
& hBOOL(hAPP(hAPP(c_member(U_13103),U_13104),U_13105)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_13103),U_13104),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13103,tc_HOL_Obool)),U_13105),hAPP(c_Set_OCollect(U_13103),U_13106)))) ) ),
inference(variable_rename,[status(thm)],[f_3346_1]) ).
fof(f_3346_3,plain,
( ! [U_13114,U_13112,U_13110,U_13108] :
( hBOOL(hAPP(hAPP(c_member(U_13108),U_13110),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13108,tc_HOL_Obool)),U_13112),hAPP(c_Set_OCollect(U_13108),U_13114))))
| ~ hBOOL(hAPP(U_13114,U_13110))
| ~ hBOOL(hAPP(hAPP(c_member(U_13108),U_13110),U_13112)) )
& ! [U_13113,U_13111,U_13109,U_13107] :
( ( hBOOL(hAPP(U_13113,U_13109))
& hBOOL(hAPP(hAPP(c_member(U_13107),U_13109),U_13111)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_13107),U_13109),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13107,tc_HOL_Obool)),U_13111),hAPP(c_Set_OCollect(U_13107),U_13113)))) ) ),
inference(miniscope,[status(thm)],[f_3346_2]) ).
cnf(f_3346_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_13107),U_13109),U_13111))
| ~ hBOOL(hAPP(hAPP(c_member(U_13107),U_13109),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13107,tc_HOL_Obool)),U_13111),hAPP(c_Set_OCollect(U_13107),U_13113)))) ),
inference(clausify,[status(thm)],[f_3346_3]) ).
cnf(f_3346_5,plain,
( hBOOL(hAPP(U_13113,U_13109))
| ~ hBOOL(hAPP(hAPP(c_member(U_13107),U_13109),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13107,tc_HOL_Obool)),U_13111),hAPP(c_Set_OCollect(U_13107),U_13113)))) ),
inference(clausify,[status(thm)],[f_3346_3]) ).
cnf(f_3346_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_13108),U_13110),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13108,tc_HOL_Obool)),U_13112),hAPP(c_Set_OCollect(U_13108),U_13114))))
| ~ hBOOL(hAPP(U_13114,U_13110))
| ~ hBOOL(hAPP(hAPP(c_member(U_13108),U_13110),U_13112)) ),
inference(clausify,[status(thm)],[f_3346_3]) ).
fof(f_3347_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_3347_2,plain,
! [U_13117,U_13116,U_13115] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13115,tc_HOL_Obool)),U_13116),U_13117) = hAPP(c_Set_OCollect(U_13115),hAPP(hAPP(c_COMBS(U_13115,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13115),c_fconj),hAPP(hAPP(c_COMBC(U_13115,tc_fun(U_13115,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13115)),U_13116))),hAPP(hAPP(c_COMBC(U_13115,tc_fun(U_13115,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13115)),U_13117))),
inference(variable_rename,[status(thm)],[f_3347_1]) ).
cnf(f_3347_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13115,tc_HOL_Obool)),U_13116),U_13117) = hAPP(c_Set_OCollect(U_13115),hAPP(hAPP(c_COMBS(U_13115,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13115),c_fconj),hAPP(hAPP(c_COMBC(U_13115,tc_fun(U_13115,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13115)),U_13116))),hAPP(hAPP(c_COMBC(U_13115,tc_fun(U_13115,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13115)),U_13117))),
inference(clausify,[status(thm)],[f_3347_2]) ).
fof(f_3348_1,plain,
! [T_b,V_a_2,V_P_2] :
( ( hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hBOOL(hAPP(V_P_2,V_a_2)) )
& ( hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
| ~ hBOOL(hAPP(V_P_2,V_a_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Collect__conv__if]) ).
fof(f_3348_2,plain,
! [U_13120,U_13119,U_13118] :
( ( hAPP(c_Set_OCollect(U_13120),hAPP(hAPP(c_COMBS(U_13120,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13120),c_fconj),hAPP(hAPP(c_COMBC(U_13120,U_13120,tc_HOL_Obool),c_fequal),U_13119))),U_13118)) = c_Orderings_Obot__class_Obot(tc_fun(U_13120,tc_HOL_Obool))
| hBOOL(hAPP(U_13118,U_13119)) )
& ( hAPP(c_Set_OCollect(U_13120),hAPP(hAPP(c_COMBS(U_13120,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13120),c_fconj),hAPP(hAPP(c_COMBC(U_13120,U_13120,tc_HOL_Obool),c_fequal),U_13119))),U_13118)) = hAPP(hAPP(c_Set_Oinsert(U_13120),U_13119),c_Orderings_Obot__class_Obot(tc_fun(U_13120,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_13118,U_13119)) ) ),
inference(variable_rename,[status(thm)],[f_3348_1]) ).
fof(f_3348_3,plain,
( ! [U_13126,U_13124,U_13122] :
( hAPP(c_Set_OCollect(U_13126),hAPP(hAPP(c_COMBS(U_13126,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13126),c_fconj),hAPP(hAPP(c_COMBC(U_13126,U_13126,tc_HOL_Obool),c_fequal),U_13124))),U_13122)) = c_Orderings_Obot__class_Obot(tc_fun(U_13126,tc_HOL_Obool))
| hBOOL(hAPP(U_13122,U_13124)) )
& ! [U_13125,U_13123,U_13121] :
( hAPP(c_Set_OCollect(U_13125),hAPP(hAPP(c_COMBS(U_13125,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13125),c_fconj),hAPP(hAPP(c_COMBC(U_13125,U_13125,tc_HOL_Obool),c_fequal),U_13123))),U_13121)) = hAPP(hAPP(c_Set_Oinsert(U_13125),U_13123),c_Orderings_Obot__class_Obot(tc_fun(U_13125,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_13121,U_13123)) ) ),
inference(miniscope,[status(thm)],[f_3348_2]) ).
cnf(f_3348_4,plain,
( hAPP(c_Set_OCollect(U_13125),hAPP(hAPP(c_COMBS(U_13125,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13125),c_fconj),hAPP(hAPP(c_COMBC(U_13125,U_13125,tc_HOL_Obool),c_fequal),U_13123))),U_13121)) = hAPP(hAPP(c_Set_Oinsert(U_13125),U_13123),c_Orderings_Obot__class_Obot(tc_fun(U_13125,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_13121,U_13123)) ),
inference(clausify,[status(thm)],[f_3348_3]) ).
cnf(f_3348_5,plain,
( hAPP(c_Set_OCollect(U_13126),hAPP(hAPP(c_COMBS(U_13126,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13126),c_fconj),hAPP(hAPP(c_COMBC(U_13126,U_13126,tc_HOL_Obool),c_fequal),U_13124))),U_13122)) = c_Orderings_Obot__class_Obot(tc_fun(U_13126,tc_HOL_Obool))
| hBOOL(hAPP(U_13122,U_13124)) ),
inference(clausify,[status(thm)],[f_3348_3]) ).
fof(f_3349_1,plain,
! [T_b,V_a_2,V_P_2] :
( ( hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hBOOL(hAPP(V_P_2,V_a_2)) )
& ( hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
| ~ hBOOL(hAPP(V_P_2,V_a_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Collect__conv__if2]) ).
fof(f_3349_2,plain,
! [U_13129,U_13128,U_13127] :
( ( hAPP(c_Set_OCollect(U_13129),hAPP(hAPP(c_COMBS(U_13129,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13129),c_fconj),hAPP(c_fequal,U_13128))),U_13127)) = c_Orderings_Obot__class_Obot(tc_fun(U_13129,tc_HOL_Obool))
| hBOOL(hAPP(U_13127,U_13128)) )
& ( hAPP(c_Set_OCollect(U_13129),hAPP(hAPP(c_COMBS(U_13129,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13129),c_fconj),hAPP(c_fequal,U_13128))),U_13127)) = hAPP(hAPP(c_Set_Oinsert(U_13129),U_13128),c_Orderings_Obot__class_Obot(tc_fun(U_13129,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_13127,U_13128)) ) ),
inference(variable_rename,[status(thm)],[f_3349_1]) ).
fof(f_3349_3,plain,
( ! [U_13135,U_13133,U_13131] :
( hAPP(c_Set_OCollect(U_13135),hAPP(hAPP(c_COMBS(U_13135,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13135),c_fconj),hAPP(c_fequal,U_13133))),U_13131)) = c_Orderings_Obot__class_Obot(tc_fun(U_13135,tc_HOL_Obool))
| hBOOL(hAPP(U_13131,U_13133)) )
& ! [U_13134,U_13132,U_13130] :
( hAPP(c_Set_OCollect(U_13134),hAPP(hAPP(c_COMBS(U_13134,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13134),c_fconj),hAPP(c_fequal,U_13132))),U_13130)) = hAPP(hAPP(c_Set_Oinsert(U_13134),U_13132),c_Orderings_Obot__class_Obot(tc_fun(U_13134,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_13130,U_13132)) ) ),
inference(miniscope,[status(thm)],[f_3349_2]) ).
cnf(f_3349_4,plain,
( hAPP(c_Set_OCollect(U_13134),hAPP(hAPP(c_COMBS(U_13134,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13134),c_fconj),hAPP(c_fequal,U_13132))),U_13130)) = hAPP(hAPP(c_Set_Oinsert(U_13134),U_13132),c_Orderings_Obot__class_Obot(tc_fun(U_13134,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_13130,U_13132)) ),
inference(clausify,[status(thm)],[f_3349_3]) ).
cnf(f_3349_5,plain,
( hAPP(c_Set_OCollect(U_13135),hAPP(hAPP(c_COMBS(U_13135,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13135),c_fconj),hAPP(c_fequal,U_13133))),U_13131)) = c_Orderings_Obot__class_Obot(tc_fun(U_13135,tc_HOL_Obool))
| hBOOL(hAPP(U_13131,U_13133)) ),
inference(clausify,[status(thm)],[f_3349_3]) ).
fof(f_3350_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_3350_2,plain,
! [U_13137,U_13136] : hAPP(c_Set_OCollect(U_13136),hAPP(hAPP(c_COMBC(U_13136,U_13136,tc_HOL_Obool),c_fequal),U_13137)) = hAPP(hAPP(c_Set_Oinsert(U_13136),U_13137),c_Orderings_Obot__class_Obot(tc_fun(U_13136,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_3350_1]) ).
cnf(f_3350_3,plain,
hAPP(c_Set_OCollect(U_13136),hAPP(hAPP(c_COMBC(U_13136,U_13136,tc_HOL_Obool),c_fequal),U_13137)) = hAPP(hAPP(c_Set_Oinsert(U_13136),U_13137),c_Orderings_Obot__class_Obot(tc_fun(U_13136,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_3350_2]) ).
fof(f_3351_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_3351_2,plain,
! [U_13139,U_13138] : hAPP(c_Set_OCollect(U_13138),hAPP(c_fequal,U_13139)) = hAPP(hAPP(c_Set_Oinsert(U_13138),U_13139),c_Orderings_Obot__class_Obot(tc_fun(U_13138,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_3351_1]) ).
cnf(f_3351_3,plain,
hAPP(c_Set_OCollect(U_13138),hAPP(c_fequal,U_13139)) = hAPP(hAPP(c_Set_Oinsert(U_13138),U_13139),c_Orderings_Obot__class_Obot(tc_fun(U_13138,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_3351_2]) ).
fof(f_3352_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_3352_2,plain,
! [U_13142,U_13141,U_13140] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13140,tc_HOL_Obool)),U_13141),U_13142) = hAPP(c_Set_OCollect(U_13140),hAPP(hAPP(c_COMBS(U_13140,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13140),c_fconj),hAPP(hAPP(c_COMBC(U_13140,tc_fun(U_13140,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13140)),U_13141))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13140),c_fNot),hAPP(hAPP(c_COMBC(U_13140,tc_fun(U_13140,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13140)),U_13142)))),
inference(variable_rename,[status(thm)],[f_3352_1]) ).
cnf(f_3352_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13140,tc_HOL_Obool)),U_13141),U_13142) = hAPP(c_Set_OCollect(U_13140),hAPP(hAPP(c_COMBS(U_13140,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13140),c_fconj),hAPP(hAPP(c_COMBC(U_13140,tc_fun(U_13140,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13140)),U_13141))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13140),c_fNot),hAPP(hAPP(c_COMBC(U_13140,tc_fun(U_13140,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13140)),U_13142)))),
inference(clausify,[status(thm)],[f_3352_2]) ).
fof(f_3353_1,plain,
! [V_P_2,T_b] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) ),
inference(fof_nnf,[status(thm)],[fact_finite__Collect__not]) ).
fof(f_3353_2,plain,
! [U_13144,U_13143] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13143),hAPP(c_Set_OCollect(U_13143),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13143),c_fNot),U_13144))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13143),c_Orderings_Otop__class_Otop(tc_fun(U_13143,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13143),c_Orderings_Otop__class_Otop(tc_fun(U_13143,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13143),hAPP(c_Set_OCollect(U_13143),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13143),c_fNot),U_13144)))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13143),hAPP(c_Set_OCollect(U_13143),U_13144))) ),
inference(variable_rename,[status(thm)],[f_3353_1]) ).
cnf(f_3353_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13143),c_Orderings_Otop__class_Otop(tc_fun(U_13143,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13143),hAPP(c_Set_OCollect(U_13143),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13143),c_fNot),U_13144))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13143),hAPP(c_Set_OCollect(U_13143),U_13144))) ),
inference(clausify,[status(thm)],[f_3353_2]) ).
cnf(f_3353_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13143),hAPP(c_Set_OCollect(U_13143),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13143),c_fNot),U_13144))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13143),c_Orderings_Otop__class_Otop(tc_fun(U_13143,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13143),hAPP(c_Set_OCollect(U_13143),U_13144))) ),
inference(clausify,[status(thm)],[f_3353_2]) ).
fof(f_3354_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_3354_2,plain,
! [U_13147,U_13146,U_13145] : hAPP(hAPP(c_Set_Oinsert(U_13145),U_13146),U_13147) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13145,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13145),hAPP(hAPP(c_COMBC(U_13145,U_13145,tc_HOL_Obool),c_fequal),U_13146))),U_13147),
inference(variable_rename,[status(thm)],[f_3354_1]) ).
cnf(f_3354_3,plain,
hAPP(hAPP(c_Set_Oinsert(U_13145),U_13146),U_13147) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13145,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13145),hAPP(hAPP(c_COMBC(U_13145,U_13145,tc_HOL_Obool),c_fequal),U_13146))),U_13147),
inference(clausify,[status(thm)],[f_3354_2]) ).
fof(f_3355_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_3355_2,plain,
! [U_13149,U_13148] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13148,tc_HOL_Obool)),U_13149) = hAPP(c_Set_OCollect(U_13148),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13148),c_fNot),hAPP(hAPP(c_COMBC(U_13148,tc_fun(U_13148,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13148)),U_13149))),
inference(variable_rename,[status(thm)],[f_3355_1]) ).
cnf(f_3355_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13148,tc_HOL_Obool)),U_13149) = hAPP(c_Set_OCollect(U_13148),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13148),c_fNot),hAPP(hAPP(c_COMBC(U_13148,tc_fun(U_13148,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13148)),U_13149))),
inference(clausify,[status(thm)],[f_3355_2]) ).
fof(f_3356_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_3356_2,plain,
! [U_13153,U_13152,U_13151,U_13150] : hAPP(c_Set_Ovimage(U_13150,U_13151,U_13152),U_13153) = hAPP(c_Set_OCollect(U_13150),hAPP(hAPP(c_COMBC(U_13150,tc_fun(U_13151,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13151,tc_fun(tc_fun(U_13151,tc_HOL_Obool),tc_HOL_Obool),U_13150),c_member(U_13151)),U_13152)),U_13153)),
inference(variable_rename,[status(thm)],[f_3356_1]) ).
cnf(f_3356_3,plain,
hAPP(c_Set_Ovimage(U_13150,U_13151,U_13152),U_13153) = hAPP(c_Set_OCollect(U_13150),hAPP(hAPP(c_COMBC(U_13150,tc_fun(U_13151,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13151,tc_fun(tc_fun(U_13151,tc_HOL_Obool),tc_HOL_Obool),U_13150),c_member(U_13151)),U_13152)),U_13153)),
inference(clausify,[status(thm)],[f_3356_2]) ).
fof(f_3357_1,plain,
! [V_P_2,V_A_2,T_c,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),V_P_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_P_2))),
inference(fof_nnf,[status(thm)],[fact_Collect__ball__eq]) ).
fof(f_3357_2,plain,
! [U_13157,U_13156,U_13155,U_13154] : hAPP(c_Set_OCollect(U_13154),hAPP(hAPP(c_COMBB(tc_fun(U_13155,tc_HOL_Obool),tc_HOL_Obool,U_13154),c_HOL_OAll(U_13155)),hAPP(hAPP(c_COMBB(tc_fun(U_13155,tc_HOL_Obool),tc_fun(U_13155,tc_HOL_Obool),U_13154),hAPP(c_COMBS(U_13155,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13155),c_fimplies),hAPP(hAPP(c_COMBC(U_13155,tc_fun(U_13155,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13155)),U_13156)))),U_13157))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13155,tc_fun(U_13154,tc_HOL_Obool)),U_13156),hAPP(hAPP(c_COMBB(tc_fun(U_13154,tc_HOL_Obool),tc_fun(U_13154,tc_HOL_Obool),U_13155),c_Set_OCollect(U_13154)),hAPP(c_COMBC(U_13154,U_13155,tc_HOL_Obool),U_13157))),
inference(variable_rename,[status(thm)],[f_3357_1]) ).
cnf(f_3357_3,plain,
hAPP(c_Set_OCollect(U_13154),hAPP(hAPP(c_COMBB(tc_fun(U_13155,tc_HOL_Obool),tc_HOL_Obool,U_13154),c_HOL_OAll(U_13155)),hAPP(hAPP(c_COMBB(tc_fun(U_13155,tc_HOL_Obool),tc_fun(U_13155,tc_HOL_Obool),U_13154),hAPP(c_COMBS(U_13155,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13155),c_fimplies),hAPP(hAPP(c_COMBC(U_13155,tc_fun(U_13155,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13155)),U_13156)))),U_13157))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13155,tc_fun(U_13154,tc_HOL_Obool)),U_13156),hAPP(hAPP(c_COMBB(tc_fun(U_13154,tc_HOL_Obool),tc_fun(U_13154,tc_HOL_Obool),U_13155),c_Set_OCollect(U_13154)),hAPP(c_COMBC(U_13154,U_13155,tc_HOL_Obool),U_13157))),
inference(clausify,[status(thm)],[f_3357_2]) ).
fof(f_3358_1,plain,
! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(c_Set_OCollect(T_b),V_Q_2)),
inference(fof_nnf,[status(thm)],[fact_Collect__imp__eq]) ).
fof(f_3358_2,plain,
! [U_13160,U_13159,U_13158] : hAPP(c_Set_OCollect(U_13158),hAPP(hAPP(c_COMBS(U_13158,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13158),c_fimplies),U_13159)),U_13160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13158,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13158,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13158),U_13159))),hAPP(c_Set_OCollect(U_13158),U_13160)),
inference(variable_rename,[status(thm)],[f_3358_1]) ).
cnf(f_3358_3,plain,
hAPP(c_Set_OCollect(U_13158),hAPP(hAPP(c_COMBS(U_13158,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13158),c_fimplies),U_13159)),U_13160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13158,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13158,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13158),U_13159))),hAPP(c_Set_OCollect(U_13158),U_13160)),
inference(clausify,[status(thm)],[f_3358_2]) ).
fof(f_3359_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_3359_2,plain,
! [U_13162,U_13161] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_13161,tc_HOL_Obool),U_13162) = hAPP(c_Set_OCollect(U_13161),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13161,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,U_13161),c_HOL_OAll(tc_fun(U_13161,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13161,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13161,tc_HOL_Obool),tc_HOL_Obool),U_13161),hAPP(c_COMBS(tc_fun(U_13161,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_13161,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(U_13161,tc_HOL_Obool),tc_fun(tc_fun(U_13161,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_13161,tc_HOL_Obool))),U_13162)))),c_member(U_13161)))),
inference(variable_rename,[status(thm)],[f_3359_1]) ).
cnf(f_3359_3,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_13161,tc_HOL_Obool),U_13162) = hAPP(c_Set_OCollect(U_13161),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13161,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,U_13161),c_HOL_OAll(tc_fun(U_13161,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13161,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13161,tc_HOL_Obool),tc_HOL_Obool),U_13161),hAPP(c_COMBS(tc_fun(U_13161,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_13161,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(U_13161,tc_HOL_Obool),tc_fun(tc_fun(U_13161,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_13161,tc_HOL_Obool))),U_13162)))),c_member(U_13161)))),
inference(clausify,[status(thm)],[f_3359_2]) ).
fof(f_3360_1,plain,
! [V_i_2,V_P_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),V_P_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))),
inference(fof_nnf,[status(thm)],[fact_finite__M__bounded__by__nat]) ).
fof(f_3360_2,plain,
! [U_13164,U_13163] : 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_13163)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13164))))),
inference(variable_rename,[status(thm)],[f_3360_1]) ).
cnf(f_3360_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_13163)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13164))))),
inference(clausify,[status(thm)],[f_3360_2]) ).
fof(f_3361_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_3361_2,plain,
! [U_13171,U_13170,U_13169,U_13168,U_13167,U_13166,U_13165] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13166,U_13165),hAPP(hAPP(c_COMBS(U_13166,tc_fun(U_13168,tc_HOL_Obool),U_13165),hAPP(hAPP(c_COMBB(tc_fun(U_13168,U_13165),tc_fun(tc_fun(U_13168,tc_HOL_Obool),U_13165),U_13166),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13168,U_13165)),U_13170)),hAPP(hAPP(c_COMBB(tc_fun(U_13168,tc_HOL_Obool),tc_fun(U_13168,tc_HOL_Obool),U_13166),c_Set_OCollect(U_13168)),hAPP(hAPP(c_COMBB(tc_fun(U_13168,tc_HOL_Obool),tc_fun(U_13168,tc_HOL_Obool),U_13166),hAPP(c_COMBS(U_13168,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13168),c_fconj),hAPP(hAPP(c_COMBC(U_13168,tc_fun(U_13168,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13168)),U_13169)))),U_13171)))),U_13167) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13168,U_13165),hAPP(hAPP(c_COMBS(U_13168,tc_fun(U_13166,tc_HOL_Obool),U_13165),hAPP(hAPP(c_COMBB(tc_fun(U_13166,U_13165),tc_fun(tc_fun(U_13166,tc_HOL_Obool),U_13165),U_13168),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13166,U_13165)),hAPP(c_COMBC(U_13166,U_13168,U_13165),U_13170))),hAPP(hAPP(c_COMBB(tc_fun(U_13166,tc_HOL_Obool),tc_fun(U_13166,tc_HOL_Obool),U_13168),c_Set_OCollect(U_13166)),hAPP(hAPP(c_COMBB(tc_fun(U_13166,tc_HOL_Obool),tc_fun(U_13166,tc_HOL_Obool),U_13168),hAPP(c_COMBS(U_13166,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13166),c_fconj),hAPP(hAPP(c_COMBC(U_13166,tc_fun(U_13166,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13166)),U_13167)))),hAPP(c_COMBC(U_13166,U_13168,tc_HOL_Obool),U_13171))))),U_13169)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13168),U_13169))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13166),U_13167))
| ~ class_Groups_Ocomm__monoid__add(U_13165) ),
inference(variable_rename,[status(thm)],[f_3361_1]) ).
cnf(f_3361_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13166,U_13165),hAPP(hAPP(c_COMBS(U_13166,tc_fun(U_13168,tc_HOL_Obool),U_13165),hAPP(hAPP(c_COMBB(tc_fun(U_13168,U_13165),tc_fun(tc_fun(U_13168,tc_HOL_Obool),U_13165),U_13166),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13168,U_13165)),U_13170)),hAPP(hAPP(c_COMBB(tc_fun(U_13168,tc_HOL_Obool),tc_fun(U_13168,tc_HOL_Obool),U_13166),c_Set_OCollect(U_13168)),hAPP(hAPP(c_COMBB(tc_fun(U_13168,tc_HOL_Obool),tc_fun(U_13168,tc_HOL_Obool),U_13166),hAPP(c_COMBS(U_13168,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13168),c_fconj),hAPP(hAPP(c_COMBC(U_13168,tc_fun(U_13168,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13168)),U_13169)))),U_13171)))),U_13167) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13168,U_13165),hAPP(hAPP(c_COMBS(U_13168,tc_fun(U_13166,tc_HOL_Obool),U_13165),hAPP(hAPP(c_COMBB(tc_fun(U_13166,U_13165),tc_fun(tc_fun(U_13166,tc_HOL_Obool),U_13165),U_13168),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13166,U_13165)),hAPP(c_COMBC(U_13166,U_13168,U_13165),U_13170))),hAPP(hAPP(c_COMBB(tc_fun(U_13166,tc_HOL_Obool),tc_fun(U_13166,tc_HOL_Obool),U_13168),c_Set_OCollect(U_13166)),hAPP(hAPP(c_COMBB(tc_fun(U_13166,tc_HOL_Obool),tc_fun(U_13166,tc_HOL_Obool),U_13168),hAPP(c_COMBS(U_13166,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13166),c_fconj),hAPP(hAPP(c_COMBC(U_13166,tc_fun(U_13166,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13166)),U_13167)))),hAPP(c_COMBC(U_13166,U_13168,tc_HOL_Obool),U_13171))))),U_13169)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13168),U_13169))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13166),U_13167))
| ~ class_Groups_Ocomm__monoid__add(U_13165) ),
inference(clausify,[status(thm)],[f_3361_2]) ).
fof(f_3362_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_3362_2,plain,
! [U_13175,U_13174,U_13173,U_13172] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13172,tc_fun(U_13173,tc_HOL_Obool)),U_13174),U_13175) = hAPP(c_Set_OCollect(U_13173),hAPP(hAPP(c_COMBB(tc_fun(U_13172,tc_HOL_Obool),tc_HOL_Obool,U_13173),c_HOL_OAll(U_13172)),hAPP(hAPP(c_COMBB(tc_fun(U_13172,tc_HOL_Obool),tc_fun(U_13172,tc_HOL_Obool),U_13173),hAPP(c_COMBS(U_13172,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13172),c_fimplies),hAPP(hAPP(c_COMBC(U_13172,tc_fun(U_13172,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13172)),U_13174)))),hAPP(hAPP(c_COMBC(U_13173,tc_fun(U_13172,tc_fun(U_13173,tc_HOL_Obool)),tc_fun(U_13172,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13173,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13172,tc_fun(U_13173,tc_HOL_Obool)),tc_fun(U_13172,tc_HOL_Obool)),U_13173),c_COMBB(tc_fun(U_13173,tc_HOL_Obool),tc_HOL_Obool,U_13172)),c_member(U_13173))),U_13175)))),
inference(variable_rename,[status(thm)],[f_3362_1]) ).
cnf(f_3362_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13172,tc_fun(U_13173,tc_HOL_Obool)),U_13174),U_13175) = hAPP(c_Set_OCollect(U_13173),hAPP(hAPP(c_COMBB(tc_fun(U_13172,tc_HOL_Obool),tc_HOL_Obool,U_13173),c_HOL_OAll(U_13172)),hAPP(hAPP(c_COMBB(tc_fun(U_13172,tc_HOL_Obool),tc_fun(U_13172,tc_HOL_Obool),U_13173),hAPP(c_COMBS(U_13172,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13172),c_fimplies),hAPP(hAPP(c_COMBC(U_13172,tc_fun(U_13172,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13172)),U_13174)))),hAPP(hAPP(c_COMBC(U_13173,tc_fun(U_13172,tc_fun(U_13173,tc_HOL_Obool)),tc_fun(U_13172,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13173,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13172,tc_fun(U_13173,tc_HOL_Obool)),tc_fun(U_13172,tc_HOL_Obool)),U_13173),c_COMBB(tc_fun(U_13173,tc_HOL_Obool),tc_HOL_Obool,U_13172)),c_member(U_13173))),U_13175)))),
inference(clausify,[status(thm)],[f_3362_2]) ).
fof(f_3363_1,plain,
! [V_S_2,V_g_2,V_f_2,V_P_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),V_P_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),V_P_2)))),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_P_2))))),
inference(fof_nnf,[status(thm)],[fact_if__image__distrib]) ).
fof(f_3363_2,plain,
! [U_13181,U_13180,U_13179,U_13178,U_13177,U_13176] : hAPP(c_Set_Oimage(U_13176,U_13177,hAPP(hAPP(c_COMBS(U_13176,U_13177,U_13177),hAPP(hAPP(c_COMBS(U_13176,U_13177,tc_fun(U_13177,U_13177)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13177,tc_fun(U_13177,U_13177)),U_13176),c_If(U_13177)),U_13178)),U_13179)),U_13180)),U_13181) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13177,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13176,U_13177,U_13179),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13176,tc_HOL_Obool)),U_13181),hAPP(c_Set_OCollect(U_13176),U_13178)))),hAPP(c_Set_Oimage(U_13176,U_13177,U_13180),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13176,tc_HOL_Obool)),U_13181),hAPP(c_Set_OCollect(U_13176),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13176),c_fNot),U_13178))))),
inference(variable_rename,[status(thm)],[f_3363_1]) ).
cnf(f_3363_3,plain,
hAPP(c_Set_Oimage(U_13176,U_13177,hAPP(hAPP(c_COMBS(U_13176,U_13177,U_13177),hAPP(hAPP(c_COMBS(U_13176,U_13177,tc_fun(U_13177,U_13177)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13177,tc_fun(U_13177,U_13177)),U_13176),c_If(U_13177)),U_13178)),U_13179)),U_13180)),U_13181) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13177,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13176,U_13177,U_13179),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13176,tc_HOL_Obool)),U_13181),hAPP(c_Set_OCollect(U_13176),U_13178)))),hAPP(c_Set_Oimage(U_13176,U_13177,U_13180),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13176,tc_HOL_Obool)),U_13181),hAPP(c_Set_OCollect(U_13176),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13176),c_fNot),U_13178))))),
inference(clausify,[status(thm)],[f_3363_2]) ).
fof(f_3364_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_3364_2,plain,
! [U_13185,U_13184,U_13183,U_13182] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13183),U_13182))
| U_13182 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_13183,U_13184),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_13185))) ),
inference(variable_rename,[status(thm)],[f_3364_1]) ).
cnf(f_3364_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13183),U_13182))
| U_13182 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_13183,U_13184),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_13185))) ),
inference(clausify,[status(thm)],[f_3364_2]) ).
fof(f_3365_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_3365_2,plain,
! [U_13190,U_13189,U_13188,U_13187,U_13186] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13187,U_13186),U_13189),hAPP(c_Set_OCollect(U_13187),hAPP(hAPP(c_COMBS(U_13187,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13187),c_fconj),hAPP(hAPP(c_COMBC(U_13187,tc_fun(U_13187,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13187)),U_13188))),hAPP(hAPP(c_COMBC(U_13187,tc_fun(U_13187,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13187)),U_13190)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13187,U_13186),hAPP(hAPP(c_COMBC(U_13187,U_13186,U_13186),hAPP(hAPP(c_COMBS(U_13187,U_13186,tc_fun(U_13186,U_13186)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13186,tc_fun(U_13186,U_13186)),U_13187),c_If(U_13186)),hAPP(hAPP(c_COMBC(U_13187,tc_fun(U_13187,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13187)),U_13190))),U_13189)),c_Groups_Ozero__class_Ozero(U_13186))),U_13188)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13187),U_13188))
| ~ class_Groups_Ocomm__monoid__add(U_13186) ),
inference(variable_rename,[status(thm)],[f_3365_1]) ).
cnf(f_3365_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13187,U_13186),U_13189),hAPP(c_Set_OCollect(U_13187),hAPP(hAPP(c_COMBS(U_13187,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13187),c_fconj),hAPP(hAPP(c_COMBC(U_13187,tc_fun(U_13187,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13187)),U_13188))),hAPP(hAPP(c_COMBC(U_13187,tc_fun(U_13187,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13187)),U_13190)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13187,U_13186),hAPP(hAPP(c_COMBC(U_13187,U_13186,U_13186),hAPP(hAPP(c_COMBS(U_13187,U_13186,tc_fun(U_13186,U_13186)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13186,tc_fun(U_13186,U_13186)),U_13187),c_If(U_13186)),hAPP(hAPP(c_COMBC(U_13187,tc_fun(U_13187,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13187)),U_13190))),U_13189)),c_Groups_Ozero__class_Ozero(U_13186))),U_13188)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13187),U_13188))
| ~ class_Groups_Ocomm__monoid__add(U_13186) ),
inference(clausify,[status(thm)],[f_3365_2]) ).
fof(f_3366_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_3366_2,plain,
! [U_13196,U_13195,U_13194,U_13193,U_13192,U_13191] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13192,U_13191),U_13194),U_13193) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13195,U_13191),hAPP(hAPP(c_COMBB(tc_fun(U_13192,tc_HOL_Obool),U_13191,U_13195),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13192,U_13191),U_13194)),hAPP(hAPP(c_COMBB(tc_fun(U_13192,tc_HOL_Obool),tc_fun(U_13192,tc_HOL_Obool),U_13195),c_Set_OCollect(U_13192)),hAPP(hAPP(c_COMBB(tc_fun(U_13192,tc_HOL_Obool),tc_fun(U_13192,tc_HOL_Obool),U_13195),hAPP(c_COMBS(U_13192,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13192),c_fconj),hAPP(hAPP(c_COMBC(U_13192,tc_fun(U_13192,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13192)),U_13193)))),hAPP(c_COMBC(U_13192,U_13195,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13195,tc_fun(U_13195,tc_HOL_Obool),U_13192),c_fequal),U_13196)))))),hAPP(c_Set_Oimage(U_13192,U_13195,U_13196),U_13193))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13192),U_13193))
| ~ class_Groups_Ocomm__monoid__add(U_13191) ),
inference(variable_rename,[status(thm)],[f_3366_1]) ).
cnf(f_3366_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13192,U_13191),U_13194),U_13193) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13195,U_13191),hAPP(hAPP(c_COMBB(tc_fun(U_13192,tc_HOL_Obool),U_13191,U_13195),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13192,U_13191),U_13194)),hAPP(hAPP(c_COMBB(tc_fun(U_13192,tc_HOL_Obool),tc_fun(U_13192,tc_HOL_Obool),U_13195),c_Set_OCollect(U_13192)),hAPP(hAPP(c_COMBB(tc_fun(U_13192,tc_HOL_Obool),tc_fun(U_13192,tc_HOL_Obool),U_13195),hAPP(c_COMBS(U_13192,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13192),c_fconj),hAPP(hAPP(c_COMBC(U_13192,tc_fun(U_13192,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13192)),U_13193)))),hAPP(c_COMBC(U_13192,U_13195,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13195,tc_fun(U_13195,tc_HOL_Obool),U_13192),c_fequal),U_13196)))))),hAPP(c_Set_Oimage(U_13192,U_13195,U_13196),U_13193))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13192),U_13193))
| ~ class_Groups_Ocomm__monoid__add(U_13191) ),
inference(clausify,[status(thm)],[f_3366_2]) ).
fof(f_3367_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_3367_2,plain,
! [U_13198,U_13197] :
( c_Complete__Lattice_OSup__class_OSup(U_13197,U_13198) = c_Complete__Lattice_OInf__class_OInf(U_13197,hAPP(c_Set_OCollect(U_13197),hAPP(hAPP(c_COMBB(tc_fun(U_13197,tc_HOL_Obool),tc_HOL_Obool,U_13197),c_HOL_OAll(U_13197)),hAPP(hAPP(c_COMBB(tc_fun(U_13197,tc_HOL_Obool),tc_fun(U_13197,tc_HOL_Obool),U_13197),hAPP(c_COMBS(U_13197,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13197),c_fimplies),hAPP(hAPP(c_COMBC(U_13197,tc_fun(U_13197,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13197)),U_13198)))),hAPP(c_COMBC(U_13197,U_13197,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_13197))))))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_13197) ),
inference(variable_rename,[status(thm)],[f_3367_1]) ).
cnf(f_3367_3,plain,
( c_Complete__Lattice_OSup__class_OSup(U_13197,U_13198) = c_Complete__Lattice_OInf__class_OInf(U_13197,hAPP(c_Set_OCollect(U_13197),hAPP(hAPP(c_COMBB(tc_fun(U_13197,tc_HOL_Obool),tc_HOL_Obool,U_13197),c_HOL_OAll(U_13197)),hAPP(hAPP(c_COMBB(tc_fun(U_13197,tc_HOL_Obool),tc_fun(U_13197,tc_HOL_Obool),U_13197),hAPP(c_COMBS(U_13197,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13197),c_fimplies),hAPP(hAPP(c_COMBC(U_13197,tc_fun(U_13197,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13197)),U_13198)))),hAPP(c_COMBC(U_13197,U_13197,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_13197))))))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_13197) ),
inference(clausify,[status(thm)],[f_3367_2]) ).
fof(f_3368_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_3368_2,plain,
! [U_13200,U_13199] :
( c_Complete__Lattice_OInf__class_OInf(U_13199,U_13200) = c_Complete__Lattice_OSup__class_OSup(U_13199,hAPP(c_Set_OCollect(U_13199),hAPP(hAPP(c_COMBB(tc_fun(U_13199,tc_HOL_Obool),tc_HOL_Obool,U_13199),c_HOL_OAll(U_13199)),hAPP(hAPP(c_COMBB(tc_fun(U_13199,tc_HOL_Obool),tc_fun(U_13199,tc_HOL_Obool),U_13199),hAPP(c_COMBS(U_13199,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13199),c_fimplies),hAPP(hAPP(c_COMBC(U_13199,tc_fun(U_13199,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13199)),U_13200)))),c_Orderings_Oord__class_Oless__eq(U_13199)))))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_13199) ),
inference(variable_rename,[status(thm)],[f_3368_1]) ).
cnf(f_3368_3,plain,
( c_Complete__Lattice_OInf__class_OInf(U_13199,U_13200) = c_Complete__Lattice_OSup__class_OSup(U_13199,hAPP(c_Set_OCollect(U_13199),hAPP(hAPP(c_COMBB(tc_fun(U_13199,tc_HOL_Obool),tc_HOL_Obool,U_13199),c_HOL_OAll(U_13199)),hAPP(hAPP(c_COMBB(tc_fun(U_13199,tc_HOL_Obool),tc_fun(U_13199,tc_HOL_Obool),U_13199),hAPP(c_COMBS(U_13199,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13199),c_fimplies),hAPP(hAPP(c_COMBC(U_13199,tc_fun(U_13199,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13199)),U_13200)))),c_Orderings_Oord__class_Oless__eq(U_13199)))))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_13199) ),
inference(clausify,[status(thm)],[f_3368_2]) ).
fof(f_3369_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_3369_2,plain,
! [U_13204,U_13203,U_13202,U_13201] : hAPP(c_Relation_OImage(U_13201,U_13202,U_13203),hAPP(hAPP(c_Set_Oinsert(U_13201),U_13204),c_Orderings_Obot__class_Obot(tc_fun(U_13201,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_13202),hAPP(hAPP(c_COMBC(U_13202,tc_fun(tc_prod(U_13201,U_13202),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_13201,U_13202),tc_fun(tc_fun(tc_prod(U_13201,U_13202),tc_HOL_Obool),tc_HOL_Obool),U_13202),c_member(tc_prod(U_13201,U_13202))),hAPP(c_Product__Type_OPair(U_13201,U_13202),U_13204))),U_13203)),
inference(variable_rename,[status(thm)],[f_3369_1]) ).
cnf(f_3369_3,plain,
hAPP(c_Relation_OImage(U_13201,U_13202,U_13203),hAPP(hAPP(c_Set_Oinsert(U_13201),U_13204),c_Orderings_Obot__class_Obot(tc_fun(U_13201,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_13202),hAPP(hAPP(c_COMBC(U_13202,tc_fun(tc_prod(U_13201,U_13202),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_13201,U_13202),tc_fun(tc_fun(tc_prod(U_13201,U_13202),tc_HOL_Obool),tc_HOL_Obool),U_13202),c_member(tc_prod(U_13201,U_13202))),hAPP(c_Product__Type_OPair(U_13201,U_13202),U_13204))),U_13203)),
inference(clausify,[status(thm)],[f_3369_2]) ).
fof(f_3370_1,plain,
! [V_g_2,V_f_2,V_P_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),V_P_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__cases]) ).
fof(f_3370_2,plain,
! [U_13210,U_13209,U_13208,U_13207,U_13206,U_13205] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13206,U_13205),hAPP(hAPP(c_COMBS(U_13206,U_13205,U_13205),hAPP(hAPP(c_COMBS(U_13206,U_13205,tc_fun(U_13205,U_13205)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13205,tc_fun(U_13205,U_13205)),U_13206),c_If(U_13205)),U_13208)),U_13209)),U_13210)),U_13207) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13205),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13206,U_13205),U_13209),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13206,tc_HOL_Obool)),U_13207),hAPP(c_Set_OCollect(U_13206),U_13208)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13206,U_13205),U_13210),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13206,tc_HOL_Obool)),U_13207),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13206,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13206),U_13208)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13206),U_13207))
| ~ class_Groups_Ocomm__monoid__add(U_13205) ),
inference(variable_rename,[status(thm)],[f_3370_1]) ).
cnf(f_3370_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13206,U_13205),hAPP(hAPP(c_COMBS(U_13206,U_13205,U_13205),hAPP(hAPP(c_COMBS(U_13206,U_13205,tc_fun(U_13205,U_13205)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13205,tc_fun(U_13205,U_13205)),U_13206),c_If(U_13205)),U_13208)),U_13209)),U_13210)),U_13207) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13205),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13206,U_13205),U_13209),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13206,tc_HOL_Obool)),U_13207),hAPP(c_Set_OCollect(U_13206),U_13208)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13206,U_13205),U_13210),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13206,tc_HOL_Obool)),U_13207),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13206,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13206),U_13208)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13206),U_13207))
| ~ class_Groups_Ocomm__monoid__add(U_13205) ),
inference(clausify,[status(thm)],[f_3370_2]) ).
fof(f_3371_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_3371_2,plain,
! [U_13212,U_13211] :
( 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_13211))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13212)))) = 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_13211))),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_13212)))))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_13211)) ),
inference(variable_rename,[status(thm)],[f_3371_1]) ).
cnf(f_3371_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_13211))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13212)))) = 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_13211))),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_13212)))))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_13211)) ),
inference(clausify,[status(thm)],[f_3371_2]) ).
fof(f_3372_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_3372_2,plain,
! [U_13214,U_13213] :
( 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_13213))),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_13214))))) != 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_13213)) ),
inference(variable_rename,[status(thm)],[f_3372_1]) ).
cnf(f_3372_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_13213))),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_13214))))) != 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_13213)) ),
inference(clausify,[status(thm)],[f_3372_2]) ).
fof(f_3373_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_3373_2,plain,
! [U_13221,U_13220,U_13219,U_13218,U_13217,U_13216] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13216,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13218,tc_HOL_Obool),tc_Nat_Onat,U_13216),c_Finite__Set_Ocard(U_13218)),hAPP(hAPP(c_COMBB(tc_fun(U_13218,tc_HOL_Obool),tc_fun(U_13218,tc_HOL_Obool),U_13216),c_Set_OCollect(U_13218)),hAPP(hAPP(c_COMBB(tc_fun(U_13218,tc_HOL_Obool),tc_fun(U_13218,tc_HOL_Obool),U_13216),hAPP(c_COMBS(U_13218,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13218),c_fconj),hAPP(hAPP(c_COMBC(U_13218,tc_fun(U_13218,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13218)),U_13219)))),U_13220)))),U_13217) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_13221),hAPP(c_Finite__Set_Ocard(U_13218),U_13219))
| ? [U_13215] :
( hAPP(c_Finite__Set_Ocard(U_13216),hAPP(c_Set_OCollect(U_13216),hAPP(hAPP(c_COMBS(U_13216,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13216),c_fconj),hAPP(hAPP(c_COMBC(U_13216,tc_fun(U_13216,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13216)),U_13217))),hAPP(hAPP(c_COMBC(U_13216,U_13218,tc_HOL_Obool),U_13220),U_13215)))) != U_13221
& hBOOL(hAPP(hAPP(c_member(U_13218),U_13215),U_13219)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13218),U_13219))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13216),U_13217)) ),
inference(variable_rename,[status(thm)],[f_3373_1]) ).
fof(f_3373_3,plain,
! [U_13221,U_13220,U_13219,U_13218,U_13217,U_13216] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13216,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13218,tc_HOL_Obool),tc_Nat_Onat,U_13216),c_Finite__Set_Ocard(U_13218)),hAPP(hAPP(c_COMBB(tc_fun(U_13218,tc_HOL_Obool),tc_fun(U_13218,tc_HOL_Obool),U_13216),c_Set_OCollect(U_13218)),hAPP(hAPP(c_COMBB(tc_fun(U_13218,tc_HOL_Obool),tc_fun(U_13218,tc_HOL_Obool),U_13216),hAPP(c_COMBS(U_13218,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13218),c_fconj),hAPP(hAPP(c_COMBC(U_13218,tc_fun(U_13218,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13218)),U_13219)))),U_13220)))),U_13217) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_13221),hAPP(c_Finite__Set_Ocard(U_13218),U_13219))
| ( hAPP(c_Finite__Set_Ocard(U_13216),hAPP(c_Set_OCollect(U_13216),hAPP(hAPP(c_COMBS(U_13216,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13216),c_fconj),hAPP(hAPP(c_COMBC(U_13216,tc_fun(U_13216,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13216)),U_13217))),hAPP(hAPP(c_COMBC(U_13216,U_13218,tc_HOL_Obool),U_13220),sK322(U_13221,U_13220,U_13219,U_13218,U_13217,U_13216))))) != U_13221
& hBOOL(hAPP(hAPP(c_member(U_13218),sK322(U_13221,U_13220,U_13219,U_13218,U_13217,U_13216)),U_13219)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13218),U_13219))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13216),U_13217)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK322]),skolemize(U_13215,sK322(U_13221,U_13220,U_13219,U_13218,U_13217,U_13216))],[f_3373_2]) ).
cnf(f_3373_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_13218),sK322(U_13221,U_13220,U_13219,U_13218,U_13217,U_13216)),U_13219))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13216,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13218,tc_HOL_Obool),tc_Nat_Onat,U_13216),c_Finite__Set_Ocard(U_13218)),hAPP(hAPP(c_COMBB(tc_fun(U_13218,tc_HOL_Obool),tc_fun(U_13218,tc_HOL_Obool),U_13216),c_Set_OCollect(U_13218)),hAPP(hAPP(c_COMBB(tc_fun(U_13218,tc_HOL_Obool),tc_fun(U_13218,tc_HOL_Obool),U_13216),hAPP(c_COMBS(U_13218,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13218),c_fconj),hAPP(hAPP(c_COMBC(U_13218,tc_fun(U_13218,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13218)),U_13219)))),U_13220)))),U_13217) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_13221),hAPP(c_Finite__Set_Ocard(U_13218),U_13219))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13218),U_13219))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13216),U_13217)) ),
inference(clausify,[status(thm)],[f_3373_3]) ).
cnf(f_3373_5,plain,
( hAPP(c_Finite__Set_Ocard(U_13216),hAPP(c_Set_OCollect(U_13216),hAPP(hAPP(c_COMBS(U_13216,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13216),c_fconj),hAPP(hAPP(c_COMBC(U_13216,tc_fun(U_13216,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13216)),U_13217))),hAPP(hAPP(c_COMBC(U_13216,U_13218,tc_HOL_Obool),U_13220),sK322(U_13221,U_13220,U_13219,U_13218,U_13217,U_13216))))) != U_13221
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13216,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13218,tc_HOL_Obool),tc_Nat_Onat,U_13216),c_Finite__Set_Ocard(U_13218)),hAPP(hAPP(c_COMBB(tc_fun(U_13218,tc_HOL_Obool),tc_fun(U_13218,tc_HOL_Obool),U_13216),c_Set_OCollect(U_13218)),hAPP(hAPP(c_COMBB(tc_fun(U_13218,tc_HOL_Obool),tc_fun(U_13218,tc_HOL_Obool),U_13216),hAPP(c_COMBS(U_13218,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13218),c_fconj),hAPP(hAPP(c_COMBC(U_13218,tc_fun(U_13218,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13218)),U_13219)))),U_13220)))),U_13217) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_13221),hAPP(c_Finite__Set_Ocard(U_13218),U_13219))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13218),U_13219))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13216),U_13217)) ),
inference(clausify,[status(thm)],[f_3373_3]) ).
fof(f_3374_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_3374_2,plain,
! [U_13224,U_13223,U_13222] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_13222),U_13224),c_Big__Operators_Olattice_OInf__fin(U_13222,c_Orderings_Oord__class_Omin(U_13222),U_13223)) = c_Big__Operators_Olattice_OInf__fin(U_13222,c_Orderings_Oord__class_Omin(U_13222),hAPP(c_Set_OCollect(U_13222),hAPP(hAPP(c_COMBB(tc_fun(U_13222,tc_HOL_Obool),tc_HOL_Obool,U_13222),c_HOL_OEx(U_13222)),hAPP(hAPP(c_COMBC(U_13222,tc_fun(U_13222,tc_HOL_Obool),tc_fun(U_13222,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13222,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13222,tc_HOL_Obool),tc_fun(U_13222,tc_HOL_Obool)),U_13222),c_COMBS(U_13222,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13222,tc_HOL_Obool),tc_fun(U_13222,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13222),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13222),c_fconj)),hAPP(hAPP(c_COMBC(U_13222,tc_fun(U_13222,U_13222),tc_fun(U_13222,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13222,tc_HOL_Obool),tc_fun(tc_fun(U_13222,U_13222),tc_fun(U_13222,tc_HOL_Obool)),U_13222),c_COMBB(U_13222,tc_HOL_Obool,U_13222)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_13222),U_13224))))),hAPP(hAPP(c_COMBC(U_13222,tc_fun(U_13222,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13222)),U_13223)))))
| U_13223 = c_Orderings_Obot__class_Obot(tc_fun(U_13222,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13222),U_13223))
| ~ class_Orderings_Olinorder(U_13222) ),
inference(variable_rename,[status(thm)],[f_3374_1]) ).
cnf(f_3374_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_13222),U_13224),c_Big__Operators_Olattice_OInf__fin(U_13222,c_Orderings_Oord__class_Omin(U_13222),U_13223)) = c_Big__Operators_Olattice_OInf__fin(U_13222,c_Orderings_Oord__class_Omin(U_13222),hAPP(c_Set_OCollect(U_13222),hAPP(hAPP(c_COMBB(tc_fun(U_13222,tc_HOL_Obool),tc_HOL_Obool,U_13222),c_HOL_OEx(U_13222)),hAPP(hAPP(c_COMBC(U_13222,tc_fun(U_13222,tc_HOL_Obool),tc_fun(U_13222,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13222,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13222,tc_HOL_Obool),tc_fun(U_13222,tc_HOL_Obool)),U_13222),c_COMBS(U_13222,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13222,tc_HOL_Obool),tc_fun(U_13222,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13222),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13222),c_fconj)),hAPP(hAPP(c_COMBC(U_13222,tc_fun(U_13222,U_13222),tc_fun(U_13222,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13222,tc_HOL_Obool),tc_fun(tc_fun(U_13222,U_13222),tc_fun(U_13222,tc_HOL_Obool)),U_13222),c_COMBB(U_13222,tc_HOL_Obool,U_13222)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_13222),U_13224))))),hAPP(hAPP(c_COMBC(U_13222,tc_fun(U_13222,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13222)),U_13223)))))
| U_13223 = c_Orderings_Obot__class_Obot(tc_fun(U_13222,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13222),U_13223))
| ~ class_Orderings_Olinorder(U_13222) ),
inference(clausify,[status(thm)],[f_3374_2]) ).
fof(f_3375_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_3375_2,plain,
! [U_13227,U_13226,U_13225] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_13225),U_13227),c_Big__Operators_Olattice_OSup__fin(U_13225,c_Orderings_Oord__class_Omax(U_13225),U_13226)) = c_Big__Operators_Olattice_OSup__fin(U_13225,c_Orderings_Oord__class_Omax(U_13225),hAPP(c_Set_OCollect(U_13225),hAPP(hAPP(c_COMBB(tc_fun(U_13225,tc_HOL_Obool),tc_HOL_Obool,U_13225),c_HOL_OEx(U_13225)),hAPP(hAPP(c_COMBC(U_13225,tc_fun(U_13225,tc_HOL_Obool),tc_fun(U_13225,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13225,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13225,tc_HOL_Obool),tc_fun(U_13225,tc_HOL_Obool)),U_13225),c_COMBS(U_13225,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13225,tc_HOL_Obool),tc_fun(U_13225,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13225),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13225),c_fconj)),hAPP(hAPP(c_COMBC(U_13225,tc_fun(U_13225,U_13225),tc_fun(U_13225,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13225,tc_HOL_Obool),tc_fun(tc_fun(U_13225,U_13225),tc_fun(U_13225,tc_HOL_Obool)),U_13225),c_COMBB(U_13225,tc_HOL_Obool,U_13225)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_13225),U_13227))))),hAPP(hAPP(c_COMBC(U_13225,tc_fun(U_13225,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13225)),U_13226)))))
| U_13226 = c_Orderings_Obot__class_Obot(tc_fun(U_13225,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13225),U_13226))
| ~ class_Orderings_Olinorder(U_13225) ),
inference(variable_rename,[status(thm)],[f_3375_1]) ).
cnf(f_3375_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_13225),U_13227),c_Big__Operators_Olattice_OSup__fin(U_13225,c_Orderings_Oord__class_Omax(U_13225),U_13226)) = c_Big__Operators_Olattice_OSup__fin(U_13225,c_Orderings_Oord__class_Omax(U_13225),hAPP(c_Set_OCollect(U_13225),hAPP(hAPP(c_COMBB(tc_fun(U_13225,tc_HOL_Obool),tc_HOL_Obool,U_13225),c_HOL_OEx(U_13225)),hAPP(hAPP(c_COMBC(U_13225,tc_fun(U_13225,tc_HOL_Obool),tc_fun(U_13225,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13225,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13225,tc_HOL_Obool),tc_fun(U_13225,tc_HOL_Obool)),U_13225),c_COMBS(U_13225,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13225,tc_HOL_Obool),tc_fun(U_13225,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13225),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13225),c_fconj)),hAPP(hAPP(c_COMBC(U_13225,tc_fun(U_13225,U_13225),tc_fun(U_13225,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13225,tc_HOL_Obool),tc_fun(tc_fun(U_13225,U_13225),tc_fun(U_13225,tc_HOL_Obool)),U_13225),c_COMBB(U_13225,tc_HOL_Obool,U_13225)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_13225),U_13227))))),hAPP(hAPP(c_COMBC(U_13225,tc_fun(U_13225,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13225)),U_13226)))))
| U_13226 = c_Orderings_Obot__class_Obot(tc_fun(U_13225,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13225),U_13226))
| ~ class_Orderings_Olinorder(U_13225) ),
inference(clausify,[status(thm)],[f_3375_2]) ).
fof(f_3376_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_3376_2,plain,
! [U_13229,U_13228] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13228,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_13228,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_13228,tc_HOL_Obool),tc_fun(U_13228,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_13228,tc_HOL_Obool))),U_13229))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13228),U_13229)) ),
inference(variable_rename,[status(thm)],[f_3376_1]) ).
cnf(f_3376_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13228,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_13228,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_13228,tc_HOL_Obool),tc_fun(U_13228,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_13228,tc_HOL_Obool))),U_13229))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13228),U_13229)) ),
inference(clausify,[status(thm)],[f_3376_2]) ).
fof(f_3377_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_3377_2,plain,
! [U_13231,U_13230] : hAPP(c_Set_OPow(U_13230),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13230,tc_HOL_Obool)),U_13231)) = hAPP(c_Set_OCollect(tc_fun(U_13230,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13230,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_13230,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_13230,tc_HOL_Obool),tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13230,tc_HOL_Obool)),c_COMBS(tc_fun(U_13230,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_13230,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_13230,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_13230,tc_HOL_Obool),tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_fun(U_13230,tc_HOL_Obool)),tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_fun(U_13230,tc_HOL_Obool)),tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13230,tc_HOL_Obool)),c_COMBB(tc_fun(U_13230,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13230,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_13230,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13230,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_13230,tc_HOL_Obool)),U_13231)),c_Set_OPow(U_13230))))),
inference(variable_rename,[status(thm)],[f_3377_1]) ).
cnf(f_3377_3,plain,
hAPP(c_Set_OPow(U_13230),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13230,tc_HOL_Obool)),U_13231)) = hAPP(c_Set_OCollect(tc_fun(U_13230,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13230,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_13230,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_13230,tc_HOL_Obool),tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13230,tc_HOL_Obool)),c_COMBS(tc_fun(U_13230,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_13230,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_13230,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_13230,tc_HOL_Obool),tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_fun(U_13230,tc_HOL_Obool)),tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_fun(U_13230,tc_HOL_Obool)),tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13230,tc_HOL_Obool)),c_COMBB(tc_fun(U_13230,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13230,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_13230,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13230,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13230,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_13230,tc_HOL_Obool)),U_13231)),c_Set_OPow(U_13230))))),
inference(clausify,[status(thm)],[f_3377_2]) ).
fof(f_3378_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_3378_2,plain,
! [U_13233,U_13232] : hAPP(c_Set_OPow(U_13232),U_13233) = hAPP(c_Set_OCollect(tc_fun(U_13232,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_13232,tc_HOL_Obool),tc_fun(U_13232,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_13232,tc_HOL_Obool))),U_13233)),
inference(variable_rename,[status(thm)],[f_3378_1]) ).
cnf(f_3378_3,plain,
hAPP(c_Set_OPow(U_13232),U_13233) = hAPP(c_Set_OCollect(tc_fun(U_13232,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_13232,tc_HOL_Obool),tc_fun(U_13232,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_13232,tc_HOL_Obool))),U_13233)),
inference(clausify,[status(thm)],[f_3378_2]) ).
fof(f_3379_1,plain,
! [V_f_2,T_c,V_P_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_b)),c_fequal)),V_f_2)))),V_P_2)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) ),
inference(fof_nnf,[status(thm)],[fact_finite__image__set]) ).
fof(f_3379_2,plain,
! [U_13237,U_13236,U_13235,U_13234] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13236),hAPP(c_Set_OCollect(U_13236),hAPP(hAPP(c_COMBB(tc_fun(U_13234,tc_HOL_Obool),tc_HOL_Obool,U_13236),c_HOL_OEx(U_13234)),hAPP(hAPP(c_COMBC(U_13236,tc_fun(U_13234,tc_HOL_Obool),tc_fun(U_13234,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13234,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13234,tc_HOL_Obool),tc_fun(U_13234,tc_HOL_Obool)),U_13236),c_COMBS(U_13234,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13234,tc_HOL_Obool),tc_fun(U_13234,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13236),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13234),c_fconj)),hAPP(hAPP(c_COMBC(U_13236,tc_fun(U_13234,U_13236),tc_fun(U_13234,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13236,tc_HOL_Obool),tc_fun(tc_fun(U_13234,U_13236),tc_fun(U_13234,tc_HOL_Obool)),U_13236),c_COMBB(U_13236,tc_HOL_Obool,U_13234)),c_fequal)),U_13237)))),U_13235)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13234),hAPP(c_Set_OCollect(U_13234),U_13235))) ),
inference(variable_rename,[status(thm)],[f_3379_1]) ).
cnf(f_3379_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13236),hAPP(c_Set_OCollect(U_13236),hAPP(hAPP(c_COMBB(tc_fun(U_13234,tc_HOL_Obool),tc_HOL_Obool,U_13236),c_HOL_OEx(U_13234)),hAPP(hAPP(c_COMBC(U_13236,tc_fun(U_13234,tc_HOL_Obool),tc_fun(U_13234,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13234,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13234,tc_HOL_Obool),tc_fun(U_13234,tc_HOL_Obool)),U_13236),c_COMBS(U_13234,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13234,tc_HOL_Obool),tc_fun(U_13234,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13236),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13234),c_fconj)),hAPP(hAPP(c_COMBC(U_13236,tc_fun(U_13234,U_13236),tc_fun(U_13234,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13236,tc_HOL_Obool),tc_fun(tc_fun(U_13234,U_13236),tc_fun(U_13234,tc_HOL_Obool)),U_13236),c_COMBB(U_13236,tc_HOL_Obool,U_13234)),c_fequal)),U_13237)))),U_13235)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13234),hAPP(c_Set_OCollect(U_13234),U_13235))) ),
inference(clausify,[status(thm)],[f_3379_2]) ).
fof(f_3380_1,plain,
! [V_Q_2,T_c,V_P_2,T_b] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2)))))
| ? [B_y] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_y))))
& hBOOL(hAPP(V_P_2,B_y)) ) )
& ( ! [B_y] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_y))))
| ~ hBOOL(hAPP(V_P_2,B_y)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) ),
inference(fof_nnf,[status(thm)],[fact_finite__Collect__bounded__ex]) ).
fof(f_3380_2,plain,
! [U_13243,U_13242,U_13241,U_13240] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13242),hAPP(c_Set_OCollect(U_13242),hAPP(hAPP(c_COMBB(tc_fun(U_13240,tc_HOL_Obool),tc_HOL_Obool,U_13242),c_HOL_OEx(U_13240)),hAPP(hAPP(c_COMBB(tc_fun(U_13240,tc_HOL_Obool),tc_fun(U_13240,tc_HOL_Obool),U_13242),hAPP(c_COMBS(U_13240,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13240),c_fconj),U_13241))),U_13243)))))
| ? [U_13239] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13242),hAPP(c_Set_OCollect(U_13242),hAPP(hAPP(c_COMBC(U_13242,U_13240,tc_HOL_Obool),U_13243),U_13239))))
& hBOOL(hAPP(U_13241,U_13239)) ) )
& ( ! [U_13238] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13242),hAPP(c_Set_OCollect(U_13242),hAPP(hAPP(c_COMBC(U_13242,U_13240,tc_HOL_Obool),U_13243),U_13238))))
| ~ hBOOL(hAPP(U_13241,U_13238)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13242),hAPP(c_Set_OCollect(U_13242),hAPP(hAPP(c_COMBB(tc_fun(U_13240,tc_HOL_Obool),tc_HOL_Obool,U_13242),c_HOL_OEx(U_13240)),hAPP(hAPP(c_COMBB(tc_fun(U_13240,tc_HOL_Obool),tc_fun(U_13240,tc_HOL_Obool),U_13242),hAPP(c_COMBS(U_13240,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13240),c_fconj),U_13241))),U_13243))))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13240),hAPP(c_Set_OCollect(U_13240),U_13241))) ),
inference(variable_rename,[status(thm)],[f_3380_1]) ).
fof(f_3380_3,plain,
! [U_13243,U_13242,U_13241,U_13240] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13242),hAPP(c_Set_OCollect(U_13242),hAPP(hAPP(c_COMBB(tc_fun(U_13240,tc_HOL_Obool),tc_HOL_Obool,U_13242),c_HOL_OEx(U_13240)),hAPP(hAPP(c_COMBB(tc_fun(U_13240,tc_HOL_Obool),tc_fun(U_13240,tc_HOL_Obool),U_13242),hAPP(c_COMBS(U_13240,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13240),c_fconj),U_13241))),U_13243)))))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13242),hAPP(c_Set_OCollect(U_13242),hAPP(hAPP(c_COMBC(U_13242,U_13240,tc_HOL_Obool),U_13243),sK323(U_13243,U_13242,U_13241,U_13240)))))
& hBOOL(hAPP(U_13241,sK323(U_13243,U_13242,U_13241,U_13240))) ) )
& ( ! [U_13238] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13242),hAPP(c_Set_OCollect(U_13242),hAPP(hAPP(c_COMBC(U_13242,U_13240,tc_HOL_Obool),U_13243),U_13238))))
| ~ hBOOL(hAPP(U_13241,U_13238)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13242),hAPP(c_Set_OCollect(U_13242),hAPP(hAPP(c_COMBB(tc_fun(U_13240,tc_HOL_Obool),tc_HOL_Obool,U_13242),c_HOL_OEx(U_13240)),hAPP(hAPP(c_COMBB(tc_fun(U_13240,tc_HOL_Obool),tc_fun(U_13240,tc_HOL_Obool),U_13242),hAPP(c_COMBS(U_13240,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13240),c_fconj),U_13241))),U_13243))))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13240),hAPP(c_Set_OCollect(U_13240),U_13241))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK323]),skolemize(U_13239,sK323(U_13243,U_13242,U_13241,U_13240))],[f_3380_2]) ).
cnf(f_3380_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13242),hAPP(c_Set_OCollect(U_13242),hAPP(hAPP(c_COMBC(U_13242,U_13240,tc_HOL_Obool),U_13243),U_13238))))
| ~ hBOOL(hAPP(U_13241,U_13238))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13242),hAPP(c_Set_OCollect(U_13242),hAPP(hAPP(c_COMBB(tc_fun(U_13240,tc_HOL_Obool),tc_HOL_Obool,U_13242),c_HOL_OEx(U_13240)),hAPP(hAPP(c_COMBB(tc_fun(U_13240,tc_HOL_Obool),tc_fun(U_13240,tc_HOL_Obool),U_13242),hAPP(c_COMBS(U_13240,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13240),c_fconj),U_13241))),U_13243)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13240),hAPP(c_Set_OCollect(U_13240),U_13241))) ),
inference(clausify,[status(thm)],[f_3380_3]) ).
cnf(f_3380_5,plain,
( hBOOL(hAPP(U_13241,sK323(U_13243,U_13242,U_13241,U_13240)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_13242),hAPP(c_Set_OCollect(U_13242),hAPP(hAPP(c_COMBB(tc_fun(U_13240,tc_HOL_Obool),tc_HOL_Obool,U_13242),c_HOL_OEx(U_13240)),hAPP(hAPP(c_COMBB(tc_fun(U_13240,tc_HOL_Obool),tc_fun(U_13240,tc_HOL_Obool),U_13242),hAPP(c_COMBS(U_13240,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13240),c_fconj),U_13241))),U_13243)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13240),hAPP(c_Set_OCollect(U_13240),U_13241))) ),
inference(clausify,[status(thm)],[f_3380_3]) ).
cnf(f_3380_6,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13242),hAPP(c_Set_OCollect(U_13242),hAPP(hAPP(c_COMBC(U_13242,U_13240,tc_HOL_Obool),U_13243),sK323(U_13243,U_13242,U_13241,U_13240)))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_13242),hAPP(c_Set_OCollect(U_13242),hAPP(hAPP(c_COMBB(tc_fun(U_13240,tc_HOL_Obool),tc_HOL_Obool,U_13242),c_HOL_OEx(U_13240)),hAPP(hAPP(c_COMBB(tc_fun(U_13240,tc_HOL_Obool),tc_fun(U_13240,tc_HOL_Obool),U_13242),hAPP(c_COMBS(U_13240,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13240),c_fconj),U_13241))),U_13243)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13240),hAPP(c_Set_OCollect(U_13240),U_13241))) ),
inference(clausify,[status(thm)],[f_3380_3]) ).
fof(f_3381_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_3381_2,plain,
! [U_13245,U_13244] : c_Fun_Oinj__on(tc_fun(U_13244,U_13245),tc_fun(tc_prod(U_13244,U_13245),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13244,U_13245),tc_HOL_Obool),tc_fun(tc_prod(U_13244,U_13245),tc_HOL_Obool),tc_fun(U_13244,U_13245)),c_Set_OCollect(tc_prod(U_13244,U_13245))),hAPP(hAPP(c_COMBB(tc_fun(U_13244,tc_fun(U_13245,tc_HOL_Obool)),tc_fun(tc_prod(U_13244,U_13245),tc_HOL_Obool),tc_fun(U_13244,U_13245)),c_Product__Type_Oprod_Oprod__case(U_13244,U_13245,tc_HOL_Obool)),hAPP(c_COMBB(U_13245,tc_fun(U_13245,tc_HOL_Obool),U_13244),hAPP(c_COMBC(U_13245,U_13245,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13244,U_13245),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_3381_1]) ).
cnf(f_3381_3,plain,
c_Fun_Oinj__on(tc_fun(U_13244,U_13245),tc_fun(tc_prod(U_13244,U_13245),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13244,U_13245),tc_HOL_Obool),tc_fun(tc_prod(U_13244,U_13245),tc_HOL_Obool),tc_fun(U_13244,U_13245)),c_Set_OCollect(tc_prod(U_13244,U_13245))),hAPP(hAPP(c_COMBB(tc_fun(U_13244,tc_fun(U_13245,tc_HOL_Obool)),tc_fun(tc_prod(U_13244,U_13245),tc_HOL_Obool),tc_fun(U_13244,U_13245)),c_Product__Type_Oprod_Oprod__case(U_13244,U_13245,tc_HOL_Obool)),hAPP(c_COMBB(U_13245,tc_fun(U_13245,tc_HOL_Obool),U_13244),hAPP(c_COMBC(U_13245,U_13245,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13244,U_13245),tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_3381_2]) ).
fof(f_3382_1,plain,
! [V_P_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J]) ).
fof(f_3382_2,plain,
! [U_13246] : 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_13246))),
inference(variable_rename,[status(thm)],[f_3382_1]) ).
cnf(f_3382_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_13246))),
inference(clausify,[status(thm)],[f_3382_2]) ).
fof(f_3383_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_3383_2,plain,
! [U_13247] : c_Wellfounded_Ofinite__psubset(U_13247) = hAPP(c_Set_OCollect(tc_prod(tc_fun(U_13247,tc_HOL_Obool),tc_fun(U_13247,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(U_13247,tc_HOL_Obool),tc_fun(U_13247,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_13247,tc_HOL_Obool),tc_fun(tc_fun(U_13247,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13247,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13247,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_13247,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13247,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13247,tc_HOL_Obool)),c_COMBS(tc_fun(U_13247,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13247,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13247,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_13247,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_13247,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(U_13247,tc_HOL_Obool))))),c_Finite__Set_Ofinite(U_13247)))),
inference(variable_rename,[status(thm)],[f_3383_1]) ).
cnf(f_3383_3,plain,
c_Wellfounded_Ofinite__psubset(U_13247) = hAPP(c_Set_OCollect(tc_prod(tc_fun(U_13247,tc_HOL_Obool),tc_fun(U_13247,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(U_13247,tc_HOL_Obool),tc_fun(U_13247,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_13247,tc_HOL_Obool),tc_fun(tc_fun(U_13247,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13247,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13247,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_13247,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13247,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13247,tc_HOL_Obool)),c_COMBS(tc_fun(U_13247,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13247,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13247,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_13247,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_13247,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(U_13247,tc_HOL_Obool))))),c_Finite__Set_Ofinite(U_13247)))),
inference(clausify,[status(thm)],[f_3383_2]) ).
fof(f_3384_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_3384_2,plain,
! [U_13251,U_13250,U_13249,U_13248] : hAPP(hAPP(c_Relation_Oinv__image(U_13248,U_13249),U_13250),U_13251) = hAPP(c_Set_OCollect(tc_prod(U_13249,U_13249)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13249,U_13249,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13249,tc_fun(tc_prod(U_13248,U_13248),tc_HOL_Obool),tc_fun(U_13249,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13249,tc_fun(tc_fun(tc_prod(U_13248,U_13248),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13248,U_13248),tc_HOL_Obool),tc_fun(U_13249,tc_HOL_Obool)),U_13249),c_COMBC(U_13249,tc_fun(tc_prod(U_13248,U_13248),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13249,tc_prod(U_13248,U_13248)),tc_fun(U_13249,tc_fun(tc_fun(tc_prod(U_13248,U_13248),tc_HOL_Obool),tc_HOL_Obool)),U_13249),hAPP(c_COMBB(tc_prod(U_13248,U_13248),tc_fun(tc_fun(tc_prod(U_13248,U_13248),tc_HOL_Obool),tc_HOL_Obool),U_13249),c_member(tc_prod(U_13248,U_13248)))),hAPP(hAPP(c_COMBC(U_13249,tc_fun(U_13249,U_13248),tc_fun(U_13249,tc_prod(U_13248,U_13248))),hAPP(hAPP(c_COMBB(tc_fun(U_13248,tc_prod(U_13248,U_13248)),tc_fun(tc_fun(U_13249,U_13248),tc_fun(U_13249,tc_prod(U_13248,U_13248))),U_13249),c_COMBB(U_13248,tc_prod(U_13248,U_13248),U_13249)),hAPP(hAPP(c_COMBB(U_13248,tc_fun(U_13248,tc_prod(U_13248,U_13248)),U_13249),c_Product__Type_OPair(U_13248,U_13248)),U_13251))),U_13251)))),U_13250))),
inference(variable_rename,[status(thm)],[f_3384_1]) ).
cnf(f_3384_3,plain,
hAPP(hAPP(c_Relation_Oinv__image(U_13248,U_13249),U_13250),U_13251) = hAPP(c_Set_OCollect(tc_prod(U_13249,U_13249)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13249,U_13249,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13249,tc_fun(tc_prod(U_13248,U_13248),tc_HOL_Obool),tc_fun(U_13249,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13249,tc_fun(tc_fun(tc_prod(U_13248,U_13248),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13248,U_13248),tc_HOL_Obool),tc_fun(U_13249,tc_HOL_Obool)),U_13249),c_COMBC(U_13249,tc_fun(tc_prod(U_13248,U_13248),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13249,tc_prod(U_13248,U_13248)),tc_fun(U_13249,tc_fun(tc_fun(tc_prod(U_13248,U_13248),tc_HOL_Obool),tc_HOL_Obool)),U_13249),hAPP(c_COMBB(tc_prod(U_13248,U_13248),tc_fun(tc_fun(tc_prod(U_13248,U_13248),tc_HOL_Obool),tc_HOL_Obool),U_13249),c_member(tc_prod(U_13248,U_13248)))),hAPP(hAPP(c_COMBC(U_13249,tc_fun(U_13249,U_13248),tc_fun(U_13249,tc_prod(U_13248,U_13248))),hAPP(hAPP(c_COMBB(tc_fun(U_13248,tc_prod(U_13248,U_13248)),tc_fun(tc_fun(U_13249,U_13248),tc_fun(U_13249,tc_prod(U_13248,U_13248))),U_13249),c_COMBB(U_13248,tc_prod(U_13248,U_13248),U_13249)),hAPP(hAPP(c_COMBB(U_13248,tc_fun(U_13248,tc_prod(U_13248,U_13248)),U_13249),c_Product__Type_OPair(U_13248,U_13248)),U_13251))),U_13251)))),U_13250))),
inference(clausify,[status(thm)],[f_3384_2]) ).
fof(f_3385_1,plain,
! [V_P_2] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J]) ).
fof(f_3385_2,plain,
! [U_13252] : 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_13252)) = 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_13252),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[f_3385_1]) ).
cnf(f_3385_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_13252)) = 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_13252),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
inference(clausify,[status(thm)],[f_3385_2]) ).
fof(f_3386_1,plain,
! [V_P_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_P_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),V_P_2),c_Int_Onat)))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J]) ).
fof(f_3386_2,plain,
! [U_13253] : hAPP(c_Set_OCollect(tc_Nat_Onat),U_13253) = 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_13253),c_Int_Onat)))),
inference(variable_rename,[status(thm)],[f_3386_1]) ).
cnf(f_3386_3,plain,
hAPP(c_Set_OCollect(tc_Nat_Onat),U_13253) = 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_13253),c_Int_Onat)))),
inference(clausify,[status(thm)],[f_3386_2]) ).
fof(f_3387_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_3387_2,plain,
! [U_13256,U_13255,U_13254] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13254),U_13256),c_Big__Operators_Olinorder__class_OMax(U_13254,U_13255)) = c_Big__Operators_Olinorder__class_OMax(U_13254,hAPP(c_Set_OCollect(U_13254),hAPP(hAPP(c_COMBB(tc_fun(U_13254,tc_HOL_Obool),tc_HOL_Obool,U_13254),c_HOL_OEx(U_13254)),hAPP(hAPP(c_COMBC(U_13254,tc_fun(U_13254,tc_HOL_Obool),tc_fun(U_13254,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13254,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13254,tc_HOL_Obool),tc_fun(U_13254,tc_HOL_Obool)),U_13254),c_COMBS(U_13254,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13254,tc_HOL_Obool),tc_fun(U_13254,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13254),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13254),c_fconj)),hAPP(hAPP(c_COMBC(U_13254,tc_fun(U_13254,U_13254),tc_fun(U_13254,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13254,tc_HOL_Obool),tc_fun(tc_fun(U_13254,U_13254),tc_fun(U_13254,tc_HOL_Obool)),U_13254),c_COMBB(U_13254,tc_HOL_Obool,U_13254)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_13254),U_13256))))),hAPP(hAPP(c_COMBC(U_13254,tc_fun(U_13254,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13254)),U_13255)))))
| U_13255 = c_Orderings_Obot__class_Obot(tc_fun(U_13254,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13254),U_13255))
| ~ class_Groups_Olinordered__ab__semigroup__add(U_13254) ),
inference(variable_rename,[status(thm)],[f_3387_1]) ).
cnf(f_3387_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13254),U_13256),c_Big__Operators_Olinorder__class_OMax(U_13254,U_13255)) = c_Big__Operators_Olinorder__class_OMax(U_13254,hAPP(c_Set_OCollect(U_13254),hAPP(hAPP(c_COMBB(tc_fun(U_13254,tc_HOL_Obool),tc_HOL_Obool,U_13254),c_HOL_OEx(U_13254)),hAPP(hAPP(c_COMBC(U_13254,tc_fun(U_13254,tc_HOL_Obool),tc_fun(U_13254,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13254,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13254,tc_HOL_Obool),tc_fun(U_13254,tc_HOL_Obool)),U_13254),c_COMBS(U_13254,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13254,tc_HOL_Obool),tc_fun(U_13254,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13254),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13254),c_fconj)),hAPP(hAPP(c_COMBC(U_13254,tc_fun(U_13254,U_13254),tc_fun(U_13254,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13254,tc_HOL_Obool),tc_fun(tc_fun(U_13254,U_13254),tc_fun(U_13254,tc_HOL_Obool)),U_13254),c_COMBB(U_13254,tc_HOL_Obool,U_13254)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_13254),U_13256))))),hAPP(hAPP(c_COMBC(U_13254,tc_fun(U_13254,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13254)),U_13255)))))
| U_13255 = c_Orderings_Obot__class_Obot(tc_fun(U_13254,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13254),U_13255))
| ~ class_Groups_Olinordered__ab__semigroup__add(U_13254) ),
inference(clausify,[status(thm)],[f_3387_2]) ).
fof(f_3388_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_3388_2,plain,
! [U_13259,U_13258,U_13257] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13257),U_13259),c_Big__Operators_Olinorder__class_OMin(U_13257,U_13258)) = c_Big__Operators_Olinorder__class_OMin(U_13257,hAPP(c_Set_OCollect(U_13257),hAPP(hAPP(c_COMBB(tc_fun(U_13257,tc_HOL_Obool),tc_HOL_Obool,U_13257),c_HOL_OEx(U_13257)),hAPP(hAPP(c_COMBC(U_13257,tc_fun(U_13257,tc_HOL_Obool),tc_fun(U_13257,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13257,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13257,tc_HOL_Obool),tc_fun(U_13257,tc_HOL_Obool)),U_13257),c_COMBS(U_13257,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13257,tc_HOL_Obool),tc_fun(U_13257,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13257),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13257),c_fconj)),hAPP(hAPP(c_COMBC(U_13257,tc_fun(U_13257,U_13257),tc_fun(U_13257,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13257,tc_HOL_Obool),tc_fun(tc_fun(U_13257,U_13257),tc_fun(U_13257,tc_HOL_Obool)),U_13257),c_COMBB(U_13257,tc_HOL_Obool,U_13257)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_13257),U_13259))))),hAPP(hAPP(c_COMBC(U_13257,tc_fun(U_13257,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13257)),U_13258)))))
| U_13258 = c_Orderings_Obot__class_Obot(tc_fun(U_13257,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13257),U_13258))
| ~ class_Groups_Olinordered__ab__semigroup__add(U_13257) ),
inference(variable_rename,[status(thm)],[f_3388_1]) ).
cnf(f_3388_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13257),U_13259),c_Big__Operators_Olinorder__class_OMin(U_13257,U_13258)) = c_Big__Operators_Olinorder__class_OMin(U_13257,hAPP(c_Set_OCollect(U_13257),hAPP(hAPP(c_COMBB(tc_fun(U_13257,tc_HOL_Obool),tc_HOL_Obool,U_13257),c_HOL_OEx(U_13257)),hAPP(hAPP(c_COMBC(U_13257,tc_fun(U_13257,tc_HOL_Obool),tc_fun(U_13257,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13257,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13257,tc_HOL_Obool),tc_fun(U_13257,tc_HOL_Obool)),U_13257),c_COMBS(U_13257,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13257,tc_HOL_Obool),tc_fun(U_13257,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13257),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13257),c_fconj)),hAPP(hAPP(c_COMBC(U_13257,tc_fun(U_13257,U_13257),tc_fun(U_13257,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13257,tc_HOL_Obool),tc_fun(tc_fun(U_13257,U_13257),tc_fun(U_13257,tc_HOL_Obool)),U_13257),c_COMBB(U_13257,tc_HOL_Obool,U_13257)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_13257),U_13259))))),hAPP(hAPP(c_COMBC(U_13257,tc_fun(U_13257,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13257)),U_13258)))))
| U_13258 = c_Orderings_Obot__class_Obot(tc_fun(U_13257,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13257),U_13258))
| ~ class_Groups_Olinordered__ab__semigroup__add(U_13257) ),
inference(clausify,[status(thm)],[f_3388_2]) ).
fof(f_3389_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_3389_2,plain,
! [U_13262,U_13261,U_13260] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13260),c_Big__Operators_Olattice__class_OInf__fin(U_13260,U_13261)),c_Big__Operators_Olattice__class_OInf__fin(U_13260,U_13262)) = c_Big__Operators_Olattice__class_OInf__fin(U_13260,hAPP(c_Set_OCollect(U_13260),hAPP(hAPP(c_COMBB(tc_fun(U_13260,tc_HOL_Obool),tc_HOL_Obool,U_13260),c_HOL_OEx(U_13260)),hAPP(hAPP(c_COMBB(tc_fun(U_13260,tc_fun(U_13260,tc_HOL_Obool)),tc_fun(U_13260,tc_HOL_Obool),U_13260),hAPP(c_COMBB(tc_fun(U_13260,tc_HOL_Obool),tc_HOL_Obool,U_13260),c_HOL_OEx(U_13260))),hAPP(hAPP(c_COMBC(U_13260,tc_fun(U_13260,tc_fun(U_13260,tc_HOL_Obool)),tc_fun(U_13260,tc_fun(U_13260,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13260,tc_fun(tc_fun(U_13260,tc_HOL_Obool),tc_fun(U_13260,tc_HOL_Obool))),tc_fun(tc_fun(U_13260,tc_fun(U_13260,tc_HOL_Obool)),tc_fun(U_13260,tc_fun(U_13260,tc_HOL_Obool))),U_13260),c_COMBS(U_13260,tc_fun(U_13260,tc_HOL_Obool),tc_fun(U_13260,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13260,tc_fun(U_13260,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13260,tc_fun(tc_fun(U_13260,tc_HOL_Obool),tc_fun(U_13260,tc_HOL_Obool))),U_13260),hAPP(c_COMBB(tc_fun(U_13260,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13260,tc_HOL_Obool),tc_fun(U_13260,tc_HOL_Obool)),U_13260),c_COMBS(U_13260,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13260,tc_fun(U_13260,tc_HOL_Obool)),tc_fun(U_13260,tc_fun(U_13260,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13260),hAPP(c_COMBB(tc_fun(U_13260,tc_HOL_Obool),tc_fun(U_13260,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13260),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13260),c_fconj))),hAPP(hAPP(c_COMBC(U_13260,tc_fun(U_13260,tc_fun(U_13260,U_13260)),tc_fun(U_13260,tc_fun(U_13260,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13260,U_13260),tc_fun(U_13260,tc_HOL_Obool)),tc_fun(tc_fun(U_13260,tc_fun(U_13260,U_13260)),tc_fun(U_13260,tc_fun(U_13260,tc_HOL_Obool))),U_13260),c_COMBB(tc_fun(U_13260,U_13260),tc_fun(U_13260,tc_HOL_Obool),U_13260)),hAPP(hAPP(c_COMBB(tc_fun(U_13260,tc_HOL_Obool),tc_fun(tc_fun(U_13260,U_13260),tc_fun(U_13260,tc_HOL_Obool)),U_13260),c_COMBB(U_13260,tc_HOL_Obool,U_13260)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_13260)))))),hAPP(hAPP(c_COMBC(U_13260,tc_fun(U_13260,tc_HOL_Obool),tc_fun(U_13260,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13260,tc_HOL_Obool),tc_fun(U_13260,tc_HOL_Obool)),U_13260),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13260)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13260),c_fconj),hAPP(hAPP(c_COMBC(U_13260,tc_fun(U_13260,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13260)),U_13261)))),hAPP(hAPP(c_COMBC(U_13260,tc_fun(U_13260,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13260)),U_13262)))))))
| U_13262 = c_Orderings_Obot__class_Obot(tc_fun(U_13260,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13260),U_13262))
| U_13261 = c_Orderings_Obot__class_Obot(tc_fun(U_13260,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13260),U_13261))
| ~ class_Lattices_Odistrib__lattice(U_13260) ),
inference(variable_rename,[status(thm)],[f_3389_1]) ).
cnf(f_3389_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13260),c_Big__Operators_Olattice__class_OInf__fin(U_13260,U_13261)),c_Big__Operators_Olattice__class_OInf__fin(U_13260,U_13262)) = c_Big__Operators_Olattice__class_OInf__fin(U_13260,hAPP(c_Set_OCollect(U_13260),hAPP(hAPP(c_COMBB(tc_fun(U_13260,tc_HOL_Obool),tc_HOL_Obool,U_13260),c_HOL_OEx(U_13260)),hAPP(hAPP(c_COMBB(tc_fun(U_13260,tc_fun(U_13260,tc_HOL_Obool)),tc_fun(U_13260,tc_HOL_Obool),U_13260),hAPP(c_COMBB(tc_fun(U_13260,tc_HOL_Obool),tc_HOL_Obool,U_13260),c_HOL_OEx(U_13260))),hAPP(hAPP(c_COMBC(U_13260,tc_fun(U_13260,tc_fun(U_13260,tc_HOL_Obool)),tc_fun(U_13260,tc_fun(U_13260,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13260,tc_fun(tc_fun(U_13260,tc_HOL_Obool),tc_fun(U_13260,tc_HOL_Obool))),tc_fun(tc_fun(U_13260,tc_fun(U_13260,tc_HOL_Obool)),tc_fun(U_13260,tc_fun(U_13260,tc_HOL_Obool))),U_13260),c_COMBS(U_13260,tc_fun(U_13260,tc_HOL_Obool),tc_fun(U_13260,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13260,tc_fun(U_13260,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13260,tc_fun(tc_fun(U_13260,tc_HOL_Obool),tc_fun(U_13260,tc_HOL_Obool))),U_13260),hAPP(c_COMBB(tc_fun(U_13260,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13260,tc_HOL_Obool),tc_fun(U_13260,tc_HOL_Obool)),U_13260),c_COMBS(U_13260,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13260,tc_fun(U_13260,tc_HOL_Obool)),tc_fun(U_13260,tc_fun(U_13260,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13260),hAPP(c_COMBB(tc_fun(U_13260,tc_HOL_Obool),tc_fun(U_13260,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13260),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13260),c_fconj))),hAPP(hAPP(c_COMBC(U_13260,tc_fun(U_13260,tc_fun(U_13260,U_13260)),tc_fun(U_13260,tc_fun(U_13260,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13260,U_13260),tc_fun(U_13260,tc_HOL_Obool)),tc_fun(tc_fun(U_13260,tc_fun(U_13260,U_13260)),tc_fun(U_13260,tc_fun(U_13260,tc_HOL_Obool))),U_13260),c_COMBB(tc_fun(U_13260,U_13260),tc_fun(U_13260,tc_HOL_Obool),U_13260)),hAPP(hAPP(c_COMBB(tc_fun(U_13260,tc_HOL_Obool),tc_fun(tc_fun(U_13260,U_13260),tc_fun(U_13260,tc_HOL_Obool)),U_13260),c_COMBB(U_13260,tc_HOL_Obool,U_13260)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_13260)))))),hAPP(hAPP(c_COMBC(U_13260,tc_fun(U_13260,tc_HOL_Obool),tc_fun(U_13260,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13260,tc_HOL_Obool),tc_fun(U_13260,tc_HOL_Obool)),U_13260),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13260)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13260),c_fconj),hAPP(hAPP(c_COMBC(U_13260,tc_fun(U_13260,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13260)),U_13261)))),hAPP(hAPP(c_COMBC(U_13260,tc_fun(U_13260,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13260)),U_13262)))))))
| U_13262 = c_Orderings_Obot__class_Obot(tc_fun(U_13260,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13260),U_13262))
| U_13261 = c_Orderings_Obot__class_Obot(tc_fun(U_13260,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13260),U_13261))
| ~ class_Lattices_Odistrib__lattice(U_13260) ),
inference(clausify,[status(thm)],[f_3389_2]) ).
fof(f_3390_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_3390_2,plain,
! [U_13265,U_13264,U_13263] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13263),U_13265),c_Big__Operators_Olattice__class_OInf__fin(U_13263,U_13264)) = c_Big__Operators_Olattice__class_OInf__fin(U_13263,hAPP(c_Set_OCollect(U_13263),hAPP(hAPP(c_COMBB(tc_fun(U_13263,tc_HOL_Obool),tc_HOL_Obool,U_13263),c_HOL_OEx(U_13263)),hAPP(hAPP(c_COMBC(U_13263,tc_fun(U_13263,tc_HOL_Obool),tc_fun(U_13263,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13263,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13263,tc_HOL_Obool),tc_fun(U_13263,tc_HOL_Obool)),U_13263),c_COMBS(U_13263,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13263,tc_HOL_Obool),tc_fun(U_13263,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13263),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13263),c_fconj)),hAPP(hAPP(c_COMBC(U_13263,tc_fun(U_13263,U_13263),tc_fun(U_13263,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13263,tc_HOL_Obool),tc_fun(tc_fun(U_13263,U_13263),tc_fun(U_13263,tc_HOL_Obool)),U_13263),c_COMBB(U_13263,tc_HOL_Obool,U_13263)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13263),U_13265))))),hAPP(hAPP(c_COMBC(U_13263,tc_fun(U_13263,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13263)),U_13264)))))
| U_13264 = c_Orderings_Obot__class_Obot(tc_fun(U_13263,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13263),U_13264))
| ~ class_Lattices_Odistrib__lattice(U_13263) ),
inference(variable_rename,[status(thm)],[f_3390_1]) ).
cnf(f_3390_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13263),U_13265),c_Big__Operators_Olattice__class_OInf__fin(U_13263,U_13264)) = c_Big__Operators_Olattice__class_OInf__fin(U_13263,hAPP(c_Set_OCollect(U_13263),hAPP(hAPP(c_COMBB(tc_fun(U_13263,tc_HOL_Obool),tc_HOL_Obool,U_13263),c_HOL_OEx(U_13263)),hAPP(hAPP(c_COMBC(U_13263,tc_fun(U_13263,tc_HOL_Obool),tc_fun(U_13263,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13263,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13263,tc_HOL_Obool),tc_fun(U_13263,tc_HOL_Obool)),U_13263),c_COMBS(U_13263,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13263,tc_HOL_Obool),tc_fun(U_13263,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13263),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13263),c_fconj)),hAPP(hAPP(c_COMBC(U_13263,tc_fun(U_13263,U_13263),tc_fun(U_13263,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13263,tc_HOL_Obool),tc_fun(tc_fun(U_13263,U_13263),tc_fun(U_13263,tc_HOL_Obool)),U_13263),c_COMBB(U_13263,tc_HOL_Obool,U_13263)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13263),U_13265))))),hAPP(hAPP(c_COMBC(U_13263,tc_fun(U_13263,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13263)),U_13264)))))
| U_13264 = c_Orderings_Obot__class_Obot(tc_fun(U_13263,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13263),U_13264))
| ~ class_Lattices_Odistrib__lattice(U_13263) ),
inference(clausify,[status(thm)],[f_3390_2]) ).
fof(f_3391_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_3391_2,plain,
! [U_13268,U_13267,U_13266] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13266),U_13268),c_Big__Operators_Olattice__class_OSup__fin(U_13266,U_13267)) = c_Big__Operators_Olattice__class_OSup__fin(U_13266,hAPP(c_Set_OCollect(U_13266),hAPP(hAPP(c_COMBB(tc_fun(U_13266,tc_HOL_Obool),tc_HOL_Obool,U_13266),c_HOL_OEx(U_13266)),hAPP(hAPP(c_COMBC(U_13266,tc_fun(U_13266,tc_HOL_Obool),tc_fun(U_13266,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13266,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13266,tc_HOL_Obool),tc_fun(U_13266,tc_HOL_Obool)),U_13266),c_COMBS(U_13266,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13266,tc_HOL_Obool),tc_fun(U_13266,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13266),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13266),c_fconj)),hAPP(hAPP(c_COMBC(U_13266,tc_fun(U_13266,U_13266),tc_fun(U_13266,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13266,tc_HOL_Obool),tc_fun(tc_fun(U_13266,U_13266),tc_fun(U_13266,tc_HOL_Obool)),U_13266),c_COMBB(U_13266,tc_HOL_Obool,U_13266)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13266),U_13268))))),hAPP(hAPP(c_COMBC(U_13266,tc_fun(U_13266,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13266)),U_13267)))))
| U_13267 = c_Orderings_Obot__class_Obot(tc_fun(U_13266,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13266),U_13267))
| ~ class_Lattices_Odistrib__lattice(U_13266) ),
inference(variable_rename,[status(thm)],[f_3391_1]) ).
cnf(f_3391_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13266),U_13268),c_Big__Operators_Olattice__class_OSup__fin(U_13266,U_13267)) = c_Big__Operators_Olattice__class_OSup__fin(U_13266,hAPP(c_Set_OCollect(U_13266),hAPP(hAPP(c_COMBB(tc_fun(U_13266,tc_HOL_Obool),tc_HOL_Obool,U_13266),c_HOL_OEx(U_13266)),hAPP(hAPP(c_COMBC(U_13266,tc_fun(U_13266,tc_HOL_Obool),tc_fun(U_13266,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13266,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13266,tc_HOL_Obool),tc_fun(U_13266,tc_HOL_Obool)),U_13266),c_COMBS(U_13266,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13266,tc_HOL_Obool),tc_fun(U_13266,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13266),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13266),c_fconj)),hAPP(hAPP(c_COMBC(U_13266,tc_fun(U_13266,U_13266),tc_fun(U_13266,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13266,tc_HOL_Obool),tc_fun(tc_fun(U_13266,U_13266),tc_fun(U_13266,tc_HOL_Obool)),U_13266),c_COMBB(U_13266,tc_HOL_Obool,U_13266)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13266),U_13268))))),hAPP(hAPP(c_COMBC(U_13266,tc_fun(U_13266,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13266)),U_13267)))))
| U_13267 = c_Orderings_Obot__class_Obot(tc_fun(U_13266,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13266),U_13267))
| ~ class_Lattices_Odistrib__lattice(U_13266) ),
inference(clausify,[status(thm)],[f_3391_2]) ).
fof(f_3392_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_3392_2,plain,
! [U_13271,U_13270,U_13269] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13269),c_Big__Operators_Olattice__class_OSup__fin(U_13269,U_13270)),c_Big__Operators_Olattice__class_OSup__fin(U_13269,U_13271)) = c_Big__Operators_Olattice__class_OSup__fin(U_13269,hAPP(c_Set_OCollect(U_13269),hAPP(hAPP(c_COMBB(tc_fun(U_13269,tc_HOL_Obool),tc_HOL_Obool,U_13269),c_HOL_OEx(U_13269)),hAPP(hAPP(c_COMBB(tc_fun(U_13269,tc_fun(U_13269,tc_HOL_Obool)),tc_fun(U_13269,tc_HOL_Obool),U_13269),hAPP(c_COMBB(tc_fun(U_13269,tc_HOL_Obool),tc_HOL_Obool,U_13269),c_HOL_OEx(U_13269))),hAPP(hAPP(c_COMBC(U_13269,tc_fun(U_13269,tc_fun(U_13269,tc_HOL_Obool)),tc_fun(U_13269,tc_fun(U_13269,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13269,tc_fun(tc_fun(U_13269,tc_HOL_Obool),tc_fun(U_13269,tc_HOL_Obool))),tc_fun(tc_fun(U_13269,tc_fun(U_13269,tc_HOL_Obool)),tc_fun(U_13269,tc_fun(U_13269,tc_HOL_Obool))),U_13269),c_COMBS(U_13269,tc_fun(U_13269,tc_HOL_Obool),tc_fun(U_13269,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13269,tc_fun(U_13269,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13269,tc_fun(tc_fun(U_13269,tc_HOL_Obool),tc_fun(U_13269,tc_HOL_Obool))),U_13269),hAPP(c_COMBB(tc_fun(U_13269,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13269,tc_HOL_Obool),tc_fun(U_13269,tc_HOL_Obool)),U_13269),c_COMBS(U_13269,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13269,tc_fun(U_13269,tc_HOL_Obool)),tc_fun(U_13269,tc_fun(U_13269,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13269),hAPP(c_COMBB(tc_fun(U_13269,tc_HOL_Obool),tc_fun(U_13269,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13269),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13269),c_fconj))),hAPP(hAPP(c_COMBC(U_13269,tc_fun(U_13269,tc_fun(U_13269,U_13269)),tc_fun(U_13269,tc_fun(U_13269,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13269,U_13269),tc_fun(U_13269,tc_HOL_Obool)),tc_fun(tc_fun(U_13269,tc_fun(U_13269,U_13269)),tc_fun(U_13269,tc_fun(U_13269,tc_HOL_Obool))),U_13269),c_COMBB(tc_fun(U_13269,U_13269),tc_fun(U_13269,tc_HOL_Obool),U_13269)),hAPP(hAPP(c_COMBB(tc_fun(U_13269,tc_HOL_Obool),tc_fun(tc_fun(U_13269,U_13269),tc_fun(U_13269,tc_HOL_Obool)),U_13269),c_COMBB(U_13269,tc_HOL_Obool,U_13269)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_13269)))))),hAPP(hAPP(c_COMBC(U_13269,tc_fun(U_13269,tc_HOL_Obool),tc_fun(U_13269,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13269,tc_HOL_Obool),tc_fun(U_13269,tc_HOL_Obool)),U_13269),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13269)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13269),c_fconj),hAPP(hAPP(c_COMBC(U_13269,tc_fun(U_13269,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13269)),U_13270)))),hAPP(hAPP(c_COMBC(U_13269,tc_fun(U_13269,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13269)),U_13271)))))))
| U_13271 = c_Orderings_Obot__class_Obot(tc_fun(U_13269,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13269),U_13271))
| U_13270 = c_Orderings_Obot__class_Obot(tc_fun(U_13269,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13269),U_13270))
| ~ class_Lattices_Odistrib__lattice(U_13269) ),
inference(variable_rename,[status(thm)],[f_3392_1]) ).
cnf(f_3392_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13269),c_Big__Operators_Olattice__class_OSup__fin(U_13269,U_13270)),c_Big__Operators_Olattice__class_OSup__fin(U_13269,U_13271)) = c_Big__Operators_Olattice__class_OSup__fin(U_13269,hAPP(c_Set_OCollect(U_13269),hAPP(hAPP(c_COMBB(tc_fun(U_13269,tc_HOL_Obool),tc_HOL_Obool,U_13269),c_HOL_OEx(U_13269)),hAPP(hAPP(c_COMBB(tc_fun(U_13269,tc_fun(U_13269,tc_HOL_Obool)),tc_fun(U_13269,tc_HOL_Obool),U_13269),hAPP(c_COMBB(tc_fun(U_13269,tc_HOL_Obool),tc_HOL_Obool,U_13269),c_HOL_OEx(U_13269))),hAPP(hAPP(c_COMBC(U_13269,tc_fun(U_13269,tc_fun(U_13269,tc_HOL_Obool)),tc_fun(U_13269,tc_fun(U_13269,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13269,tc_fun(tc_fun(U_13269,tc_HOL_Obool),tc_fun(U_13269,tc_HOL_Obool))),tc_fun(tc_fun(U_13269,tc_fun(U_13269,tc_HOL_Obool)),tc_fun(U_13269,tc_fun(U_13269,tc_HOL_Obool))),U_13269),c_COMBS(U_13269,tc_fun(U_13269,tc_HOL_Obool),tc_fun(U_13269,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13269,tc_fun(U_13269,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13269,tc_fun(tc_fun(U_13269,tc_HOL_Obool),tc_fun(U_13269,tc_HOL_Obool))),U_13269),hAPP(c_COMBB(tc_fun(U_13269,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13269,tc_HOL_Obool),tc_fun(U_13269,tc_HOL_Obool)),U_13269),c_COMBS(U_13269,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13269,tc_fun(U_13269,tc_HOL_Obool)),tc_fun(U_13269,tc_fun(U_13269,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13269),hAPP(c_COMBB(tc_fun(U_13269,tc_HOL_Obool),tc_fun(U_13269,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13269),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13269),c_fconj))),hAPP(hAPP(c_COMBC(U_13269,tc_fun(U_13269,tc_fun(U_13269,U_13269)),tc_fun(U_13269,tc_fun(U_13269,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13269,U_13269),tc_fun(U_13269,tc_HOL_Obool)),tc_fun(tc_fun(U_13269,tc_fun(U_13269,U_13269)),tc_fun(U_13269,tc_fun(U_13269,tc_HOL_Obool))),U_13269),c_COMBB(tc_fun(U_13269,U_13269),tc_fun(U_13269,tc_HOL_Obool),U_13269)),hAPP(hAPP(c_COMBB(tc_fun(U_13269,tc_HOL_Obool),tc_fun(tc_fun(U_13269,U_13269),tc_fun(U_13269,tc_HOL_Obool)),U_13269),c_COMBB(U_13269,tc_HOL_Obool,U_13269)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_13269)))))),hAPP(hAPP(c_COMBC(U_13269,tc_fun(U_13269,tc_HOL_Obool),tc_fun(U_13269,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13269,tc_HOL_Obool),tc_fun(U_13269,tc_HOL_Obool)),U_13269),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13269)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13269),c_fconj),hAPP(hAPP(c_COMBC(U_13269,tc_fun(U_13269,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13269)),U_13270)))),hAPP(hAPP(c_COMBC(U_13269,tc_fun(U_13269,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13269)),U_13271)))))))
| U_13271 = c_Orderings_Obot__class_Obot(tc_fun(U_13269,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13269),U_13271))
| U_13270 = c_Orderings_Obot__class_Obot(tc_fun(U_13269,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13269),U_13270))
| ~ class_Lattices_Odistrib__lattice(U_13269) ),
inference(clausify,[status(thm)],[f_3392_2]) ).
fof(f_3393_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_3393_2,plain,
! [U_13274,U_13273,U_13272] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_13272),c_Big__Operators_Olattice_OSup__fin(U_13272,c_Orderings_Oord__class_Omax(U_13272),U_13273)),c_Big__Operators_Olattice_OSup__fin(U_13272,c_Orderings_Oord__class_Omax(U_13272),U_13274)) = c_Big__Operators_Olattice_OSup__fin(U_13272,c_Orderings_Oord__class_Omax(U_13272),hAPP(c_Set_OCollect(U_13272),hAPP(hAPP(c_COMBB(tc_fun(U_13272,tc_HOL_Obool),tc_HOL_Obool,U_13272),c_HOL_OEx(U_13272)),hAPP(hAPP(c_COMBB(tc_fun(U_13272,tc_fun(U_13272,tc_HOL_Obool)),tc_fun(U_13272,tc_HOL_Obool),U_13272),hAPP(c_COMBB(tc_fun(U_13272,tc_HOL_Obool),tc_HOL_Obool,U_13272),c_HOL_OEx(U_13272))),hAPP(hAPP(c_COMBC(U_13272,tc_fun(U_13272,tc_fun(U_13272,tc_HOL_Obool)),tc_fun(U_13272,tc_fun(U_13272,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13272,tc_fun(tc_fun(U_13272,tc_HOL_Obool),tc_fun(U_13272,tc_HOL_Obool))),tc_fun(tc_fun(U_13272,tc_fun(U_13272,tc_HOL_Obool)),tc_fun(U_13272,tc_fun(U_13272,tc_HOL_Obool))),U_13272),c_COMBS(U_13272,tc_fun(U_13272,tc_HOL_Obool),tc_fun(U_13272,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13272,tc_fun(U_13272,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13272,tc_fun(tc_fun(U_13272,tc_HOL_Obool),tc_fun(U_13272,tc_HOL_Obool))),U_13272),hAPP(c_COMBB(tc_fun(U_13272,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13272,tc_HOL_Obool),tc_fun(U_13272,tc_HOL_Obool)),U_13272),c_COMBS(U_13272,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13272,tc_fun(U_13272,tc_HOL_Obool)),tc_fun(U_13272,tc_fun(U_13272,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13272),hAPP(c_COMBB(tc_fun(U_13272,tc_HOL_Obool),tc_fun(U_13272,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13272),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13272),c_fconj))),hAPP(hAPP(c_COMBC(U_13272,tc_fun(U_13272,tc_fun(U_13272,U_13272)),tc_fun(U_13272,tc_fun(U_13272,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13272,U_13272),tc_fun(U_13272,tc_HOL_Obool)),tc_fun(tc_fun(U_13272,tc_fun(U_13272,U_13272)),tc_fun(U_13272,tc_fun(U_13272,tc_HOL_Obool))),U_13272),c_COMBB(tc_fun(U_13272,U_13272),tc_fun(U_13272,tc_HOL_Obool),U_13272)),hAPP(hAPP(c_COMBB(tc_fun(U_13272,tc_HOL_Obool),tc_fun(tc_fun(U_13272,U_13272),tc_fun(U_13272,tc_HOL_Obool)),U_13272),c_COMBB(U_13272,tc_HOL_Obool,U_13272)),c_fequal))),c_Orderings_Oord__class_Omin(U_13272)))))),hAPP(hAPP(c_COMBC(U_13272,tc_fun(U_13272,tc_HOL_Obool),tc_fun(U_13272,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13272,tc_HOL_Obool),tc_fun(U_13272,tc_HOL_Obool)),U_13272),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13272)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13272),c_fconj),hAPP(hAPP(c_COMBC(U_13272,tc_fun(U_13272,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13272)),U_13273)))),hAPP(hAPP(c_COMBC(U_13272,tc_fun(U_13272,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13272)),U_13274)))))))
| U_13274 = c_Orderings_Obot__class_Obot(tc_fun(U_13272,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13272),U_13274))
| U_13273 = c_Orderings_Obot__class_Obot(tc_fun(U_13272,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13272),U_13273))
| ~ class_Orderings_Olinorder(U_13272) ),
inference(variable_rename,[status(thm)],[f_3393_1]) ).
cnf(f_3393_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_13272),c_Big__Operators_Olattice_OSup__fin(U_13272,c_Orderings_Oord__class_Omax(U_13272),U_13273)),c_Big__Operators_Olattice_OSup__fin(U_13272,c_Orderings_Oord__class_Omax(U_13272),U_13274)) = c_Big__Operators_Olattice_OSup__fin(U_13272,c_Orderings_Oord__class_Omax(U_13272),hAPP(c_Set_OCollect(U_13272),hAPP(hAPP(c_COMBB(tc_fun(U_13272,tc_HOL_Obool),tc_HOL_Obool,U_13272),c_HOL_OEx(U_13272)),hAPP(hAPP(c_COMBB(tc_fun(U_13272,tc_fun(U_13272,tc_HOL_Obool)),tc_fun(U_13272,tc_HOL_Obool),U_13272),hAPP(c_COMBB(tc_fun(U_13272,tc_HOL_Obool),tc_HOL_Obool,U_13272),c_HOL_OEx(U_13272))),hAPP(hAPP(c_COMBC(U_13272,tc_fun(U_13272,tc_fun(U_13272,tc_HOL_Obool)),tc_fun(U_13272,tc_fun(U_13272,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13272,tc_fun(tc_fun(U_13272,tc_HOL_Obool),tc_fun(U_13272,tc_HOL_Obool))),tc_fun(tc_fun(U_13272,tc_fun(U_13272,tc_HOL_Obool)),tc_fun(U_13272,tc_fun(U_13272,tc_HOL_Obool))),U_13272),c_COMBS(U_13272,tc_fun(U_13272,tc_HOL_Obool),tc_fun(U_13272,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13272,tc_fun(U_13272,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13272,tc_fun(tc_fun(U_13272,tc_HOL_Obool),tc_fun(U_13272,tc_HOL_Obool))),U_13272),hAPP(c_COMBB(tc_fun(U_13272,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13272,tc_HOL_Obool),tc_fun(U_13272,tc_HOL_Obool)),U_13272),c_COMBS(U_13272,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13272,tc_fun(U_13272,tc_HOL_Obool)),tc_fun(U_13272,tc_fun(U_13272,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13272),hAPP(c_COMBB(tc_fun(U_13272,tc_HOL_Obool),tc_fun(U_13272,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13272),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13272),c_fconj))),hAPP(hAPP(c_COMBC(U_13272,tc_fun(U_13272,tc_fun(U_13272,U_13272)),tc_fun(U_13272,tc_fun(U_13272,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13272,U_13272),tc_fun(U_13272,tc_HOL_Obool)),tc_fun(tc_fun(U_13272,tc_fun(U_13272,U_13272)),tc_fun(U_13272,tc_fun(U_13272,tc_HOL_Obool))),U_13272),c_COMBB(tc_fun(U_13272,U_13272),tc_fun(U_13272,tc_HOL_Obool),U_13272)),hAPP(hAPP(c_COMBB(tc_fun(U_13272,tc_HOL_Obool),tc_fun(tc_fun(U_13272,U_13272),tc_fun(U_13272,tc_HOL_Obool)),U_13272),c_COMBB(U_13272,tc_HOL_Obool,U_13272)),c_fequal))),c_Orderings_Oord__class_Omin(U_13272)))))),hAPP(hAPP(c_COMBC(U_13272,tc_fun(U_13272,tc_HOL_Obool),tc_fun(U_13272,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13272,tc_HOL_Obool),tc_fun(U_13272,tc_HOL_Obool)),U_13272),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13272)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13272),c_fconj),hAPP(hAPP(c_COMBC(U_13272,tc_fun(U_13272,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13272)),U_13273)))),hAPP(hAPP(c_COMBC(U_13272,tc_fun(U_13272,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13272)),U_13274)))))))
| U_13274 = c_Orderings_Obot__class_Obot(tc_fun(U_13272,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13272),U_13274))
| U_13273 = c_Orderings_Obot__class_Obot(tc_fun(U_13272,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13272),U_13273))
| ~ class_Orderings_Olinorder(U_13272) ),
inference(clausify,[status(thm)],[f_3393_2]) ).
fof(f_3394_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_3394_2,plain,
! [U_13277,U_13276,U_13275] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_13275),c_Big__Operators_Olattice_OInf__fin(U_13275,c_Orderings_Oord__class_Omin(U_13275),U_13276)),c_Big__Operators_Olattice_OInf__fin(U_13275,c_Orderings_Oord__class_Omin(U_13275),U_13277)) = c_Big__Operators_Olattice_OInf__fin(U_13275,c_Orderings_Oord__class_Omin(U_13275),hAPP(c_Set_OCollect(U_13275),hAPP(hAPP(c_COMBB(tc_fun(U_13275,tc_HOL_Obool),tc_HOL_Obool,U_13275),c_HOL_OEx(U_13275)),hAPP(hAPP(c_COMBB(tc_fun(U_13275,tc_fun(U_13275,tc_HOL_Obool)),tc_fun(U_13275,tc_HOL_Obool),U_13275),hAPP(c_COMBB(tc_fun(U_13275,tc_HOL_Obool),tc_HOL_Obool,U_13275),c_HOL_OEx(U_13275))),hAPP(hAPP(c_COMBC(U_13275,tc_fun(U_13275,tc_fun(U_13275,tc_HOL_Obool)),tc_fun(U_13275,tc_fun(U_13275,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13275,tc_fun(tc_fun(U_13275,tc_HOL_Obool),tc_fun(U_13275,tc_HOL_Obool))),tc_fun(tc_fun(U_13275,tc_fun(U_13275,tc_HOL_Obool)),tc_fun(U_13275,tc_fun(U_13275,tc_HOL_Obool))),U_13275),c_COMBS(U_13275,tc_fun(U_13275,tc_HOL_Obool),tc_fun(U_13275,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13275,tc_fun(U_13275,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13275,tc_fun(tc_fun(U_13275,tc_HOL_Obool),tc_fun(U_13275,tc_HOL_Obool))),U_13275),hAPP(c_COMBB(tc_fun(U_13275,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13275,tc_HOL_Obool),tc_fun(U_13275,tc_HOL_Obool)),U_13275),c_COMBS(U_13275,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13275,tc_fun(U_13275,tc_HOL_Obool)),tc_fun(U_13275,tc_fun(U_13275,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13275),hAPP(c_COMBB(tc_fun(U_13275,tc_HOL_Obool),tc_fun(U_13275,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13275),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13275),c_fconj))),hAPP(hAPP(c_COMBC(U_13275,tc_fun(U_13275,tc_fun(U_13275,U_13275)),tc_fun(U_13275,tc_fun(U_13275,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13275,U_13275),tc_fun(U_13275,tc_HOL_Obool)),tc_fun(tc_fun(U_13275,tc_fun(U_13275,U_13275)),tc_fun(U_13275,tc_fun(U_13275,tc_HOL_Obool))),U_13275),c_COMBB(tc_fun(U_13275,U_13275),tc_fun(U_13275,tc_HOL_Obool),U_13275)),hAPP(hAPP(c_COMBB(tc_fun(U_13275,tc_HOL_Obool),tc_fun(tc_fun(U_13275,U_13275),tc_fun(U_13275,tc_HOL_Obool)),U_13275),c_COMBB(U_13275,tc_HOL_Obool,U_13275)),c_fequal))),c_Orderings_Oord__class_Omax(U_13275)))))),hAPP(hAPP(c_COMBC(U_13275,tc_fun(U_13275,tc_HOL_Obool),tc_fun(U_13275,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13275,tc_HOL_Obool),tc_fun(U_13275,tc_HOL_Obool)),U_13275),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13275)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13275),c_fconj),hAPP(hAPP(c_COMBC(U_13275,tc_fun(U_13275,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13275)),U_13276)))),hAPP(hAPP(c_COMBC(U_13275,tc_fun(U_13275,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13275)),U_13277)))))))
| U_13277 = c_Orderings_Obot__class_Obot(tc_fun(U_13275,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13275),U_13277))
| U_13276 = c_Orderings_Obot__class_Obot(tc_fun(U_13275,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13275),U_13276))
| ~ class_Orderings_Olinorder(U_13275) ),
inference(variable_rename,[status(thm)],[f_3394_1]) ).
cnf(f_3394_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_13275),c_Big__Operators_Olattice_OInf__fin(U_13275,c_Orderings_Oord__class_Omin(U_13275),U_13276)),c_Big__Operators_Olattice_OInf__fin(U_13275,c_Orderings_Oord__class_Omin(U_13275),U_13277)) = c_Big__Operators_Olattice_OInf__fin(U_13275,c_Orderings_Oord__class_Omin(U_13275),hAPP(c_Set_OCollect(U_13275),hAPP(hAPP(c_COMBB(tc_fun(U_13275,tc_HOL_Obool),tc_HOL_Obool,U_13275),c_HOL_OEx(U_13275)),hAPP(hAPP(c_COMBB(tc_fun(U_13275,tc_fun(U_13275,tc_HOL_Obool)),tc_fun(U_13275,tc_HOL_Obool),U_13275),hAPP(c_COMBB(tc_fun(U_13275,tc_HOL_Obool),tc_HOL_Obool,U_13275),c_HOL_OEx(U_13275))),hAPP(hAPP(c_COMBC(U_13275,tc_fun(U_13275,tc_fun(U_13275,tc_HOL_Obool)),tc_fun(U_13275,tc_fun(U_13275,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13275,tc_fun(tc_fun(U_13275,tc_HOL_Obool),tc_fun(U_13275,tc_HOL_Obool))),tc_fun(tc_fun(U_13275,tc_fun(U_13275,tc_HOL_Obool)),tc_fun(U_13275,tc_fun(U_13275,tc_HOL_Obool))),U_13275),c_COMBS(U_13275,tc_fun(U_13275,tc_HOL_Obool),tc_fun(U_13275,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13275,tc_fun(U_13275,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13275,tc_fun(tc_fun(U_13275,tc_HOL_Obool),tc_fun(U_13275,tc_HOL_Obool))),U_13275),hAPP(c_COMBB(tc_fun(U_13275,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13275,tc_HOL_Obool),tc_fun(U_13275,tc_HOL_Obool)),U_13275),c_COMBS(U_13275,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13275,tc_fun(U_13275,tc_HOL_Obool)),tc_fun(U_13275,tc_fun(U_13275,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13275),hAPP(c_COMBB(tc_fun(U_13275,tc_HOL_Obool),tc_fun(U_13275,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13275),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13275),c_fconj))),hAPP(hAPP(c_COMBC(U_13275,tc_fun(U_13275,tc_fun(U_13275,U_13275)),tc_fun(U_13275,tc_fun(U_13275,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13275,U_13275),tc_fun(U_13275,tc_HOL_Obool)),tc_fun(tc_fun(U_13275,tc_fun(U_13275,U_13275)),tc_fun(U_13275,tc_fun(U_13275,tc_HOL_Obool))),U_13275),c_COMBB(tc_fun(U_13275,U_13275),tc_fun(U_13275,tc_HOL_Obool),U_13275)),hAPP(hAPP(c_COMBB(tc_fun(U_13275,tc_HOL_Obool),tc_fun(tc_fun(U_13275,U_13275),tc_fun(U_13275,tc_HOL_Obool)),U_13275),c_COMBB(U_13275,tc_HOL_Obool,U_13275)),c_fequal))),c_Orderings_Oord__class_Omax(U_13275)))))),hAPP(hAPP(c_COMBC(U_13275,tc_fun(U_13275,tc_HOL_Obool),tc_fun(U_13275,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13275,tc_HOL_Obool),tc_fun(U_13275,tc_HOL_Obool)),U_13275),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13275)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13275),c_fconj),hAPP(hAPP(c_COMBC(U_13275,tc_fun(U_13275,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13275)),U_13276)))),hAPP(hAPP(c_COMBC(U_13275,tc_fun(U_13275,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13275)),U_13277)))))))
| U_13277 = c_Orderings_Obot__class_Obot(tc_fun(U_13275,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13275),U_13277))
| U_13276 = c_Orderings_Obot__class_Obot(tc_fun(U_13275,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13275),U_13276))
| ~ class_Orderings_Olinorder(U_13275) ),
inference(clausify,[status(thm)],[f_3394_2]) ).
fof(f_3395_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_3395_2,plain,
! [U_13281,U_13280,U_13279,U_13278] : c_Nitpick_Oprod(U_13278,U_13279,U_13280,U_13281) = hAPP(c_Set_OCollect(tc_prod(U_13278,U_13279)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13278,U_13279,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13278,tc_fun(U_13279,tc_HOL_Obool),tc_fun(U_13279,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13279,tc_HOL_Obool),tc_fun(U_13279,tc_HOL_Obool)),U_13278),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13279)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13278),c_fconj),hAPP(hAPP(c_COMBC(U_13278,tc_fun(U_13278,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13278)),U_13280)))),hAPP(hAPP(c_COMBC(U_13279,tc_fun(U_13279,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13279)),U_13281)))),
inference(variable_rename,[status(thm)],[f_3395_1]) ).
cnf(f_3395_3,plain,
c_Nitpick_Oprod(U_13278,U_13279,U_13280,U_13281) = hAPP(c_Set_OCollect(tc_prod(U_13278,U_13279)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13278,U_13279,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13278,tc_fun(U_13279,tc_HOL_Obool),tc_fun(U_13279,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13279,tc_HOL_Obool),tc_fun(U_13279,tc_HOL_Obool)),U_13278),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13279)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13278),c_fconj),hAPP(hAPP(c_COMBC(U_13278,tc_fun(U_13278,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13278)),U_13280)))),hAPP(hAPP(c_COMBC(U_13279,tc_fun(U_13279,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13279)),U_13281)))),
inference(clausify,[status(thm)],[f_3395_2]) ).
fof(f_3396_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_3396_2,plain,
! [U_13282] : c_Int_Oint__ge__less__than(U_13282) = 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_13282)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[f_3396_1]) ).
cnf(f_3396_3,plain,
c_Int_Oint__ge__less__than(U_13282) = 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_13282)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(clausify,[status(thm)],[f_3396_2]) ).
fof(f_3397_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_3397_2,plain,
! [U_13283] : c_Int_Oint__ge__less__than2(U_13283) = 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_13283)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[f_3397_1]) ).
cnf(f_3397_3,plain,
c_Int_Oint__ge__less__than2(U_13283) = 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_13283)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(clausify,[status(thm)],[f_3397_2]) ).
fof(f_3398_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_3398_2,plain,
! [U_13285,U_13284] :
( ( c_Predicate_Oreflp(U_13284,U_13285)
| ~ c_Relation_Orefl__on(U_13284,c_Orderings_Otop__class_Otop(tc_fun(U_13284,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_13284,U_13284)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13284,U_13284,tc_HOL_Obool),U_13285))) )
& ( c_Relation_Orefl__on(U_13284,c_Orderings_Otop__class_Otop(tc_fun(U_13284,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_13284,U_13284)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13284,U_13284,tc_HOL_Obool),U_13285)))
| ~ c_Predicate_Oreflp(U_13284,U_13285) ) ),
inference(variable_rename,[status(thm)],[f_3398_1]) ).
fof(f_3398_3,plain,
( ! [U_13289,U_13287] :
( c_Predicate_Oreflp(U_13287,U_13289)
| ~ c_Relation_Orefl__on(U_13287,c_Orderings_Otop__class_Otop(tc_fun(U_13287,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_13287,U_13287)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13287,U_13287,tc_HOL_Obool),U_13289))) )
& ! [U_13288,U_13286] :
( c_Relation_Orefl__on(U_13286,c_Orderings_Otop__class_Otop(tc_fun(U_13286,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_13286,U_13286)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13286,U_13286,tc_HOL_Obool),U_13288)))
| ~ c_Predicate_Oreflp(U_13286,U_13288) ) ),
inference(miniscope,[status(thm)],[f_3398_2]) ).
cnf(f_3398_4,plain,
( c_Relation_Orefl__on(U_13286,c_Orderings_Otop__class_Otop(tc_fun(U_13286,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_13286,U_13286)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13286,U_13286,tc_HOL_Obool),U_13288)))
| ~ c_Predicate_Oreflp(U_13286,U_13288) ),
inference(clausify,[status(thm)],[f_3398_3]) ).
cnf(f_3398_5,plain,
( c_Predicate_Oreflp(U_13287,U_13289)
| ~ c_Relation_Orefl__on(U_13287,c_Orderings_Otop__class_Otop(tc_fun(U_13287,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_13287,U_13287)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13287,U_13287,tc_HOL_Obool),U_13289))) ),
inference(clausify,[status(thm)],[f_3398_3]) ).
fof(f_3399_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_3399_2,plain,
! [U_13296,U_13295,U_13294,U_13293,U_13292,U_13291,U_13290] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13290),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13291,U_13290),U_13293),U_13295)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13292,U_13290),U_13294),U_13296)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13290,U_13290),c_Fun_Oid(U_13290)),hAPP(c_Set_OCollect(U_13290),hAPP(hAPP(c_COMBB(tc_fun(U_13291,tc_HOL_Obool),tc_HOL_Obool,U_13290),c_HOL_OEx(U_13291)),hAPP(hAPP(c_COMBB(tc_fun(U_13291,tc_fun(U_13292,tc_HOL_Obool)),tc_fun(U_13291,tc_HOL_Obool),U_13290),hAPP(c_COMBB(tc_fun(U_13292,tc_HOL_Obool),tc_HOL_Obool,U_13291),c_HOL_OEx(U_13292))),hAPP(hAPP(c_COMBC(U_13290,tc_fun(U_13291,tc_fun(U_13292,tc_HOL_Obool)),tc_fun(U_13291,tc_fun(U_13292,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13291,tc_fun(tc_fun(U_13292,tc_HOL_Obool),tc_fun(U_13292,tc_HOL_Obool))),tc_fun(tc_fun(U_13291,tc_fun(U_13292,tc_HOL_Obool)),tc_fun(U_13291,tc_fun(U_13292,tc_HOL_Obool))),U_13290),c_COMBS(U_13291,tc_fun(U_13292,tc_HOL_Obool),tc_fun(U_13292,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13291,tc_fun(U_13292,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13291,tc_fun(tc_fun(U_13292,tc_HOL_Obool),tc_fun(U_13292,tc_HOL_Obool))),U_13290),hAPP(c_COMBB(tc_fun(U_13292,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13292,tc_HOL_Obool),tc_fun(U_13292,tc_HOL_Obool)),U_13291),c_COMBS(U_13292,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13291,tc_fun(U_13292,tc_HOL_Obool)),tc_fun(U_13291,tc_fun(U_13292,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13290),hAPP(c_COMBB(tc_fun(U_13292,tc_HOL_Obool),tc_fun(U_13292,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13291),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13292),c_fconj))),hAPP(hAPP(c_COMBC(U_13290,tc_fun(U_13291,tc_fun(U_13292,U_13290)),tc_fun(U_13291,tc_fun(U_13292,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13292,U_13290),tc_fun(U_13292,tc_HOL_Obool)),tc_fun(tc_fun(U_13291,tc_fun(U_13292,U_13290)),tc_fun(U_13291,tc_fun(U_13292,tc_HOL_Obool))),U_13290),c_COMBB(tc_fun(U_13292,U_13290),tc_fun(U_13292,tc_HOL_Obool),U_13291)),hAPP(hAPP(c_COMBB(tc_fun(U_13290,tc_HOL_Obool),tc_fun(tc_fun(U_13292,U_13290),tc_fun(U_13292,tc_HOL_Obool)),U_13290),c_COMBB(U_13290,tc_HOL_Obool,U_13292)),c_fequal))),hAPP(hAPP(c_COMBC(U_13291,tc_fun(U_13292,U_13290),tc_fun(U_13292,U_13290)),hAPP(hAPP(c_COMBB(tc_fun(U_13290,U_13290),tc_fun(tc_fun(U_13292,U_13290),tc_fun(U_13292,U_13290)),U_13291),c_COMBB(U_13290,U_13290,U_13292)),hAPP(hAPP(c_COMBB(U_13290,tc_fun(U_13290,U_13290),U_13291),c_Groups_Otimes__class_Otimes(U_13290)),U_13293))),U_13294)))))),hAPP(hAPP(c_COMBC(U_13291,tc_fun(U_13292,tc_HOL_Obool),tc_fun(U_13292,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13292,tc_HOL_Obool),tc_fun(U_13292,tc_HOL_Obool)),U_13291),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13292)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13291),c_fconj),hAPP(hAPP(c_COMBC(U_13291,tc_fun(U_13291,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13291)),U_13295)))),hAPP(hAPP(c_COMBC(U_13292,tc_fun(U_13292,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13292)),U_13296)))))))
| ~ c_Fun_Oinj__on(tc_prod(U_13291,U_13292),U_13290,hAPP(c_Product__Type_Oprod_Oprod__case(U_13291,U_13292,U_13290),hAPP(hAPP(c_COMBC(U_13291,tc_fun(U_13292,U_13290),tc_fun(U_13292,U_13290)),hAPP(hAPP(c_COMBB(tc_fun(U_13290,U_13290),tc_fun(tc_fun(U_13292,U_13290),tc_fun(U_13292,U_13290)),U_13291),c_COMBB(U_13290,U_13290,U_13292)),hAPP(hAPP(c_COMBB(U_13290,tc_fun(U_13290,U_13290),U_13291),c_Groups_Otimes__class_Otimes(U_13290)),U_13293))),U_13294)),hAPP(hAPP(c_Product__Type_OSigma(U_13291,U_13292),U_13295),hAPP(c_COMBK(tc_fun(U_13292,tc_HOL_Obool),U_13291),U_13296)))
| ~ class_Rings_Osemiring__0(U_13290) ),
inference(variable_rename,[status(thm)],[f_3399_1]) ).
cnf(f_3399_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13290),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13291,U_13290),U_13293),U_13295)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13292,U_13290),U_13294),U_13296)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13290,U_13290),c_Fun_Oid(U_13290)),hAPP(c_Set_OCollect(U_13290),hAPP(hAPP(c_COMBB(tc_fun(U_13291,tc_HOL_Obool),tc_HOL_Obool,U_13290),c_HOL_OEx(U_13291)),hAPP(hAPP(c_COMBB(tc_fun(U_13291,tc_fun(U_13292,tc_HOL_Obool)),tc_fun(U_13291,tc_HOL_Obool),U_13290),hAPP(c_COMBB(tc_fun(U_13292,tc_HOL_Obool),tc_HOL_Obool,U_13291),c_HOL_OEx(U_13292))),hAPP(hAPP(c_COMBC(U_13290,tc_fun(U_13291,tc_fun(U_13292,tc_HOL_Obool)),tc_fun(U_13291,tc_fun(U_13292,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13291,tc_fun(tc_fun(U_13292,tc_HOL_Obool),tc_fun(U_13292,tc_HOL_Obool))),tc_fun(tc_fun(U_13291,tc_fun(U_13292,tc_HOL_Obool)),tc_fun(U_13291,tc_fun(U_13292,tc_HOL_Obool))),U_13290),c_COMBS(U_13291,tc_fun(U_13292,tc_HOL_Obool),tc_fun(U_13292,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13291,tc_fun(U_13292,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13291,tc_fun(tc_fun(U_13292,tc_HOL_Obool),tc_fun(U_13292,tc_HOL_Obool))),U_13290),hAPP(c_COMBB(tc_fun(U_13292,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13292,tc_HOL_Obool),tc_fun(U_13292,tc_HOL_Obool)),U_13291),c_COMBS(U_13292,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13291,tc_fun(U_13292,tc_HOL_Obool)),tc_fun(U_13291,tc_fun(U_13292,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13290),hAPP(c_COMBB(tc_fun(U_13292,tc_HOL_Obool),tc_fun(U_13292,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13291),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13292),c_fconj))),hAPP(hAPP(c_COMBC(U_13290,tc_fun(U_13291,tc_fun(U_13292,U_13290)),tc_fun(U_13291,tc_fun(U_13292,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13292,U_13290),tc_fun(U_13292,tc_HOL_Obool)),tc_fun(tc_fun(U_13291,tc_fun(U_13292,U_13290)),tc_fun(U_13291,tc_fun(U_13292,tc_HOL_Obool))),U_13290),c_COMBB(tc_fun(U_13292,U_13290),tc_fun(U_13292,tc_HOL_Obool),U_13291)),hAPP(hAPP(c_COMBB(tc_fun(U_13290,tc_HOL_Obool),tc_fun(tc_fun(U_13292,U_13290),tc_fun(U_13292,tc_HOL_Obool)),U_13290),c_COMBB(U_13290,tc_HOL_Obool,U_13292)),c_fequal))),hAPP(hAPP(c_COMBC(U_13291,tc_fun(U_13292,U_13290),tc_fun(U_13292,U_13290)),hAPP(hAPP(c_COMBB(tc_fun(U_13290,U_13290),tc_fun(tc_fun(U_13292,U_13290),tc_fun(U_13292,U_13290)),U_13291),c_COMBB(U_13290,U_13290,U_13292)),hAPP(hAPP(c_COMBB(U_13290,tc_fun(U_13290,U_13290),U_13291),c_Groups_Otimes__class_Otimes(U_13290)),U_13293))),U_13294)))))),hAPP(hAPP(c_COMBC(U_13291,tc_fun(U_13292,tc_HOL_Obool),tc_fun(U_13292,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13292,tc_HOL_Obool),tc_fun(U_13292,tc_HOL_Obool)),U_13291),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13292)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13291),c_fconj),hAPP(hAPP(c_COMBC(U_13291,tc_fun(U_13291,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13291)),U_13295)))),hAPP(hAPP(c_COMBC(U_13292,tc_fun(U_13292,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13292)),U_13296)))))))
| ~ c_Fun_Oinj__on(tc_prod(U_13291,U_13292),U_13290,hAPP(c_Product__Type_Oprod_Oprod__case(U_13291,U_13292,U_13290),hAPP(hAPP(c_COMBC(U_13291,tc_fun(U_13292,U_13290),tc_fun(U_13292,U_13290)),hAPP(hAPP(c_COMBB(tc_fun(U_13290,U_13290),tc_fun(tc_fun(U_13292,U_13290),tc_fun(U_13292,U_13290)),U_13291),c_COMBB(U_13290,U_13290,U_13292)),hAPP(hAPP(c_COMBB(U_13290,tc_fun(U_13290,U_13290),U_13291),c_Groups_Otimes__class_Otimes(U_13290)),U_13293))),U_13294)),hAPP(hAPP(c_Product__Type_OSigma(U_13291,U_13292),U_13295),hAPP(c_COMBK(tc_fun(U_13292,tc_HOL_Obool),U_13291),U_13296)))
| ~ class_Rings_Osemiring__0(U_13290) ),
inference(clausify,[status(thm)],[f_3399_2]) ).
fof(f_3400_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_3400_2,plain,
! [U_13303,U_13302,U_13301,U_13300,U_13299,U_13298] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13298,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13300,tc_HOL_Obool),tc_Nat_Onat,U_13298),c_Finite__Set_Ocard(U_13300)),hAPP(hAPP(c_COMBB(tc_fun(U_13300,tc_HOL_Obool),tc_fun(U_13300,tc_HOL_Obool),U_13298),c_Set_OCollect(U_13300)),hAPP(hAPP(c_COMBB(tc_fun(U_13300,tc_HOL_Obool),tc_fun(U_13300,tc_HOL_Obool),U_13298),hAPP(c_COMBS(U_13300,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13300),c_fconj),hAPP(hAPP(c_COMBC(U_13300,tc_fun(U_13300,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13300)),U_13301)))),U_13302)))),U_13299) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13300,tc_Nat_Onat),U_13303),U_13301)
| ? [U_13297] :
( hAPP(c_Finite__Set_Ocard(U_13298),hAPP(c_Set_OCollect(U_13298),hAPP(hAPP(c_COMBS(U_13298,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13298),c_fconj),hAPP(hAPP(c_COMBC(U_13298,tc_fun(U_13298,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13298)),U_13299))),hAPP(hAPP(c_COMBC(U_13298,U_13300,tc_HOL_Obool),U_13302),U_13297)))) != hAPP(U_13303,U_13297)
& hBOOL(hAPP(hAPP(c_member(U_13300),U_13297),U_13301)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13300),U_13301))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13298),U_13299)) ),
inference(variable_rename,[status(thm)],[f_3400_1]) ).
fof(f_3400_3,plain,
! [U_13303,U_13302,U_13301,U_13300,U_13299,U_13298] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13298,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13300,tc_HOL_Obool),tc_Nat_Onat,U_13298),c_Finite__Set_Ocard(U_13300)),hAPP(hAPP(c_COMBB(tc_fun(U_13300,tc_HOL_Obool),tc_fun(U_13300,tc_HOL_Obool),U_13298),c_Set_OCollect(U_13300)),hAPP(hAPP(c_COMBB(tc_fun(U_13300,tc_HOL_Obool),tc_fun(U_13300,tc_HOL_Obool),U_13298),hAPP(c_COMBS(U_13300,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13300),c_fconj),hAPP(hAPP(c_COMBC(U_13300,tc_fun(U_13300,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13300)),U_13301)))),U_13302)))),U_13299) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13300,tc_Nat_Onat),U_13303),U_13301)
| ( hAPP(c_Finite__Set_Ocard(U_13298),hAPP(c_Set_OCollect(U_13298),hAPP(hAPP(c_COMBS(U_13298,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13298),c_fconj),hAPP(hAPP(c_COMBC(U_13298,tc_fun(U_13298,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13298)),U_13299))),hAPP(hAPP(c_COMBC(U_13298,U_13300,tc_HOL_Obool),U_13302),sK324(U_13303,U_13302,U_13301,U_13300,U_13299,U_13298))))) != hAPP(U_13303,sK324(U_13303,U_13302,U_13301,U_13300,U_13299,U_13298))
& hBOOL(hAPP(hAPP(c_member(U_13300),sK324(U_13303,U_13302,U_13301,U_13300,U_13299,U_13298)),U_13301)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13300),U_13301))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13298),U_13299)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK324]),skolemize(U_13297,sK324(U_13303,U_13302,U_13301,U_13300,U_13299,U_13298))],[f_3400_2]) ).
cnf(f_3400_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_13300),sK324(U_13303,U_13302,U_13301,U_13300,U_13299,U_13298)),U_13301))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13298,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13300,tc_HOL_Obool),tc_Nat_Onat,U_13298),c_Finite__Set_Ocard(U_13300)),hAPP(hAPP(c_COMBB(tc_fun(U_13300,tc_HOL_Obool),tc_fun(U_13300,tc_HOL_Obool),U_13298),c_Set_OCollect(U_13300)),hAPP(hAPP(c_COMBB(tc_fun(U_13300,tc_HOL_Obool),tc_fun(U_13300,tc_HOL_Obool),U_13298),hAPP(c_COMBS(U_13300,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13300),c_fconj),hAPP(hAPP(c_COMBC(U_13300,tc_fun(U_13300,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13300)),U_13301)))),U_13302)))),U_13299) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13300,tc_Nat_Onat),U_13303),U_13301)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13300),U_13301))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13298),U_13299)) ),
inference(clausify,[status(thm)],[f_3400_3]) ).
cnf(f_3400_5,plain,
( hAPP(c_Finite__Set_Ocard(U_13298),hAPP(c_Set_OCollect(U_13298),hAPP(hAPP(c_COMBS(U_13298,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13298),c_fconj),hAPP(hAPP(c_COMBC(U_13298,tc_fun(U_13298,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13298)),U_13299))),hAPP(hAPP(c_COMBC(U_13298,U_13300,tc_HOL_Obool),U_13302),sK324(U_13303,U_13302,U_13301,U_13300,U_13299,U_13298))))) != hAPP(U_13303,sK324(U_13303,U_13302,U_13301,U_13300,U_13299,U_13298))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13298,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13300,tc_HOL_Obool),tc_Nat_Onat,U_13298),c_Finite__Set_Ocard(U_13300)),hAPP(hAPP(c_COMBB(tc_fun(U_13300,tc_HOL_Obool),tc_fun(U_13300,tc_HOL_Obool),U_13298),c_Set_OCollect(U_13300)),hAPP(hAPP(c_COMBB(tc_fun(U_13300,tc_HOL_Obool),tc_fun(U_13300,tc_HOL_Obool),U_13298),hAPP(c_COMBS(U_13300,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13300),c_fconj),hAPP(hAPP(c_COMBC(U_13300,tc_fun(U_13300,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13300)),U_13301)))),U_13302)))),U_13299) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13300,tc_Nat_Onat),U_13303),U_13301)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13300),U_13301))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13298),U_13299)) ),
inference(clausify,[status(thm)],[f_3400_3]) ).
fof(f_3401_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_3401_2,plain,
! [U_13305,U_13304] : c_Fun_Oinj__on(U_13304,U_13304,c_Fun_Oid(U_13304),U_13305),
inference(variable_rename,[status(thm)],[f_3401_1]) ).
cnf(f_3401_3,plain,
c_Fun_Oinj__on(U_13304,U_13304,c_Fun_Oid(U_13304),U_13305),
inference(clausify,[status(thm)],[f_3401_2]) ).
fof(f_3402_1,plain,
! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
( hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2)
| hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) != hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_c_2) ),
inference(fof_nnf,[status(thm)],[fact_o__eq__id__dest]) ).
fof(f_3402_2,plain,
! [U_13312,U_13311,U_13310,U_13309,U_13308,U_13307,U_13306] :
( hAPP(U_13309,hAPP(U_13310,U_13312)) = hAPP(U_13311,U_13312)
| hAPP(c_Fun_Ocomp(U_13306,U_13307,U_13308,U_13309),U_13310) != hAPP(c_Fun_Ocomp(U_13307,U_13307,U_13308,c_Fun_Oid(U_13307)),U_13311) ),
inference(variable_rename,[status(thm)],[f_3402_1]) ).
fof(f_3402_3,plain,
! [U_13312,U_13311,U_13310,U_13309] :
( ! [U_13308,U_13307,U_13306] : hAPP(c_Fun_Ocomp(U_13306,U_13307,U_13308,U_13309),U_13310) != hAPP(c_Fun_Ocomp(U_13307,U_13307,U_13308,c_Fun_Oid(U_13307)),U_13311)
| hAPP(U_13309,hAPP(U_13310,U_13312)) = hAPP(U_13311,U_13312) ),
inference(miniscope,[status(thm)],[f_3402_2]) ).
cnf(f_3402_4,plain,
( hAPP(c_Fun_Ocomp(U_13306,U_13307,U_13308,U_13309),U_13310) != hAPP(c_Fun_Ocomp(U_13307,U_13307,U_13308,c_Fun_Oid(U_13307)),U_13311)
| hAPP(U_13309,hAPP(U_13310,U_13312)) = hAPP(U_13311,U_13312) ),
inference(clausify,[status(thm)],[f_3402_3]) ).
fof(f_3403_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_3403_2,plain,
! [U_13315,U_13314,U_13313] : hAPP(c_Fun_Ocomp(U_13313,U_13314,U_13313,U_13315),c_Fun_Oid(U_13313)) = U_13315,
inference(variable_rename,[status(thm)],[f_3403_1]) ).
cnf(f_3403_3,plain,
hAPP(c_Fun_Ocomp(U_13313,U_13314,U_13313,U_13315),c_Fun_Oid(U_13313)) = U_13315,
inference(clausify,[status(thm)],[f_3403_2]) ).
fof(f_3404_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_3404_2,plain,
! [U_13318,U_13317,U_13316] : hAPP(c_Fun_Ocomp(U_13316,U_13316,U_13317,c_Fun_Oid(U_13316)),U_13318) = U_13318,
inference(variable_rename,[status(thm)],[f_3404_1]) ).
cnf(f_3404_3,plain,
hAPP(c_Fun_Ocomp(U_13316,U_13316,U_13317,c_Fun_Oid(U_13316)),U_13318) = U_13318,
inference(clausify,[status(thm)],[f_3404_2]) ).
fof(f_3405_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_3405_2,plain,
! [U_13320,U_13319] : c_Product__Type_Oapfst(U_13319,U_13319,U_13320,c_Fun_Oid(U_13319)) = c_Fun_Oid(tc_prod(U_13319,U_13320)),
inference(variable_rename,[status(thm)],[f_3405_1]) ).
cnf(f_3405_3,plain,
c_Product__Type_Oapfst(U_13319,U_13319,U_13320,c_Fun_Oid(U_13319)) = c_Fun_Oid(tc_prod(U_13319,U_13320)),
inference(clausify,[status(thm)],[f_3405_2]) ).
fof(f_3406_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_3406_2,plain,
! [U_13322,U_13321] : hAPP(c_Fun_Oid(U_13321),U_13322) = U_13322,
inference(variable_rename,[status(thm)],[f_3406_1]) ).
cnf(f_3406_3,plain,
hAPP(c_Fun_Oid(U_13321),U_13322) = U_13322,
inference(clausify,[status(thm)],[f_3406_2]) ).
fof(f_3407_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_3407_2,plain,
! [U_13324,U_13323] : c_Product__Type_Oapsnd(U_13323,U_13323,U_13324,c_Fun_Oid(U_13323)) = c_Fun_Oid(tc_prod(U_13324,U_13323)),
inference(variable_rename,[status(thm)],[f_3407_1]) ).
cnf(f_3407_3,plain,
c_Product__Type_Oapsnd(U_13323,U_13323,U_13324,c_Fun_Oid(U_13323)) = c_Fun_Oid(tc_prod(U_13324,U_13323)),
inference(clausify,[status(thm)],[f_3407_2]) ).
fof(f_3408_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_3408_2,plain,
! [U_13327,U_13326,U_13325] :
( hBOOL(hAPP(hAPP(U_13326,U_13327),U_13327))
| ~ c_Predicate_Oreflp(U_13325,U_13326) ),
inference(variable_rename,[status(thm)],[f_3408_1]) ).
fof(f_3408_3,plain,
! [U_13327,U_13326] :
( ! [U_13325] : ~ c_Predicate_Oreflp(U_13325,U_13326)
| hBOOL(hAPP(hAPP(U_13326,U_13327),U_13327)) ),
inference(miniscope,[status(thm)],[f_3408_2]) ).
cnf(f_3408_4,plain,
( ~ c_Predicate_Oreflp(U_13325,U_13326)
| hBOOL(hAPP(hAPP(U_13326,U_13327),U_13327)) ),
inference(clausify,[status(thm)],[f_3408_3]) ).
fof(f_3409_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_3409_2,plain,
! [U_13329,U_13328] : hAPP(c_Fun_Oid(U_13328),U_13329) = U_13329,
inference(variable_rename,[status(thm)],[f_3409_1]) ).
cnf(f_3409_3,plain,
hAPP(c_Fun_Oid(U_13328),U_13329) = U_13329,
inference(clausify,[status(thm)],[f_3409_2]) ).
fof(f_3410_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_3410_2,plain,
! [U_13331,U_13330] : hAPP(c_Set_Ovimage(U_13330,U_13330,c_Fun_Oid(U_13330)),U_13331) = U_13331,
inference(variable_rename,[status(thm)],[f_3410_1]) ).
cnf(f_3410_3,plain,
hAPP(c_Set_Ovimage(U_13330,U_13330,c_Fun_Oid(U_13330)),U_13331) = U_13331,
inference(clausify,[status(thm)],[f_3410_2]) ).
fof(f_3411_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_3411_2,plain,
! [U_13333,U_13332] : c_Product__Type_Omap__pair(U_13332,U_13332,U_13333,U_13333,c_Fun_Oid(U_13332),c_Fun_Oid(U_13333)) = c_Fun_Oid(tc_prod(U_13332,U_13333)),
inference(variable_rename,[status(thm)],[f_3411_1]) ).
cnf(f_3411_3,plain,
c_Product__Type_Omap__pair(U_13332,U_13332,U_13333,U_13333,c_Fun_Oid(U_13332),c_Fun_Oid(U_13333)) = c_Fun_Oid(tc_prod(U_13332,U_13333)),
inference(clausify,[status(thm)],[f_3411_2]) ).
fof(f_3412_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_3412_2,plain,
! [U_13335,U_13334] : c_Product__Type_Omap__pair(U_13334,U_13334,U_13335,U_13335,c_COMBI(U_13334),c_COMBI(U_13335)) = c_Fun_Oid(tc_prod(U_13334,U_13335)),
inference(variable_rename,[status(thm)],[f_3412_1]) ).
cnf(f_3412_3,plain,
c_Product__Type_Omap__pair(U_13334,U_13334,U_13335,U_13335,c_COMBI(U_13334),c_COMBI(U_13335)) = c_Fun_Oid(tc_prod(U_13334,U_13335)),
inference(clausify,[status(thm)],[f_3412_2]) ).
fof(f_3413_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_3413_2,plain,
c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
inference(clausify,[status(thm)],[f_3413_1]) ).
fof(f_3414_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_3414_2,plain,
! [U_13337,U_13336] : hAPP(c_Set_Oimage(U_13336,U_13336,c_Fun_Oid(U_13336)),U_13337) = U_13337,
inference(variable_rename,[status(thm)],[f_3414_1]) ).
cnf(f_3414_3,plain,
hAPP(c_Set_Oimage(U_13336,U_13336,c_Fun_Oid(U_13336)),U_13337) = U_13337,
inference(clausify,[status(thm)],[f_3414_2]) ).
fof(f_3415_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_3415_2,plain,
! [U_13338] : hAPP(c_Set_Oimage(U_13338,U_13338,c_Fun_Oid(U_13338)),c_Orderings_Otop__class_Otop(tc_fun(U_13338,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13338,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3415_1]) ).
cnf(f_3415_3,plain,
hAPP(c_Set_Oimage(U_13338,U_13338,c_Fun_Oid(U_13338)),c_Orderings_Otop__class_Otop(tc_fun(U_13338,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13338,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3415_2]) ).
fof(f_3416_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_3416_2,plain,
! [U_13342,U_13341,U_13340,U_13339] :
( hAPP(U_13342,c_Orderings_Obot__class_Obot(tc_fun(U_13339,tc_HOL_Obool))) = c_Fun_Oid(U_13340)
| ~ c_Finite__Set_Ofolding(U_13339,U_13340,U_13341,U_13342) ),
inference(variable_rename,[status(thm)],[f_3416_1]) ).
cnf(f_3416_3,plain,
( hAPP(U_13342,c_Orderings_Obot__class_Obot(tc_fun(U_13339,tc_HOL_Obool))) = c_Fun_Oid(U_13340)
| ~ c_Finite__Set_Ofolding(U_13339,U_13340,U_13341,U_13342) ),
inference(clausify,[status(thm)],[f_3416_2]) ).
fof(f_3417_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_3417_2,plain,
! [U_13346,U_13345,U_13344,U_13343] : c_Product__Type_Oapfst(U_13343,U_13344,U_13345,U_13346) = c_Product__Type_Omap__pair(U_13343,U_13344,U_13345,U_13345,U_13346,c_Fun_Oid(U_13345)),
inference(variable_rename,[status(thm)],[f_3417_1]) ).
cnf(f_3417_3,plain,
c_Product__Type_Oapfst(U_13343,U_13344,U_13345,U_13346) = c_Product__Type_Omap__pair(U_13343,U_13344,U_13345,U_13345,U_13346,c_Fun_Oid(U_13345)),
inference(clausify,[status(thm)],[f_3417_2]) ).
fof(f_3418_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_3418_2,plain,
! [U_13350,U_13349,U_13348,U_13347] : c_Product__Type_Oapsnd(U_13347,U_13348,U_13349,U_13350) = c_Product__Type_Omap__pair(U_13349,U_13349,U_13347,U_13348,c_Fun_Oid(U_13349),U_13350),
inference(variable_rename,[status(thm)],[f_3418_1]) ).
cnf(f_3418_3,plain,
c_Product__Type_Oapsnd(U_13347,U_13348,U_13349,U_13350) = c_Product__Type_Omap__pair(U_13349,U_13349,U_13347,U_13348,c_Fun_Oid(U_13349),U_13350),
inference(clausify,[status(thm)],[f_3418_2]) ).
fof(f_3419_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_3419_2,plain,
! [U_13352,U_13351] : hAPP(c_Product__Type_Oprod_Oprod__case(U_13351,U_13352,tc_prod(U_13351,U_13352)),c_Product__Type_OPair(U_13351,U_13352)) = c_Fun_Oid(tc_prod(U_13351,U_13352)),
inference(variable_rename,[status(thm)],[f_3419_1]) ).
cnf(f_3419_3,plain,
hAPP(c_Product__Type_Oprod_Oprod__case(U_13351,U_13352,tc_prod(U_13351,U_13352)),c_Product__Type_OPair(U_13351,U_13352)) = c_Fun_Oid(tc_prod(U_13351,U_13352)),
inference(clausify,[status(thm)],[f_3419_2]) ).
fof(f_3420_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_3420_2,plain,
! [U_13356,U_13355,U_13354,U_13353] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13354,U_13353),U_13355),U_13356) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13353,U_13353),c_Fun_Oid(U_13353)),hAPP(c_Set_Oimage(U_13354,U_13353,U_13355),U_13356))
| ~ c_Fun_Oinj__on(U_13354,U_13353,U_13355,U_13356)
| ~ class_Groups_Ocomm__monoid__add(U_13353) ),
inference(variable_rename,[status(thm)],[f_3420_1]) ).
cnf(f_3420_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13354,U_13353),U_13355),U_13356) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13353,U_13353),c_Fun_Oid(U_13353)),hAPP(c_Set_Oimage(U_13354,U_13353,U_13355),U_13356))
| ~ c_Fun_Oinj__on(U_13354,U_13353,U_13355,U_13356)
| ~ class_Groups_Ocomm__monoid__add(U_13353) ),
inference(clausify,[status(thm)],[f_3420_2]) ).
fof(f_3421_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_3421_2,plain,
! [U_13360,U_13359,U_13358,U_13357] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13358,U_13357),U_13359),U_13360) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13357,U_13357),c_Fun_Oid(U_13357)),hAPP(c_Set_Oimage(U_13358,U_13357,U_13359),U_13360))
| ~ c_Fun_Oinj__on(U_13358,U_13357,U_13359,U_13360)
| ~ class_Groups_Ocomm__monoid__mult(U_13357) ),
inference(variable_rename,[status(thm)],[f_3421_1]) ).
cnf(f_3421_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13358,U_13357),U_13359),U_13360) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13357,U_13357),c_Fun_Oid(U_13357)),hAPP(c_Set_Oimage(U_13358,U_13357,U_13359),U_13360))
| ~ c_Fun_Oinj__on(U_13358,U_13357,U_13359,U_13360)
| ~ class_Groups_Ocomm__monoid__mult(U_13357) ),
inference(clausify,[status(thm)],[f_3421_2]) ).
fof(f_3422_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_3422_2,plain,
! [U_13366,U_13365] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13365),U_13366))
| ! [U_13364,U_13363] : U_13366 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_13365,U_13363),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_13364))) )
& ( ? [U_13362,U_13361] : U_13366 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_13365,U_13361),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_13362)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13365),U_13366)) ) ),
inference(variable_rename,[status(thm)],[f_3422_1]) ).
fof(f_3422_3,plain,
( ! [U_13370,U_13368] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13368),U_13370))
| ! [U_13364,U_13363] : U_13370 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_13368,U_13363),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_13364))) )
& ! [U_13369,U_13367] :
( ? [U_13362,U_13361] : U_13369 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_13367,U_13361),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_13362)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13367),U_13369)) ) ),
inference(miniscope,[status(thm)],[f_3422_2]) ).
fof(f_3422_4,plain,
( ! [U_13370,U_13368] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13368),U_13370))
| ! [U_13364,U_13363] : U_13370 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_13368,U_13363),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_13364))) )
& ! [U_13369,U_13367] :
( ? [U_13361] : U_13369 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_13367,U_13361),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)),sK325(U_13369,U_13367))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13367),U_13369)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK325]),skolemize(U_13362,sK325(U_13369,U_13367))],[f_3422_3]) ).
fof(f_3422_5,plain,
( ! [U_13370,U_13368] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13368),U_13370))
| ! [U_13364,U_13363] : U_13370 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_13368,U_13363),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_13364))) )
& ! [U_13369,U_13367] :
( U_13369 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_13367,sK326(U_13369,U_13367)),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)),sK325(U_13369,U_13367))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13367),U_13369)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK326]),skolemize(U_13361,sK326(U_13369,U_13367))],[f_3422_4]) ).
cnf(f_3422_6,plain,
( U_13369 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_13367,sK326(U_13369,U_13367)),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)),sK325(U_13369,U_13367))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13367),U_13369)) ),
inference(clausify,[status(thm)],[f_3422_5]) ).
cnf(f_3422_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13368),U_13370))
| U_13370 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_13368,U_13363),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_13364))) ),
inference(clausify,[status(thm)],[f_3422_5]) ).
fof(f_3423_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_3423_2,plain,
! [U_13375,U_13374,U_13373,U_13372,U_13371] : hAPP(hAPP(c_Relation_Orel__comp(U_13371,U_13372,U_13373),U_13374),U_13375) = hAPP(c_Set_OCollect(tc_prod(U_13371,U_13373)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13371,U_13373,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13373,tc_fun(U_13372,tc_HOL_Obool)),tc_fun(U_13373,tc_HOL_Obool),U_13371),hAPP(c_COMBB(tc_fun(U_13372,tc_HOL_Obool),tc_HOL_Obool,U_13373),c_HOL_OEx(U_13372))),hAPP(hAPP(c_COMBC(U_13371,tc_fun(U_13373,tc_fun(U_13372,tc_HOL_Obool)),tc_fun(U_13373,tc_fun(U_13372,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13372,tc_HOL_Obool),tc_fun(U_13372,tc_HOL_Obool)),tc_fun(tc_fun(U_13373,tc_fun(U_13372,tc_HOL_Obool)),tc_fun(U_13373,tc_fun(U_13372,tc_HOL_Obool))),U_13371),c_COMBB(tc_fun(U_13372,tc_HOL_Obool),tc_fun(U_13372,tc_HOL_Obool),U_13373)),hAPP(hAPP(c_COMBB(tc_fun(U_13372,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13372,tc_HOL_Obool),tc_fun(U_13372,tc_HOL_Obool)),U_13371),c_COMBS(U_13372,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13372,tc_HOL_Obool),tc_fun(U_13372,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13371),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13372),c_fconj)),hAPP(hAPP(c_COMBC(U_13371,tc_fun(tc_prod(U_13371,U_13372),tc_HOL_Obool),tc_fun(U_13372,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13372,tc_fun(tc_fun(tc_prod(U_13371,U_13372),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13371,U_13372),tc_HOL_Obool),tc_fun(U_13372,tc_HOL_Obool)),U_13371),c_COMBC(U_13372,tc_fun(tc_prod(U_13371,U_13372),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13372,tc_prod(U_13371,U_13372)),tc_fun(U_13372,tc_fun(tc_fun(tc_prod(U_13371,U_13372),tc_HOL_Obool),tc_HOL_Obool)),U_13371),hAPP(c_COMBB(tc_prod(U_13371,U_13372),tc_fun(tc_fun(tc_prod(U_13371,U_13372),tc_HOL_Obool),tc_HOL_Obool),U_13372),c_member(tc_prod(U_13371,U_13372)))),c_Product__Type_OPair(U_13371,U_13372)))),U_13374))))),hAPP(hAPP(c_COMBC(U_13373,tc_fun(tc_prod(U_13372,U_13373),tc_HOL_Obool),tc_fun(U_13372,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13372,tc_fun(tc_fun(tc_prod(U_13372,U_13373),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13372,U_13373),tc_HOL_Obool),tc_fun(U_13372,tc_HOL_Obool)),U_13373),c_COMBC(U_13372,tc_fun(tc_prod(U_13372,U_13373),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13372,tc_prod(U_13372,U_13373)),tc_fun(U_13372,tc_fun(tc_fun(tc_prod(U_13372,U_13373),tc_HOL_Obool),tc_HOL_Obool)),U_13373),hAPP(c_COMBB(tc_prod(U_13372,U_13373),tc_fun(tc_fun(tc_prod(U_13372,U_13373),tc_HOL_Obool),tc_HOL_Obool),U_13372),c_member(tc_prod(U_13372,U_13373)))),hAPP(c_COMBC(U_13372,U_13373,tc_prod(U_13372,U_13373)),c_Product__Type_OPair(U_13372,U_13373))))),U_13375))))),
inference(variable_rename,[status(thm)],[f_3423_1]) ).
cnf(f_3423_3,plain,
hAPP(hAPP(c_Relation_Orel__comp(U_13371,U_13372,U_13373),U_13374),U_13375) = hAPP(c_Set_OCollect(tc_prod(U_13371,U_13373)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13371,U_13373,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13373,tc_fun(U_13372,tc_HOL_Obool)),tc_fun(U_13373,tc_HOL_Obool),U_13371),hAPP(c_COMBB(tc_fun(U_13372,tc_HOL_Obool),tc_HOL_Obool,U_13373),c_HOL_OEx(U_13372))),hAPP(hAPP(c_COMBC(U_13371,tc_fun(U_13373,tc_fun(U_13372,tc_HOL_Obool)),tc_fun(U_13373,tc_fun(U_13372,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13372,tc_HOL_Obool),tc_fun(U_13372,tc_HOL_Obool)),tc_fun(tc_fun(U_13373,tc_fun(U_13372,tc_HOL_Obool)),tc_fun(U_13373,tc_fun(U_13372,tc_HOL_Obool))),U_13371),c_COMBB(tc_fun(U_13372,tc_HOL_Obool),tc_fun(U_13372,tc_HOL_Obool),U_13373)),hAPP(hAPP(c_COMBB(tc_fun(U_13372,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13372,tc_HOL_Obool),tc_fun(U_13372,tc_HOL_Obool)),U_13371),c_COMBS(U_13372,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13372,tc_HOL_Obool),tc_fun(U_13372,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13371),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13372),c_fconj)),hAPP(hAPP(c_COMBC(U_13371,tc_fun(tc_prod(U_13371,U_13372),tc_HOL_Obool),tc_fun(U_13372,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13372,tc_fun(tc_fun(tc_prod(U_13371,U_13372),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13371,U_13372),tc_HOL_Obool),tc_fun(U_13372,tc_HOL_Obool)),U_13371),c_COMBC(U_13372,tc_fun(tc_prod(U_13371,U_13372),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13372,tc_prod(U_13371,U_13372)),tc_fun(U_13372,tc_fun(tc_fun(tc_prod(U_13371,U_13372),tc_HOL_Obool),tc_HOL_Obool)),U_13371),hAPP(c_COMBB(tc_prod(U_13371,U_13372),tc_fun(tc_fun(tc_prod(U_13371,U_13372),tc_HOL_Obool),tc_HOL_Obool),U_13372),c_member(tc_prod(U_13371,U_13372)))),c_Product__Type_OPair(U_13371,U_13372)))),U_13374))))),hAPP(hAPP(c_COMBC(U_13373,tc_fun(tc_prod(U_13372,U_13373),tc_HOL_Obool),tc_fun(U_13372,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13372,tc_fun(tc_fun(tc_prod(U_13372,U_13373),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13372,U_13373),tc_HOL_Obool),tc_fun(U_13372,tc_HOL_Obool)),U_13373),c_COMBC(U_13372,tc_fun(tc_prod(U_13372,U_13373),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13372,tc_prod(U_13372,U_13373)),tc_fun(U_13372,tc_fun(tc_fun(tc_prod(U_13372,U_13373),tc_HOL_Obool),tc_HOL_Obool)),U_13373),hAPP(c_COMBB(tc_prod(U_13372,U_13373),tc_fun(tc_fun(tc_prod(U_13372,U_13373),tc_HOL_Obool),tc_HOL_Obool),U_13372),c_member(tc_prod(U_13372,U_13373)))),hAPP(c_COMBC(U_13372,U_13373,tc_prod(U_13372,U_13373)),c_Product__Type_OPair(U_13372,U_13373))))),U_13375))))),
inference(clausify,[status(thm)],[f_3423_2]) ).
fof(f_3424_1,plain,
! [V_P_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_P_2))),
inference(fof_nnf,[status(thm)],[fact_Range__Collect__split]) ).
fof(f_3424_2,plain,
! [U_13378,U_13377,U_13376] : hAPP(c_Relation_ORange(U_13376,U_13377),hAPP(c_Set_OCollect(tc_prod(U_13376,U_13377)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13376,U_13377,tc_HOL_Obool),U_13378))) = hAPP(c_Set_OCollect(U_13377),hAPP(hAPP(c_COMBB(tc_fun(U_13376,tc_HOL_Obool),tc_HOL_Obool,U_13377),c_HOL_OEx(U_13376)),hAPP(c_COMBC(U_13376,U_13377,tc_HOL_Obool),U_13378))),
inference(variable_rename,[status(thm)],[f_3424_1]) ).
cnf(f_3424_3,plain,
hAPP(c_Relation_ORange(U_13376,U_13377),hAPP(c_Set_OCollect(tc_prod(U_13376,U_13377)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13376,U_13377,tc_HOL_Obool),U_13378))) = hAPP(c_Set_OCollect(U_13377),hAPP(hAPP(c_COMBB(tc_fun(U_13376,tc_HOL_Obool),tc_HOL_Obool,U_13377),c_HOL_OEx(U_13376)),hAPP(c_COMBC(U_13376,U_13377,tc_HOL_Obool),U_13378))),
inference(clausify,[status(thm)],[f_3424_2]) ).
fof(f_3425_1,plain,
! [V_s_2,V_c_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_a_2),V_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_b_2),V_c_2)),V_s_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_rel__compI]) ).
fof(f_3425_2,plain,
! [U_13386,U_13385,U_13384,U_13383,U_13382,U_13381,U_13380,U_13379] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13379,U_13384)),hAPP(hAPP(c_Product__Type_OPair(U_13379,U_13384),U_13381),U_13385)),hAPP(hAPP(c_Relation_Orel__comp(U_13379,U_13380,U_13384),U_13383),U_13386)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13380,U_13384)),hAPP(hAPP(c_Product__Type_OPair(U_13380,U_13384),U_13382),U_13385)),U_13386))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13379,U_13380)),hAPP(hAPP(c_Product__Type_OPair(U_13379,U_13380),U_13381),U_13382)),U_13383)) ),
inference(variable_rename,[status(thm)],[f_3425_1]) ).
cnf(f_3425_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13379,U_13384)),hAPP(hAPP(c_Product__Type_OPair(U_13379,U_13384),U_13381),U_13385)),hAPP(hAPP(c_Relation_Orel__comp(U_13379,U_13380,U_13384),U_13383),U_13386)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13380,U_13384)),hAPP(hAPP(c_Product__Type_OPair(U_13380,U_13384),U_13382),U_13385)),U_13386))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13379,U_13380)),hAPP(hAPP(c_Product__Type_OPair(U_13379,U_13380),U_13381),U_13382)),U_13383)) ),
inference(clausify,[status(thm)],[f_3425_2]) ).
fof(f_3426_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_3426_2,plain,
! [U_13391,U_13390,U_13389,U_13388,U_13387] :
( hBOOL(hAPP(hAPP(c_member(U_13388),U_13390),hAPP(c_Relation_ORange(U_13387,U_13388),U_13391)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13387,U_13388)),hAPP(hAPP(c_Product__Type_OPair(U_13387,U_13388),U_13389),U_13390)),U_13391)) ),
inference(variable_rename,[status(thm)],[f_3426_1]) ).
cnf(f_3426_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_13388),U_13390),hAPP(c_Relation_ORange(U_13387,U_13388),U_13391)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13387,U_13388)),hAPP(hAPP(c_Product__Type_OPair(U_13387,U_13388),U_13389),U_13390)),U_13391)) ),
inference(clausify,[status(thm)],[f_3426_2]) ).
fof(f_3427_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_3427_2,plain,
! [U_13398,U_13397,U_13396,U_13395,U_13394,U_13393,U_13392] : hAPP(hAPP(c_Relation_Orel__comp(U_13392,U_13393,U_13394),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13395,tc_fun(tc_prod(U_13392,U_13393),tc_HOL_Obool)),U_13396),U_13397)),U_13398) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13395,tc_fun(tc_prod(U_13392,U_13394),tc_HOL_Obool)),U_13396),hAPP(hAPP(c_COMBC(U_13395,tc_fun(tc_prod(U_13393,U_13394),tc_HOL_Obool),tc_fun(tc_prod(U_13392,U_13394),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13392,U_13393),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_13393,U_13394),tc_HOL_Obool),tc_fun(tc_prod(U_13392,U_13394),tc_HOL_Obool)),U_13395),c_Relation_Orel__comp(U_13392,U_13393,U_13394)),U_13397)),U_13398)),
inference(variable_rename,[status(thm)],[f_3427_1]) ).
cnf(f_3427_3,plain,
hAPP(hAPP(c_Relation_Orel__comp(U_13392,U_13393,U_13394),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13395,tc_fun(tc_prod(U_13392,U_13393),tc_HOL_Obool)),U_13396),U_13397)),U_13398) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13395,tc_fun(tc_prod(U_13392,U_13394),tc_HOL_Obool)),U_13396),hAPP(hAPP(c_COMBC(U_13395,tc_fun(tc_prod(U_13393,U_13394),tc_HOL_Obool),tc_fun(tc_prod(U_13392,U_13394),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13392,U_13393),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_13393,U_13394),tc_HOL_Obool),tc_fun(tc_prod(U_13392,U_13394),tc_HOL_Obool)),U_13395),c_Relation_Orel__comp(U_13392,U_13393,U_13394)),U_13397)),U_13398)),
inference(clausify,[status(thm)],[f_3427_2]) ).
fof(f_3428_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_3428_2,plain,
! [U_13405,U_13404,U_13403,U_13402,U_13401,U_13400,U_13399] : hAPP(hAPP(c_Relation_Orel__comp(U_13399,U_13400,U_13401),U_13402),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13403,tc_fun(tc_prod(U_13400,U_13401),tc_HOL_Obool)),U_13404),U_13405)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13403,tc_fun(tc_prod(U_13399,U_13401),tc_HOL_Obool)),U_13404),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13400,U_13401),tc_HOL_Obool),tc_fun(tc_prod(U_13399,U_13401),tc_HOL_Obool),U_13403),hAPP(c_Relation_Orel__comp(U_13399,U_13400,U_13401),U_13402)),U_13405)),
inference(variable_rename,[status(thm)],[f_3428_1]) ).
cnf(f_3428_3,plain,
hAPP(hAPP(c_Relation_Orel__comp(U_13399,U_13400,U_13401),U_13402),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13403,tc_fun(tc_prod(U_13400,U_13401),tc_HOL_Obool)),U_13404),U_13405)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13403,tc_fun(tc_prod(U_13399,U_13401),tc_HOL_Obool)),U_13404),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13400,U_13401),tc_HOL_Obool),tc_fun(tc_prod(U_13399,U_13401),tc_HOL_Obool),U_13403),hAPP(c_Relation_Orel__comp(U_13399,U_13400,U_13401),U_13402)),U_13405)),
inference(clausify,[status(thm)],[f_3428_2]) ).
fof(f_3429_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_3429_2,plain,
! [U_13407,U_13406] : hAPP(c_Relation_ORange(U_13406,U_13406),c_Relation_OId__on(U_13406,U_13407)) = U_13407,
inference(variable_rename,[status(thm)],[f_3429_1]) ).
cnf(f_3429_3,plain,
hAPP(c_Relation_ORange(U_13406,U_13406),c_Relation_OId__on(U_13406,U_13407)) = U_13407,
inference(clausify,[status(thm)],[f_3429_2]) ).
fof(f_3430_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_3430_2,plain,
! [U_13414,U_13413,U_13412,U_13411,U_13410,U_13409,U_13408] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13408,U_13412),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13408,U_13409,U_13412),U_13410),U_13413)),hAPP(hAPP(c_Relation_Orel__comp(U_13408,U_13409,U_13412),U_13411),U_13414)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13409,U_13412),tc_HOL_Obool)),U_13413),U_13414))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13408,U_13409),tc_HOL_Obool)),U_13410),U_13411)) ),
inference(variable_rename,[status(thm)],[f_3430_1]) ).
cnf(f_3430_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13408,U_13412),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13408,U_13409,U_13412),U_13410),U_13413)),hAPP(hAPP(c_Relation_Orel__comp(U_13408,U_13409,U_13412),U_13411),U_13414)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13409,U_13412),tc_HOL_Obool)),U_13413),U_13414))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13408,U_13409),tc_HOL_Obool)),U_13410),U_13411)) ),
inference(clausify,[status(thm)],[f_3430_2]) ).
fof(f_3431_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_3431_2,plain,
! [U_13421,U_13420,U_13419,U_13418,U_13417,U_13416,U_13415] : hAPP(hAPP(c_Relation_Orel__comp(U_13415,U_13416,U_13417),hAPP(hAPP(c_Relation_Orel__comp(U_13415,U_13418,U_13416),U_13419),U_13420)),U_13421) = hAPP(hAPP(c_Relation_Orel__comp(U_13415,U_13418,U_13417),U_13419),hAPP(hAPP(c_Relation_Orel__comp(U_13418,U_13416,U_13417),U_13420),U_13421)),
inference(variable_rename,[status(thm)],[f_3431_1]) ).
cnf(f_3431_3,plain,
hAPP(hAPP(c_Relation_Orel__comp(U_13415,U_13416,U_13417),hAPP(hAPP(c_Relation_Orel__comp(U_13415,U_13418,U_13416),U_13419),U_13420)),U_13421) = hAPP(hAPP(c_Relation_Orel__comp(U_13415,U_13418,U_13417),U_13419),hAPP(hAPP(c_Relation_Orel__comp(U_13418,U_13416,U_13417),U_13420),U_13421)),
inference(clausify,[status(thm)],[f_3431_2]) ).
fof(f_3432_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_3432_2,plain,
! [U_13427,U_13426,U_13425,U_13424,U_13423,U_13422] : hAPP(hAPP(c_Relation_Orel__comp(U_13422,U_13423,U_13424),U_13425),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13423,U_13424),tc_HOL_Obool)),U_13426),U_13427)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13422,U_13424),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13422,U_13423,U_13424),U_13425),U_13426)),hAPP(hAPP(c_Relation_Orel__comp(U_13422,U_13423,U_13424),U_13425),U_13427)),
inference(variable_rename,[status(thm)],[f_3432_1]) ).
cnf(f_3432_3,plain,
hAPP(hAPP(c_Relation_Orel__comp(U_13422,U_13423,U_13424),U_13425),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13423,U_13424),tc_HOL_Obool)),U_13426),U_13427)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13422,U_13424),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13422,U_13423,U_13424),U_13425),U_13426)),hAPP(hAPP(c_Relation_Orel__comp(U_13422,U_13423,U_13424),U_13425),U_13427)),
inference(clausify,[status(thm)],[f_3432_2]) ).
fof(f_3433_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_3433_2,plain,
! [U_13433,U_13432,U_13431,U_13430,U_13429,U_13428] : hAPP(hAPP(c_Relation_Orel__comp(U_13428,U_13429,U_13430),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13428,U_13429),tc_HOL_Obool)),U_13431),U_13432)),U_13433) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13428,U_13430),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13428,U_13429,U_13430),U_13431),U_13433)),hAPP(hAPP(c_Relation_Orel__comp(U_13428,U_13429,U_13430),U_13432),U_13433)),
inference(variable_rename,[status(thm)],[f_3433_1]) ).
cnf(f_3433_3,plain,
hAPP(hAPP(c_Relation_Orel__comp(U_13428,U_13429,U_13430),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13428,U_13429),tc_HOL_Obool)),U_13431),U_13432)),U_13433) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13428,U_13430),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13428,U_13429,U_13430),U_13431),U_13433)),hAPP(hAPP(c_Relation_Orel__comp(U_13428,U_13429,U_13430),U_13432),U_13433)),
inference(clausify,[status(thm)],[f_3433_2]) ).
fof(f_3434_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_3434_2,plain,
! [U_13437,U_13436,U_13435,U_13434] : hAPP(hAPP(c_Relation_Orel__comp(U_13434,U_13435,U_13436),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13434,U_13435),tc_HOL_Obool))),U_13437) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13434,U_13436),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3434_1]) ).
cnf(f_3434_3,plain,
hAPP(hAPP(c_Relation_Orel__comp(U_13434,U_13435,U_13436),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13434,U_13435),tc_HOL_Obool))),U_13437) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13434,U_13436),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3434_2]) ).
fof(f_3435_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_3435_2,plain,
! [U_13441,U_13440,U_13439,U_13438] : hAPP(hAPP(c_Relation_Orel__comp(U_13438,U_13439,U_13440),U_13441),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13439,U_13440),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13438,U_13440),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3435_1]) ).
cnf(f_3435_3,plain,
hAPP(hAPP(c_Relation_Orel__comp(U_13438,U_13439,U_13440),U_13441),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13439,U_13440),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13438,U_13440),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3435_2]) ).
fof(f_3436_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_3436_2,plain,
! [U_13445,U_13444,U_13443,U_13442] :
( hAPP(hAPP(c_Relation_Orel__comp(U_13442,U_13442,U_13442),U_13443),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13442,U_13442),tc_HOL_Obool)),U_13444),U_13445)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13442,U_13442),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(U_13442,U_13442,U_13442),U_13443),U_13445) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13442,U_13442),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(U_13442,U_13442,U_13442),U_13443),U_13444) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13442,U_13442),tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_3436_1]) ).
cnf(f_3436_3,plain,
( hAPP(hAPP(c_Relation_Orel__comp(U_13442,U_13442,U_13442),U_13443),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13442,U_13442),tc_HOL_Obool)),U_13444),U_13445)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13442,U_13442),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(U_13442,U_13442,U_13442),U_13443),U_13445) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13442,U_13442),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(U_13442,U_13442,U_13442),U_13443),U_13444) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13442,U_13442),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3436_2]) ).
fof(f_3437_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_3437_2,plain,
! [U_13449,U_13448,U_13447,U_13446] :
( hAPP(hAPP(c_Relation_Orel__comp(U_13446,U_13446,U_13446),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13446,U_13446),tc_HOL_Obool)),U_13447),U_13449)),U_13448) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13446,U_13446),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(U_13446,U_13446,U_13446),U_13449),U_13448) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13446,U_13446),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(U_13446,U_13446,U_13446),U_13447),U_13448) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13446,U_13446),tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_3437_1]) ).
cnf(f_3437_3,plain,
( hAPP(hAPP(c_Relation_Orel__comp(U_13446,U_13446,U_13446),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13446,U_13446),tc_HOL_Obool)),U_13447),U_13449)),U_13448) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13446,U_13446),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(U_13446,U_13446,U_13446),U_13449),U_13448) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13446,U_13446),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(U_13446,U_13446,U_13446),U_13447),U_13448) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13446,U_13446),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3437_2]) ).
fof(f_3438_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_3438_2,plain,
! [U_13452,U_13451,U_13450] : hAPP(c_Relation_ORange(U_13450,U_13451),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_13450,U_13451),tc_HOL_Obool),U_13452)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_13450,U_13451),tc_HOL_Obool),tc_fun(U_13451,tc_HOL_Obool)),U_13452),c_Relation_ORange(U_13450,U_13451)),
inference(variable_rename,[status(thm)],[f_3438_1]) ).
cnf(f_3438_3,plain,
hAPP(c_Relation_ORange(U_13450,U_13451),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_13450,U_13451),tc_HOL_Obool),U_13452)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_13450,U_13451),tc_HOL_Obool),tc_fun(U_13451,tc_HOL_Obool)),U_13452),c_Relation_ORange(U_13450,U_13451)),
inference(clausify,[status(thm)],[f_3438_2]) ).
fof(f_3439_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_3439_2,plain,
! [U_13454,U_13453] : hAPP(c_Relation_ORange(U_13453,U_13454),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13453,U_13454),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13454,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3439_1]) ).
cnf(f_3439_3,plain,
hAPP(c_Relation_ORange(U_13453,U_13454),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13453,U_13454),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13454,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3439_2]) ).
fof(f_3440_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_3440_2,plain,
! [U_13457,U_13456,U_13455] :
( ( hAPP(c_Relation_ORange(U_13455,U_13456),U_13457) = c_Orderings_Obot__class_Obot(tc_fun(U_13456,tc_HOL_Obool))
| U_13457 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13455,U_13456),tc_HOL_Obool)) )
& ( U_13457 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13455,U_13456),tc_HOL_Obool))
| hAPP(c_Relation_ORange(U_13455,U_13456),U_13457) != c_Orderings_Obot__class_Obot(tc_fun(U_13456,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_3440_1]) ).
fof(f_3440_3,plain,
( ! [U_13463,U_13461,U_13459] :
( hAPP(c_Relation_ORange(U_13459,U_13461),U_13463) = c_Orderings_Obot__class_Obot(tc_fun(U_13461,tc_HOL_Obool))
| U_13463 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13459,U_13461),tc_HOL_Obool)) )
& ! [U_13462,U_13460,U_13458] :
( U_13462 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13458,U_13460),tc_HOL_Obool))
| hAPP(c_Relation_ORange(U_13458,U_13460),U_13462) != c_Orderings_Obot__class_Obot(tc_fun(U_13460,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_3440_2]) ).
cnf(f_3440_4,plain,
( U_13462 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13458,U_13460),tc_HOL_Obool))
| hAPP(c_Relation_ORange(U_13458,U_13460),U_13462) != c_Orderings_Obot__class_Obot(tc_fun(U_13460,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3440_3]) ).
cnf(f_3440_5,plain,
( hAPP(c_Relation_ORange(U_13459,U_13461),U_13463) = c_Orderings_Obot__class_Obot(tc_fun(U_13461,tc_HOL_Obool))
| U_13463 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13459,U_13461),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3440_3]) ).
fof(f_3441_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_3441_2,plain,
! [U_13471,U_13470,U_13469,U_13468,U_13467,U_13466,U_13465,U_13464] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13464,U_13469),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13464,U_13465,U_13469),U_13466),U_13470)),hAPP(hAPP(c_Product__Type_OSigma(U_13464,U_13469),U_13467),hAPP(c_COMBK(tc_fun(U_13469,tc_HOL_Obool),U_13464),U_13471))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13465,U_13469),tc_HOL_Obool)),U_13470),hAPP(hAPP(c_Product__Type_OSigma(U_13465,U_13469),U_13468),hAPP(c_COMBK(tc_fun(U_13469,tc_HOL_Obool),U_13465),U_13471))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13464,U_13465),tc_HOL_Obool)),U_13466),hAPP(hAPP(c_Product__Type_OSigma(U_13464,U_13465),U_13467),hAPP(c_COMBK(tc_fun(U_13465,tc_HOL_Obool),U_13464),U_13468)))) ),
inference(variable_rename,[status(thm)],[f_3441_1]) ).
cnf(f_3441_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13464,U_13469),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13464,U_13465,U_13469),U_13466),U_13470)),hAPP(hAPP(c_Product__Type_OSigma(U_13464,U_13469),U_13467),hAPP(c_COMBK(tc_fun(U_13469,tc_HOL_Obool),U_13464),U_13471))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13465,U_13469),tc_HOL_Obool)),U_13470),hAPP(hAPP(c_Product__Type_OSigma(U_13465,U_13469),U_13468),hAPP(c_COMBK(tc_fun(U_13469,tc_HOL_Obool),U_13465),U_13471))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13464,U_13465),tc_HOL_Obool)),U_13466),hAPP(hAPP(c_Product__Type_OSigma(U_13464,U_13465),U_13467),hAPP(c_COMBK(tc_fun(U_13465,tc_HOL_Obool),U_13464),U_13468)))) ),
inference(clausify,[status(thm)],[f_3441_2]) ).
fof(f_3442_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_3442_2,plain,
! [U_13475,U_13474,U_13473,U_13472] : hAPP(c_Relation_ORange(U_13472,U_13473),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13472,U_13473),tc_HOL_Obool)),U_13474),U_13475)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13473,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13472,U_13473),U_13474)),hAPP(c_Relation_ORange(U_13472,U_13473),U_13475)),
inference(variable_rename,[status(thm)],[f_3442_1]) ).
cnf(f_3442_3,plain,
hAPP(c_Relation_ORange(U_13472,U_13473),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13472,U_13473),tc_HOL_Obool)),U_13474),U_13475)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13473,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13472,U_13473),U_13474)),hAPP(c_Relation_ORange(U_13472,U_13473),U_13475)),
inference(clausify,[status(thm)],[f_3442_2]) ).
fof(f_3443_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_3443_2,plain,
! [U_13478,U_13477,U_13476] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13477),hAPP(c_Relation_ORange(U_13476,U_13477),U_13478)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13476,U_13477)),U_13478)) ),
inference(variable_rename,[status(thm)],[f_3443_1]) ).
cnf(f_3443_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13477),hAPP(c_Relation_ORange(U_13476,U_13477),U_13478)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13476,U_13477)),U_13478)) ),
inference(clausify,[status(thm)],[f_3443_2]) ).
fof(f_3444_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_3444_2,plain,
! [U_13481,U_13480,U_13479] : hAPP(c_Set_Oimage(tc_prod(U_13479,U_13480),U_13480,c_Product__Type_Osnd(U_13479,U_13480)),U_13481) = hAPP(c_Relation_ORange(U_13479,U_13480),U_13481),
inference(variable_rename,[status(thm)],[f_3444_1]) ).
cnf(f_3444_3,plain,
hAPP(c_Set_Oimage(tc_prod(U_13479,U_13480),U_13480,c_Product__Type_Osnd(U_13479,U_13480)),U_13481) = hAPP(c_Relation_ORange(U_13479,U_13480),U_13481),
inference(clausify,[status(thm)],[f_3444_2]) ).
fof(f_3445_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_3445_2,plain,
! [U_13487,U_13486,U_13485,U_13484] :
( ( hBOOL(hAPP(hAPP(c_member(U_13484),U_13485),hAPP(c_Relation_ORange(U_13486,U_13484),U_13487)))
| ! [U_13483] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13486,U_13484)),hAPP(hAPP(c_Product__Type_OPair(U_13486,U_13484),U_13483),U_13485)),U_13487)) )
& ( ? [U_13482] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13486,U_13484)),hAPP(hAPP(c_Product__Type_OPair(U_13486,U_13484),U_13482),U_13485)),U_13487))
| ~ hBOOL(hAPP(hAPP(c_member(U_13484),U_13485),hAPP(c_Relation_ORange(U_13486,U_13484),U_13487))) ) ),
inference(variable_rename,[status(thm)],[f_3445_1]) ).
fof(f_3445_3,plain,
( ! [U_13495,U_13493,U_13491,U_13489] :
( hBOOL(hAPP(hAPP(c_member(U_13489),U_13491),hAPP(c_Relation_ORange(U_13493,U_13489),U_13495)))
| ! [U_13483] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13493,U_13489)),hAPP(hAPP(c_Product__Type_OPair(U_13493,U_13489),U_13483),U_13491)),U_13495)) )
& ! [U_13494,U_13492,U_13490,U_13488] :
( ? [U_13482] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13492,U_13488)),hAPP(hAPP(c_Product__Type_OPair(U_13492,U_13488),U_13482),U_13490)),U_13494))
| ~ hBOOL(hAPP(hAPP(c_member(U_13488),U_13490),hAPP(c_Relation_ORange(U_13492,U_13488),U_13494))) ) ),
inference(miniscope,[status(thm)],[f_3445_2]) ).
fof(f_3445_4,plain,
( ! [U_13495,U_13493,U_13491,U_13489] :
( hBOOL(hAPP(hAPP(c_member(U_13489),U_13491),hAPP(c_Relation_ORange(U_13493,U_13489),U_13495)))
| ! [U_13483] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13493,U_13489)),hAPP(hAPP(c_Product__Type_OPair(U_13493,U_13489),U_13483),U_13491)),U_13495)) )
& ! [U_13494,U_13492,U_13490,U_13488] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13492,U_13488)),hAPP(hAPP(c_Product__Type_OPair(U_13492,U_13488),sK327(U_13494,U_13492,U_13490,U_13488)),U_13490)),U_13494))
| ~ hBOOL(hAPP(hAPP(c_member(U_13488),U_13490),hAPP(c_Relation_ORange(U_13492,U_13488),U_13494))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK327]),skolemize(U_13482,sK327(U_13494,U_13492,U_13490,U_13488))],[f_3445_3]) ).
cnf(f_3445_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13492,U_13488)),hAPP(hAPP(c_Product__Type_OPair(U_13492,U_13488),sK327(U_13494,U_13492,U_13490,U_13488)),U_13490)),U_13494))
| ~ hBOOL(hAPP(hAPP(c_member(U_13488),U_13490),hAPP(c_Relation_ORange(U_13492,U_13488),U_13494))) ),
inference(clausify,[status(thm)],[f_3445_4]) ).
cnf(f_3445_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_13489),U_13491),hAPP(c_Relation_ORange(U_13493,U_13489),U_13495)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13493,U_13489)),hAPP(hAPP(c_Product__Type_OPair(U_13493,U_13489),U_13483),U_13491)),U_13495)) ),
inference(clausify,[status(thm)],[f_3445_4]) ).
fof(f_3446_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_3446_2,plain,
! [U_13500,U_13499,U_13498,U_13497,U_13496] : hAPP(c_Relation_ORange(U_13496,U_13497),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13496,U_13497)),hAPP(hAPP(c_Product__Type_OPair(U_13496,U_13497),U_13498),U_13499)),U_13500)) = hAPP(hAPP(c_Set_Oinsert(U_13497),U_13499),hAPP(c_Relation_ORange(U_13496,U_13497),U_13500)),
inference(variable_rename,[status(thm)],[f_3446_1]) ).
cnf(f_3446_3,plain,
hAPP(c_Relation_ORange(U_13496,U_13497),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13496,U_13497)),hAPP(hAPP(c_Product__Type_OPair(U_13496,U_13497),U_13498),U_13499)),U_13500)) = hAPP(hAPP(c_Set_Oinsert(U_13497),U_13499),hAPP(c_Relation_ORange(U_13496,U_13497),U_13500)),
inference(clausify,[status(thm)],[f_3446_2]) ).
fof(f_3447_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_3447_2,plain,
! [U_13504,U_13503,U_13502,U_13501] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13501,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13502,U_13501),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13502,U_13501),tc_HOL_Obool)),U_13503),U_13504))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13501,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13502,U_13501),U_13503)),hAPP(c_Relation_ORange(U_13502,U_13501),U_13504)))),
inference(variable_rename,[status(thm)],[f_3447_1]) ).
cnf(f_3447_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13501,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13502,U_13501),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13502,U_13501),tc_HOL_Obool)),U_13503),U_13504))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13501,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13502,U_13501),U_13503)),hAPP(c_Relation_ORange(U_13502,U_13501),U_13504)))),
inference(clausify,[status(thm)],[f_3447_2]) ).
fof(f_3448_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_3448_2,plain,
! [U_13508,U_13507,U_13506,U_13505] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13505,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13505,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13506,U_13505),U_13507)),hAPP(c_Relation_ORange(U_13506,U_13505),U_13508))),hAPP(c_Relation_ORange(U_13506,U_13505),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13506,U_13505),tc_HOL_Obool)),U_13507),U_13508)))),
inference(variable_rename,[status(thm)],[f_3448_1]) ).
cnf(f_3448_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13505,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13505,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13506,U_13505),U_13507)),hAPP(c_Relation_ORange(U_13506,U_13505),U_13508))),hAPP(c_Relation_ORange(U_13506,U_13505),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13506,U_13505),tc_HOL_Obool)),U_13507),U_13508)))),
inference(clausify,[status(thm)],[f_3448_2]) ).
fof(f_3449_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_3449_2,plain,
! [U_13511,U_13510,U_13509] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_13509,tc_HOL_Obool),tc_fun(U_13509,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_13509,tc_HOL_Obool),tc_fun(U_13509,tc_HOL_Obool),tc_fun(U_13509,tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_13509,U_13510)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_13509,tc_HOL_Obool),tc_fun(U_13509,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_13509,U_13511)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_13509,tc_HOL_Obool),tc_fun(U_13509,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13509,tc_HOL_Obool),tc_fun(U_13509,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13509,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_13509,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_13509,tc_HOL_Obool),tc_fun(U_13509,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(U_13509,U_13510)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13509,U_13509),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13509,U_13509,U_13509),U_13510),U_13511)),U_13510)) ),
inference(variable_rename,[status(thm)],[f_3449_1]) ).
cnf(f_3449_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_13509,tc_HOL_Obool),tc_fun(U_13509,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_13509,tc_HOL_Obool),tc_fun(U_13509,tc_HOL_Obool),tc_fun(U_13509,tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_13509,U_13510)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_13509,tc_HOL_Obool),tc_fun(U_13509,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_13509,U_13511)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_13509,tc_HOL_Obool),tc_fun(U_13509,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13509,tc_HOL_Obool),tc_fun(U_13509,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13509,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_13509,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_13509,tc_HOL_Obool),tc_fun(U_13509,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(U_13509,U_13510)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13509,U_13509),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13509,U_13509,U_13509),U_13510),U_13511)),U_13510)) ),
inference(clausify,[status(thm)],[f_3449_2]) ).
fof(f_3450_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_3450_2,plain,
! [U_13514,U_13513,U_13512] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_13512,tc_HOL_Obool),tc_fun(U_13512,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_13512,tc_HOL_Obool),tc_fun(U_13512,tc_HOL_Obool),tc_fun(U_13512,tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_13512,U_13513)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_13512,tc_HOL_Obool),tc_fun(U_13512,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_13512,U_13514)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_13512,tc_HOL_Obool),tc_fun(U_13512,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13512,tc_HOL_Obool),tc_fun(U_13512,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13512,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_13512,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_13512,tc_HOL_Obool),tc_fun(U_13512,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(U_13512,U_13513)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13512,U_13512),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13512,U_13512,U_13512),U_13513),U_13514)),U_13513)) ),
inference(variable_rename,[status(thm)],[f_3450_1]) ).
cnf(f_3450_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_13512,tc_HOL_Obool),tc_fun(U_13512,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_13512,tc_HOL_Obool),tc_fun(U_13512,tc_HOL_Obool),tc_fun(U_13512,tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_13512,U_13513)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_13512,tc_HOL_Obool),tc_fun(U_13512,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_13512,U_13514)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_13512,tc_HOL_Obool),tc_fun(U_13512,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13512,tc_HOL_Obool),tc_fun(U_13512,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13512,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_13512,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_13512,tc_HOL_Obool),tc_fun(U_13512,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(U_13512,U_13513)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13512,U_13512),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13512,U_13512,U_13512),U_13513),U_13514)),U_13513)) ),
inference(clausify,[status(thm)],[f_3450_2]) ).
fof(f_3451_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_3451_2,plain,
! [U_13518,U_13517,U_13516,U_13515] :
( ( hBOOL(hAPP(c_Predicate_ORangeP(U_13515,U_13516,hAPP(hAPP(c_COMBC(U_13515,tc_fun(tc_prod(U_13515,U_13516),tc_HOL_Obool),tc_fun(U_13516,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13516,tc_fun(tc_fun(tc_prod(U_13515,U_13516),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13515,U_13516),tc_HOL_Obool),tc_fun(U_13516,tc_HOL_Obool)),U_13515),c_COMBC(U_13516,tc_fun(tc_prod(U_13515,U_13516),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13516,tc_prod(U_13515,U_13516)),tc_fun(U_13516,tc_fun(tc_fun(tc_prod(U_13515,U_13516),tc_HOL_Obool),tc_HOL_Obool)),U_13515),hAPP(c_COMBB(tc_prod(U_13515,U_13516),tc_fun(tc_fun(tc_prod(U_13515,U_13516),tc_HOL_Obool),tc_HOL_Obool),U_13516),c_member(tc_prod(U_13515,U_13516)))),c_Product__Type_OPair(U_13515,U_13516)))),U_13517)),U_13518))
| ~ hBOOL(hAPP(hAPP(c_member(U_13516),U_13518),hAPP(c_Relation_ORange(U_13515,U_13516),U_13517))) )
& ( hBOOL(hAPP(hAPP(c_member(U_13516),U_13518),hAPP(c_Relation_ORange(U_13515,U_13516),U_13517)))
| ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13515,U_13516,hAPP(hAPP(c_COMBC(U_13515,tc_fun(tc_prod(U_13515,U_13516),tc_HOL_Obool),tc_fun(U_13516,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13516,tc_fun(tc_fun(tc_prod(U_13515,U_13516),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13515,U_13516),tc_HOL_Obool),tc_fun(U_13516,tc_HOL_Obool)),U_13515),c_COMBC(U_13516,tc_fun(tc_prod(U_13515,U_13516),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13516,tc_prod(U_13515,U_13516)),tc_fun(U_13516,tc_fun(tc_fun(tc_prod(U_13515,U_13516),tc_HOL_Obool),tc_HOL_Obool)),U_13515),hAPP(c_COMBB(tc_prod(U_13515,U_13516),tc_fun(tc_fun(tc_prod(U_13515,U_13516),tc_HOL_Obool),tc_HOL_Obool),U_13516),c_member(tc_prod(U_13515,U_13516)))),c_Product__Type_OPair(U_13515,U_13516)))),U_13517)),U_13518)) ) ),
inference(variable_rename,[status(thm)],[f_3451_1]) ).
fof(f_3451_3,plain,
( ! [U_13526,U_13524,U_13522,U_13520] :
( hBOOL(hAPP(c_Predicate_ORangeP(U_13520,U_13522,hAPP(hAPP(c_COMBC(U_13520,tc_fun(tc_prod(U_13520,U_13522),tc_HOL_Obool),tc_fun(U_13522,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13522,tc_fun(tc_fun(tc_prod(U_13520,U_13522),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13520,U_13522),tc_HOL_Obool),tc_fun(U_13522,tc_HOL_Obool)),U_13520),c_COMBC(U_13522,tc_fun(tc_prod(U_13520,U_13522),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13522,tc_prod(U_13520,U_13522)),tc_fun(U_13522,tc_fun(tc_fun(tc_prod(U_13520,U_13522),tc_HOL_Obool),tc_HOL_Obool)),U_13520),hAPP(c_COMBB(tc_prod(U_13520,U_13522),tc_fun(tc_fun(tc_prod(U_13520,U_13522),tc_HOL_Obool),tc_HOL_Obool),U_13522),c_member(tc_prod(U_13520,U_13522)))),c_Product__Type_OPair(U_13520,U_13522)))),U_13524)),U_13526))
| ~ hBOOL(hAPP(hAPP(c_member(U_13522),U_13526),hAPP(c_Relation_ORange(U_13520,U_13522),U_13524))) )
& ! [U_13525,U_13523,U_13521,U_13519] :
( hBOOL(hAPP(hAPP(c_member(U_13521),U_13525),hAPP(c_Relation_ORange(U_13519,U_13521),U_13523)))
| ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13519,U_13521,hAPP(hAPP(c_COMBC(U_13519,tc_fun(tc_prod(U_13519,U_13521),tc_HOL_Obool),tc_fun(U_13521,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13521,tc_fun(tc_fun(tc_prod(U_13519,U_13521),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13519,U_13521),tc_HOL_Obool),tc_fun(U_13521,tc_HOL_Obool)),U_13519),c_COMBC(U_13521,tc_fun(tc_prod(U_13519,U_13521),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13521,tc_prod(U_13519,U_13521)),tc_fun(U_13521,tc_fun(tc_fun(tc_prod(U_13519,U_13521),tc_HOL_Obool),tc_HOL_Obool)),U_13519),hAPP(c_COMBB(tc_prod(U_13519,U_13521),tc_fun(tc_fun(tc_prod(U_13519,U_13521),tc_HOL_Obool),tc_HOL_Obool),U_13521),c_member(tc_prod(U_13519,U_13521)))),c_Product__Type_OPair(U_13519,U_13521)))),U_13523)),U_13525)) ) ),
inference(miniscope,[status(thm)],[f_3451_2]) ).
cnf(f_3451_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_13521),U_13525),hAPP(c_Relation_ORange(U_13519,U_13521),U_13523)))
| ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13519,U_13521,hAPP(hAPP(c_COMBC(U_13519,tc_fun(tc_prod(U_13519,U_13521),tc_HOL_Obool),tc_fun(U_13521,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13521,tc_fun(tc_fun(tc_prod(U_13519,U_13521),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13519,U_13521),tc_HOL_Obool),tc_fun(U_13521,tc_HOL_Obool)),U_13519),c_COMBC(U_13521,tc_fun(tc_prod(U_13519,U_13521),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13521,tc_prod(U_13519,U_13521)),tc_fun(U_13521,tc_fun(tc_fun(tc_prod(U_13519,U_13521),tc_HOL_Obool),tc_HOL_Obool)),U_13519),hAPP(c_COMBB(tc_prod(U_13519,U_13521),tc_fun(tc_fun(tc_prod(U_13519,U_13521),tc_HOL_Obool),tc_HOL_Obool),U_13521),c_member(tc_prod(U_13519,U_13521)))),c_Product__Type_OPair(U_13519,U_13521)))),U_13523)),U_13525)) ),
inference(clausify,[status(thm)],[f_3451_3]) ).
cnf(f_3451_5,plain,
( hBOOL(hAPP(c_Predicate_ORangeP(U_13520,U_13522,hAPP(hAPP(c_COMBC(U_13520,tc_fun(tc_prod(U_13520,U_13522),tc_HOL_Obool),tc_fun(U_13522,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13522,tc_fun(tc_fun(tc_prod(U_13520,U_13522),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13520,U_13522),tc_HOL_Obool),tc_fun(U_13522,tc_HOL_Obool)),U_13520),c_COMBC(U_13522,tc_fun(tc_prod(U_13520,U_13522),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13522,tc_prod(U_13520,U_13522)),tc_fun(U_13522,tc_fun(tc_fun(tc_prod(U_13520,U_13522),tc_HOL_Obool),tc_HOL_Obool)),U_13520),hAPP(c_COMBB(tc_prod(U_13520,U_13522),tc_fun(tc_fun(tc_prod(U_13520,U_13522),tc_HOL_Obool),tc_HOL_Obool),U_13522),c_member(tc_prod(U_13520,U_13522)))),c_Product__Type_OPair(U_13520,U_13522)))),U_13524)),U_13526))
| ~ hBOOL(hAPP(hAPP(c_member(U_13522),U_13526),hAPP(c_Relation_ORange(U_13520,U_13522),U_13524))) ),
inference(clausify,[status(thm)],[f_3451_3]) ).
fof(f_3452_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_3452_2,plain,
! [U_13531,U_13530,U_13529,U_13528] :
( ? [U_13527] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13530,U_13528)),hAPP(hAPP(c_Product__Type_OPair(U_13530,U_13528),U_13527),U_13529)),U_13531))
| ~ hBOOL(hAPP(hAPP(c_member(U_13528),U_13529),hAPP(c_Relation_ORange(U_13530,U_13528),U_13531))) ),
inference(variable_rename,[status(thm)],[f_3452_1]) ).
fof(f_3452_3,plain,
! [U_13531,U_13530,U_13529,U_13528] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13530,U_13528)),hAPP(hAPP(c_Product__Type_OPair(U_13530,U_13528),sK328(U_13531,U_13530,U_13529,U_13528)),U_13529)),U_13531))
| ~ hBOOL(hAPP(hAPP(c_member(U_13528),U_13529),hAPP(c_Relation_ORange(U_13530,U_13528),U_13531))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK328]),skolemize(U_13527,sK328(U_13531,U_13530,U_13529,U_13528))],[f_3452_2]) ).
cnf(f_3452_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13530,U_13528)),hAPP(hAPP(c_Product__Type_OPair(U_13530,U_13528),sK328(U_13531,U_13530,U_13529,U_13528)),U_13529)),U_13531))
| ~ hBOOL(hAPP(hAPP(c_member(U_13528),U_13529),hAPP(c_Relation_ORange(U_13530,U_13528),U_13531))) ),
inference(clausify,[status(thm)],[f_3452_3]) ).
fof(f_3453_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_3453_2,plain,
! [U_13538,U_13537,U_13536,U_13535,U_13534,U_13533,U_13532] :
( ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13532,U_13533,U_13534,hAPP(hAPP(c_COMBC(U_13532,tc_fun(tc_prod(U_13532,U_13533),tc_HOL_Obool),tc_fun(U_13533,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13533,tc_fun(tc_fun(tc_prod(U_13532,U_13533),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13532,U_13533),tc_HOL_Obool),tc_fun(U_13533,tc_HOL_Obool)),U_13532),c_COMBC(U_13533,tc_fun(tc_prod(U_13532,U_13533),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13533,tc_prod(U_13532,U_13533)),tc_fun(U_13533,tc_fun(tc_fun(tc_prod(U_13532,U_13533),tc_HOL_Obool),tc_HOL_Obool)),U_13532),hAPP(c_COMBB(tc_prod(U_13532,U_13533),tc_fun(tc_fun(tc_prod(U_13532,U_13533),tc_HOL_Obool),tc_HOL_Obool),U_13533),c_member(tc_prod(U_13532,U_13533)))),c_Product__Type_OPair(U_13532,U_13533)))),U_13535),hAPP(hAPP(c_COMBC(U_13533,tc_fun(tc_prod(U_13533,U_13534),tc_HOL_Obool),tc_fun(U_13534,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13534,tc_fun(tc_fun(tc_prod(U_13533,U_13534),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13533,U_13534),tc_HOL_Obool),tc_fun(U_13534,tc_HOL_Obool)),U_13533),c_COMBC(U_13534,tc_fun(tc_prod(U_13533,U_13534),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13534,tc_prod(U_13533,U_13534)),tc_fun(U_13534,tc_fun(tc_fun(tc_prod(U_13533,U_13534),tc_HOL_Obool),tc_HOL_Obool)),U_13533),hAPP(c_COMBB(tc_prod(U_13533,U_13534),tc_fun(tc_fun(tc_prod(U_13533,U_13534),tc_HOL_Obool),tc_HOL_Obool),U_13534),c_member(tc_prod(U_13533,U_13534)))),c_Product__Type_OPair(U_13533,U_13534)))),U_13536)),U_13537),U_13538))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13532,U_13534)),hAPP(hAPP(c_Product__Type_OPair(U_13532,U_13534),U_13537),U_13538)),hAPP(hAPP(c_Relation_Orel__comp(U_13532,U_13533,U_13534),U_13535),U_13536))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13532,U_13534)),hAPP(hAPP(c_Product__Type_OPair(U_13532,U_13534),U_13537),U_13538)),hAPP(hAPP(c_Relation_Orel__comp(U_13532,U_13533,U_13534),U_13535),U_13536)))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13532,U_13533,U_13534,hAPP(hAPP(c_COMBC(U_13532,tc_fun(tc_prod(U_13532,U_13533),tc_HOL_Obool),tc_fun(U_13533,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13533,tc_fun(tc_fun(tc_prod(U_13532,U_13533),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13532,U_13533),tc_HOL_Obool),tc_fun(U_13533,tc_HOL_Obool)),U_13532),c_COMBC(U_13533,tc_fun(tc_prod(U_13532,U_13533),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13533,tc_prod(U_13532,U_13533)),tc_fun(U_13533,tc_fun(tc_fun(tc_prod(U_13532,U_13533),tc_HOL_Obool),tc_HOL_Obool)),U_13532),hAPP(c_COMBB(tc_prod(U_13532,U_13533),tc_fun(tc_fun(tc_prod(U_13532,U_13533),tc_HOL_Obool),tc_HOL_Obool),U_13533),c_member(tc_prod(U_13532,U_13533)))),c_Product__Type_OPair(U_13532,U_13533)))),U_13535),hAPP(hAPP(c_COMBC(U_13533,tc_fun(tc_prod(U_13533,U_13534),tc_HOL_Obool),tc_fun(U_13534,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13534,tc_fun(tc_fun(tc_prod(U_13533,U_13534),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13533,U_13534),tc_HOL_Obool),tc_fun(U_13534,tc_HOL_Obool)),U_13533),c_COMBC(U_13534,tc_fun(tc_prod(U_13533,U_13534),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13534,tc_prod(U_13533,U_13534)),tc_fun(U_13534,tc_fun(tc_fun(tc_prod(U_13533,U_13534),tc_HOL_Obool),tc_HOL_Obool)),U_13533),hAPP(c_COMBB(tc_prod(U_13533,U_13534),tc_fun(tc_fun(tc_prod(U_13533,U_13534),tc_HOL_Obool),tc_HOL_Obool),U_13534),c_member(tc_prod(U_13533,U_13534)))),c_Product__Type_OPair(U_13533,U_13534)))),U_13536)),U_13537),U_13538)) ) ),
inference(variable_rename,[status(thm)],[f_3453_1]) ).
fof(f_3453_3,plain,
( ! [U_13552,U_13550,U_13548,U_13546,U_13544,U_13542,U_13540] :
( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13540,U_13542,U_13544,hAPP(hAPP(c_COMBC(U_13540,tc_fun(tc_prod(U_13540,U_13542),tc_HOL_Obool),tc_fun(U_13542,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13542,tc_fun(tc_fun(tc_prod(U_13540,U_13542),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13540,U_13542),tc_HOL_Obool),tc_fun(U_13542,tc_HOL_Obool)),U_13540),c_COMBC(U_13542,tc_fun(tc_prod(U_13540,U_13542),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13542,tc_prod(U_13540,U_13542)),tc_fun(U_13542,tc_fun(tc_fun(tc_prod(U_13540,U_13542),tc_HOL_Obool),tc_HOL_Obool)),U_13540),hAPP(c_COMBB(tc_prod(U_13540,U_13542),tc_fun(tc_fun(tc_prod(U_13540,U_13542),tc_HOL_Obool),tc_HOL_Obool),U_13542),c_member(tc_prod(U_13540,U_13542)))),c_Product__Type_OPair(U_13540,U_13542)))),U_13546),hAPP(hAPP(c_COMBC(U_13542,tc_fun(tc_prod(U_13542,U_13544),tc_HOL_Obool),tc_fun(U_13544,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13544,tc_fun(tc_fun(tc_prod(U_13542,U_13544),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13542,U_13544),tc_HOL_Obool),tc_fun(U_13544,tc_HOL_Obool)),U_13542),c_COMBC(U_13544,tc_fun(tc_prod(U_13542,U_13544),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13544,tc_prod(U_13542,U_13544)),tc_fun(U_13544,tc_fun(tc_fun(tc_prod(U_13542,U_13544),tc_HOL_Obool),tc_HOL_Obool)),U_13542),hAPP(c_COMBB(tc_prod(U_13542,U_13544),tc_fun(tc_fun(tc_prod(U_13542,U_13544),tc_HOL_Obool),tc_HOL_Obool),U_13544),c_member(tc_prod(U_13542,U_13544)))),c_Product__Type_OPair(U_13542,U_13544)))),U_13548)),U_13550),U_13552))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13540,U_13544)),hAPP(hAPP(c_Product__Type_OPair(U_13540,U_13544),U_13550),U_13552)),hAPP(hAPP(c_Relation_Orel__comp(U_13540,U_13542,U_13544),U_13546),U_13548))) )
& ! [U_13551,U_13549,U_13547,U_13545,U_13543,U_13541,U_13539] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13539,U_13543)),hAPP(hAPP(c_Product__Type_OPair(U_13539,U_13543),U_13549),U_13551)),hAPP(hAPP(c_Relation_Orel__comp(U_13539,U_13541,U_13543),U_13545),U_13547)))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13539,U_13541,U_13543,hAPP(hAPP(c_COMBC(U_13539,tc_fun(tc_prod(U_13539,U_13541),tc_HOL_Obool),tc_fun(U_13541,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13541,tc_fun(tc_fun(tc_prod(U_13539,U_13541),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13539,U_13541),tc_HOL_Obool),tc_fun(U_13541,tc_HOL_Obool)),U_13539),c_COMBC(U_13541,tc_fun(tc_prod(U_13539,U_13541),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13541,tc_prod(U_13539,U_13541)),tc_fun(U_13541,tc_fun(tc_fun(tc_prod(U_13539,U_13541),tc_HOL_Obool),tc_HOL_Obool)),U_13539),hAPP(c_COMBB(tc_prod(U_13539,U_13541),tc_fun(tc_fun(tc_prod(U_13539,U_13541),tc_HOL_Obool),tc_HOL_Obool),U_13541),c_member(tc_prod(U_13539,U_13541)))),c_Product__Type_OPair(U_13539,U_13541)))),U_13545),hAPP(hAPP(c_COMBC(U_13541,tc_fun(tc_prod(U_13541,U_13543),tc_HOL_Obool),tc_fun(U_13543,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13543,tc_fun(tc_fun(tc_prod(U_13541,U_13543),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13541,U_13543),tc_HOL_Obool),tc_fun(U_13543,tc_HOL_Obool)),U_13541),c_COMBC(U_13543,tc_fun(tc_prod(U_13541,U_13543),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13543,tc_prod(U_13541,U_13543)),tc_fun(U_13543,tc_fun(tc_fun(tc_prod(U_13541,U_13543),tc_HOL_Obool),tc_HOL_Obool)),U_13541),hAPP(c_COMBB(tc_prod(U_13541,U_13543),tc_fun(tc_fun(tc_prod(U_13541,U_13543),tc_HOL_Obool),tc_HOL_Obool),U_13543),c_member(tc_prod(U_13541,U_13543)))),c_Product__Type_OPair(U_13541,U_13543)))),U_13547)),U_13549),U_13551)) ) ),
inference(miniscope,[status(thm)],[f_3453_2]) ).
cnf(f_3453_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13539,U_13543)),hAPP(hAPP(c_Product__Type_OPair(U_13539,U_13543),U_13549),U_13551)),hAPP(hAPP(c_Relation_Orel__comp(U_13539,U_13541,U_13543),U_13545),U_13547)))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13539,U_13541,U_13543,hAPP(hAPP(c_COMBC(U_13539,tc_fun(tc_prod(U_13539,U_13541),tc_HOL_Obool),tc_fun(U_13541,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13541,tc_fun(tc_fun(tc_prod(U_13539,U_13541),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13539,U_13541),tc_HOL_Obool),tc_fun(U_13541,tc_HOL_Obool)),U_13539),c_COMBC(U_13541,tc_fun(tc_prod(U_13539,U_13541),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13541,tc_prod(U_13539,U_13541)),tc_fun(U_13541,tc_fun(tc_fun(tc_prod(U_13539,U_13541),tc_HOL_Obool),tc_HOL_Obool)),U_13539),hAPP(c_COMBB(tc_prod(U_13539,U_13541),tc_fun(tc_fun(tc_prod(U_13539,U_13541),tc_HOL_Obool),tc_HOL_Obool),U_13541),c_member(tc_prod(U_13539,U_13541)))),c_Product__Type_OPair(U_13539,U_13541)))),U_13545),hAPP(hAPP(c_COMBC(U_13541,tc_fun(tc_prod(U_13541,U_13543),tc_HOL_Obool),tc_fun(U_13543,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13543,tc_fun(tc_fun(tc_prod(U_13541,U_13543),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13541,U_13543),tc_HOL_Obool),tc_fun(U_13543,tc_HOL_Obool)),U_13541),c_COMBC(U_13543,tc_fun(tc_prod(U_13541,U_13543),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13543,tc_prod(U_13541,U_13543)),tc_fun(U_13543,tc_fun(tc_fun(tc_prod(U_13541,U_13543),tc_HOL_Obool),tc_HOL_Obool)),U_13541),hAPP(c_COMBB(tc_prod(U_13541,U_13543),tc_fun(tc_fun(tc_prod(U_13541,U_13543),tc_HOL_Obool),tc_HOL_Obool),U_13543),c_member(tc_prod(U_13541,U_13543)))),c_Product__Type_OPair(U_13541,U_13543)))),U_13547)),U_13549),U_13551)) ),
inference(clausify,[status(thm)],[f_3453_3]) ).
cnf(f_3453_5,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13540,U_13542,U_13544,hAPP(hAPP(c_COMBC(U_13540,tc_fun(tc_prod(U_13540,U_13542),tc_HOL_Obool),tc_fun(U_13542,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13542,tc_fun(tc_fun(tc_prod(U_13540,U_13542),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13540,U_13542),tc_HOL_Obool),tc_fun(U_13542,tc_HOL_Obool)),U_13540),c_COMBC(U_13542,tc_fun(tc_prod(U_13540,U_13542),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13542,tc_prod(U_13540,U_13542)),tc_fun(U_13542,tc_fun(tc_fun(tc_prod(U_13540,U_13542),tc_HOL_Obool),tc_HOL_Obool)),U_13540),hAPP(c_COMBB(tc_prod(U_13540,U_13542),tc_fun(tc_fun(tc_prod(U_13540,U_13542),tc_HOL_Obool),tc_HOL_Obool),U_13542),c_member(tc_prod(U_13540,U_13542)))),c_Product__Type_OPair(U_13540,U_13542)))),U_13546),hAPP(hAPP(c_COMBC(U_13542,tc_fun(tc_prod(U_13542,U_13544),tc_HOL_Obool),tc_fun(U_13544,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13544,tc_fun(tc_fun(tc_prod(U_13542,U_13544),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13542,U_13544),tc_HOL_Obool),tc_fun(U_13544,tc_HOL_Obool)),U_13542),c_COMBC(U_13544,tc_fun(tc_prod(U_13542,U_13544),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13544,tc_prod(U_13542,U_13544)),tc_fun(U_13544,tc_fun(tc_fun(tc_prod(U_13542,U_13544),tc_HOL_Obool),tc_HOL_Obool)),U_13542),hAPP(c_COMBB(tc_prod(U_13542,U_13544),tc_fun(tc_fun(tc_prod(U_13542,U_13544),tc_HOL_Obool),tc_HOL_Obool),U_13544),c_member(tc_prod(U_13542,U_13544)))),c_Product__Type_OPair(U_13542,U_13544)))),U_13548)),U_13550),U_13552))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13540,U_13544)),hAPP(hAPP(c_Product__Type_OPair(U_13540,U_13544),U_13550),U_13552)),hAPP(hAPP(c_Relation_Orel__comp(U_13540,U_13542,U_13544),U_13546),U_13548))) ),
inference(clausify,[status(thm)],[f_3453_3]) ).
fof(f_3454_1,plain,
! [T_d,T_c,T_b,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] :
( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_pred__comp_Ointros]) ).
fof(f_3454_2,plain,
! [U_13560,U_13559,U_13558,U_13557,U_13556,U_13555,U_13554,U_13553] :
( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13558,U_13559,U_13560,U_13553,U_13556),U_13554),U_13557))
| ~ hBOOL(hAPP(hAPP(U_13556,U_13555),U_13557))
| ~ hBOOL(hAPP(hAPP(U_13553,U_13554),U_13555)) ),
inference(variable_rename,[status(thm)],[f_3454_1]) ).
cnf(f_3454_3,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13558,U_13559,U_13560,U_13553,U_13556),U_13554),U_13557))
| ~ hBOOL(hAPP(hAPP(U_13556,U_13555),U_13557))
| ~ hBOOL(hAPP(hAPP(U_13553,U_13554),U_13555)) ),
inference(clausify,[status(thm)],[f_3454_2]) ).
fof(f_3455_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_3455_2,plain,
! [U_13565,U_13564,U_13563,U_13562,U_13561] :
( hBOOL(hAPP(c_Predicate_ORangeP(U_13564,U_13565,U_13561),U_13563))
| ~ hBOOL(hAPP(hAPP(U_13561,U_13562),U_13563)) ),
inference(variable_rename,[status(thm)],[f_3455_1]) ).
cnf(f_3455_3,plain,
( hBOOL(hAPP(c_Predicate_ORangeP(U_13564,U_13565,U_13561),U_13563))
| ~ hBOOL(hAPP(hAPP(U_13561,U_13562),U_13563)) ),
inference(clausify,[status(thm)],[f_3455_2]) ).
fof(f_3456_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_3456_2,plain,
! [U_13574,U_13573,U_13572,U_13571,U_13570,U_13569,U_13568] :
( ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13568,U_13569,U_13570,U_13571,U_13572),U_13573),U_13574))
| ! [U_13567] :
( ~ hBOOL(hAPP(hAPP(U_13572,U_13567),U_13574))
| ~ hBOOL(hAPP(hAPP(U_13571,U_13573),U_13567)) ) )
& ( ? [U_13566] :
( hBOOL(hAPP(hAPP(U_13572,U_13566),U_13574))
& hBOOL(hAPP(hAPP(U_13571,U_13573),U_13566)) )
| ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13568,U_13569,U_13570,U_13571,U_13572),U_13573),U_13574)) ) ),
inference(variable_rename,[status(thm)],[f_3456_1]) ).
fof(f_3456_3,plain,
( ! [U_13588,U_13586,U_13584,U_13582] :
( ! [U_13580,U_13578,U_13576] : hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13576,U_13578,U_13580,U_13582,U_13584),U_13586),U_13588))
| ! [U_13567] :
( ~ hBOOL(hAPP(hAPP(U_13584,U_13567),U_13588))
| ~ hBOOL(hAPP(hAPP(U_13582,U_13586),U_13567)) ) )
& ! [U_13587,U_13585,U_13583,U_13581] :
( ! [U_13579,U_13577,U_13575] : ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13575,U_13577,U_13579,U_13581,U_13583),U_13585),U_13587))
| ? [U_13566] :
( hBOOL(hAPP(hAPP(U_13583,U_13566),U_13587))
& hBOOL(hAPP(hAPP(U_13581,U_13585),U_13566)) ) ) ),
inference(miniscope,[status(thm)],[f_3456_2]) ).
fof(f_3456_4,plain,
( ! [U_13588,U_13586,U_13584,U_13582] :
( ! [U_13580,U_13578,U_13576] : hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13576,U_13578,U_13580,U_13582,U_13584),U_13586),U_13588))
| ! [U_13567] :
( ~ hBOOL(hAPP(hAPP(U_13584,U_13567),U_13588))
| ~ hBOOL(hAPP(hAPP(U_13582,U_13586),U_13567)) ) )
& ! [U_13587,U_13585,U_13583,U_13581] :
( ! [U_13579,U_13577,U_13575] : ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13575,U_13577,U_13579,U_13581,U_13583),U_13585),U_13587))
| ( hBOOL(hAPP(hAPP(U_13583,sK329(U_13587,U_13585,U_13583,U_13581)),U_13587))
& hBOOL(hAPP(hAPP(U_13581,U_13585),sK329(U_13587,U_13585,U_13583,U_13581))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK329]),skolemize(U_13566,sK329(U_13587,U_13585,U_13583,U_13581))],[f_3456_3]) ).
cnf(f_3456_5,plain,
( hBOOL(hAPP(hAPP(U_13581,U_13585),sK329(U_13587,U_13585,U_13583,U_13581)))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13575,U_13577,U_13579,U_13581,U_13583),U_13585),U_13587)) ),
inference(clausify,[status(thm)],[f_3456_4]) ).
cnf(f_3456_6,plain,
( hBOOL(hAPP(hAPP(U_13583,sK329(U_13587,U_13585,U_13583,U_13581)),U_13587))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13575,U_13577,U_13579,U_13581,U_13583),U_13585),U_13587)) ),
inference(clausify,[status(thm)],[f_3456_4]) ).
cnf(f_3456_7,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13576,U_13578,U_13580,U_13582,U_13584),U_13586),U_13588))
| ~ hBOOL(hAPP(hAPP(U_13584,U_13567),U_13588))
| ~ hBOOL(hAPP(hAPP(U_13582,U_13586),U_13567)) ),
inference(clausify,[status(thm)],[f_3456_4]) ).
fof(f_3457_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_3457_2,plain,
! [U_13594,U_13593,U_13592,U_13591] :
( ( hBOOL(hAPP(c_Predicate_ORangeP(U_13591,U_13592,U_13593),U_13594))
| ! [U_13590] : ~ hBOOL(hAPP(hAPP(U_13593,U_13590),U_13594)) )
& ( ? [U_13589] : hBOOL(hAPP(hAPP(U_13593,U_13589),U_13594))
| ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13591,U_13592,U_13593),U_13594)) ) ),
inference(variable_rename,[status(thm)],[f_3457_1]) ).
fof(f_3457_3,plain,
( ! [U_13602,U_13600] :
( ! [U_13598,U_13596] : hBOOL(hAPP(c_Predicate_ORangeP(U_13596,U_13598,U_13600),U_13602))
| ! [U_13590] : ~ hBOOL(hAPP(hAPP(U_13600,U_13590),U_13602)) )
& ! [U_13601,U_13599] :
( ! [U_13597,U_13595] : ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13595,U_13597,U_13599),U_13601))
| ? [U_13589] : hBOOL(hAPP(hAPP(U_13599,U_13589),U_13601)) ) ),
inference(miniscope,[status(thm)],[f_3457_2]) ).
fof(f_3457_4,plain,
( ! [U_13602,U_13600] :
( ! [U_13598,U_13596] : hBOOL(hAPP(c_Predicate_ORangeP(U_13596,U_13598,U_13600),U_13602))
| ! [U_13590] : ~ hBOOL(hAPP(hAPP(U_13600,U_13590),U_13602)) )
& ! [U_13601,U_13599] :
( ! [U_13597,U_13595] : ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13595,U_13597,U_13599),U_13601))
| hBOOL(hAPP(hAPP(U_13599,sK330(U_13601,U_13599)),U_13601)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK330]),skolemize(U_13589,sK330(U_13601,U_13599))],[f_3457_3]) ).
cnf(f_3457_5,plain,
( ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13595,U_13597,U_13599),U_13601))
| hBOOL(hAPP(hAPP(U_13599,sK330(U_13601,U_13599)),U_13601)) ),
inference(clausify,[status(thm)],[f_3457_4]) ).
cnf(f_3457_6,plain,
( hBOOL(hAPP(c_Predicate_ORangeP(U_13596,U_13598,U_13600),U_13602))
| ~ hBOOL(hAPP(hAPP(U_13600,U_13590),U_13602)) ),
inference(clausify,[status(thm)],[f_3457_4]) ).
fof(f_3458_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_3458_2,plain,
! [U_13605,U_13604,U_13603] :
( c_FunDef_Oreduction__pair(U_13603,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(U_13603,U_13603),tc_HOL_Obool),tc_fun(tc_prod(U_13603,U_13603),tc_HOL_Obool)),U_13604),U_13605))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13603,U_13603),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13603,U_13603,U_13603),U_13604),U_13605)),U_13604))
| ~ c_Wellfounded_Owf(U_13603,U_13604) ),
inference(variable_rename,[status(thm)],[f_3458_1]) ).
cnf(f_3458_3,plain,
( c_FunDef_Oreduction__pair(U_13603,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(U_13603,U_13603),tc_HOL_Obool),tc_fun(tc_prod(U_13603,U_13603),tc_HOL_Obool)),U_13604),U_13605))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13603,U_13603),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13603,U_13603,U_13603),U_13604),U_13605)),U_13604))
| ~ c_Wellfounded_Owf(U_13603,U_13604) ),
inference(clausify,[status(thm)],[f_3458_2]) ).
fof(f_3459_1,plain,
! [V_P_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),V_P_2)),
inference(fof_nnf,[status(thm)],[fact_Domain__Collect__split]) ).
fof(f_3459_2,plain,
! [U_13608,U_13607,U_13606] : hAPP(c_Relation_ODomain(U_13606,U_13607),hAPP(c_Set_OCollect(tc_prod(U_13606,U_13607)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13606,U_13607,tc_HOL_Obool),U_13608))) = hAPP(c_Set_OCollect(U_13606),hAPP(hAPP(c_COMBB(tc_fun(U_13607,tc_HOL_Obool),tc_HOL_Obool,U_13606),c_HOL_OEx(U_13607)),U_13608)),
inference(variable_rename,[status(thm)],[f_3459_1]) ).
cnf(f_3459_3,plain,
hAPP(c_Relation_ODomain(U_13606,U_13607),hAPP(c_Set_OCollect(tc_prod(U_13606,U_13607)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13606,U_13607,tc_HOL_Obool),U_13608))) = hAPP(c_Set_OCollect(U_13606),hAPP(hAPP(c_COMBB(tc_fun(U_13607,tc_HOL_Obool),tc_HOL_Obool,U_13606),c_HOL_OEx(U_13607)),U_13608)),
inference(clausify,[status(thm)],[f_3459_2]) ).
fof(f_3460_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_3460_2,plain,
! [U_13610,U_13609] : c_HOL_OThe(U_13609,hAPP(hAPP(c_COMBC(U_13609,U_13609,tc_HOL_Obool),c_fequal),U_13610)) = U_13610,
inference(variable_rename,[status(thm)],[f_3460_1]) ).
cnf(f_3460_3,plain,
c_HOL_OThe(U_13609,hAPP(hAPP(c_COMBC(U_13609,U_13609,tc_HOL_Obool),c_fequal),U_13610)) = U_13610,
inference(clausify,[status(thm)],[f_3460_2]) ).
fof(f_3461_1,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(fof_nnf,[status(thm)],[fact_wf__less__than]) ).
cnf(f_3461_2,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(clausify,[status(thm)],[f_3461_1]) ).
fof(f_3462_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_3462_2,plain,
! [U_13611] : c_Wellfounded_Owf(U_13611,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13611,U_13611),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_3462_1]) ).
cnf(f_3462_3,plain,
c_Wellfounded_Owf(U_13611,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13611,U_13611),tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_3462_2]) ).
fof(f_3463_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_3463_2,plain,
! [U_13615,U_13614,U_13613,U_13612] :
( c_Wellfounded_Owf(U_13614,hAPP(hAPP(c_Relation_Oinv__image(U_13612,U_13614),U_13613),U_13615))
| ~ c_Wellfounded_Owf(U_13612,U_13613) ),
inference(variable_rename,[status(thm)],[f_3463_1]) ).
cnf(f_3463_3,plain,
( c_Wellfounded_Owf(U_13614,hAPP(hAPP(c_Relation_Oinv__image(U_13612,U_13614),U_13613),U_13615))
| ~ c_Wellfounded_Owf(U_13612,U_13613) ),
inference(clausify,[status(thm)],[f_3463_2]) ).
fof(f_3464_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_3464_2,plain,
! [U_13619,U_13618,U_13617,U_13616] :
( c_Wellfounded_Owf(tc_prod(U_13616,U_13618),c_Wellfounded_Olex__prod(U_13616,U_13618,U_13617,U_13619))
| ~ c_Wellfounded_Owf(U_13618,U_13619)
| ~ c_Wellfounded_Owf(U_13616,U_13617) ),
inference(variable_rename,[status(thm)],[f_3464_1]) ).
cnf(f_3464_3,plain,
( c_Wellfounded_Owf(tc_prod(U_13616,U_13618),c_Wellfounded_Olex__prod(U_13616,U_13618,U_13617,U_13619))
| ~ c_Wellfounded_Owf(U_13618,U_13619)
| ~ c_Wellfounded_Owf(U_13616,U_13617) ),
inference(clausify,[status(thm)],[f_3464_2]) ).
fof(f_3465_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_3465_2,plain,
! [U_13621,U_13620] : c_Wellfounded_Owf(U_13620,hAPP(c_Wellfounded_Omeasure(U_13620),U_13621)),
inference(variable_rename,[status(thm)],[f_3465_1]) ).
cnf(f_3465_3,plain,
c_Wellfounded_Owf(U_13620,hAPP(c_Wellfounded_Omeasure(U_13620),U_13621)),
inference(clausify,[status(thm)],[f_3465_2]) ).
fof(f_3466_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_3466_2,plain,
! [U_13626,U_13625,U_13624,U_13623,U_13622] :
( hBOOL(hAPP(hAPP(c_member(U_13622),U_13624),hAPP(c_Relation_ODomain(U_13622,U_13623),U_13626)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13622,U_13623)),hAPP(hAPP(c_Product__Type_OPair(U_13622,U_13623),U_13624),U_13625)),U_13626)) ),
inference(variable_rename,[status(thm)],[f_3466_1]) ).
cnf(f_3466_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_13622),U_13624),hAPP(c_Relation_ODomain(U_13622,U_13623),U_13626)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13622,U_13623)),hAPP(hAPP(c_Product__Type_OPair(U_13622,U_13623),U_13624),U_13625)),U_13626)) ),
inference(clausify,[status(thm)],[f_3466_2]) ).
fof(f_3467_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_3467_2,plain,
! [U_13628,U_13627] :
( ( c_Wellfounded_Owf(U_13627,U_13628)
| ~ c_Wellfounded_Owf(U_13627,hAPP(hAPP(c_Relation_Orel__comp(U_13627,U_13627,U_13627),U_13628),U_13628)) )
& ( c_Wellfounded_Owf(U_13627,hAPP(hAPP(c_Relation_Orel__comp(U_13627,U_13627,U_13627),U_13628),U_13628))
| ~ c_Wellfounded_Owf(U_13627,U_13628) ) ),
inference(variable_rename,[status(thm)],[f_3467_1]) ).
fof(f_3467_3,plain,
( ! [U_13632,U_13630] :
( c_Wellfounded_Owf(U_13630,U_13632)
| ~ c_Wellfounded_Owf(U_13630,hAPP(hAPP(c_Relation_Orel__comp(U_13630,U_13630,U_13630),U_13632),U_13632)) )
& ! [U_13631,U_13629] :
( c_Wellfounded_Owf(U_13629,hAPP(hAPP(c_Relation_Orel__comp(U_13629,U_13629,U_13629),U_13631),U_13631))
| ~ c_Wellfounded_Owf(U_13629,U_13631) ) ),
inference(miniscope,[status(thm)],[f_3467_2]) ).
cnf(f_3467_4,plain,
( c_Wellfounded_Owf(U_13629,hAPP(hAPP(c_Relation_Orel__comp(U_13629,U_13629,U_13629),U_13631),U_13631))
| ~ c_Wellfounded_Owf(U_13629,U_13631) ),
inference(clausify,[status(thm)],[f_3467_3]) ).
cnf(f_3467_5,plain,
( c_Wellfounded_Owf(U_13630,U_13632)
| ~ c_Wellfounded_Owf(U_13630,hAPP(hAPP(c_Relation_Orel__comp(U_13630,U_13630,U_13630),U_13632),U_13632)) ),
inference(clausify,[status(thm)],[f_3467_3]) ).
fof(f_3468_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_3468_2,plain,
! [U_13635,U_13634,U_13633] :
( c_Wellfounded_Owf(U_13633,U_13635)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13633,U_13633),tc_HOL_Obool)),U_13635),U_13634))
| ~ c_Wellfounded_Owf(U_13633,U_13634) ),
inference(variable_rename,[status(thm)],[f_3468_1]) ).
cnf(f_3468_3,plain,
( c_Wellfounded_Owf(U_13633,U_13635)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13633,U_13633),tc_HOL_Obool)),U_13635),U_13634))
| ~ c_Wellfounded_Owf(U_13633,U_13634) ),
inference(clausify,[status(thm)],[f_3468_2]) ).
fof(f_3469_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_3469_2,plain,
! [U_13637,U_13636] :
( c_Wellfounded_Owf(tc_fun(U_13636,tc_HOL_Obool),c_Wellfounded_Omin__ext(U_13636,U_13637))
| ~ c_Wellfounded_Owf(U_13636,U_13637) ),
inference(variable_rename,[status(thm)],[f_3469_1]) ).
cnf(f_3469_3,plain,
( c_Wellfounded_Owf(tc_fun(U_13636,tc_HOL_Obool),c_Wellfounded_Omin__ext(U_13636,U_13637))
| ~ c_Wellfounded_Owf(U_13636,U_13637) ),
inference(clausify,[status(thm)],[f_3469_2]) ).
fof(f_3470_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_3470_2,plain,
! [U_13640,U_13639,U_13638] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13638,U_13638)),hAPP(hAPP(c_Product__Type_OPair(U_13638,U_13638),U_13640),U_13640)),U_13639))
| ~ c_Wellfounded_Owf(U_13638,U_13639) ),
inference(variable_rename,[status(thm)],[f_3470_1]) ).
cnf(f_3470_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13638,U_13638)),hAPP(hAPP(c_Product__Type_OPair(U_13638,U_13638),U_13640),U_13640)),U_13639))
| ~ c_Wellfounded_Owf(U_13638,U_13639) ),
inference(clausify,[status(thm)],[f_3470_2]) ).
fof(f_3471_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_3471_2,plain,
! [U_13644,U_13643,U_13642,U_13641] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13641,U_13641)),hAPP(hAPP(c_Product__Type_OPair(U_13641,U_13641),U_13644),U_13643)),U_13642))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13641,U_13641)),hAPP(hAPP(c_Product__Type_OPair(U_13641,U_13641),U_13643),U_13644)),U_13642))
| ~ c_Wellfounded_Owf(U_13641,U_13642) ),
inference(variable_rename,[status(thm)],[f_3471_1]) ).
cnf(f_3471_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13641,U_13641)),hAPP(hAPP(c_Product__Type_OPair(U_13641,U_13641),U_13644),U_13643)),U_13642))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13641,U_13641)),hAPP(hAPP(c_Product__Type_OPair(U_13641,U_13641),U_13643),U_13644)),U_13642))
| ~ c_Wellfounded_Owf(U_13641,U_13642) ),
inference(clausify,[status(thm)],[f_3471_2]) ).
fof(f_3472_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_3472_2,plain,
! [U_13648,U_13647,U_13646,U_13645] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13645,U_13645)),hAPP(hAPP(c_Product__Type_OPair(U_13645,U_13645),U_13648),U_13647)),U_13646))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13645,U_13645)),hAPP(hAPP(c_Product__Type_OPair(U_13645,U_13645),U_13647),U_13648)),U_13646))
| ~ c_Wellfounded_Owf(U_13645,U_13646) ),
inference(variable_rename,[status(thm)],[f_3472_1]) ).
cnf(f_3472_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13645,U_13645)),hAPP(hAPP(c_Product__Type_OPair(U_13645,U_13645),U_13648),U_13647)),U_13646))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13645,U_13645)),hAPP(hAPP(c_Product__Type_OPair(U_13645,U_13645),U_13647),U_13648)),U_13646))
| ~ c_Wellfounded_Owf(U_13645,U_13646) ),
inference(clausify,[status(thm)],[f_3472_2]) ).
fof(f_3473_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_3473_2,plain,
! [U_13651,U_13650,U_13649] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13649,U_13649)),hAPP(hAPP(c_Product__Type_OPair(U_13649,U_13649),U_13651),U_13651)),U_13650))
| ~ c_Wellfounded_Owf(U_13649,U_13650) ),
inference(variable_rename,[status(thm)],[f_3473_1]) ).
cnf(f_3473_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13649,U_13649)),hAPP(hAPP(c_Product__Type_OPair(U_13649,U_13649),U_13651),U_13651)),U_13650))
| ~ c_Wellfounded_Owf(U_13649,U_13650) ),
inference(clausify,[status(thm)],[f_3473_2]) ).
fof(f_3474_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_3474_2,plain,
! [U_13653,U_13652] : hAPP(c_Relation_ODomain(U_13652,U_13652),c_Relation_OId__on(U_13652,U_13653)) = U_13653,
inference(variable_rename,[status(thm)],[f_3474_1]) ).
cnf(f_3474_3,plain,
hAPP(c_Relation_ODomain(U_13652,U_13652),c_Relation_OId__on(U_13652,U_13653)) = U_13653,
inference(clausify,[status(thm)],[f_3474_2]) ).
fof(f_3475_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_3475_2,plain,
! [U_13656,U_13655,U_13654] :
( c_Wellfounded_Owf(U_13654,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13654,U_13654),tc_HOL_Obool)),U_13655),U_13656))
| ~ c_Wellfounded_Owf(U_13654,U_13655) ),
inference(variable_rename,[status(thm)],[f_3475_1]) ).
cnf(f_3475_3,plain,
( c_Wellfounded_Owf(U_13654,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13654,U_13654),tc_HOL_Obool)),U_13655),U_13656))
| ~ c_Wellfounded_Owf(U_13654,U_13655) ),
inference(clausify,[status(thm)],[f_3475_2]) ).
fof(f_3476_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_3476_2,plain,
! [U_13659,U_13658,U_13657] :
( c_Wellfounded_Owf(U_13657,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13657,U_13657),tc_HOL_Obool)),U_13659),U_13658))
| ~ c_Wellfounded_Owf(U_13657,U_13658) ),
inference(variable_rename,[status(thm)],[f_3476_1]) ).
cnf(f_3476_3,plain,
( c_Wellfounded_Owf(U_13657,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13657,U_13657),tc_HOL_Obool)),U_13659),U_13658))
| ~ c_Wellfounded_Owf(U_13657,U_13658) ),
inference(clausify,[status(thm)],[f_3476_2]) ).
fof(f_3477_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_3477_2,plain,
! [U_13662,U_13661,U_13660] :
( c_Wellfounded_Owf(U_13660,c_Wellfounded_Omlex__prod(U_13660,U_13662,U_13661))
| ~ c_Wellfounded_Owf(U_13660,U_13661) ),
inference(variable_rename,[status(thm)],[f_3477_1]) ).
cnf(f_3477_3,plain,
( c_Wellfounded_Owf(U_13660,c_Wellfounded_Omlex__prod(U_13660,U_13662,U_13661))
| ~ c_Wellfounded_Owf(U_13660,U_13661) ),
inference(clausify,[status(thm)],[f_3477_2]) ).
fof(f_3478_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_3478_2,plain,
! [U_13663] : c_Wellfounded_Owf(tc_fun(U_13663,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(U_13663)),
inference(variable_rename,[status(thm)],[f_3478_1]) ).
cnf(f_3478_3,plain,
c_Wellfounded_Owf(tc_fun(U_13663,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(U_13663)),
inference(clausify,[status(thm)],[f_3478_2]) ).
fof(f_3479_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_3479_2,plain,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(clausify,[status(thm)],[f_3479_1]) ).
fof(f_3480_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_3480_2,plain,
! [U_13665,U_13664] :
( c_Wellfounded_Owf(tc_fun(U_13664,tc_HOL_Obool),c_Wellfounded_Omax__ext(U_13664,U_13665))
| ~ c_Wellfounded_Owf(U_13664,U_13665) ),
inference(variable_rename,[status(thm)],[f_3480_1]) ).
cnf(f_3480_3,plain,
( c_Wellfounded_Owf(tc_fun(U_13664,tc_HOL_Obool),c_Wellfounded_Omax__ext(U_13664,U_13665))
| ~ c_Wellfounded_Owf(U_13664,U_13665) ),
inference(clausify,[status(thm)],[f_3480_2]) ).
fof(f_3481_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_3481_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_3481_1]) ).
fof(f_3482_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_3482_2,plain,
! [U_13666] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(U_13666)),
inference(variable_rename,[status(thm)],[f_3482_1]) ).
cnf(f_3482_3,plain,
c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(U_13666)),
inference(clausify,[status(thm)],[f_3482_2]) ).
fof(f_3483_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_3483_2,plain,
! [U_13667] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(U_13667)),
inference(variable_rename,[status(thm)],[f_3483_1]) ).
cnf(f_3483_3,plain,
c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(U_13667)),
inference(clausify,[status(thm)],[f_3483_2]) ).
fof(f_3484_1,plain,
! [V_s_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
| 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_3484_2,plain,
! [U_13670,U_13669,U_13668] :
( c_Wellfounded_Owf(U_13668,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13668,U_13668),tc_HOL_Obool)),U_13669),U_13670))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13668,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13668,U_13668),U_13669)),hAPP(c_Relation_ORange(U_13668,U_13668),U_13670)) != c_Orderings_Obot__class_Obot(tc_fun(U_13668,tc_HOL_Obool))
| ~ c_Wellfounded_Owf(U_13668,U_13670)
| ~ c_Wellfounded_Owf(U_13668,U_13669) ),
inference(variable_rename,[status(thm)],[f_3484_1]) ).
cnf(f_3484_3,plain,
( c_Wellfounded_Owf(U_13668,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13668,U_13668),tc_HOL_Obool)),U_13669),U_13670))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13668,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13668,U_13668),U_13669)),hAPP(c_Relation_ORange(U_13668,U_13668),U_13670)) != c_Orderings_Obot__class_Obot(tc_fun(U_13668,tc_HOL_Obool))
| ~ c_Wellfounded_Owf(U_13668,U_13670)
| ~ c_Wellfounded_Owf(U_13668,U_13669) ),
inference(clausify,[status(thm)],[f_3484_2]) ).
fof(f_3485_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_3485_2,plain,
! [U_13674,U_13673] :
( ( c_Wellfounded_Owf(U_13673,U_13674)
| ? [U_13672] : ~ hBOOL(hAPP(hAPP(c_member(U_13673),U_13672),c_Wellfounded_Oacc(U_13673,U_13674))) )
& ( ! [U_13671] : hBOOL(hAPP(hAPP(c_member(U_13673),U_13671),c_Wellfounded_Oacc(U_13673,U_13674)))
| ~ c_Wellfounded_Owf(U_13673,U_13674) ) ),
inference(variable_rename,[status(thm)],[f_3485_1]) ).
fof(f_3485_3,plain,
( ! [U_13678,U_13676] :
( c_Wellfounded_Owf(U_13676,U_13678)
| ? [U_13672] : ~ hBOOL(hAPP(hAPP(c_member(U_13676),U_13672),c_Wellfounded_Oacc(U_13676,U_13678))) )
& ! [U_13677,U_13675] :
( ! [U_13671] : hBOOL(hAPP(hAPP(c_member(U_13675),U_13671),c_Wellfounded_Oacc(U_13675,U_13677)))
| ~ c_Wellfounded_Owf(U_13675,U_13677) ) ),
inference(miniscope,[status(thm)],[f_3485_2]) ).
fof(f_3485_4,plain,
( ! [U_13678,U_13676] :
( c_Wellfounded_Owf(U_13676,U_13678)
| ~ hBOOL(hAPP(hAPP(c_member(U_13676),sK331(U_13678,U_13676)),c_Wellfounded_Oacc(U_13676,U_13678))) )
& ! [U_13677,U_13675] :
( ! [U_13671] : hBOOL(hAPP(hAPP(c_member(U_13675),U_13671),c_Wellfounded_Oacc(U_13675,U_13677)))
| ~ c_Wellfounded_Owf(U_13675,U_13677) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK331]),skolemize(U_13672,sK331(U_13678,U_13676))],[f_3485_3]) ).
cnf(f_3485_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_13675),U_13671),c_Wellfounded_Oacc(U_13675,U_13677)))
| ~ c_Wellfounded_Owf(U_13675,U_13677) ),
inference(clausify,[status(thm)],[f_3485_4]) ).
cnf(f_3485_6,plain,
( c_Wellfounded_Owf(U_13676,U_13678)
| ~ hBOOL(hAPP(hAPP(c_member(U_13676),sK331(U_13678,U_13676)),c_Wellfounded_Oacc(U_13676,U_13678))) ),
inference(clausify,[status(thm)],[f_3485_4]) ).
fof(f_3486_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_3486_2,plain,
! [U_13681,U_13680,U_13679] :
( hBOOL(hAPP(hAPP(c_member(U_13679),U_13681),c_Wellfounded_Oacc(U_13679,U_13680)))
| ~ c_Wellfounded_Owf(U_13679,U_13680) ),
inference(variable_rename,[status(thm)],[f_3486_1]) ).
cnf(f_3486_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_13679),U_13681),c_Wellfounded_Oacc(U_13679,U_13680)))
| ~ c_Wellfounded_Owf(U_13679,U_13680) ),
inference(clausify,[status(thm)],[f_3486_2]) ).
fof(f_3487_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_3487_2,plain,
! [U_13683,U_13682] :
( c_Wellfounded_Owf(U_13682,U_13683)
| hAPP(hAPP(c_Relation_Orel__comp(U_13682,U_13682,U_13682),U_13683),U_13683) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13682,U_13682),tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_3487_1]) ).
cnf(f_3487_3,plain,
( c_Wellfounded_Owf(U_13682,U_13683)
| hAPP(hAPP(c_Relation_Orel__comp(U_13682,U_13682,U_13682),U_13683),U_13683) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13682,U_13682),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3487_2]) ).
fof(f_3488_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_3488_2,plain,
! [U_13686,U_13685,U_13684] :
( ( c_Wellfounded_Owf(U_13684,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13684,U_13684),tc_HOL_Obool)),U_13685),U_13686))
| ~ c_Wellfounded_Owf(U_13684,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13684,U_13684),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13684,U_13684),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13684,U_13684,U_13684),U_13685),U_13685)),hAPP(hAPP(c_Relation_Orel__comp(U_13684,U_13684,U_13684),U_13686),U_13685))),U_13686)) )
& ( c_Wellfounded_Owf(U_13684,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13684,U_13684),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13684,U_13684),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13684,U_13684,U_13684),U_13685),U_13685)),hAPP(hAPP(c_Relation_Orel__comp(U_13684,U_13684,U_13684),U_13686),U_13685))),U_13686))
| ~ c_Wellfounded_Owf(U_13684,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13684,U_13684),tc_HOL_Obool)),U_13685),U_13686)) ) ),
inference(variable_rename,[status(thm)],[f_3488_1]) ).
fof(f_3488_3,plain,
( ! [U_13692,U_13690,U_13688] :
( c_Wellfounded_Owf(U_13688,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13688,U_13688),tc_HOL_Obool)),U_13690),U_13692))
| ~ c_Wellfounded_Owf(U_13688,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13688,U_13688),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13688,U_13688),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13688,U_13688,U_13688),U_13690),U_13690)),hAPP(hAPP(c_Relation_Orel__comp(U_13688,U_13688,U_13688),U_13692),U_13690))),U_13692)) )
& ! [U_13691,U_13689,U_13687] :
( c_Wellfounded_Owf(U_13687,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13687,U_13687),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13687,U_13687),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13687,U_13687,U_13687),U_13689),U_13689)),hAPP(hAPP(c_Relation_Orel__comp(U_13687,U_13687,U_13687),U_13691),U_13689))),U_13691))
| ~ c_Wellfounded_Owf(U_13687,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13687,U_13687),tc_HOL_Obool)),U_13689),U_13691)) ) ),
inference(miniscope,[status(thm)],[f_3488_2]) ).
cnf(f_3488_4,plain,
( c_Wellfounded_Owf(U_13687,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13687,U_13687),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13687,U_13687),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13687,U_13687,U_13687),U_13689),U_13689)),hAPP(hAPP(c_Relation_Orel__comp(U_13687,U_13687,U_13687),U_13691),U_13689))),U_13691))
| ~ c_Wellfounded_Owf(U_13687,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13687,U_13687),tc_HOL_Obool)),U_13689),U_13691)) ),
inference(clausify,[status(thm)],[f_3488_3]) ).
cnf(f_3488_5,plain,
( c_Wellfounded_Owf(U_13688,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13688,U_13688),tc_HOL_Obool)),U_13690),U_13692))
| ~ c_Wellfounded_Owf(U_13688,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13688,U_13688),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13688,U_13688),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13688,U_13688,U_13688),U_13690),U_13690)),hAPP(hAPP(c_Relation_Orel__comp(U_13688,U_13688,U_13688),U_13692),U_13690))),U_13692)) ),
inference(clausify,[status(thm)],[f_3488_3]) ).
fof(f_3489_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_3489_2,plain,
! [U_13694,U_13693] : hAPP(c_Relation_ODomain(U_13693,U_13694),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13693,U_13694),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13693,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3489_1]) ).
cnf(f_3489_3,plain,
hAPP(c_Relation_ODomain(U_13693,U_13694),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13693,U_13694),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13693,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3489_2]) ).
fof(f_3490_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_3490_2,plain,
! [U_13697,U_13696,U_13695] :
( ( hAPP(c_Relation_ODomain(U_13695,U_13696),U_13697) = c_Orderings_Obot__class_Obot(tc_fun(U_13695,tc_HOL_Obool))
| U_13697 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13695,U_13696),tc_HOL_Obool)) )
& ( U_13697 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13695,U_13696),tc_HOL_Obool))
| hAPP(c_Relation_ODomain(U_13695,U_13696),U_13697) != c_Orderings_Obot__class_Obot(tc_fun(U_13695,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_3490_1]) ).
fof(f_3490_3,plain,
( ! [U_13703,U_13701,U_13699] :
( hAPP(c_Relation_ODomain(U_13699,U_13701),U_13703) = c_Orderings_Obot__class_Obot(tc_fun(U_13699,tc_HOL_Obool))
| U_13703 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13699,U_13701),tc_HOL_Obool)) )
& ! [U_13702,U_13700,U_13698] :
( U_13702 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13698,U_13700),tc_HOL_Obool))
| hAPP(c_Relation_ODomain(U_13698,U_13700),U_13702) != c_Orderings_Obot__class_Obot(tc_fun(U_13698,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_3490_2]) ).
cnf(f_3490_4,plain,
( U_13702 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13698,U_13700),tc_HOL_Obool))
| hAPP(c_Relation_ODomain(U_13698,U_13700),U_13702) != c_Orderings_Obot__class_Obot(tc_fun(U_13698,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3490_3]) ).
cnf(f_3490_5,plain,
( hAPP(c_Relation_ODomain(U_13699,U_13701),U_13703) = c_Orderings_Obot__class_Obot(tc_fun(U_13699,tc_HOL_Obool))
| U_13703 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13699,U_13701),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3490_3]) ).
fof(f_3491_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_3491_2,plain,
! [U_13707,U_13706,U_13705,U_13704] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13704,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13704,U_13705),U_13706)),hAPP(c_Relation_ODomain(U_13704,U_13705),U_13707)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13704,U_13705),tc_HOL_Obool)),U_13706),U_13707)) ),
inference(variable_rename,[status(thm)],[f_3491_1]) ).
cnf(f_3491_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13704,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13704,U_13705),U_13706)),hAPP(c_Relation_ODomain(U_13704,U_13705),U_13707)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13704,U_13705),tc_HOL_Obool)),U_13706),U_13707)) ),
inference(clausify,[status(thm)],[f_3491_2]) ).
fof(f_3492_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_3492_2,plain,
! [U_13711,U_13710,U_13709,U_13708] : hAPP(c_Relation_ODomain(U_13708,U_13709),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13708,U_13709),tc_HOL_Obool)),U_13710),U_13711)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13708,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13708,U_13709),U_13710)),hAPP(c_Relation_ODomain(U_13708,U_13709),U_13711)),
inference(variable_rename,[status(thm)],[f_3492_1]) ).
cnf(f_3492_3,plain,
hAPP(c_Relation_ODomain(U_13708,U_13709),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13708,U_13709),tc_HOL_Obool)),U_13710),U_13711)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13708,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13708,U_13709),U_13710)),hAPP(c_Relation_ODomain(U_13708,U_13709),U_13711)),
inference(clausify,[status(thm)],[f_3492_2]) ).
fof(f_3493_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_3493_2,plain,
! [U_13714,U_13713,U_13712] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13712),hAPP(c_Relation_ODomain(U_13712,U_13713),U_13714)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13712,U_13713)),U_13714)) ),
inference(variable_rename,[status(thm)],[f_3493_1]) ).
cnf(f_3493_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13712),hAPP(c_Relation_ODomain(U_13712,U_13713),U_13714)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13712,U_13713)),U_13714)) ),
inference(clausify,[status(thm)],[f_3493_2]) ).
fof(f_3494_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_3494_2,plain,
! [U_13717,U_13716,U_13715] : hAPP(c_Set_Oimage(tc_prod(U_13715,U_13716),U_13715,c_Product__Type_Ofst(U_13715,U_13716)),U_13717) = hAPP(c_Relation_ODomain(U_13715,U_13716),U_13717),
inference(variable_rename,[status(thm)],[f_3494_1]) ).
cnf(f_3494_3,plain,
hAPP(c_Set_Oimage(tc_prod(U_13715,U_13716),U_13715,c_Product__Type_Ofst(U_13715,U_13716)),U_13717) = hAPP(c_Relation_ODomain(U_13715,U_13716),U_13717),
inference(clausify,[status(thm)],[f_3494_2]) ).
fof(f_3495_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_3495_2,plain,
! [U_13723,U_13722] :
( ( c_Wellfounded_Owf(U_13722,U_13723)
| ? [U_13721] :
! [U_13720] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13722,U_13722)),hAPP(hAPP(c_Product__Type_OPair(U_13722,U_13722),hAPP(U_13721,hAPP(c_Nat_OSuc,U_13720))),hAPP(U_13721,U_13720))),U_13723)) )
& ( ! [U_13719] :
? [U_13718] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13722,U_13722)),hAPP(hAPP(c_Product__Type_OPair(U_13722,U_13722),hAPP(U_13719,hAPP(c_Nat_OSuc,U_13718))),hAPP(U_13719,U_13718))),U_13723))
| ~ c_Wellfounded_Owf(U_13722,U_13723) ) ),
inference(variable_rename,[status(thm)],[f_3495_1]) ).
fof(f_3495_3,plain,
( ! [U_13727,U_13725] :
( c_Wellfounded_Owf(U_13725,U_13727)
| ? [U_13721] :
! [U_13720] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13725,U_13725)),hAPP(hAPP(c_Product__Type_OPair(U_13725,U_13725),hAPP(U_13721,hAPP(c_Nat_OSuc,U_13720))),hAPP(U_13721,U_13720))),U_13727)) )
& ! [U_13726,U_13724] :
( ! [U_13719] :
? [U_13718] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13724,U_13724)),hAPP(hAPP(c_Product__Type_OPair(U_13724,U_13724),hAPP(U_13719,hAPP(c_Nat_OSuc,U_13718))),hAPP(U_13719,U_13718))),U_13726))
| ~ c_Wellfounded_Owf(U_13724,U_13726) ) ),
inference(miniscope,[status(thm)],[f_3495_2]) ).
fof(f_3495_4,plain,
( ! [U_13727,U_13725] :
( c_Wellfounded_Owf(U_13725,U_13727)
| ? [U_13721] :
! [U_13720] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13725,U_13725)),hAPP(hAPP(c_Product__Type_OPair(U_13725,U_13725),hAPP(U_13721,hAPP(c_Nat_OSuc,U_13720))),hAPP(U_13721,U_13720))),U_13727)) )
& ! [U_13726,U_13724] :
( ! [U_13719] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13724,U_13724)),hAPP(hAPP(c_Product__Type_OPair(U_13724,U_13724),hAPP(U_13719,hAPP(c_Nat_OSuc,sK332(U_13726,U_13724,U_13719)))),hAPP(U_13719,sK332(U_13726,U_13724,U_13719)))),U_13726))
| ~ c_Wellfounded_Owf(U_13724,U_13726) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK332]),skolemize(U_13718,sK332(U_13726,U_13724,U_13719))],[f_3495_3]) ).
fof(f_3495_5,plain,
( ! [U_13727,U_13725] :
( c_Wellfounded_Owf(U_13725,U_13727)
| ! [U_13720] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13725,U_13725)),hAPP(hAPP(c_Product__Type_OPair(U_13725,U_13725),hAPP(sK333(U_13727,U_13725),hAPP(c_Nat_OSuc,U_13720))),hAPP(sK333(U_13727,U_13725),U_13720))),U_13727)) )
& ! [U_13726,U_13724] :
( ! [U_13719] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13724,U_13724)),hAPP(hAPP(c_Product__Type_OPair(U_13724,U_13724),hAPP(U_13719,hAPP(c_Nat_OSuc,sK332(U_13726,U_13724,U_13719)))),hAPP(U_13719,sK332(U_13726,U_13724,U_13719)))),U_13726))
| ~ c_Wellfounded_Owf(U_13724,U_13726) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK333]),skolemize(U_13721,sK333(U_13727,U_13725))],[f_3495_4]) ).
cnf(f_3495_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13724,U_13724)),hAPP(hAPP(c_Product__Type_OPair(U_13724,U_13724),hAPP(U_13719,hAPP(c_Nat_OSuc,sK332(U_13726,U_13724,U_13719)))),hAPP(U_13719,sK332(U_13726,U_13724,U_13719)))),U_13726))
| ~ c_Wellfounded_Owf(U_13724,U_13726) ),
inference(clausify,[status(thm)],[f_3495_5]) ).
cnf(f_3495_7,plain,
( c_Wellfounded_Owf(U_13725,U_13727)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_13725,U_13725)),hAPP(hAPP(c_Product__Type_OPair(U_13725,U_13725),hAPP(sK333(U_13727,U_13725),hAPP(c_Nat_OSuc,U_13720))),hAPP(sK333(U_13727,U_13725),U_13720))),U_13727)) ),
inference(clausify,[status(thm)],[f_3495_5]) ).
fof(f_3496_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_3496_2,plain,
! [U_13730,U_13729,U_13728] :
( U_13730 = c_Orderings_Obot__class_Obot(tc_fun(U_13728,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13728,tc_HOL_Obool)),U_13730),hAPP(c_Relation_OImage(U_13728,U_13728,U_13729),U_13730)))
| ~ c_Wellfounded_Owf(U_13728,U_13729) ),
inference(variable_rename,[status(thm)],[f_3496_1]) ).
cnf(f_3496_3,plain,
( U_13730 = c_Orderings_Obot__class_Obot(tc_fun(U_13728,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13728,tc_HOL_Obool)),U_13730),hAPP(c_Relation_OImage(U_13728,U_13728,U_13729),U_13730)))
| ~ c_Wellfounded_Owf(U_13728,U_13729) ),
inference(clausify,[status(thm)],[f_3496_2]) ).
fof(f_3497_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_3497_2,plain,
! [U_13733,U_13732,U_13731] :
( c_Wellfounded_Owf(U_13731,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13731,U_13731),tc_HOL_Obool)),U_13732),U_13733))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13731,U_13731),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13731,U_13731,U_13731),U_13732),U_13733)),U_13732))
| ~ c_Wellfounded_Owf(U_13731,U_13733)
| ~ c_Wellfounded_Owf(U_13731,U_13732) ),
inference(variable_rename,[status(thm)],[f_3497_1]) ).
cnf(f_3497_3,plain,
( c_Wellfounded_Owf(U_13731,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13731,U_13731),tc_HOL_Obool)),U_13732),U_13733))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13731,U_13731),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13731,U_13731,U_13731),U_13732),U_13733)),U_13732))
| ~ c_Wellfounded_Owf(U_13731,U_13733)
| ~ c_Wellfounded_Owf(U_13731,U_13732) ),
inference(clausify,[status(thm)],[f_3497_2]) ).
fof(f_3498_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_3498_2,plain,
! [U_13739,U_13738,U_13737,U_13736] :
( ( hBOOL(hAPP(hAPP(c_member(U_13736),U_13737),hAPP(c_Relation_ODomain(U_13736,U_13738),U_13739)))
| ! [U_13735] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13736,U_13738)),hAPP(hAPP(c_Product__Type_OPair(U_13736,U_13738),U_13737),U_13735)),U_13739)) )
& ( ? [U_13734] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13736,U_13738)),hAPP(hAPP(c_Product__Type_OPair(U_13736,U_13738),U_13737),U_13734)),U_13739))
| ~ hBOOL(hAPP(hAPP(c_member(U_13736),U_13737),hAPP(c_Relation_ODomain(U_13736,U_13738),U_13739))) ) ),
inference(variable_rename,[status(thm)],[f_3498_1]) ).
fof(f_3498_3,plain,
( ! [U_13747,U_13745,U_13743,U_13741] :
( hBOOL(hAPP(hAPP(c_member(U_13741),U_13743),hAPP(c_Relation_ODomain(U_13741,U_13745),U_13747)))
| ! [U_13735] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13741,U_13745)),hAPP(hAPP(c_Product__Type_OPair(U_13741,U_13745),U_13743),U_13735)),U_13747)) )
& ! [U_13746,U_13744,U_13742,U_13740] :
( ? [U_13734] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13740,U_13744)),hAPP(hAPP(c_Product__Type_OPair(U_13740,U_13744),U_13742),U_13734)),U_13746))
| ~ hBOOL(hAPP(hAPP(c_member(U_13740),U_13742),hAPP(c_Relation_ODomain(U_13740,U_13744),U_13746))) ) ),
inference(miniscope,[status(thm)],[f_3498_2]) ).
fof(f_3498_4,plain,
( ! [U_13747,U_13745,U_13743,U_13741] :
( hBOOL(hAPP(hAPP(c_member(U_13741),U_13743),hAPP(c_Relation_ODomain(U_13741,U_13745),U_13747)))
| ! [U_13735] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13741,U_13745)),hAPP(hAPP(c_Product__Type_OPair(U_13741,U_13745),U_13743),U_13735)),U_13747)) )
& ! [U_13746,U_13744,U_13742,U_13740] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13740,U_13744)),hAPP(hAPP(c_Product__Type_OPair(U_13740,U_13744),U_13742),sK334(U_13746,U_13744,U_13742,U_13740))),U_13746))
| ~ hBOOL(hAPP(hAPP(c_member(U_13740),U_13742),hAPP(c_Relation_ODomain(U_13740,U_13744),U_13746))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK334]),skolemize(U_13734,sK334(U_13746,U_13744,U_13742,U_13740))],[f_3498_3]) ).
cnf(f_3498_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13740,U_13744)),hAPP(hAPP(c_Product__Type_OPair(U_13740,U_13744),U_13742),sK334(U_13746,U_13744,U_13742,U_13740))),U_13746))
| ~ hBOOL(hAPP(hAPP(c_member(U_13740),U_13742),hAPP(c_Relation_ODomain(U_13740,U_13744),U_13746))) ),
inference(clausify,[status(thm)],[f_3498_4]) ).
cnf(f_3498_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_13741),U_13743),hAPP(c_Relation_ODomain(U_13741,U_13745),U_13747)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13741,U_13745)),hAPP(hAPP(c_Product__Type_OPair(U_13741,U_13745),U_13743),U_13735)),U_13747)) ),
inference(clausify,[status(thm)],[f_3498_4]) ).
fof(f_3499_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_3499_2,plain,
! [U_13748] :
( c_Wellfounded_Owf(U_13748,hAPP(c_Set_OCollect(tc_prod(U_13748,U_13748)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13748,U_13748,tc_HOL_Obool),c_Orderings_Oord__class_Oless(U_13748))))
| ~ class_Orderings_Owellorder(U_13748) ),
inference(variable_rename,[status(thm)],[f_3499_1]) ).
cnf(f_3499_3,plain,
( c_Wellfounded_Owf(U_13748,hAPP(c_Set_OCollect(tc_prod(U_13748,U_13748)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13748,U_13748,tc_HOL_Obool),c_Orderings_Oord__class_Oless(U_13748))))
| ~ class_Orderings_Owellorder(U_13748) ),
inference(clausify,[status(thm)],[f_3499_2]) ).
fof(f_3500_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_3500_2,plain,
! [U_13753,U_13752,U_13751,U_13750,U_13749] : hAPP(c_Relation_ODomain(U_13749,U_13750),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13749,U_13750)),hAPP(hAPP(c_Product__Type_OPair(U_13749,U_13750),U_13751),U_13752)),U_13753)) = hAPP(hAPP(c_Set_Oinsert(U_13749),U_13751),hAPP(c_Relation_ODomain(U_13749,U_13750),U_13753)),
inference(variable_rename,[status(thm)],[f_3500_1]) ).
cnf(f_3500_3,plain,
hAPP(c_Relation_ODomain(U_13749,U_13750),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13749,U_13750)),hAPP(hAPP(c_Product__Type_OPair(U_13749,U_13750),U_13751),U_13752)),U_13753)) = hAPP(hAPP(c_Set_Oinsert(U_13749),U_13751),hAPP(c_Relation_ODomain(U_13749,U_13750),U_13753)),
inference(clausify,[status(thm)],[f_3500_2]) ).
fof(f_3501_1,plain,
! [V_P_2,T_b] :
( ( c_FunDef_Oreduction__pair(T_b,V_P_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
| ~ c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
& c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)) )
| ~ c_FunDef_Oreduction__pair(T_b,V_P_2) ) ),
inference(fof_nnf,[status(thm)],[fact_reduction__pair__def]) ).
fof(f_3501_2,plain,
! [U_13755,U_13754] :
( ( c_FunDef_Oreduction__pair(U_13754,U_13755)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13754,U_13754),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13754,U_13754,U_13754),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13754,U_13754),tc_HOL_Obool),tc_fun(tc_prod(U_13754,U_13754),tc_HOL_Obool)),U_13755)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13754,U_13754),tc_HOL_Obool),tc_fun(tc_prod(U_13754,U_13754),tc_HOL_Obool)),U_13755))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13754,U_13754),tc_HOL_Obool),tc_fun(tc_prod(U_13754,U_13754),tc_HOL_Obool)),U_13755)))
| ~ c_Wellfounded_Owf(U_13754,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13754,U_13754),tc_HOL_Obool),tc_fun(tc_prod(U_13754,U_13754),tc_HOL_Obool)),U_13755)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13754,U_13754),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13754,U_13754,U_13754),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13754,U_13754),tc_HOL_Obool),tc_fun(tc_prod(U_13754,U_13754),tc_HOL_Obool)),U_13755)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13754,U_13754),tc_HOL_Obool),tc_fun(tc_prod(U_13754,U_13754),tc_HOL_Obool)),U_13755))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13754,U_13754),tc_HOL_Obool),tc_fun(tc_prod(U_13754,U_13754),tc_HOL_Obool)),U_13755)))
& c_Wellfounded_Owf(U_13754,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13754,U_13754),tc_HOL_Obool),tc_fun(tc_prod(U_13754,U_13754),tc_HOL_Obool)),U_13755)) )
| ~ c_FunDef_Oreduction__pair(U_13754,U_13755) ) ),
inference(variable_rename,[status(thm)],[f_3501_1]) ).
fof(f_3501_3,plain,
( ! [U_13759,U_13757] :
( c_FunDef_Oreduction__pair(U_13757,U_13759)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13757,U_13757),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13757,U_13757,U_13757),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13757,U_13757),tc_HOL_Obool),tc_fun(tc_prod(U_13757,U_13757),tc_HOL_Obool)),U_13759)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13757,U_13757),tc_HOL_Obool),tc_fun(tc_prod(U_13757,U_13757),tc_HOL_Obool)),U_13759))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13757,U_13757),tc_HOL_Obool),tc_fun(tc_prod(U_13757,U_13757),tc_HOL_Obool)),U_13759)))
| ~ c_Wellfounded_Owf(U_13757,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13757,U_13757),tc_HOL_Obool),tc_fun(tc_prod(U_13757,U_13757),tc_HOL_Obool)),U_13759)) )
& ! [U_13758,U_13756] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13756,U_13756),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13756,U_13756,U_13756),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13756,U_13756),tc_HOL_Obool),tc_fun(tc_prod(U_13756,U_13756),tc_HOL_Obool)),U_13758)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13756,U_13756),tc_HOL_Obool),tc_fun(tc_prod(U_13756,U_13756),tc_HOL_Obool)),U_13758))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13756,U_13756),tc_HOL_Obool),tc_fun(tc_prod(U_13756,U_13756),tc_HOL_Obool)),U_13758)))
& c_Wellfounded_Owf(U_13756,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13756,U_13756),tc_HOL_Obool),tc_fun(tc_prod(U_13756,U_13756),tc_HOL_Obool)),U_13758)) )
| ~ c_FunDef_Oreduction__pair(U_13756,U_13758) ) ),
inference(miniscope,[status(thm)],[f_3501_2]) ).
cnf(f_3501_4,plain,
( c_Wellfounded_Owf(U_13756,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13756,U_13756),tc_HOL_Obool),tc_fun(tc_prod(U_13756,U_13756),tc_HOL_Obool)),U_13758))
| ~ c_FunDef_Oreduction__pair(U_13756,U_13758) ),
inference(clausify,[status(thm)],[f_3501_3]) ).
cnf(f_3501_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13756,U_13756),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13756,U_13756,U_13756),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13756,U_13756),tc_HOL_Obool),tc_fun(tc_prod(U_13756,U_13756),tc_HOL_Obool)),U_13758)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13756,U_13756),tc_HOL_Obool),tc_fun(tc_prod(U_13756,U_13756),tc_HOL_Obool)),U_13758))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13756,U_13756),tc_HOL_Obool),tc_fun(tc_prod(U_13756,U_13756),tc_HOL_Obool)),U_13758)))
| ~ c_FunDef_Oreduction__pair(U_13756,U_13758) ),
inference(clausify,[status(thm)],[f_3501_3]) ).
cnf(f_3501_6,plain,
( c_FunDef_Oreduction__pair(U_13757,U_13759)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13757,U_13757),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13757,U_13757,U_13757),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13757,U_13757),tc_HOL_Obool),tc_fun(tc_prod(U_13757,U_13757),tc_HOL_Obool)),U_13759)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13757,U_13757),tc_HOL_Obool),tc_fun(tc_prod(U_13757,U_13757),tc_HOL_Obool)),U_13759))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13757,U_13757),tc_HOL_Obool),tc_fun(tc_prod(U_13757,U_13757),tc_HOL_Obool)),U_13759)))
| ~ c_Wellfounded_Owf(U_13757,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13757,U_13757),tc_HOL_Obool),tc_fun(tc_prod(U_13757,U_13757),tc_HOL_Obool)),U_13759)) ),
inference(clausify,[status(thm)],[f_3501_3]) ).
fof(f_3502_1,plain,
! [V_S_2,V_R_2,V_P_2,T_b] :
( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
| ~ c_Wellfounded_Owf(T_b,V_S_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
| ~ c_FunDef_Oreduction__pair(T_b,V_P_2) ),
inference(fof_nnf,[status(thm)],[fact_reduction__pair__lemma]) ).
fof(f_3502_2,plain,
! [U_13763,U_13762,U_13761,U_13760] :
( c_Wellfounded_Owf(U_13760,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13760,U_13760),tc_HOL_Obool)),U_13762),U_13763))
| ~ c_Wellfounded_Owf(U_13760,U_13763)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13760,U_13760),tc_HOL_Obool)),U_13763),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13760,U_13760),tc_HOL_Obool),tc_fun(tc_prod(U_13760,U_13760),tc_HOL_Obool)),U_13761)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13760,U_13760),tc_HOL_Obool)),U_13762),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13760,U_13760),tc_HOL_Obool),tc_fun(tc_prod(U_13760,U_13760),tc_HOL_Obool)),U_13761)))
| ~ c_FunDef_Oreduction__pair(U_13760,U_13761) ),
inference(variable_rename,[status(thm)],[f_3502_1]) ).
cnf(f_3502_3,plain,
( c_Wellfounded_Owf(U_13760,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13760,U_13760),tc_HOL_Obool)),U_13762),U_13763))
| ~ c_Wellfounded_Owf(U_13760,U_13763)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13760,U_13760),tc_HOL_Obool)),U_13763),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13760,U_13760),tc_HOL_Obool),tc_fun(tc_prod(U_13760,U_13760),tc_HOL_Obool)),U_13761)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13760,U_13760),tc_HOL_Obool)),U_13762),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13760,U_13760),tc_HOL_Obool),tc_fun(tc_prod(U_13760,U_13760),tc_HOL_Obool)),U_13761)))
| ~ c_FunDef_Oreduction__pair(U_13760,U_13761) ),
inference(clausify,[status(thm)],[f_3502_2]) ).
fof(f_3503_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_3503_2,plain,
! [U_13767,U_13766,U_13765,U_13764] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13764,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13764,U_13765),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13764,U_13765),tc_HOL_Obool)),U_13766),U_13767))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13764,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13764,U_13765),U_13766)),hAPP(c_Relation_ODomain(U_13764,U_13765),U_13767)))),
inference(variable_rename,[status(thm)],[f_3503_1]) ).
cnf(f_3503_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13764,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13764,U_13765),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13764,U_13765),tc_HOL_Obool)),U_13766),U_13767))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13764,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13764,U_13765),U_13766)),hAPP(c_Relation_ODomain(U_13764,U_13765),U_13767)))),
inference(clausify,[status(thm)],[f_3503_2]) ).
fof(f_3504_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_3504_2,plain,
! [U_13771,U_13770,U_13769,U_13768] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13768,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13768,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13768,U_13769),U_13770)),hAPP(c_Relation_ODomain(U_13768,U_13769),U_13771))),hAPP(c_Relation_ODomain(U_13768,U_13769),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13768,U_13769),tc_HOL_Obool)),U_13770),U_13771)))),
inference(variable_rename,[status(thm)],[f_3504_1]) ).
cnf(f_3504_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13768,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13768,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13768,U_13769),U_13770)),hAPP(c_Relation_ODomain(U_13768,U_13769),U_13771))),hAPP(c_Relation_ODomain(U_13768,U_13769),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13768,U_13769),tc_HOL_Obool)),U_13770),U_13771)))),
inference(clausify,[status(thm)],[f_3504_2]) ).
fof(f_3505_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_3505_2,plain,
! [U_13773,U_13772] : hAPP(c_Relation_OField(U_13772),U_13773) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13772,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13772,U_13772),U_13773)),hAPP(c_Relation_ORange(U_13772,U_13772),U_13773)),
inference(variable_rename,[status(thm)],[f_3505_1]) ).
cnf(f_3505_3,plain,
hAPP(c_Relation_OField(U_13772),U_13773) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13772,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13772,U_13772),U_13773)),hAPP(c_Relation_ORange(U_13772,U_13772),U_13773)),
inference(clausify,[status(thm)],[f_3505_2]) ).
fof(f_3506_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_3506_2,plain,
! [U_13777,U_13776,U_13775,U_13774] :
( c_Wellfounded_Owf(U_13776,hAPP(c_Set_Oimage(tc_prod(U_13774,U_13774),tc_prod(U_13776,U_13776),c_Product__Type_Omap__pair(U_13774,U_13776,U_13774,U_13776,U_13777,U_13777)),U_13775))
| ~ c_Fun_Oinj__on(U_13774,U_13776,U_13777,c_Orderings_Otop__class_Otop(tc_fun(U_13774,tc_HOL_Obool)))
| ~ c_Wellfounded_Owf(U_13774,U_13775) ),
inference(variable_rename,[status(thm)],[f_3506_1]) ).
cnf(f_3506_3,plain,
( c_Wellfounded_Owf(U_13776,hAPP(c_Set_Oimage(tc_prod(U_13774,U_13774),tc_prod(U_13776,U_13776),c_Product__Type_Omap__pair(U_13774,U_13776,U_13774,U_13776,U_13777,U_13777)),U_13775))
| ~ c_Fun_Oinj__on(U_13774,U_13776,U_13777,c_Orderings_Otop__class_Otop(tc_fun(U_13774,tc_HOL_Obool)))
| ~ c_Wellfounded_Owf(U_13774,U_13775) ),
inference(clausify,[status(thm)],[f_3506_2]) ).
fof(f_3507_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_3507_2,plain,
! [U_13780,U_13779,U_13778] : hAPP(c_Relation_ODomain(U_13778,U_13779),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_13778,U_13779),tc_HOL_Obool),U_13780)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_13778,U_13779),tc_HOL_Obool),tc_fun(U_13778,tc_HOL_Obool)),U_13780),c_Relation_ODomain(U_13778,U_13779)),
inference(variable_rename,[status(thm)],[f_3507_1]) ).
cnf(f_3507_3,plain,
hAPP(c_Relation_ODomain(U_13778,U_13779),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_13778,U_13779),tc_HOL_Obool),U_13780)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_13778,U_13779),tc_HOL_Obool),tc_fun(U_13778,tc_HOL_Obool)),U_13780),c_Relation_ODomain(U_13778,U_13779)),
inference(clausify,[status(thm)],[f_3507_2]) ).
fof(f_3508_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_3508_2,plain,
! [U_13782,U_13781] : c_HOL_OThe(U_13781,hAPP(c_fequal,U_13782)) = U_13782,
inference(variable_rename,[status(thm)],[f_3508_1]) ).
cnf(f_3508_3,plain,
c_HOL_OThe(U_13781,hAPP(c_fequal,U_13782)) = U_13782,
inference(clausify,[status(thm)],[f_3508_2]) ).
fof(f_3509_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_3509_2,plain,
! [U_13786,U_13785,U_13784,U_13783] :
( ( hBOOL(hAPP(c_Predicate_ODomainP(U_13783,U_13784,hAPP(hAPP(c_COMBC(U_13783,tc_fun(tc_prod(U_13783,U_13784),tc_HOL_Obool),tc_fun(U_13784,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13784,tc_fun(tc_fun(tc_prod(U_13783,U_13784),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13783,U_13784),tc_HOL_Obool),tc_fun(U_13784,tc_HOL_Obool)),U_13783),c_COMBC(U_13784,tc_fun(tc_prod(U_13783,U_13784),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13784,tc_prod(U_13783,U_13784)),tc_fun(U_13784,tc_fun(tc_fun(tc_prod(U_13783,U_13784),tc_HOL_Obool),tc_HOL_Obool)),U_13783),hAPP(c_COMBB(tc_prod(U_13783,U_13784),tc_fun(tc_fun(tc_prod(U_13783,U_13784),tc_HOL_Obool),tc_HOL_Obool),U_13784),c_member(tc_prod(U_13783,U_13784)))),c_Product__Type_OPair(U_13783,U_13784)))),U_13785)),U_13786))
| ~ hBOOL(hAPP(hAPP(c_member(U_13783),U_13786),hAPP(c_Relation_ODomain(U_13783,U_13784),U_13785))) )
& ( hBOOL(hAPP(hAPP(c_member(U_13783),U_13786),hAPP(c_Relation_ODomain(U_13783,U_13784),U_13785)))
| ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13783,U_13784,hAPP(hAPP(c_COMBC(U_13783,tc_fun(tc_prod(U_13783,U_13784),tc_HOL_Obool),tc_fun(U_13784,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13784,tc_fun(tc_fun(tc_prod(U_13783,U_13784),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13783,U_13784),tc_HOL_Obool),tc_fun(U_13784,tc_HOL_Obool)),U_13783),c_COMBC(U_13784,tc_fun(tc_prod(U_13783,U_13784),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13784,tc_prod(U_13783,U_13784)),tc_fun(U_13784,tc_fun(tc_fun(tc_prod(U_13783,U_13784),tc_HOL_Obool),tc_HOL_Obool)),U_13783),hAPP(c_COMBB(tc_prod(U_13783,U_13784),tc_fun(tc_fun(tc_prod(U_13783,U_13784),tc_HOL_Obool),tc_HOL_Obool),U_13784),c_member(tc_prod(U_13783,U_13784)))),c_Product__Type_OPair(U_13783,U_13784)))),U_13785)),U_13786)) ) ),
inference(variable_rename,[status(thm)],[f_3509_1]) ).
fof(f_3509_3,plain,
( ! [U_13794,U_13792,U_13790,U_13788] :
( hBOOL(hAPP(c_Predicate_ODomainP(U_13788,U_13790,hAPP(hAPP(c_COMBC(U_13788,tc_fun(tc_prod(U_13788,U_13790),tc_HOL_Obool),tc_fun(U_13790,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13790,tc_fun(tc_fun(tc_prod(U_13788,U_13790),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13788,U_13790),tc_HOL_Obool),tc_fun(U_13790,tc_HOL_Obool)),U_13788),c_COMBC(U_13790,tc_fun(tc_prod(U_13788,U_13790),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13790,tc_prod(U_13788,U_13790)),tc_fun(U_13790,tc_fun(tc_fun(tc_prod(U_13788,U_13790),tc_HOL_Obool),tc_HOL_Obool)),U_13788),hAPP(c_COMBB(tc_prod(U_13788,U_13790),tc_fun(tc_fun(tc_prod(U_13788,U_13790),tc_HOL_Obool),tc_HOL_Obool),U_13790),c_member(tc_prod(U_13788,U_13790)))),c_Product__Type_OPair(U_13788,U_13790)))),U_13792)),U_13794))
| ~ hBOOL(hAPP(hAPP(c_member(U_13788),U_13794),hAPP(c_Relation_ODomain(U_13788,U_13790),U_13792))) )
& ! [U_13793,U_13791,U_13789,U_13787] :
( hBOOL(hAPP(hAPP(c_member(U_13787),U_13793),hAPP(c_Relation_ODomain(U_13787,U_13789),U_13791)))
| ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13787,U_13789,hAPP(hAPP(c_COMBC(U_13787,tc_fun(tc_prod(U_13787,U_13789),tc_HOL_Obool),tc_fun(U_13789,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13789,tc_fun(tc_fun(tc_prod(U_13787,U_13789),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13787,U_13789),tc_HOL_Obool),tc_fun(U_13789,tc_HOL_Obool)),U_13787),c_COMBC(U_13789,tc_fun(tc_prod(U_13787,U_13789),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13789,tc_prod(U_13787,U_13789)),tc_fun(U_13789,tc_fun(tc_fun(tc_prod(U_13787,U_13789),tc_HOL_Obool),tc_HOL_Obool)),U_13787),hAPP(c_COMBB(tc_prod(U_13787,U_13789),tc_fun(tc_fun(tc_prod(U_13787,U_13789),tc_HOL_Obool),tc_HOL_Obool),U_13789),c_member(tc_prod(U_13787,U_13789)))),c_Product__Type_OPair(U_13787,U_13789)))),U_13791)),U_13793)) ) ),
inference(miniscope,[status(thm)],[f_3509_2]) ).
cnf(f_3509_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_13787),U_13793),hAPP(c_Relation_ODomain(U_13787,U_13789),U_13791)))
| ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13787,U_13789,hAPP(hAPP(c_COMBC(U_13787,tc_fun(tc_prod(U_13787,U_13789),tc_HOL_Obool),tc_fun(U_13789,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13789,tc_fun(tc_fun(tc_prod(U_13787,U_13789),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13787,U_13789),tc_HOL_Obool),tc_fun(U_13789,tc_HOL_Obool)),U_13787),c_COMBC(U_13789,tc_fun(tc_prod(U_13787,U_13789),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13789,tc_prod(U_13787,U_13789)),tc_fun(U_13789,tc_fun(tc_fun(tc_prod(U_13787,U_13789),tc_HOL_Obool),tc_HOL_Obool)),U_13787),hAPP(c_COMBB(tc_prod(U_13787,U_13789),tc_fun(tc_fun(tc_prod(U_13787,U_13789),tc_HOL_Obool),tc_HOL_Obool),U_13789),c_member(tc_prod(U_13787,U_13789)))),c_Product__Type_OPair(U_13787,U_13789)))),U_13791)),U_13793)) ),
inference(clausify,[status(thm)],[f_3509_3]) ).
cnf(f_3509_5,plain,
( hBOOL(hAPP(c_Predicate_ODomainP(U_13788,U_13790,hAPP(hAPP(c_COMBC(U_13788,tc_fun(tc_prod(U_13788,U_13790),tc_HOL_Obool),tc_fun(U_13790,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13790,tc_fun(tc_fun(tc_prod(U_13788,U_13790),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13788,U_13790),tc_HOL_Obool),tc_fun(U_13790,tc_HOL_Obool)),U_13788),c_COMBC(U_13790,tc_fun(tc_prod(U_13788,U_13790),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13790,tc_prod(U_13788,U_13790)),tc_fun(U_13790,tc_fun(tc_fun(tc_prod(U_13788,U_13790),tc_HOL_Obool),tc_HOL_Obool)),U_13788),hAPP(c_COMBB(tc_prod(U_13788,U_13790),tc_fun(tc_fun(tc_prod(U_13788,U_13790),tc_HOL_Obool),tc_HOL_Obool),U_13790),c_member(tc_prod(U_13788,U_13790)))),c_Product__Type_OPair(U_13788,U_13790)))),U_13792)),U_13794))
| ~ hBOOL(hAPP(hAPP(c_member(U_13788),U_13794),hAPP(c_Relation_ODomain(U_13788,U_13790),U_13792))) ),
inference(clausify,[status(thm)],[f_3509_3]) ).
fof(f_3510_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_3510_2,plain,
! [U_13796,U_13795] :
( c_Wellfounded_Owf(tc_List_Olist(U_13795),c_List_Olenlex(U_13795,U_13796))
| ~ c_Wellfounded_Owf(U_13795,U_13796) ),
inference(variable_rename,[status(thm)],[f_3510_1]) ).
cnf(f_3510_3,plain,
( c_Wellfounded_Owf(tc_List_Olist(U_13795),c_List_Olenlex(U_13795,U_13796))
| ~ c_Wellfounded_Owf(U_13795,U_13796) ),
inference(clausify,[status(thm)],[f_3510_2]) ).
fof(f_3511_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_3511_2,plain,
! [U_13801,U_13800,U_13799,U_13798] :
( ? [U_13797] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13798,U_13800)),hAPP(hAPP(c_Product__Type_OPair(U_13798,U_13800),U_13799),U_13797)),U_13801))
| ~ hBOOL(hAPP(hAPP(c_member(U_13798),U_13799),hAPP(c_Relation_ODomain(U_13798,U_13800),U_13801))) ),
inference(variable_rename,[status(thm)],[f_3511_1]) ).
fof(f_3511_3,plain,
! [U_13801,U_13800,U_13799,U_13798] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13798,U_13800)),hAPP(hAPP(c_Product__Type_OPair(U_13798,U_13800),U_13799),sK335(U_13801,U_13800,U_13799,U_13798))),U_13801))
| ~ hBOOL(hAPP(hAPP(c_member(U_13798),U_13799),hAPP(c_Relation_ODomain(U_13798,U_13800),U_13801))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK335]),skolemize(U_13797,sK335(U_13801,U_13800,U_13799,U_13798))],[f_3511_2]) ).
cnf(f_3511_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13798,U_13800)),hAPP(hAPP(c_Product__Type_OPair(U_13798,U_13800),U_13799),sK335(U_13801,U_13800,U_13799,U_13798))),U_13801))
| ~ hBOOL(hAPP(hAPP(c_member(U_13798),U_13799),hAPP(c_Relation_ODomain(U_13798,U_13800),U_13801))) ),
inference(clausify,[status(thm)],[f_3511_3]) ).
fof(f_3512_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_3512_2,plain,
! [U_13806,U_13805,U_13804,U_13803,U_13802] :
( hBOOL(hAPP(c_Predicate_ODomainP(U_13805,U_13806,U_13802),U_13803))
| ~ hBOOL(hAPP(hAPP(U_13802,U_13803),U_13804)) ),
inference(variable_rename,[status(thm)],[f_3512_1]) ).
cnf(f_3512_3,plain,
( hBOOL(hAPP(c_Predicate_ODomainP(U_13805,U_13806,U_13802),U_13803))
| ~ hBOOL(hAPP(hAPP(U_13802,U_13803),U_13804)) ),
inference(clausify,[status(thm)],[f_3512_2]) ).
fof(f_3513_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_3513_2,plain,
! [U_13812,U_13811,U_13810,U_13809] :
( ( hBOOL(hAPP(c_Predicate_ODomainP(U_13809,U_13810,U_13811),U_13812))
| ! [U_13808] : ~ hBOOL(hAPP(hAPP(U_13811,U_13812),U_13808)) )
& ( ? [U_13807] : hBOOL(hAPP(hAPP(U_13811,U_13812),U_13807))
| ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13809,U_13810,U_13811),U_13812)) ) ),
inference(variable_rename,[status(thm)],[f_3513_1]) ).
fof(f_3513_3,plain,
( ! [U_13820,U_13818] :
( ! [U_13816,U_13814] : hBOOL(hAPP(c_Predicate_ODomainP(U_13814,U_13816,U_13818),U_13820))
| ! [U_13808] : ~ hBOOL(hAPP(hAPP(U_13818,U_13820),U_13808)) )
& ! [U_13819,U_13817] :
( ! [U_13815,U_13813] : ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13813,U_13815,U_13817),U_13819))
| ? [U_13807] : hBOOL(hAPP(hAPP(U_13817,U_13819),U_13807)) ) ),
inference(miniscope,[status(thm)],[f_3513_2]) ).
fof(f_3513_4,plain,
( ! [U_13820,U_13818] :
( ! [U_13816,U_13814] : hBOOL(hAPP(c_Predicate_ODomainP(U_13814,U_13816,U_13818),U_13820))
| ! [U_13808] : ~ hBOOL(hAPP(hAPP(U_13818,U_13820),U_13808)) )
& ! [U_13819,U_13817] :
( ! [U_13815,U_13813] : ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13813,U_13815,U_13817),U_13819))
| hBOOL(hAPP(hAPP(U_13817,U_13819),sK336(U_13819,U_13817))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK336]),skolemize(U_13807,sK336(U_13819,U_13817))],[f_3513_3]) ).
cnf(f_3513_5,plain,
( ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13813,U_13815,U_13817),U_13819))
| hBOOL(hAPP(hAPP(U_13817,U_13819),sK336(U_13819,U_13817))) ),
inference(clausify,[status(thm)],[f_3513_4]) ).
cnf(f_3513_6,plain,
( hBOOL(hAPP(c_Predicate_ODomainP(U_13814,U_13816,U_13818),U_13820))
| ~ hBOOL(hAPP(hAPP(U_13818,U_13820),U_13808)) ),
inference(clausify,[status(thm)],[f_3513_4]) ).
fof(f_3514_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_3514_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_3514_1]) ).
fof(f_3515_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_3515_2,plain,
! [U_13822,U_13821] :
( c_Wellfounded_Owf(tc_List_Olist(U_13821),c_List_Olex(U_13821,U_13822))
| ~ c_Wellfounded_Owf(U_13821,U_13822) ),
inference(variable_rename,[status(thm)],[f_3515_1]) ).
cnf(f_3515_3,plain,
( c_Wellfounded_Owf(tc_List_Olist(U_13821),c_List_Olex(U_13821,U_13822))
| ~ c_Wellfounded_Owf(U_13821,U_13822) ),
inference(clausify,[status(thm)],[f_3515_2]) ).
fof(f_3516_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_3516_2,plain,
! [U_13825,U_13824,U_13823] :
( c_Wellfounded_Owf(tc_List_Olist(U_13823),hAPP(c_List_Olexn(U_13823,U_13824),U_13825))
| ~ c_Wellfounded_Owf(U_13823,U_13824) ),
inference(variable_rename,[status(thm)],[f_3516_1]) ).
cnf(f_3516_3,plain,
( c_Wellfounded_Owf(tc_List_Olist(U_13823),hAPP(c_List_Olexn(U_13823,U_13824),U_13825))
| ~ c_Wellfounded_Owf(U_13823,U_13824) ),
inference(clausify,[status(thm)],[f_3516_2]) ).
fof(f_3517_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_3517_2,plain,
! [U_13827,U_13826] : c_List_Olex(U_13826,U_13827) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(U_13826),tc_List_Olist(U_13826)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(U_13826,U_13827)),
inference(variable_rename,[status(thm)],[f_3517_1]) ).
cnf(f_3517_3,plain,
c_List_Olex(U_13826,U_13827) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(U_13826),tc_List_Olist(U_13826)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(U_13826,U_13827)),
inference(clausify,[status(thm)],[f_3517_2]) ).
fof(f_3518_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_3518_2,plain,
! [U_13829,U_13828] : hAPP(c_List_Olexn(U_13828,U_13829),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(U_13828),tc_List_Olist(U_13828)),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3518_1]) ).
cnf(f_3518_3,plain,
hAPP(c_List_Olexn(U_13828,U_13829),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(U_13828),tc_List_Olist(U_13828)),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3518_2]) ).
fof(f_3519_1,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(fof_nnf,[status(thm)],[fact_wf__pred__nat]) ).
cnf(f_3519_2,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(clausify,[status(thm)],[f_3519_1]) ).
fof(f_3520_1,plain,
! [T_b,V_R_2,T_c,V_P_2] :
( c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2))
| ? [B_x] :
( ~ c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x))
& hBOOL(hAPP(V_P_2,B_x)) ) ),
inference(fof_nnf,[status(thm)],[fact_wf__same__fst]) ).
fof(f_3520_2,plain,
! [U_13834,U_13833,U_13832,U_13831] :
( c_Wellfounded_Owf(tc_prod(U_13834,U_13832),c_Recdef_Osame__fst(U_13834,U_13832,U_13831,U_13833))
| ? [U_13830] :
( ~ c_Wellfounded_Owf(U_13832,hAPP(U_13833,U_13830))
& hBOOL(hAPP(U_13831,U_13830)) ) ),
inference(variable_rename,[status(thm)],[f_3520_1]) ).
fof(f_3520_3,plain,
! [U_13834,U_13833,U_13832,U_13831] :
( c_Wellfounded_Owf(tc_prod(U_13834,U_13832),c_Recdef_Osame__fst(U_13834,U_13832,U_13831,U_13833))
| ( ~ c_Wellfounded_Owf(U_13832,hAPP(U_13833,sK337(U_13834,U_13833,U_13832,U_13831)))
& hBOOL(hAPP(U_13831,sK337(U_13834,U_13833,U_13832,U_13831))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK337]),skolemize(U_13830,sK337(U_13834,U_13833,U_13832,U_13831))],[f_3520_2]) ).
cnf(f_3520_4,plain,
( hBOOL(hAPP(U_13831,sK337(U_13834,U_13833,U_13832,U_13831)))
| c_Wellfounded_Owf(tc_prod(U_13834,U_13832),c_Recdef_Osame__fst(U_13834,U_13832,U_13831,U_13833)) ),
inference(clausify,[status(thm)],[f_3520_3]) ).
cnf(f_3520_5,plain,
( ~ c_Wellfounded_Owf(U_13832,hAPP(U_13833,sK337(U_13834,U_13833,U_13832,U_13831)))
| c_Wellfounded_Owf(tc_prod(U_13834,U_13832),c_Recdef_Osame__fst(U_13834,U_13832,U_13831,U_13833)) ),
inference(clausify,[status(thm)],[f_3520_3]) ).
fof(f_3521_1,plain,
! [T_b,V_g_2,V_f_2,V_P_2] :
( c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),V_g_2)))))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,hAPP(V_g_2,B_x))),hAPP(V_f_2,B_x)))
& hBOOL(hAPP(V_P_2,B_x)) ) ),
inference(fof_nnf,[status(thm)],[fact_wf__if__measure]) ).
fof(f_3521_2,plain,
! [U_13839,U_13838,U_13837,U_13836] :
( c_Wellfounded_Owf(U_13839,hAPP(c_Set_OCollect(tc_prod(U_13839,U_13839)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13839,U_13839,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13839,tc_HOL_Obool),tc_fun(U_13839,tc_HOL_Obool),U_13839),hAPP(c_COMBS(U_13839,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13839),c_fconj),U_13836))),hAPP(hAPP(c_COMBC(U_13839,tc_fun(U_13839,U_13839),tc_fun(U_13839,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13839,tc_HOL_Obool),tc_fun(tc_fun(U_13839,U_13839),tc_fun(U_13839,tc_HOL_Obool)),U_13839),c_COMBB(U_13839,tc_HOL_Obool,U_13839)),c_fequal)),U_13838)))))
| ? [U_13835] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_13837,hAPP(U_13838,U_13835))),hAPP(U_13837,U_13835)))
& hBOOL(hAPP(U_13836,U_13835)) ) ),
inference(variable_rename,[status(thm)],[f_3521_1]) ).
fof(f_3521_3,plain,
! [U_13839,U_13838,U_13837,U_13836] :
( c_Wellfounded_Owf(U_13839,hAPP(c_Set_OCollect(tc_prod(U_13839,U_13839)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13839,U_13839,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13839,tc_HOL_Obool),tc_fun(U_13839,tc_HOL_Obool),U_13839),hAPP(c_COMBS(U_13839,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13839),c_fconj),U_13836))),hAPP(hAPP(c_COMBC(U_13839,tc_fun(U_13839,U_13839),tc_fun(U_13839,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13839,tc_HOL_Obool),tc_fun(tc_fun(U_13839,U_13839),tc_fun(U_13839,tc_HOL_Obool)),U_13839),c_COMBB(U_13839,tc_HOL_Obool,U_13839)),c_fequal)),U_13838)))))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_13837,hAPP(U_13838,sK338(U_13839,U_13838,U_13837,U_13836)))),hAPP(U_13837,sK338(U_13839,U_13838,U_13837,U_13836))))
& hBOOL(hAPP(U_13836,sK338(U_13839,U_13838,U_13837,U_13836))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK338]),skolemize(U_13835,sK338(U_13839,U_13838,U_13837,U_13836))],[f_3521_2]) ).
cnf(f_3521_4,plain,
( hBOOL(hAPP(U_13836,sK338(U_13839,U_13838,U_13837,U_13836)))
| c_Wellfounded_Owf(U_13839,hAPP(c_Set_OCollect(tc_prod(U_13839,U_13839)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13839,U_13839,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13839,tc_HOL_Obool),tc_fun(U_13839,tc_HOL_Obool),U_13839),hAPP(c_COMBS(U_13839,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13839),c_fconj),U_13836))),hAPP(hAPP(c_COMBC(U_13839,tc_fun(U_13839,U_13839),tc_fun(U_13839,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13839,tc_HOL_Obool),tc_fun(tc_fun(U_13839,U_13839),tc_fun(U_13839,tc_HOL_Obool)),U_13839),c_COMBB(U_13839,tc_HOL_Obool,U_13839)),c_fequal)),U_13838))))) ),
inference(clausify,[status(thm)],[f_3521_3]) ).
cnf(f_3521_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_13837,hAPP(U_13838,sK338(U_13839,U_13838,U_13837,U_13836)))),hAPP(U_13837,sK338(U_13839,U_13838,U_13837,U_13836))))
| c_Wellfounded_Owf(U_13839,hAPP(c_Set_OCollect(tc_prod(U_13839,U_13839)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13839,U_13839,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13839,tc_HOL_Obool),tc_fun(U_13839,tc_HOL_Obool),U_13839),hAPP(c_COMBS(U_13839,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13839),c_fconj),U_13836))),hAPP(hAPP(c_COMBC(U_13839,tc_fun(U_13839,U_13839),tc_fun(U_13839,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13839,tc_HOL_Obool),tc_fun(tc_fun(U_13839,U_13839),tc_fun(U_13839,tc_HOL_Obool)),U_13839),c_COMBB(U_13839,tc_HOL_Obool,U_13839)),c_fequal)),U_13838))))) ),
inference(clausify,[status(thm)],[f_3521_3]) ).
fof(f_3522_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_3522_2,plain,
! [U_13841,U_13840] :
( ( c_Wellfounded_OwfP(U_13840,U_13841)
| ~ c_Wellfounded_Owf(U_13840,hAPP(c_Set_OCollect(tc_prod(U_13840,U_13840)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13840,U_13840,tc_HOL_Obool),U_13841))) )
& ( c_Wellfounded_Owf(U_13840,hAPP(c_Set_OCollect(tc_prod(U_13840,U_13840)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13840,U_13840,tc_HOL_Obool),U_13841)))
| ~ c_Wellfounded_OwfP(U_13840,U_13841) ) ),
inference(variable_rename,[status(thm)],[f_3522_1]) ).
fof(f_3522_3,plain,
( ! [U_13845,U_13843] :
( c_Wellfounded_OwfP(U_13843,U_13845)
| ~ c_Wellfounded_Owf(U_13843,hAPP(c_Set_OCollect(tc_prod(U_13843,U_13843)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13843,U_13843,tc_HOL_Obool),U_13845))) )
& ! [U_13844,U_13842] :
( c_Wellfounded_Owf(U_13842,hAPP(c_Set_OCollect(tc_prod(U_13842,U_13842)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13842,U_13842,tc_HOL_Obool),U_13844)))
| ~ c_Wellfounded_OwfP(U_13842,U_13844) ) ),
inference(miniscope,[status(thm)],[f_3522_2]) ).
cnf(f_3522_4,plain,
( c_Wellfounded_Owf(U_13842,hAPP(c_Set_OCollect(tc_prod(U_13842,U_13842)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13842,U_13842,tc_HOL_Obool),U_13844)))
| ~ c_Wellfounded_OwfP(U_13842,U_13844) ),
inference(clausify,[status(thm)],[f_3522_3]) ).
cnf(f_3522_5,plain,
( c_Wellfounded_OwfP(U_13843,U_13845)
| ~ c_Wellfounded_Owf(U_13843,hAPP(c_Set_OCollect(tc_prod(U_13843,U_13843)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13843,U_13843,tc_HOL_Obool),U_13845))) ),
inference(clausify,[status(thm)],[f_3522_3]) ).
fof(f_3523_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_3523_2,plain,
! [U_13846] : c_Wellfounded_OwfP(U_13846,hAPP(c_COMBK(tc_fun(U_13846,tc_HOL_Obool),U_13846),hAPP(c_COMBK(tc_HOL_Obool,U_13846),c_fFalse))),
inference(variable_rename,[status(thm)],[f_3523_1]) ).
cnf(f_3523_3,plain,
c_Wellfounded_OwfP(U_13846,hAPP(c_COMBK(tc_fun(U_13846,tc_HOL_Obool),U_13846),hAPP(c_COMBK(tc_HOL_Obool,U_13846),c_fFalse))),
inference(clausify,[status(thm)],[f_3523_2]) ).
fof(f_3524_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_3524_2,plain,
! [U_13849,U_13848,U_13847] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_13847,U_13848),U_13849))
| ~ c_Wellfounded_OwfP(U_13847,U_13848) ),
inference(variable_rename,[status(thm)],[f_3524_1]) ).
cnf(f_3524_3,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_13847,U_13848),U_13849))
| ~ c_Wellfounded_OwfP(U_13847,U_13848) ),
inference(clausify,[status(thm)],[f_3524_2]) ).
fof(f_3525_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_3525_2,plain,
! [U_13853,U_13852] :
( ( c_Wellfounded_OwfP(U_13852,U_13853)
| ? [U_13851] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_13852,U_13853),U_13851)) )
& ( ! [U_13850] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_13852,U_13853),U_13850))
| ~ c_Wellfounded_OwfP(U_13852,U_13853) ) ),
inference(variable_rename,[status(thm)],[f_3525_1]) ).
fof(f_3525_3,plain,
( ! [U_13857,U_13855] :
( c_Wellfounded_OwfP(U_13855,U_13857)
| ? [U_13851] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_13855,U_13857),U_13851)) )
& ! [U_13856,U_13854] :
( ! [U_13850] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_13854,U_13856),U_13850))
| ~ c_Wellfounded_OwfP(U_13854,U_13856) ) ),
inference(miniscope,[status(thm)],[f_3525_2]) ).
fof(f_3525_4,plain,
( ! [U_13857,U_13855] :
( c_Wellfounded_OwfP(U_13855,U_13857)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_13855,U_13857),sK339(U_13857,U_13855))) )
& ! [U_13856,U_13854] :
( ! [U_13850] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_13854,U_13856),U_13850))
| ~ c_Wellfounded_OwfP(U_13854,U_13856) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK339]),skolemize(U_13851,sK339(U_13857,U_13855))],[f_3525_3]) ).
cnf(f_3525_5,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_13854,U_13856),U_13850))
| ~ c_Wellfounded_OwfP(U_13854,U_13856) ),
inference(clausify,[status(thm)],[f_3525_4]) ).
cnf(f_3525_6,plain,
( c_Wellfounded_OwfP(U_13855,U_13857)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_13855,U_13857),sK339(U_13857,U_13855))) ),
inference(clausify,[status(thm)],[f_3525_4]) ).
fof(f_3526_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_3526_2,plain,
! [U_13860,U_13859,U_13858] :
( c_Wellfounded_OwfP(U_13858,U_13860)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13858,tc_fun(U_13858,tc_HOL_Obool))),U_13860),U_13859))
| ~ c_Wellfounded_OwfP(U_13858,U_13859) ),
inference(variable_rename,[status(thm)],[f_3526_1]) ).
cnf(f_3526_3,plain,
( c_Wellfounded_OwfP(U_13858,U_13860)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13858,tc_fun(U_13858,tc_HOL_Obool))),U_13860),U_13859))
| ~ c_Wellfounded_OwfP(U_13858,U_13859) ),
inference(clausify,[status(thm)],[f_3526_2]) ).
fof(f_3527_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_3527_2,plain,
! [U_13862,U_13861] :
( c_Wellfounded_OwfP(U_13861,c_FunDef_Oin__rel(U_13861,U_13861,U_13862))
| ~ c_Wellfounded_Owf(U_13861,U_13862) ),
inference(variable_rename,[status(thm)],[f_3527_1]) ).
cnf(f_3527_3,plain,
( c_Wellfounded_OwfP(U_13861,c_FunDef_Oin__rel(U_13861,U_13861,U_13862))
| ~ c_Wellfounded_Owf(U_13861,U_13862) ),
inference(clausify,[status(thm)],[f_3527_2]) ).
fof(f_3528_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_3528_2,plain,
! [U_13864,U_13863] :
( ( c_Wellfounded_OwfP(U_13863,hAPP(hAPP(c_COMBC(U_13863,tc_fun(tc_prod(U_13863,U_13863),tc_HOL_Obool),tc_fun(U_13863,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13863,tc_fun(tc_fun(tc_prod(U_13863,U_13863),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13863,U_13863),tc_HOL_Obool),tc_fun(U_13863,tc_HOL_Obool)),U_13863),c_COMBC(U_13863,tc_fun(tc_prod(U_13863,U_13863),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13863,tc_prod(U_13863,U_13863)),tc_fun(U_13863,tc_fun(tc_fun(tc_prod(U_13863,U_13863),tc_HOL_Obool),tc_HOL_Obool)),U_13863),hAPP(c_COMBB(tc_prod(U_13863,U_13863),tc_fun(tc_fun(tc_prod(U_13863,U_13863),tc_HOL_Obool),tc_HOL_Obool),U_13863),c_member(tc_prod(U_13863,U_13863)))),c_Product__Type_OPair(U_13863,U_13863)))),U_13864))
| ~ c_Wellfounded_Owf(U_13863,U_13864) )
& ( c_Wellfounded_Owf(U_13863,U_13864)
| ~ c_Wellfounded_OwfP(U_13863,hAPP(hAPP(c_COMBC(U_13863,tc_fun(tc_prod(U_13863,U_13863),tc_HOL_Obool),tc_fun(U_13863,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13863,tc_fun(tc_fun(tc_prod(U_13863,U_13863),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13863,U_13863),tc_HOL_Obool),tc_fun(U_13863,tc_HOL_Obool)),U_13863),c_COMBC(U_13863,tc_fun(tc_prod(U_13863,U_13863),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13863,tc_prod(U_13863,U_13863)),tc_fun(U_13863,tc_fun(tc_fun(tc_prod(U_13863,U_13863),tc_HOL_Obool),tc_HOL_Obool)),U_13863),hAPP(c_COMBB(tc_prod(U_13863,U_13863),tc_fun(tc_fun(tc_prod(U_13863,U_13863),tc_HOL_Obool),tc_HOL_Obool),U_13863),c_member(tc_prod(U_13863,U_13863)))),c_Product__Type_OPair(U_13863,U_13863)))),U_13864)) ) ),
inference(variable_rename,[status(thm)],[f_3528_1]) ).
fof(f_3528_3,plain,
( ! [U_13868,U_13866] :
( c_Wellfounded_OwfP(U_13866,hAPP(hAPP(c_COMBC(U_13866,tc_fun(tc_prod(U_13866,U_13866),tc_HOL_Obool),tc_fun(U_13866,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13866,tc_fun(tc_fun(tc_prod(U_13866,U_13866),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13866,U_13866),tc_HOL_Obool),tc_fun(U_13866,tc_HOL_Obool)),U_13866),c_COMBC(U_13866,tc_fun(tc_prod(U_13866,U_13866),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13866,tc_prod(U_13866,U_13866)),tc_fun(U_13866,tc_fun(tc_fun(tc_prod(U_13866,U_13866),tc_HOL_Obool),tc_HOL_Obool)),U_13866),hAPP(c_COMBB(tc_prod(U_13866,U_13866),tc_fun(tc_fun(tc_prod(U_13866,U_13866),tc_HOL_Obool),tc_HOL_Obool),U_13866),c_member(tc_prod(U_13866,U_13866)))),c_Product__Type_OPair(U_13866,U_13866)))),U_13868))
| ~ c_Wellfounded_Owf(U_13866,U_13868) )
& ! [U_13867,U_13865] :
( c_Wellfounded_Owf(U_13865,U_13867)
| ~ c_Wellfounded_OwfP(U_13865,hAPP(hAPP(c_COMBC(U_13865,tc_fun(tc_prod(U_13865,U_13865),tc_HOL_Obool),tc_fun(U_13865,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13865,tc_fun(tc_fun(tc_prod(U_13865,U_13865),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13865,U_13865),tc_HOL_Obool),tc_fun(U_13865,tc_HOL_Obool)),U_13865),c_COMBC(U_13865,tc_fun(tc_prod(U_13865,U_13865),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13865,tc_prod(U_13865,U_13865)),tc_fun(U_13865,tc_fun(tc_fun(tc_prod(U_13865,U_13865),tc_HOL_Obool),tc_HOL_Obool)),U_13865),hAPP(c_COMBB(tc_prod(U_13865,U_13865),tc_fun(tc_fun(tc_prod(U_13865,U_13865),tc_HOL_Obool),tc_HOL_Obool),U_13865),c_member(tc_prod(U_13865,U_13865)))),c_Product__Type_OPair(U_13865,U_13865)))),U_13867)) ) ),
inference(miniscope,[status(thm)],[f_3528_2]) ).
cnf(f_3528_4,plain,
( c_Wellfounded_Owf(U_13865,U_13867)
| ~ c_Wellfounded_OwfP(U_13865,hAPP(hAPP(c_COMBC(U_13865,tc_fun(tc_prod(U_13865,U_13865),tc_HOL_Obool),tc_fun(U_13865,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13865,tc_fun(tc_fun(tc_prod(U_13865,U_13865),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13865,U_13865),tc_HOL_Obool),tc_fun(U_13865,tc_HOL_Obool)),U_13865),c_COMBC(U_13865,tc_fun(tc_prod(U_13865,U_13865),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13865,tc_prod(U_13865,U_13865)),tc_fun(U_13865,tc_fun(tc_fun(tc_prod(U_13865,U_13865),tc_HOL_Obool),tc_HOL_Obool)),U_13865),hAPP(c_COMBB(tc_prod(U_13865,U_13865),tc_fun(tc_fun(tc_prod(U_13865,U_13865),tc_HOL_Obool),tc_HOL_Obool),U_13865),c_member(tc_prod(U_13865,U_13865)))),c_Product__Type_OPair(U_13865,U_13865)))),U_13867)) ),
inference(clausify,[status(thm)],[f_3528_3]) ).
cnf(f_3528_5,plain,
( c_Wellfounded_OwfP(U_13866,hAPP(hAPP(c_COMBC(U_13866,tc_fun(tc_prod(U_13866,U_13866),tc_HOL_Obool),tc_fun(U_13866,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13866,tc_fun(tc_fun(tc_prod(U_13866,U_13866),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13866,U_13866),tc_HOL_Obool),tc_fun(U_13866,tc_HOL_Obool)),U_13866),c_COMBC(U_13866,tc_fun(tc_prod(U_13866,U_13866),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13866,tc_prod(U_13866,U_13866)),tc_fun(U_13866,tc_fun(tc_fun(tc_prod(U_13866,U_13866),tc_HOL_Obool),tc_HOL_Obool)),U_13866),hAPP(c_COMBB(tc_prod(U_13866,U_13866),tc_fun(tc_fun(tc_prod(U_13866,U_13866),tc_HOL_Obool),tc_HOL_Obool),U_13866),c_member(tc_prod(U_13866,U_13866)))),c_Product__Type_OPair(U_13866,U_13866)))),U_13868))
| ~ c_Wellfounded_Owf(U_13866,U_13868) ),
inference(clausify,[status(thm)],[f_3528_3]) ).
fof(f_3529_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_3529_2,plain,
! [U_13870,U_13869] :
( c_Wellfounded_Oacyclic(U_13869,hAPP(c_Set_OCollect(tc_prod(U_13869,U_13869)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13869,U_13869,tc_HOL_Obool),U_13870)))
| ~ c_Wellfounded_OwfP(U_13869,U_13870) ),
inference(variable_rename,[status(thm)],[f_3529_1]) ).
cnf(f_3529_3,plain,
( c_Wellfounded_Oacyclic(U_13869,hAPP(c_Set_OCollect(tc_prod(U_13869,U_13869)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13869,U_13869,tc_HOL_Obool),U_13870)))
| ~ c_Wellfounded_OwfP(U_13869,U_13870) ),
inference(clausify,[status(thm)],[f_3529_2]) ).
fof(f_3530_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_3530_2,plain,
! [U_13875,U_13874,U_13873,U_13872] :
( ? [U_13871] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13872),hAPP(c_Set_OCollect(U_13872),hAPP(hAPP(c_COMBS(U_13872,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13872),c_fconj),hAPP(hAPP(c_COMBC(U_13872,tc_fun(U_13872,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13872)),U_13873))),hAPP(hAPP(c_COMBC(U_13872,U_13874,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13874,tc_fun(U_13874,tc_HOL_Obool),U_13872),c_fequal),U_13875)),hAPP(U_13875,U_13871))))))
& hBOOL(hAPP(hAPP(c_member(U_13872),U_13871),U_13873)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13874),hAPP(c_Set_Oimage(U_13872,U_13874,U_13875),U_13873)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_13872),U_13873)) ),
inference(variable_rename,[status(thm)],[f_3530_1]) ).
fof(f_3530_3,plain,
! [U_13875,U_13874,U_13873,U_13872] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13872),hAPP(c_Set_OCollect(U_13872),hAPP(hAPP(c_COMBS(U_13872,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13872),c_fconj),hAPP(hAPP(c_COMBC(U_13872,tc_fun(U_13872,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13872)),U_13873))),hAPP(hAPP(c_COMBC(U_13872,U_13874,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13874,tc_fun(U_13874,tc_HOL_Obool),U_13872),c_fequal),U_13875)),hAPP(U_13875,sK340(U_13875,U_13874,U_13873,U_13872)))))))
& hBOOL(hAPP(hAPP(c_member(U_13872),sK340(U_13875,U_13874,U_13873,U_13872)),U_13873)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13874),hAPP(c_Set_Oimage(U_13872,U_13874,U_13875),U_13873)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_13872),U_13873)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK340]),skolemize(U_13871,sK340(U_13875,U_13874,U_13873,U_13872))],[f_3530_2]) ).
cnf(f_3530_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_13872),sK340(U_13875,U_13874,U_13873,U_13872)),U_13873))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13874),hAPP(c_Set_Oimage(U_13872,U_13874,U_13875),U_13873)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_13872),U_13873)) ),
inference(clausify,[status(thm)],[f_3530_3]) ).
cnf(f_3530_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13872),hAPP(c_Set_OCollect(U_13872),hAPP(hAPP(c_COMBS(U_13872,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13872),c_fconj),hAPP(hAPP(c_COMBC(U_13872,tc_fun(U_13872,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13872)),U_13873))),hAPP(hAPP(c_COMBC(U_13872,U_13874,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13874,tc_fun(U_13874,tc_HOL_Obool),U_13872),c_fequal),U_13875)),hAPP(U_13875,sK340(U_13875,U_13874,U_13873,U_13872)))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13874),hAPP(c_Set_Oimage(U_13872,U_13874,U_13875),U_13873)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_13872),U_13873)) ),
inference(clausify,[status(thm)],[f_3530_3]) ).
fof(f_3531_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_3531_2,plain,
! [U_13877] :
? [U_13876] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_13876),c_Int_OInteg))
& U_13877 = hAPP(c_Int_OAbs__Integ,U_13876) ),
inference(variable_rename,[status(thm)],[f_3531_1]) ).
fof(f_3531_3,plain,
! [U_13877] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK341(U_13877)),c_Int_OInteg))
& U_13877 = hAPP(c_Int_OAbs__Integ,sK341(U_13877)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK341]),skolemize(U_13876,sK341(U_13877))],[f_3531_2]) ).
cnf(f_3531_4,plain,
U_13877 = hAPP(c_Int_OAbs__Integ,sK341(U_13877)),
inference(clausify,[status(thm)],[f_3531_3]) ).
cnf(f_3531_5,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK341(U_13877)),c_Int_OInteg)),
inference(clausify,[status(thm)],[f_3531_3]) ).
fof(f_3532_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_3532_2,plain,
! [U_13879,U_13878] :
( c_Wellfounded_Oacyclic(U_13878,U_13879)
| ~ c_Wellfounded_Owf(U_13878,U_13879) ),
inference(variable_rename,[status(thm)],[f_3532_1]) ).
cnf(f_3532_3,plain,
( c_Wellfounded_Oacyclic(U_13878,U_13879)
| ~ c_Wellfounded_Owf(U_13878,U_13879) ),
inference(clausify,[status(thm)],[f_3532_2]) ).
fof(f_3533_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_3533_2,plain,
! [U_13882,U_13881,U_13880] :
( c_Wellfounded_Oacyclic(U_13880,U_13882)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13880,U_13880),tc_HOL_Obool)),U_13882),U_13881))
| ~ c_Wellfounded_Oacyclic(U_13880,U_13881) ),
inference(variable_rename,[status(thm)],[f_3533_1]) ).
cnf(f_3533_3,plain,
( c_Wellfounded_Oacyclic(U_13880,U_13882)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13880,U_13880),tc_HOL_Obool)),U_13882),U_13881))
| ~ c_Wellfounded_Oacyclic(U_13880,U_13881) ),
inference(clausify,[status(thm)],[f_3533_2]) ).
fof(f_3534_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_3534_2,plain,
! [U_13884,U_13883] :
( ( ( c_Wellfounded_Owf(U_13883,U_13884)
| ~ c_Wellfounded_Oacyclic(U_13883,U_13884) )
& ( c_Wellfounded_Oacyclic(U_13883,U_13884)
| ~ c_Wellfounded_Owf(U_13883,U_13884) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13883,U_13883)),U_13884)) ),
inference(variable_rename,[status(thm)],[f_3534_1]) ).
cnf(f_3534_3,plain,
( c_Wellfounded_Oacyclic(U_13883,U_13884)
| ~ c_Wellfounded_Owf(U_13883,U_13884)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13883,U_13883)),U_13884)) ),
inference(clausify,[status(thm)],[f_3534_2]) ).
cnf(f_3534_4,plain,
( c_Wellfounded_Owf(U_13883,U_13884)
| ~ c_Wellfounded_Oacyclic(U_13883,U_13884)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13883,U_13883)),U_13884)) ),
inference(clausify,[status(thm)],[f_3534_2]) ).
fof(f_3535_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_3535_2,plain,
! [U_13886,U_13885] :
( c_Wellfounded_Owf(U_13885,U_13886)
| ~ c_Wellfounded_Oacyclic(U_13885,U_13886)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13885,U_13885)),U_13886)) ),
inference(variable_rename,[status(thm)],[f_3535_1]) ).
cnf(f_3535_3,plain,
( c_Wellfounded_Owf(U_13885,U_13886)
| ~ c_Wellfounded_Oacyclic(U_13885,U_13886)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13885,U_13885)),U_13886)) ),
inference(clausify,[status(thm)],[f_3535_2]) ).
fof(f_3536_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_3536_2,plain,
! [U_13888,U_13887] :
( ( c_Nitpick_Owf_H(U_13887,U_13888)
| ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13887,U_13887)),U_13888)) )
| ~ c_Wellfounded_Oacyclic(U_13887,U_13888) )
& ( ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13887,U_13887)),U_13888)) )
& c_Wellfounded_Oacyclic(U_13887,U_13888) )
| ~ c_Nitpick_Owf_H(U_13887,U_13888) ) ),
inference(variable_rename,[status(thm)],[f_3536_1]) ).
fof(f_3536_3,plain,
( ! [U_13892,U_13890] :
( c_Nitpick_Owf_H(U_13890,U_13892)
| ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13890,U_13890)),U_13892)) )
| ~ c_Wellfounded_Oacyclic(U_13890,U_13892) )
& ! [U_13891,U_13889] :
( ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13889,U_13889)),U_13891)) )
& c_Wellfounded_Oacyclic(U_13889,U_13891) )
| ~ c_Nitpick_Owf_H(U_13889,U_13891) ) ),
inference(miniscope,[status(thm)],[f_3536_2]) ).
cnf(f_3536_4,plain,
( c_Wellfounded_Oacyclic(U_13889,U_13891)
| ~ c_Nitpick_Owf_H(U_13889,U_13891) ),
inference(clausify,[status(thm)],[f_3536_3]) ).
cnf(f_3536_5,plain,
( c_Nitpick_Ounknown(tc_HOL_Obool)
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13889,U_13889)),U_13891))
| ~ c_Nitpick_Owf_H(U_13889,U_13891) ),
inference(clausify,[status(thm)],[f_3536_3]) ).
cnf(f_3536_6,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13890,U_13890)),U_13892))
| ~ c_Wellfounded_Oacyclic(U_13890,U_13892)
| c_Nitpick_Owf_H(U_13890,U_13892) ),
inference(clausify,[status(thm)],[f_3536_3]) ).
cnf(f_3536_7,plain,
( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
| ~ c_Wellfounded_Oacyclic(U_13890,U_13892)
| c_Nitpick_Owf_H(U_13890,U_13892) ),
inference(clausify,[status(thm)],[f_3536_3]) ).
fof(f_3537_1,plain,
! [V_x_2,V_P_2] :
( hBOOL(hAPP(V_P_2,V_x_2))
| ? [B_y] :
( ~ hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ),
inference(fof_nnf,[status(thm)],[fact_Abs__Integ__induct]) ).
fof(f_3537_2,plain,
! [U_13895,U_13894] :
( hBOOL(hAPP(U_13894,U_13895))
| ? [U_13893] :
( ~ hBOOL(hAPP(U_13894,hAPP(c_Int_OAbs__Integ,U_13893)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_13893),c_Int_OInteg)) ) ),
inference(variable_rename,[status(thm)],[f_3537_1]) ).
fof(f_3537_3,plain,
! [U_13895,U_13894] :
( hBOOL(hAPP(U_13894,U_13895))
| ( ~ hBOOL(hAPP(U_13894,hAPP(c_Int_OAbs__Integ,sK342(U_13895,U_13894))))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK342(U_13895,U_13894)),c_Int_OInteg)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK342]),skolemize(U_13893,sK342(U_13895,U_13894))],[f_3537_2]) ).
cnf(f_3537_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK342(U_13895,U_13894)),c_Int_OInteg))
| hBOOL(hAPP(U_13894,U_13895)) ),
inference(clausify,[status(thm)],[f_3537_3]) ).
cnf(f_3537_5,plain,
( ~ hBOOL(hAPP(U_13894,hAPP(c_Int_OAbs__Integ,sK342(U_13895,U_13894))))
| hBOOL(hAPP(U_13894,U_13895)) ),
inference(clausify,[status(thm)],[f_3537_3]) ).
fof(f_3538_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_3538_2,plain,
! [U_13900,U_13899,U_13898,U_13897] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13899),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13897,tc_fun(U_13899,tc_HOL_Obool)),U_13898),U_13900)))
| ? [U_13896] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13899),hAPP(U_13900,U_13896)))
& hBOOL(hAPP(hAPP(c_member(U_13897),U_13896),U_13898)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13897),U_13898)) ),
inference(variable_rename,[status(thm)],[f_3538_1]) ).
fof(f_3538_3,plain,
! [U_13900,U_13899,U_13898,U_13897] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13899),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13897,tc_fun(U_13899,tc_HOL_Obool)),U_13898),U_13900)))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13899),hAPP(U_13900,sK343(U_13900,U_13899,U_13898,U_13897))))
& hBOOL(hAPP(hAPP(c_member(U_13897),sK343(U_13900,U_13899,U_13898,U_13897)),U_13898)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13897),U_13898)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK343]),skolemize(U_13896,sK343(U_13900,U_13899,U_13898,U_13897))],[f_3538_2]) ).
cnf(f_3538_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_13897),sK343(U_13900,U_13899,U_13898,U_13897)),U_13898))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_13899),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13897,tc_fun(U_13899,tc_HOL_Obool)),U_13898),U_13900)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13897),U_13898)) ),
inference(clausify,[status(thm)],[f_3538_3]) ).
cnf(f_3538_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13899),hAPP(U_13900,sK343(U_13900,U_13899,U_13898,U_13897))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_13899),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13897,tc_fun(U_13899,tc_HOL_Obool)),U_13898),U_13900)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13897),U_13898)) ),
inference(clausify,[status(thm)],[f_3538_3]) ).
fof(f_3539_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_3539_2,plain,
! [U_13903,U_13902] :
( 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_13903),U_13902)
| ? [U_13901] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_13903),U_13901))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_13901),U_13902)) ) ),
inference(variable_rename,[status(thm)],[f_3539_1]) ).
fof(f_3539_3,plain,
! [U_13903,U_13902] :
( 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_13903),U_13902)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_13903),sK344(U_13903,U_13902)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK344(U_13903,U_13902)),U_13902)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK344]),skolemize(U_13901,sK344(U_13903,U_13902))],[f_3539_2]) ).
cnf(f_3539_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK344(U_13903,U_13902)),U_13902))
| 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_13903),U_13902) ),
inference(clausify,[status(thm)],[f_3539_3]) ).
cnf(f_3539_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_13903),sK344(U_13903,U_13902)))
| 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_13903),U_13902) ),
inference(clausify,[status(thm)],[f_3539_3]) ).
fof(f_3540_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_3540_2,plain,
! [U_13909,U_13908,U_13907] :
( c_Wellfounded_OwfP(U_13907,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13909,tc_fun(U_13907,tc_fun(U_13907,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13909,tc_HOL_Obool))),U_13908))
| ? [U_13906,U_13905] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13907,tc_HOL_Obool)),c_Predicate_ODomainP(U_13907,U_13907,hAPP(U_13908,U_13906))),c_Predicate_ORangeP(U_13907,U_13907,hAPP(U_13908,U_13905))) != c_Orderings_Obot__class_Obot(tc_fun(U_13907,tc_HOL_Obool))
& hAPP(U_13908,U_13906) != hAPP(U_13908,U_13905) )
| ? [U_13904] : ~ c_Wellfounded_OwfP(U_13907,hAPP(U_13908,U_13904)) ),
inference(variable_rename,[status(thm)],[f_3540_1]) ).
fof(f_3540_3,plain,
! [U_13909,U_13908,U_13907] :
( c_Wellfounded_OwfP(U_13907,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13909,tc_fun(U_13907,tc_fun(U_13907,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13909,tc_HOL_Obool))),U_13908))
| ? [U_13906,U_13905] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13907,tc_HOL_Obool)),c_Predicate_ODomainP(U_13907,U_13907,hAPP(U_13908,U_13906))),c_Predicate_ORangeP(U_13907,U_13907,hAPP(U_13908,U_13905))) != c_Orderings_Obot__class_Obot(tc_fun(U_13907,tc_HOL_Obool))
& hAPP(U_13908,U_13906) != hAPP(U_13908,U_13905) )
| ~ c_Wellfounded_OwfP(U_13907,hAPP(U_13908,sK345(U_13909,U_13908,U_13907))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK345]),skolemize(U_13904,sK345(U_13909,U_13908,U_13907))],[f_3540_2]) ).
fof(f_3540_4,plain,
! [U_13909,U_13908,U_13907] :
( c_Wellfounded_OwfP(U_13907,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13909,tc_fun(U_13907,tc_fun(U_13907,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13909,tc_HOL_Obool))),U_13908))
| ? [U_13905] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13907,tc_HOL_Obool)),c_Predicate_ODomainP(U_13907,U_13907,hAPP(U_13908,sK346(U_13909,U_13908,U_13907)))),c_Predicate_ORangeP(U_13907,U_13907,hAPP(U_13908,U_13905))) != c_Orderings_Obot__class_Obot(tc_fun(U_13907,tc_HOL_Obool))
& hAPP(U_13908,sK346(U_13909,U_13908,U_13907)) != hAPP(U_13908,U_13905) )
| ~ c_Wellfounded_OwfP(U_13907,hAPP(U_13908,sK345(U_13909,U_13908,U_13907))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK346]),skolemize(U_13906,sK346(U_13909,U_13908,U_13907))],[f_3540_3]) ).
fof(f_3540_5,plain,
! [U_13909,U_13908,U_13907] :
( c_Wellfounded_OwfP(U_13907,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13909,tc_fun(U_13907,tc_fun(U_13907,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13909,tc_HOL_Obool))),U_13908))
| ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13907,tc_HOL_Obool)),c_Predicate_ODomainP(U_13907,U_13907,hAPP(U_13908,sK346(U_13909,U_13908,U_13907)))),c_Predicate_ORangeP(U_13907,U_13907,hAPP(U_13908,sK347(U_13909,U_13908,U_13907)))) != c_Orderings_Obot__class_Obot(tc_fun(U_13907,tc_HOL_Obool))
& hAPP(U_13908,sK346(U_13909,U_13908,U_13907)) != hAPP(U_13908,sK347(U_13909,U_13908,U_13907)) )
| ~ c_Wellfounded_OwfP(U_13907,hAPP(U_13908,sK345(U_13909,U_13908,U_13907))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK347]),skolemize(U_13905,sK347(U_13909,U_13908,U_13907))],[f_3540_4]) ).
cnf(f_3540_6,plain,
( hAPP(U_13908,sK346(U_13909,U_13908,U_13907)) != hAPP(U_13908,sK347(U_13909,U_13908,U_13907))
| c_Wellfounded_OwfP(U_13907,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13909,tc_fun(U_13907,tc_fun(U_13907,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13909,tc_HOL_Obool))),U_13908))
| ~ c_Wellfounded_OwfP(U_13907,hAPP(U_13908,sK345(U_13909,U_13908,U_13907))) ),
inference(clausify,[status(thm)],[f_3540_5]) ).
cnf(f_3540_7,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13907,tc_HOL_Obool)),c_Predicate_ODomainP(U_13907,U_13907,hAPP(U_13908,sK346(U_13909,U_13908,U_13907)))),c_Predicate_ORangeP(U_13907,U_13907,hAPP(U_13908,sK347(U_13909,U_13908,U_13907)))) != c_Orderings_Obot__class_Obot(tc_fun(U_13907,tc_HOL_Obool))
| c_Wellfounded_OwfP(U_13907,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13909,tc_fun(U_13907,tc_fun(U_13907,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13909,tc_HOL_Obool))),U_13908))
| ~ c_Wellfounded_OwfP(U_13907,hAPP(U_13908,sK345(U_13909,U_13908,U_13907))) ),
inference(clausify,[status(thm)],[f_3540_5]) ).
fof(f_3541_1,plain,
! [V_p_2,V_c_2,T_d,T_c,V_z_2,T_b] :
( ? [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y)))
& V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),V_p_2))) ),
inference(fof_nnf,[status(thm)],[fact_mem__splitE]) ).
fof(f_3541_2,plain,
! [U_13917,U_13916,U_13915,U_13914,U_13913,U_13912] :
( ? [U_13911,U_13910] :
( hBOOL(hAPP(hAPP(c_member(U_13912),U_13913),hAPP(hAPP(U_13916,U_13911),U_13910)))
& U_13917 = hAPP(hAPP(c_Product__Type_OPair(U_13914,U_13915),U_13911),U_13910) )
| ~ hBOOL(hAPP(hAPP(c_member(U_13912),U_13913),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13914,U_13915,tc_fun(U_13912,tc_HOL_Obool)),U_13916),U_13917))) ),
inference(variable_rename,[status(thm)],[f_3541_1]) ).
fof(f_3541_3,plain,
! [U_13917,U_13916,U_13915,U_13914,U_13913,U_13912] :
( ? [U_13910] :
( hBOOL(hAPP(hAPP(c_member(U_13912),U_13913),hAPP(hAPP(U_13916,sK348(U_13917,U_13916,U_13915,U_13914,U_13913,U_13912)),U_13910)))
& U_13917 = hAPP(hAPP(c_Product__Type_OPair(U_13914,U_13915),sK348(U_13917,U_13916,U_13915,U_13914,U_13913,U_13912)),U_13910) )
| ~ hBOOL(hAPP(hAPP(c_member(U_13912),U_13913),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13914,U_13915,tc_fun(U_13912,tc_HOL_Obool)),U_13916),U_13917))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK348]),skolemize(U_13911,sK348(U_13917,U_13916,U_13915,U_13914,U_13913,U_13912))],[f_3541_2]) ).
fof(f_3541_4,plain,
! [U_13917,U_13916,U_13915,U_13914,U_13913,U_13912] :
( ( hBOOL(hAPP(hAPP(c_member(U_13912),U_13913),hAPP(hAPP(U_13916,sK348(U_13917,U_13916,U_13915,U_13914,U_13913,U_13912)),sK349(U_13917,U_13916,U_13915,U_13914,U_13913,U_13912))))
& U_13917 = hAPP(hAPP(c_Product__Type_OPair(U_13914,U_13915),sK348(U_13917,U_13916,U_13915,U_13914,U_13913,U_13912)),sK349(U_13917,U_13916,U_13915,U_13914,U_13913,U_13912)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_13912),U_13913),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13914,U_13915,tc_fun(U_13912,tc_HOL_Obool)),U_13916),U_13917))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK349]),skolemize(U_13910,sK349(U_13917,U_13916,U_13915,U_13914,U_13913,U_13912))],[f_3541_3]) ).
cnf(f_3541_5,plain,
( U_13917 = hAPP(hAPP(c_Product__Type_OPair(U_13914,U_13915),sK348(U_13917,U_13916,U_13915,U_13914,U_13913,U_13912)),sK349(U_13917,U_13916,U_13915,U_13914,U_13913,U_13912))
| ~ hBOOL(hAPP(hAPP(c_member(U_13912),U_13913),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13914,U_13915,tc_fun(U_13912,tc_HOL_Obool)),U_13916),U_13917))) ),
inference(clausify,[status(thm)],[f_3541_4]) ).
cnf(f_3541_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_13912),U_13913),hAPP(hAPP(U_13916,sK348(U_13917,U_13916,U_13915,U_13914,U_13913,U_13912)),sK349(U_13917,U_13916,U_13915,U_13914,U_13913,U_13912))))
| ~ hBOOL(hAPP(hAPP(c_member(U_13912),U_13913),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13914,U_13915,tc_fun(U_13912,tc_HOL_Obool)),U_13916),U_13917))) ),
inference(clausify,[status(thm)],[f_3541_4]) ).
fof(f_3542_1,plain,
! [V_c_2,V_z_2,T_d,T_c,T_b,V_p_2] :
( hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_c_2),V_p_2)))
| ? [B_a,B_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b)))
& V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b) ) ),
inference(fof_nnf,[status(thm)],[fact_mem__splitI2]) ).
fof(f_3542_2,plain,
! [U_13925,U_13924,U_13923,U_13922,U_13921,U_13920] :
( hBOOL(hAPP(hAPP(c_member(U_13923),U_13924),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13921,U_13922,tc_fun(U_13923,tc_HOL_Obool)),U_13925),U_13920)))
| ? [U_13919,U_13918] :
( ~ hBOOL(hAPP(hAPP(c_member(U_13923),U_13924),hAPP(hAPP(U_13925,U_13919),U_13918)))
& U_13920 = hAPP(hAPP(c_Product__Type_OPair(U_13921,U_13922),U_13919),U_13918) ) ),
inference(variable_rename,[status(thm)],[f_3542_1]) ).
fof(f_3542_3,plain,
! [U_13925,U_13924,U_13923,U_13922,U_13921,U_13920] :
( hBOOL(hAPP(hAPP(c_member(U_13923),U_13924),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13921,U_13922,tc_fun(U_13923,tc_HOL_Obool)),U_13925),U_13920)))
| ? [U_13918] :
( ~ hBOOL(hAPP(hAPP(c_member(U_13923),U_13924),hAPP(hAPP(U_13925,sK350(U_13925,U_13924,U_13923,U_13922,U_13921,U_13920)),U_13918)))
& U_13920 = hAPP(hAPP(c_Product__Type_OPair(U_13921,U_13922),sK350(U_13925,U_13924,U_13923,U_13922,U_13921,U_13920)),U_13918) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK350]),skolemize(U_13919,sK350(U_13925,U_13924,U_13923,U_13922,U_13921,U_13920))],[f_3542_2]) ).
fof(f_3542_4,plain,
! [U_13925,U_13924,U_13923,U_13922,U_13921,U_13920] :
( hBOOL(hAPP(hAPP(c_member(U_13923),U_13924),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13921,U_13922,tc_fun(U_13923,tc_HOL_Obool)),U_13925),U_13920)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_13923),U_13924),hAPP(hAPP(U_13925,sK350(U_13925,U_13924,U_13923,U_13922,U_13921,U_13920)),sK351(U_13925,U_13924,U_13923,U_13922,U_13921,U_13920))))
& U_13920 = hAPP(hAPP(c_Product__Type_OPair(U_13921,U_13922),sK350(U_13925,U_13924,U_13923,U_13922,U_13921,U_13920)),sK351(U_13925,U_13924,U_13923,U_13922,U_13921,U_13920)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK351]),skolemize(U_13918,sK351(U_13925,U_13924,U_13923,U_13922,U_13921,U_13920))],[f_3542_3]) ).
cnf(f_3542_5,plain,
( U_13920 = hAPP(hAPP(c_Product__Type_OPair(U_13921,U_13922),sK350(U_13925,U_13924,U_13923,U_13922,U_13921,U_13920)),sK351(U_13925,U_13924,U_13923,U_13922,U_13921,U_13920))
| hBOOL(hAPP(hAPP(c_member(U_13923),U_13924),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13921,U_13922,tc_fun(U_13923,tc_HOL_Obool)),U_13925),U_13920))) ),
inference(clausify,[status(thm)],[f_3542_4]) ).
cnf(f_3542_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_13923),U_13924),hAPP(hAPP(U_13925,sK350(U_13925,U_13924,U_13923,U_13922,U_13921,U_13920)),sK351(U_13925,U_13924,U_13923,U_13922,U_13921,U_13920))))
| hBOOL(hAPP(hAPP(c_member(U_13923),U_13924),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13921,U_13922,tc_fun(U_13923,tc_HOL_Obool)),U_13925),U_13920))) ),
inference(clausify,[status(thm)],[f_3542_4]) ).
fof(f_3543_1,plain,
! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))),
inference(fof_nnf,[status(thm)],[fact_Eps__split]) ).
fof(f_3543_2,plain,
! [U_13928,U_13927,U_13926] : c_Hilbert__Choice_OEps(tc_prod(U_13926,U_13927),hAPP(c_Product__Type_Oprod_Oprod__case(U_13926,U_13927,tc_HOL_Obool),U_13928)) = c_Hilbert__Choice_OEps(tc_prod(U_13926,U_13927),hAPP(hAPP(c_COMBS(tc_prod(U_13926,U_13927),U_13927,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13926,tc_fun(U_13927,tc_HOL_Obool),tc_prod(U_13926,U_13927)),U_13928),c_Product__Type_Ofst(U_13926,U_13927))),c_Product__Type_Osnd(U_13926,U_13927))),
inference(variable_rename,[status(thm)],[f_3543_1]) ).
cnf(f_3543_3,plain,
c_Hilbert__Choice_OEps(tc_prod(U_13926,U_13927),hAPP(c_Product__Type_Oprod_Oprod__case(U_13926,U_13927,tc_HOL_Obool),U_13928)) = c_Hilbert__Choice_OEps(tc_prod(U_13926,U_13927),hAPP(hAPP(c_COMBS(tc_prod(U_13926,U_13927),U_13927,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13926,tc_fun(U_13927,tc_HOL_Obool),tc_prod(U_13926,U_13927)),U_13928),c_Product__Type_Ofst(U_13926,U_13927))),c_Product__Type_Osnd(U_13926,U_13927))),
inference(clausify,[status(thm)],[f_3543_2]) ).
fof(f_3544_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_3544_2,plain,
! [U_13931,U_13930] :
( c_Wellfounded_Owf(U_13930,U_13931)
| ? [U_13929] :
( U_13929 != c_Orderings_Obot__class_Obot(tc_fun(U_13930,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13930,tc_HOL_Obool)),U_13929),hAPP(c_Relation_OImage(U_13930,U_13930,U_13931),U_13929))) ) ),
inference(variable_rename,[status(thm)],[f_3544_1]) ).
fof(f_3544_3,plain,
! [U_13931,U_13930] :
( c_Wellfounded_Owf(U_13930,U_13931)
| ( sK352(U_13931,U_13930) != c_Orderings_Obot__class_Obot(tc_fun(U_13930,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13930,tc_HOL_Obool)),sK352(U_13931,U_13930)),hAPP(c_Relation_OImage(U_13930,U_13930,U_13931),sK352(U_13931,U_13930)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK352]),skolemize(U_13929,sK352(U_13931,U_13930))],[f_3544_2]) ).
cnf(f_3544_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13930,tc_HOL_Obool)),sK352(U_13931,U_13930)),hAPP(c_Relation_OImage(U_13930,U_13930,U_13931),sK352(U_13931,U_13930))))
| c_Wellfounded_Owf(U_13930,U_13931) ),
inference(clausify,[status(thm)],[f_3544_3]) ).
cnf(f_3544_5,plain,
( sK352(U_13931,U_13930) != c_Orderings_Obot__class_Obot(tc_fun(U_13930,tc_HOL_Obool))
| c_Wellfounded_Owf(U_13930,U_13931) ),
inference(clausify,[status(thm)],[f_3544_3]) ).
fof(f_3545_1,plain,
! [T_b,V_c_2,V_P_2] :
( hBOOL(hAPP(V_P_2,V_c_2))
| V_c_2 != c_Hilbert__Choice_OEps(T_b,V_P_2)
| ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ),
inference(fof_nnf,[status(thm)],[fact_exE__some]) ).
fof(f_3545_2,plain,
! [U_13935,U_13934,U_13933] :
( hBOOL(hAPP(U_13933,U_13934))
| U_13934 != c_Hilbert__Choice_OEps(U_13935,U_13933)
| ! [U_13932] : ~ hBOOL(hAPP(U_13933,U_13932)) ),
inference(variable_rename,[status(thm)],[f_3545_1]) ).
cnf(f_3545_3,plain,
( hBOOL(hAPP(U_13933,U_13934))
| U_13934 != c_Hilbert__Choice_OEps(U_13935,U_13933)
| ~ hBOOL(hAPP(U_13933,U_13932)) ),
inference(clausify,[status(thm)],[f_3545_2]) ).
fof(f_3546_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_3546_2,plain,
! [U_13937,U_13936] : c_Hilbert__Choice_OEps(U_13936,hAPP(c_fequal,U_13937)) = U_13937,
inference(variable_rename,[status(thm)],[f_3546_1]) ).
cnf(f_3546_3,plain,
c_Hilbert__Choice_OEps(U_13936,hAPP(c_fequal,U_13937)) = U_13937,
inference(clausify,[status(thm)],[f_3546_2]) ).
fof(f_3547_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_3547_2,plain,
! [U_13939,U_13938] : c_Hilbert__Choice_OEps(U_13938,hAPP(hAPP(c_COMBC(U_13938,U_13938,tc_HOL_Obool),c_fequal),U_13939)) = U_13939,
inference(variable_rename,[status(thm)],[f_3547_1]) ).
cnf(f_3547_3,plain,
c_Hilbert__Choice_OEps(U_13938,hAPP(hAPP(c_COMBC(U_13938,U_13938,tc_HOL_Obool),c_fequal),U_13939)) = U_13939,
inference(clausify,[status(thm)],[f_3547_2]) ).
fof(f_3548_1,plain,
! [T_b,V_P_2] :
( ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
| ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) )
& ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
| ~ hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_some__eq__ex]) ).
fof(f_3548_2,plain,
! [U_13943,U_13942] :
( ( hBOOL(hAPP(U_13942,c_Hilbert__Choice_OEps(U_13943,U_13942)))
| ! [U_13941] : ~ hBOOL(hAPP(U_13942,U_13941)) )
& ( ? [U_13940] : hBOOL(hAPP(U_13942,U_13940))
| ~ hBOOL(hAPP(U_13942,c_Hilbert__Choice_OEps(U_13943,U_13942))) ) ),
inference(variable_rename,[status(thm)],[f_3548_1]) ).
fof(f_3548_3,plain,
( ! [U_13947,U_13945] :
( hBOOL(hAPP(U_13945,c_Hilbert__Choice_OEps(U_13947,U_13945)))
| ! [U_13941] : ~ hBOOL(hAPP(U_13945,U_13941)) )
& ! [U_13946,U_13944] :
( ? [U_13940] : hBOOL(hAPP(U_13944,U_13940))
| ~ hBOOL(hAPP(U_13944,c_Hilbert__Choice_OEps(U_13946,U_13944))) ) ),
inference(miniscope,[status(thm)],[f_3548_2]) ).
fof(f_3548_4,plain,
( ! [U_13947,U_13945] :
( hBOOL(hAPP(U_13945,c_Hilbert__Choice_OEps(U_13947,U_13945)))
| ! [U_13941] : ~ hBOOL(hAPP(U_13945,U_13941)) )
& ! [U_13946,U_13944] :
( hBOOL(hAPP(U_13944,sK353(U_13946,U_13944)))
| ~ hBOOL(hAPP(U_13944,c_Hilbert__Choice_OEps(U_13946,U_13944))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK353]),skolemize(U_13940,sK353(U_13946,U_13944))],[f_3548_3]) ).
cnf(f_3548_5,plain,
( hBOOL(hAPP(U_13944,sK353(U_13946,U_13944)))
| ~ hBOOL(hAPP(U_13944,c_Hilbert__Choice_OEps(U_13946,U_13944))) ),
inference(clausify,[status(thm)],[f_3548_4]) ).
cnf(f_3548_6,plain,
( hBOOL(hAPP(U_13945,c_Hilbert__Choice_OEps(U_13947,U_13945)))
| ~ hBOOL(hAPP(U_13945,U_13941)) ),
inference(clausify,[status(thm)],[f_3548_4]) ).
fof(f_3549_1,plain,
! [T_b,V_P_2] :
( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
| ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ),
inference(fof_nnf,[status(thm)],[fact_someI__ex]) ).
fof(f_3549_2,plain,
! [U_13950,U_13949] :
( hBOOL(hAPP(U_13949,c_Hilbert__Choice_OEps(U_13950,U_13949)))
| ! [U_13948] : ~ hBOOL(hAPP(U_13949,U_13948)) ),
inference(variable_rename,[status(thm)],[f_3549_1]) ).
cnf(f_3549_3,plain,
( hBOOL(hAPP(U_13949,c_Hilbert__Choice_OEps(U_13950,U_13949)))
| ~ hBOOL(hAPP(U_13949,U_13948)) ),
inference(clausify,[status(thm)],[f_3549_2]) ).
fof(f_3550_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_3550_2,plain,
! [U_13953,U_13952] :
( hBOOL(hAPP(U_13952,c_Hilbert__Choice_OEps(U_13953,U_13952)))
| ! [U_13951] : ~ hBOOL(hAPP(U_13952,U_13951)) ),
inference(variable_rename,[status(thm)],[f_3550_1]) ).
cnf(f_3550_3,plain,
( hBOOL(hAPP(U_13952,c_Hilbert__Choice_OEps(U_13953,U_13952)))
| ~ hBOOL(hAPP(U_13952,U_13951)) ),
inference(clausify,[status(thm)],[f_3550_2]) ).
fof(f_3551_1,plain,
! [T_b,V_x_2,V_P_2] :
( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
| ~ hBOOL(hAPP(V_P_2,V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_someI]) ).
fof(f_3551_2,plain,
! [U_13956,U_13955,U_13954] :
( hBOOL(hAPP(U_13954,c_Hilbert__Choice_OEps(U_13956,U_13954)))
| ~ hBOOL(hAPP(U_13954,U_13955)) ),
inference(variable_rename,[status(thm)],[f_3551_1]) ).
cnf(f_3551_3,plain,
( hBOOL(hAPP(U_13954,c_Hilbert__Choice_OEps(U_13956,U_13954)))
| ~ hBOOL(hAPP(U_13954,U_13955)) ),
inference(clausify,[status(thm)],[f_3551_2]) ).
fof(f_3552_1,plain,
! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_P_2) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))),
inference(fof_nnf,[status(thm)],[fact_split__paired__Eps]) ).
fof(f_3552_2,plain,
! [U_13959,U_13958,U_13957] : c_Hilbert__Choice_OEps(tc_prod(U_13957,U_13958),U_13959) = c_Hilbert__Choice_OEps(tc_prod(U_13957,U_13958),hAPP(c_Product__Type_Oprod_Oprod__case(U_13957,U_13958,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13958,tc_prod(U_13957,U_13958)),tc_fun(U_13958,tc_HOL_Obool),U_13957),hAPP(c_COMBB(tc_prod(U_13957,U_13958),tc_HOL_Obool,U_13958),U_13959)),c_Product__Type_OPair(U_13957,U_13958)))),
inference(variable_rename,[status(thm)],[f_3552_1]) ).
cnf(f_3552_3,plain,
c_Hilbert__Choice_OEps(tc_prod(U_13957,U_13958),U_13959) = c_Hilbert__Choice_OEps(tc_prod(U_13957,U_13958),hAPP(c_Product__Type_Oprod_Oprod__case(U_13957,U_13958,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13958,tc_prod(U_13957,U_13958)),tc_fun(U_13958,tc_HOL_Obool),U_13957),hAPP(c_COMBB(tc_prod(U_13957,U_13958),tc_HOL_Obool,U_13958),U_13959)),c_Product__Type_OPair(U_13957,U_13958)))),
inference(clausify,[status(thm)],[f_3552_2]) ).
fof(f_3553_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_3553_2,plain,
! [U_13963,U_13962,U_13961,U_13960] : c_Hilbert__Choice_OEps(tc_prod(U_13960,U_13961),hAPP(c_Product__Type_Oprod_Oprod__case(U_13960,U_13961,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13960,tc_fun(U_13961,tc_HOL_Obool),tc_fun(U_13961,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13961,tc_HOL_Obool),tc_fun(U_13961,tc_HOL_Obool)),U_13960),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13961)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13960),c_fconj),hAPP(c_fequal,U_13962)))),hAPP(c_fequal,U_13963)))) = hAPP(hAPP(c_Product__Type_OPair(U_13960,U_13961),U_13962),U_13963),
inference(variable_rename,[status(thm)],[f_3553_1]) ).
cnf(f_3553_3,plain,
c_Hilbert__Choice_OEps(tc_prod(U_13960,U_13961),hAPP(c_Product__Type_Oprod_Oprod__case(U_13960,U_13961,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13960,tc_fun(U_13961,tc_HOL_Obool),tc_fun(U_13961,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13961,tc_HOL_Obool),tc_fun(U_13961,tc_HOL_Obool)),U_13960),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13961)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13960),c_fconj),hAPP(c_fequal,U_13962)))),hAPP(c_fequal,U_13963)))) = hAPP(hAPP(c_Product__Type_OPair(U_13960,U_13961),U_13962),U_13963),
inference(clausify,[status(thm)],[f_3553_2]) ).
fof(f_3554_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_3554_2,plain,
! [U_13970,U_13969,U_13968,U_13967,U_13966,U_13965] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13965,U_13968),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13965,U_13968),U_13966),U_13969)),hAPP(hAPP(c_Product__Type_OSigma(U_13965,U_13968),U_13967),U_13970)))
| ? [U_13964] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13968,tc_HOL_Obool)),hAPP(U_13969,U_13964)),hAPP(U_13970,U_13964)))
& hBOOL(hAPP(hAPP(c_member(U_13965),U_13964),U_13966)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13965,tc_HOL_Obool)),U_13966),U_13967)) ),
inference(variable_rename,[status(thm)],[f_3554_1]) ).
fof(f_3554_3,plain,
! [U_13970,U_13969,U_13968,U_13967,U_13966,U_13965] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13965,U_13968),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13965,U_13968),U_13966),U_13969)),hAPP(hAPP(c_Product__Type_OSigma(U_13965,U_13968),U_13967),U_13970)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13968,tc_HOL_Obool)),hAPP(U_13969,sK354(U_13970,U_13969,U_13968,U_13967,U_13966,U_13965))),hAPP(U_13970,sK354(U_13970,U_13969,U_13968,U_13967,U_13966,U_13965))))
& hBOOL(hAPP(hAPP(c_member(U_13965),sK354(U_13970,U_13969,U_13968,U_13967,U_13966,U_13965)),U_13966)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13965,tc_HOL_Obool)),U_13966),U_13967)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK354]),skolemize(U_13964,sK354(U_13970,U_13969,U_13968,U_13967,U_13966,U_13965))],[f_3554_2]) ).
cnf(f_3554_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_13965),sK354(U_13970,U_13969,U_13968,U_13967,U_13966,U_13965)),U_13966))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13965,U_13968),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13965,U_13968),U_13966),U_13969)),hAPP(hAPP(c_Product__Type_OSigma(U_13965,U_13968),U_13967),U_13970)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13965,tc_HOL_Obool)),U_13966),U_13967)) ),
inference(clausify,[status(thm)],[f_3554_3]) ).
cnf(f_3554_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13968,tc_HOL_Obool)),hAPP(U_13969,sK354(U_13970,U_13969,U_13968,U_13967,U_13966,U_13965))),hAPP(U_13970,sK354(U_13970,U_13969,U_13968,U_13967,U_13966,U_13965))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13965,U_13968),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13965,U_13968),U_13966),U_13969)),hAPP(hAPP(c_Product__Type_OSigma(U_13965,U_13968),U_13967),U_13970)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13965,tc_HOL_Obool)),U_13966),U_13967)) ),
inference(clausify,[status(thm)],[f_3554_3]) ).
fof(f_3555_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_3555_2,plain,
! [U_13974,U_13973,U_13972] :
( ? [U_13971] :
( ~ hBOOL(hAPP(hAPP(c_member(U_13972),U_13971),c_Wellfounded_Oacc(U_13972,U_13974)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_13972,U_13972)),hAPP(hAPP(c_Product__Type_OPair(U_13972,U_13972),U_13971),U_13973)),U_13974)) )
| hBOOL(hAPP(hAPP(c_member(U_13972),U_13973),c_Wellfounded_Oacc(U_13972,U_13974))) ),
inference(variable_rename,[status(thm)],[f_3555_1]) ).
fof(f_3555_3,plain,
! [U_13974,U_13973,U_13972] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_13972),sK355(U_13974,U_13973,U_13972)),c_Wellfounded_Oacc(U_13972,U_13974)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_13972,U_13972)),hAPP(hAPP(c_Product__Type_OPair(U_13972,U_13972),sK355(U_13974,U_13973,U_13972)),U_13973)),U_13974)) )
| hBOOL(hAPP(hAPP(c_member(U_13972),U_13973),c_Wellfounded_Oacc(U_13972,U_13974))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK355]),skolemize(U_13971,sK355(U_13974,U_13973,U_13972))],[f_3555_2]) ).
cnf(f_3555_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13972,U_13972)),hAPP(hAPP(c_Product__Type_OPair(U_13972,U_13972),sK355(U_13974,U_13973,U_13972)),U_13973)),U_13974))
| hBOOL(hAPP(hAPP(c_member(U_13972),U_13973),c_Wellfounded_Oacc(U_13972,U_13974))) ),
inference(clausify,[status(thm)],[f_3555_3]) ).
cnf(f_3555_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_13972),sK355(U_13974,U_13973,U_13972)),c_Wellfounded_Oacc(U_13972,U_13974)))
| hBOOL(hAPP(hAPP(c_member(U_13972),U_13973),c_Wellfounded_Oacc(U_13972,U_13974))) ),
inference(clausify,[status(thm)],[f_3555_3]) ).
fof(f_3556_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_3556_2,plain,
! [U_13978,U_13977,U_13976] :
( hBOOL(hAPP(hAPP(c_member(U_13976),U_13977),c_Wellfounded_Oacc(U_13976,U_13978)))
| ? [U_13975] :
( ~ hBOOL(hAPP(hAPP(c_member(U_13976),U_13975),c_Wellfounded_Oacc(U_13976,U_13978)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_13976,U_13976)),hAPP(hAPP(c_Product__Type_OPair(U_13976,U_13976),U_13975),U_13977)),U_13978)) ) ),
inference(variable_rename,[status(thm)],[f_3556_1]) ).
fof(f_3556_3,plain,
! [U_13978,U_13977,U_13976] :
( hBOOL(hAPP(hAPP(c_member(U_13976),U_13977),c_Wellfounded_Oacc(U_13976,U_13978)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_13976),sK356(U_13978,U_13977,U_13976)),c_Wellfounded_Oacc(U_13976,U_13978)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_13976,U_13976)),hAPP(hAPP(c_Product__Type_OPair(U_13976,U_13976),sK356(U_13978,U_13977,U_13976)),U_13977)),U_13978)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK356]),skolemize(U_13975,sK356(U_13978,U_13977,U_13976))],[f_3556_2]) ).
cnf(f_3556_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13976,U_13976)),hAPP(hAPP(c_Product__Type_OPair(U_13976,U_13976),sK356(U_13978,U_13977,U_13976)),U_13977)),U_13978))
| hBOOL(hAPP(hAPP(c_member(U_13976),U_13977),c_Wellfounded_Oacc(U_13976,U_13978))) ),
inference(clausify,[status(thm)],[f_3556_3]) ).
cnf(f_3556_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_13976),sK356(U_13978,U_13977,U_13976)),c_Wellfounded_Oacc(U_13976,U_13978)))
| hBOOL(hAPP(hAPP(c_member(U_13976),U_13977),c_Wellfounded_Oacc(U_13976,U_13978))) ),
inference(clausify,[status(thm)],[f_3556_3]) ).
fof(f_3557_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_3557_2,plain,
! [U_13986,U_13985,U_13984,U_13983] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13983,tc_HOL_Obool),tc_fun(U_13983,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13983,tc_HOL_Obool),tc_fun(U_13983,tc_HOL_Obool)),U_13984),U_13985)),c_Wellfounded_Omax__ext(U_13983,U_13986)))
| ? [U_13982] :
( ! [U_13981] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13983,U_13983)),hAPP(hAPP(c_Product__Type_OPair(U_13983,U_13983),U_13982),U_13981)),U_13986))
| ~ hBOOL(hAPP(hAPP(c_member(U_13983),U_13981),U_13985)) )
& hBOOL(hAPP(hAPP(c_member(U_13983),U_13982),U_13984)) )
| U_13985 = c_Orderings_Obot__class_Obot(tc_fun(U_13983,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13983),U_13985))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13983),U_13984)) )
& ( ( ! [U_13980] :
( ? [U_13979] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13983,U_13983)),hAPP(hAPP(c_Product__Type_OPair(U_13983,U_13983),U_13980),U_13979)),U_13986))
& hBOOL(hAPP(hAPP(c_member(U_13983),U_13979),U_13985)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_13983),U_13980),U_13984)) )
& U_13985 != c_Orderings_Obot__class_Obot(tc_fun(U_13983,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_13983),U_13985))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_13983),U_13984)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13983,tc_HOL_Obool),tc_fun(U_13983,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13983,tc_HOL_Obool),tc_fun(U_13983,tc_HOL_Obool)),U_13984),U_13985)),c_Wellfounded_Omax__ext(U_13983,U_13986))) ) ),
inference(variable_rename,[status(thm)],[f_3557_1]) ).
fof(f_3557_3,plain,
( ! [U_13994,U_13992,U_13990,U_13988] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13988,tc_HOL_Obool),tc_fun(U_13988,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13988,tc_HOL_Obool),tc_fun(U_13988,tc_HOL_Obool)),U_13990),U_13992)),c_Wellfounded_Omax__ext(U_13988,U_13994)))
| ? [U_13982] :
( ! [U_13981] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13988,U_13988)),hAPP(hAPP(c_Product__Type_OPair(U_13988,U_13988),U_13982),U_13981)),U_13994))
| ~ hBOOL(hAPP(hAPP(c_member(U_13988),U_13981),U_13992)) )
& hBOOL(hAPP(hAPP(c_member(U_13988),U_13982),U_13990)) )
| U_13992 = c_Orderings_Obot__class_Obot(tc_fun(U_13988,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13988),U_13992))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13988),U_13990)) )
& ! [U_13993,U_13991,U_13989,U_13987] :
( ( ! [U_13980] :
( ? [U_13979] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13987,U_13987)),hAPP(hAPP(c_Product__Type_OPair(U_13987,U_13987),U_13980),U_13979)),U_13993))
& hBOOL(hAPP(hAPP(c_member(U_13987),U_13979),U_13991)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_13987),U_13980),U_13989)) )
& U_13991 != c_Orderings_Obot__class_Obot(tc_fun(U_13987,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_13987),U_13991))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_13987),U_13989)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13987,tc_HOL_Obool),tc_fun(U_13987,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13987,tc_HOL_Obool),tc_fun(U_13987,tc_HOL_Obool)),U_13989),U_13991)),c_Wellfounded_Omax__ext(U_13987,U_13993))) ) ),
inference(miniscope,[status(thm)],[f_3557_2]) ).
fof(f_3557_4,plain,
( ! [U_13994,U_13992,U_13990,U_13988] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13988,tc_HOL_Obool),tc_fun(U_13988,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13988,tc_HOL_Obool),tc_fun(U_13988,tc_HOL_Obool)),U_13990),U_13992)),c_Wellfounded_Omax__ext(U_13988,U_13994)))
| ? [U_13982] :
( ! [U_13981] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13988,U_13988)),hAPP(hAPP(c_Product__Type_OPair(U_13988,U_13988),U_13982),U_13981)),U_13994))
| ~ hBOOL(hAPP(hAPP(c_member(U_13988),U_13981),U_13992)) )
& hBOOL(hAPP(hAPP(c_member(U_13988),U_13982),U_13990)) )
| U_13992 = c_Orderings_Obot__class_Obot(tc_fun(U_13988,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13988),U_13992))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13988),U_13990)) )
& ! [U_13993,U_13991,U_13989,U_13987] :
( ( ! [U_13980] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13987,U_13987)),hAPP(hAPP(c_Product__Type_OPair(U_13987,U_13987),U_13980),sK357(U_13993,U_13991,U_13989,U_13987,U_13980))),U_13993))
& hBOOL(hAPP(hAPP(c_member(U_13987),sK357(U_13993,U_13991,U_13989,U_13987,U_13980)),U_13991)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_13987),U_13980),U_13989)) )
& U_13991 != c_Orderings_Obot__class_Obot(tc_fun(U_13987,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_13987),U_13991))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_13987),U_13989)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13987,tc_HOL_Obool),tc_fun(U_13987,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13987,tc_HOL_Obool),tc_fun(U_13987,tc_HOL_Obool)),U_13989),U_13991)),c_Wellfounded_Omax__ext(U_13987,U_13993))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK357]),skolemize(U_13979,sK357(U_13993,U_13991,U_13989,U_13987,U_13980))],[f_3557_3]) ).
fof(f_3557_5,plain,
( ! [U_13994,U_13992,U_13990,U_13988] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13988,tc_HOL_Obool),tc_fun(U_13988,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13988,tc_HOL_Obool),tc_fun(U_13988,tc_HOL_Obool)),U_13990),U_13992)),c_Wellfounded_Omax__ext(U_13988,U_13994)))
| ( ! [U_13981] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13988,U_13988)),hAPP(hAPP(c_Product__Type_OPair(U_13988,U_13988),sK358(U_13994,U_13992,U_13990,U_13988)),U_13981)),U_13994))
| ~ hBOOL(hAPP(hAPP(c_member(U_13988),U_13981),U_13992)) )
& hBOOL(hAPP(hAPP(c_member(U_13988),sK358(U_13994,U_13992,U_13990,U_13988)),U_13990)) )
| U_13992 = c_Orderings_Obot__class_Obot(tc_fun(U_13988,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13988),U_13992))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13988),U_13990)) )
& ! [U_13993,U_13991,U_13989,U_13987] :
( ( ! [U_13980] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13987,U_13987)),hAPP(hAPP(c_Product__Type_OPair(U_13987,U_13987),U_13980),sK357(U_13993,U_13991,U_13989,U_13987,U_13980))),U_13993))
& hBOOL(hAPP(hAPP(c_member(U_13987),sK357(U_13993,U_13991,U_13989,U_13987,U_13980)),U_13991)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_13987),U_13980),U_13989)) )
& U_13991 != c_Orderings_Obot__class_Obot(tc_fun(U_13987,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_13987),U_13991))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_13987),U_13989)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13987,tc_HOL_Obool),tc_fun(U_13987,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13987,tc_HOL_Obool),tc_fun(U_13987,tc_HOL_Obool)),U_13989),U_13991)),c_Wellfounded_Omax__ext(U_13987,U_13993))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK358]),skolemize(U_13982,sK358(U_13994,U_13992,U_13990,U_13988))],[f_3557_4]) ).
cnf(f_3557_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13987),U_13989))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13987,tc_HOL_Obool),tc_fun(U_13987,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13987,tc_HOL_Obool),tc_fun(U_13987,tc_HOL_Obool)),U_13989),U_13991)),c_Wellfounded_Omax__ext(U_13987,U_13993))) ),
inference(clausify,[status(thm)],[f_3557_5]) ).
cnf(f_3557_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13987),U_13991))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13987,tc_HOL_Obool),tc_fun(U_13987,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13987,tc_HOL_Obool),tc_fun(U_13987,tc_HOL_Obool)),U_13989),U_13991)),c_Wellfounded_Omax__ext(U_13987,U_13993))) ),
inference(clausify,[status(thm)],[f_3557_5]) ).
cnf(f_3557_8,plain,
( U_13991 != c_Orderings_Obot__class_Obot(tc_fun(U_13987,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13987,tc_HOL_Obool),tc_fun(U_13987,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13987,tc_HOL_Obool),tc_fun(U_13987,tc_HOL_Obool)),U_13989),U_13991)),c_Wellfounded_Omax__ext(U_13987,U_13993))) ),
inference(clausify,[status(thm)],[f_3557_5]) ).
cnf(f_3557_9,plain,
( hBOOL(hAPP(hAPP(c_member(U_13987),sK357(U_13993,U_13991,U_13989,U_13987,U_13980)),U_13991))
| ~ hBOOL(hAPP(hAPP(c_member(U_13987),U_13980),U_13989))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13987,tc_HOL_Obool),tc_fun(U_13987,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13987,tc_HOL_Obool),tc_fun(U_13987,tc_HOL_Obool)),U_13989),U_13991)),c_Wellfounded_Omax__ext(U_13987,U_13993))) ),
inference(clausify,[status(thm)],[f_3557_5]) ).
cnf(f_3557_10,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13987,U_13987)),hAPP(hAPP(c_Product__Type_OPair(U_13987,U_13987),U_13980),sK357(U_13993,U_13991,U_13989,U_13987,U_13980))),U_13993))
| ~ hBOOL(hAPP(hAPP(c_member(U_13987),U_13980),U_13989))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13987,tc_HOL_Obool),tc_fun(U_13987,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13987,tc_HOL_Obool),tc_fun(U_13987,tc_HOL_Obool)),U_13989),U_13991)),c_Wellfounded_Omax__ext(U_13987,U_13993))) ),
inference(clausify,[status(thm)],[f_3557_5]) ).
cnf(f_3557_11,plain,
( hBOOL(hAPP(hAPP(c_member(U_13988),sK358(U_13994,U_13992,U_13990,U_13988)),U_13990))
| U_13992 = c_Orderings_Obot__class_Obot(tc_fun(U_13988,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13988),U_13992))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13988),U_13990))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13988,tc_HOL_Obool),tc_fun(U_13988,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13988,tc_HOL_Obool),tc_fun(U_13988,tc_HOL_Obool)),U_13990),U_13992)),c_Wellfounded_Omax__ext(U_13988,U_13994))) ),
inference(clausify,[status(thm)],[f_3557_5]) ).
cnf(f_3557_12,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13988,U_13988)),hAPP(hAPP(c_Product__Type_OPair(U_13988,U_13988),sK358(U_13994,U_13992,U_13990,U_13988)),U_13981)),U_13994))
| ~ hBOOL(hAPP(hAPP(c_member(U_13988),U_13981),U_13992))
| U_13992 = c_Orderings_Obot__class_Obot(tc_fun(U_13988,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13988),U_13992))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13988),U_13990))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13988,tc_HOL_Obool),tc_fun(U_13988,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13988,tc_HOL_Obool),tc_fun(U_13988,tc_HOL_Obool)),U_13990),U_13992)),c_Wellfounded_Omax__ext(U_13988,U_13994))) ),
inference(clausify,[status(thm)],[f_3557_5]) ).
fof(f_3558_1,plain,
! [V_X_2,V_a_2,V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_coinduct__set]) ).
fof(f_3558_2,plain,
! [U_13998,U_13997,U_13996,U_13995] :
( hBOOL(hAPP(hAPP(c_member(U_13995),U_13997),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_13995,tc_HOL_Obool),U_13996)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13995,tc_HOL_Obool)),U_13998),hAPP(U_13996,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13995,tc_HOL_Obool)),U_13998),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_13995,tc_HOL_Obool),U_13996)))))
| ~ hBOOL(hAPP(hAPP(c_member(U_13995),U_13997),U_13998))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_13995,tc_HOL_Obool),tc_fun(U_13995,tc_HOL_Obool),U_13996) ),
inference(variable_rename,[status(thm)],[f_3558_1]) ).
cnf(f_3558_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_13995),U_13997),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_13995,tc_HOL_Obool),U_13996)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13995,tc_HOL_Obool)),U_13998),hAPP(U_13996,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13995,tc_HOL_Obool)),U_13998),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_13995,tc_HOL_Obool),U_13996)))))
| ~ hBOOL(hAPP(hAPP(c_member(U_13995),U_13997),U_13998))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_13995,tc_HOL_Obool),tc_fun(U_13995,tc_HOL_Obool),U_13996) ),
inference(clausify,[status(thm)],[f_3558_2]) ).
fof(f_3559_1,plain,
! [V_X_2,V_a_2,V_f_2,T_b,V_A_2] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_A_2))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
| V_A_2 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_def__coinduct__set]) ).
fof(f_3559_2,plain,
! [U_14003,U_14002,U_14001,U_14000,U_13999] :
( hBOOL(hAPP(hAPP(c_member(U_14000),U_14002),U_13999))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14000,tc_HOL_Obool)),U_14003),hAPP(U_14001,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14000,tc_HOL_Obool)),U_14003),U_13999))))
| ~ hBOOL(hAPP(hAPP(c_member(U_14000),U_14002),U_14003))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14000,tc_HOL_Obool),tc_fun(U_14000,tc_HOL_Obool),U_14001)
| U_13999 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14000,tc_HOL_Obool),U_14001) ),
inference(variable_rename,[status(thm)],[f_3559_1]) ).
cnf(f_3559_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_14000),U_14002),U_13999))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14000,tc_HOL_Obool)),U_14003),hAPP(U_14001,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14000,tc_HOL_Obool)),U_14003),U_13999))))
| ~ hBOOL(hAPP(hAPP(c_member(U_14000),U_14002),U_14003))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14000,tc_HOL_Obool),tc_fun(U_14000,tc_HOL_Obool),U_14001)
| U_13999 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14000,tc_HOL_Obool),U_14001) ),
inference(clausify,[status(thm)],[f_3559_2]) ).
fof(f_3560_1,plain,
! [V_f_2,V_A_2,T_b] :
( V_A_2 = hAPP(V_f_2,V_A_2)
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| V_A_2 != c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_def__gfp__unfold]) ).
fof(f_3560_2,plain,
! [U_14006,U_14005,U_14004] :
( U_14005 = hAPP(U_14006,U_14005)
| ~ c_Orderings_Oorder__class_Omono(U_14004,U_14004,U_14006)
| U_14005 != c_Inductive_Ocomplete__lattice__class_Ogfp(U_14004,U_14006)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14004) ),
inference(variable_rename,[status(thm)],[f_3560_1]) ).
cnf(f_3560_3,plain,
( U_14005 = hAPP(U_14006,U_14005)
| ~ c_Orderings_Oorder__class_Omono(U_14004,U_14004,U_14006)
| U_14005 != c_Inductive_Ocomplete__lattice__class_Ogfp(U_14004,U_14006)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14004) ),
inference(clausify,[status(thm)],[f_3560_2]) ).
fof(f_3561_1,plain,
! [V_f_2,T_b] :
( c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2) = hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_gfp__unfold]) ).
fof(f_3561_2,plain,
! [U_14008,U_14007] :
( c_Inductive_Ocomplete__lattice__class_Ogfp(U_14007,U_14008) = hAPP(U_14008,c_Inductive_Ocomplete__lattice__class_Ogfp(U_14007,U_14008))
| ~ c_Orderings_Oorder__class_Omono(U_14007,U_14007,U_14008)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14007) ),
inference(variable_rename,[status(thm)],[f_3561_1]) ).
cnf(f_3561_3,plain,
( c_Inductive_Ocomplete__lattice__class_Ogfp(U_14007,U_14008) = hAPP(U_14008,c_Inductive_Ocomplete__lattice__class_Ogfp(U_14007,U_14008))
| ~ c_Orderings_Oorder__class_Omono(U_14007,U_14007,U_14008)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14007) ),
inference(clausify,[status(thm)],[f_3561_2]) ).
fof(f_3562_1,plain,
! [V_f_2,V_X_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,V_X_2)))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_gfp__upperbound]) ).
fof(f_3562_2,plain,
! [U_14011,U_14010,U_14009] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14009),U_14010),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14009,U_14011)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14009),U_14010),hAPP(U_14011,U_14010)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14009) ),
inference(variable_rename,[status(thm)],[f_3562_1]) ).
cnf(f_3562_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14009),U_14010),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14009,U_14011)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14009),U_14010),hAPP(U_14011,U_14010)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14009) ),
inference(clausify,[status(thm)],[f_3562_2]) ).
fof(f_3563_1,plain,
! [V_f_2,V_X_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,V_X_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2)) ),
inference(fof_nnf,[status(thm)],[fact_weak__coinduct]) ).
fof(f_3563_2,plain,
! [U_14015,U_14014,U_14013,U_14012] :
( hBOOL(hAPP(hAPP(c_member(U_14012),U_14013),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14012,tc_HOL_Obool),U_14015)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14012,tc_HOL_Obool)),U_14014),hAPP(U_14015,U_14014)))
| ~ hBOOL(hAPP(hAPP(c_member(U_14012),U_14013),U_14014)) ),
inference(variable_rename,[status(thm)],[f_3563_1]) ).
cnf(f_3563_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_14012),U_14013),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14012,tc_HOL_Obool),U_14015)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14012,tc_HOL_Obool)),U_14014),hAPP(U_14015,U_14014)))
| ~ hBOOL(hAPP(hAPP(c_member(U_14012),U_14013),U_14014)) ),
inference(clausify,[status(thm)],[f_3563_2]) ).
fof(f_3564_1,plain,
! [V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_gfp__lemma2]) ).
fof(f_3564_2,plain,
! [U_14017,U_14016] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14016),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14016,U_14017)),hAPP(U_14017,c_Inductive_Ocomplete__lattice__class_Ogfp(U_14016,U_14017))))
| ~ c_Orderings_Oorder__class_Omono(U_14016,U_14016,U_14017)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14016) ),
inference(variable_rename,[status(thm)],[f_3564_1]) ).
cnf(f_3564_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14016),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14016,U_14017)),hAPP(U_14017,c_Inductive_Ocomplete__lattice__class_Ogfp(U_14016,U_14017))))
| ~ c_Orderings_Oorder__class_Omono(U_14016,U_14016,U_14017)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14016) ),
inference(clausify,[status(thm)],[f_3564_2]) ).
fof(f_3565_1,plain,
! [V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_gfp__lemma3]) ).
fof(f_3565_2,plain,
! [U_14019,U_14018] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14018),hAPP(U_14019,c_Inductive_Ocomplete__lattice__class_Ogfp(U_14018,U_14019))),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14018,U_14019)))
| ~ c_Orderings_Oorder__class_Omono(U_14018,U_14018,U_14019)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14018) ),
inference(variable_rename,[status(thm)],[f_3565_1]) ).
cnf(f_3565_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14018),hAPP(U_14019,c_Inductive_Ocomplete__lattice__class_Ogfp(U_14018,U_14019))),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14018,U_14019)))
| ~ c_Orderings_Oorder__class_Omono(U_14018,U_14018,U_14019)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14018) ),
inference(clausify,[status(thm)],[f_3565_2]) ).
fof(f_3566_1,plain,
! [V_f_2,V_g_2,T_c,V_X_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_g_2,V_a_2)),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_c,tc_HOL_Obool),V_f_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),V_X_2)),hAPP(V_f_2,hAPP(c_Set_Oimage(T_b,T_c,V_g_2),V_X_2))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2)) ),
inference(fof_nnf,[status(thm)],[fact_weak__coinduct__image]) ).
fof(f_3566_2,plain,
! [U_14025,U_14024,U_14023,U_14022,U_14021,U_14020] :
( hBOOL(hAPP(hAPP(c_member(U_14023),hAPP(U_14024,U_14021)),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14023,tc_HOL_Obool),U_14025)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14023,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14020,U_14023,U_14024),U_14022)),hAPP(U_14025,hAPP(c_Set_Oimage(U_14020,U_14023,U_14024),U_14022))))
| ~ hBOOL(hAPP(hAPP(c_member(U_14020),U_14021),U_14022)) ),
inference(variable_rename,[status(thm)],[f_3566_1]) ).
cnf(f_3566_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_14023),hAPP(U_14024,U_14021)),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14023,tc_HOL_Obool),U_14025)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14023,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14020,U_14023,U_14024),U_14022)),hAPP(U_14025,hAPP(c_Set_Oimage(U_14020,U_14023,U_14024),U_14022))))
| ~ hBOOL(hAPP(hAPP(c_member(U_14020),U_14021),U_14022)) ),
inference(clausify,[status(thm)],[f_3566_2]) ).
fof(f_3567_1,plain,
! [V_X_2,V_a_2,V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_gfp__fun__UnI2]) ).
fof(f_3567_2,plain,
! [U_14029,U_14028,U_14027,U_14026] :
( hBOOL(hAPP(hAPP(c_member(U_14026),U_14028),hAPP(U_14027,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14026,tc_HOL_Obool)),U_14029),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14026,tc_HOL_Obool),U_14027)))))
| ~ hBOOL(hAPP(hAPP(c_member(U_14026),U_14028),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14026,tc_HOL_Obool),U_14027)))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14026,tc_HOL_Obool),tc_fun(U_14026,tc_HOL_Obool),U_14027) ),
inference(variable_rename,[status(thm)],[f_3567_1]) ).
cnf(f_3567_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_14026),U_14028),hAPP(U_14027,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14026,tc_HOL_Obool)),U_14029),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14026,tc_HOL_Obool),U_14027)))))
| ~ hBOOL(hAPP(hAPP(c_member(U_14026),U_14028),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14026,tc_HOL_Obool),U_14027)))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14026,tc_HOL_Obool),tc_fun(U_14026,tc_HOL_Obool),U_14027) ),
inference(clausify,[status(thm)],[f_3567_2]) ).
fof(f_3568_1,plain,
! [V_X_2,V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_coinduct]) ).
fof(f_3568_2,plain,
! [U_14032,U_14031,U_14030] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14030),U_14032),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14030,U_14031)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14030),U_14032),hAPP(U_14031,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14030),U_14032),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14030,U_14031)))))
| ~ c_Orderings_Oorder__class_Omono(U_14030,U_14030,U_14031)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14030) ),
inference(variable_rename,[status(thm)],[f_3568_1]) ).
cnf(f_3568_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14030),U_14032),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14030,U_14031)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14030),U_14032),hAPP(U_14031,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14030),U_14032),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14030,U_14031)))))
| ~ c_Orderings_Oorder__class_Omono(U_14030,U_14030,U_14031)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14030) ),
inference(clausify,[status(thm)],[f_3568_2]) ).
fof(f_3569_1,plain,
! [V_f_2,V_X_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_coinduct__lemma]) ).
fof(f_3569_2,plain,
! [U_14035,U_14034,U_14033] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14033),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14033),U_14034),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14033,U_14035))),hAPP(U_14035,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14033),U_14034),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14033,U_14035)))))
| ~ c_Orderings_Oorder__class_Omono(U_14033,U_14033,U_14035)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14033),U_14034),hAPP(U_14035,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14033),U_14034),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14033,U_14035)))))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14033) ),
inference(variable_rename,[status(thm)],[f_3569_1]) ).
cnf(f_3569_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14033),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14033),U_14034),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14033,U_14035))),hAPP(U_14035,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14033),U_14034),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14033,U_14035)))))
| ~ c_Orderings_Oorder__class_Omono(U_14033,U_14033,U_14035)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14033),U_14034),hAPP(U_14035,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14033),U_14034),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14033,U_14035)))))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14033) ),
inference(clausify,[status(thm)],[f_3569_2]) ).
fof(f_3570_1,plain,
! [V_X_2,V_f_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),V_A_2))))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| V_A_2 != c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_def__coinduct]) ).
fof(f_3570_2,plain,
! [U_14039,U_14038,U_14037,U_14036] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14036),U_14039),U_14037))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14036),U_14039),hAPP(U_14038,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14036),U_14039),U_14037))))
| ~ c_Orderings_Oorder__class_Omono(U_14036,U_14036,U_14038)
| U_14037 != c_Inductive_Ocomplete__lattice__class_Ogfp(U_14036,U_14038)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14036) ),
inference(variable_rename,[status(thm)],[f_3570_1]) ).
cnf(f_3570_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14036),U_14039),U_14037))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14036),U_14039),hAPP(U_14038,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14036),U_14039),U_14037))))
| ~ c_Orderings_Oorder__class_Omono(U_14036,U_14036,U_14038)
| U_14037 != c_Inductive_Ocomplete__lattice__class_Ogfp(U_14036,U_14038)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14036) ),
inference(clausify,[status(thm)],[f_3570_2]) ).
fof(f_3571_1,plain,
! [V_X_2,V_a_2,V_f_2,T_b,V_A_2] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),V_A_2)))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
| V_A_2 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_def__coinduct3]) ).
fof(f_3571_2,plain,
! [U_14044,U_14043,U_14042,U_14041,U_14040] :
( hBOOL(hAPP(hAPP(c_member(U_14041),U_14043),U_14040))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14041,tc_HOL_Obool)),U_14044),hAPP(U_14042,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14041,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_14041,tc_HOL_Obool),tc_fun(U_14041,tc_HOL_Obool),tc_fun(U_14041,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14041,tc_HOL_Obool),tc_fun(tc_fun(U_14041,tc_HOL_Obool),tc_fun(U_14041,tc_HOL_Obool)),tc_fun(U_14041,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14041,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_14041,tc_HOL_Obool),tc_fun(U_14041,tc_HOL_Obool),tc_fun(U_14041,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14041,tc_HOL_Obool),tc_fun(tc_fun(U_14041,tc_HOL_Obool),tc_fun(U_14041,tc_HOL_Obool)),tc_fun(U_14041,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14041,tc_HOL_Obool))),U_14042)),U_14044))),U_14040)))))
| ~ hBOOL(hAPP(hAPP(c_member(U_14041),U_14043),U_14044))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14041,tc_HOL_Obool),tc_fun(U_14041,tc_HOL_Obool),U_14042)
| U_14040 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14041,tc_HOL_Obool),U_14042) ),
inference(variable_rename,[status(thm)],[f_3571_1]) ).
cnf(f_3571_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_14041),U_14043),U_14040))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14041,tc_HOL_Obool)),U_14044),hAPP(U_14042,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14041,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_14041,tc_HOL_Obool),tc_fun(U_14041,tc_HOL_Obool),tc_fun(U_14041,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14041,tc_HOL_Obool),tc_fun(tc_fun(U_14041,tc_HOL_Obool),tc_fun(U_14041,tc_HOL_Obool)),tc_fun(U_14041,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14041,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_14041,tc_HOL_Obool),tc_fun(U_14041,tc_HOL_Obool),tc_fun(U_14041,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14041,tc_HOL_Obool),tc_fun(tc_fun(U_14041,tc_HOL_Obool),tc_fun(U_14041,tc_HOL_Obool)),tc_fun(U_14041,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14041,tc_HOL_Obool))),U_14042)),U_14044))),U_14040)))))
| ~ hBOOL(hAPP(hAPP(c_member(U_14041),U_14043),U_14044))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14041,tc_HOL_Obool),tc_fun(U_14041,tc_HOL_Obool),U_14042)
| U_14040 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14041,tc_HOL_Obool),U_14042) ),
inference(clausify,[status(thm)],[f_3571_2]) ).
fof(f_3572_1,plain,
! [V_X_2,V_a_2,V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_coinduct3]) ).
fof(f_3572_2,plain,
! [U_14048,U_14047,U_14046,U_14045] :
( hBOOL(hAPP(hAPP(c_member(U_14045),U_14047),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14045,tc_HOL_Obool),U_14046)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14045,tc_HOL_Obool)),U_14048),hAPP(U_14046,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14045,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_14045,tc_HOL_Obool),tc_fun(U_14045,tc_HOL_Obool),tc_fun(U_14045,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14045,tc_HOL_Obool),tc_fun(tc_fun(U_14045,tc_HOL_Obool),tc_fun(U_14045,tc_HOL_Obool)),tc_fun(U_14045,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14045,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_14045,tc_HOL_Obool),tc_fun(U_14045,tc_HOL_Obool),tc_fun(U_14045,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14045,tc_HOL_Obool),tc_fun(tc_fun(U_14045,tc_HOL_Obool),tc_fun(U_14045,tc_HOL_Obool)),tc_fun(U_14045,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14045,tc_HOL_Obool))),U_14046)),U_14048))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14045,tc_HOL_Obool),U_14046))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_14045),U_14047),U_14048))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14045,tc_HOL_Obool),tc_fun(U_14045,tc_HOL_Obool),U_14046) ),
inference(variable_rename,[status(thm)],[f_3572_1]) ).
cnf(f_3572_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_14045),U_14047),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14045,tc_HOL_Obool),U_14046)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14045,tc_HOL_Obool)),U_14048),hAPP(U_14046,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14045,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_14045,tc_HOL_Obool),tc_fun(U_14045,tc_HOL_Obool),tc_fun(U_14045,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14045,tc_HOL_Obool),tc_fun(tc_fun(U_14045,tc_HOL_Obool),tc_fun(U_14045,tc_HOL_Obool)),tc_fun(U_14045,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14045,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_14045,tc_HOL_Obool),tc_fun(U_14045,tc_HOL_Obool),tc_fun(U_14045,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14045,tc_HOL_Obool),tc_fun(tc_fun(U_14045,tc_HOL_Obool),tc_fun(U_14045,tc_HOL_Obool)),tc_fun(U_14045,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14045,tc_HOL_Obool))),U_14046)),U_14048))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14045,tc_HOL_Obool),U_14046))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_14045),U_14047),U_14048))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14045,tc_HOL_Obool),tc_fun(U_14045,tc_HOL_Obool),U_14046) ),
inference(clausify,[status(thm)],[f_3572_2]) ).
fof(f_3573_1,plain,
! [V_X_2,V_a_2,V_P_2,T_b,V_A_2] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ? [B_z] :
( ~ hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_A_2)),B_z))
& hBOOL(hAPP(hAPP(c_member(T_b),B_z),V_X_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_OCollect(T_b)),V_P_2))
| V_A_2 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_OCollect(T_b)),V_P_2)) ),
inference(fof_nnf,[status(thm)],[fact_def__Collect__coinduct]) ).
fof(f_3573_2,plain,
! [U_14054,U_14053,U_14052,U_14051,U_14050] :
( hBOOL(hAPP(hAPP(c_member(U_14051),U_14053),U_14050))
| ? [U_14049] :
( ~ hBOOL(hAPP(hAPP(U_14052,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14051,tc_HOL_Obool)),U_14054),U_14050)),U_14049))
& hBOOL(hAPP(hAPP(c_member(U_14051),U_14049),U_14054)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_14051),U_14053),U_14054))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14051,tc_HOL_Obool),tc_fun(U_14051,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14051,tc_HOL_Obool),tc_fun(U_14051,tc_HOL_Obool),tc_fun(U_14051,tc_HOL_Obool)),c_Set_OCollect(U_14051)),U_14052))
| U_14050 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14051,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14051,tc_HOL_Obool),tc_fun(U_14051,tc_HOL_Obool),tc_fun(U_14051,tc_HOL_Obool)),c_Set_OCollect(U_14051)),U_14052)) ),
inference(variable_rename,[status(thm)],[f_3573_1]) ).
fof(f_3573_3,plain,
! [U_14054,U_14053,U_14052,U_14051,U_14050] :
( hBOOL(hAPP(hAPP(c_member(U_14051),U_14053),U_14050))
| ( ~ hBOOL(hAPP(hAPP(U_14052,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14051,tc_HOL_Obool)),U_14054),U_14050)),sK359(U_14054,U_14053,U_14052,U_14051,U_14050)))
& hBOOL(hAPP(hAPP(c_member(U_14051),sK359(U_14054,U_14053,U_14052,U_14051,U_14050)),U_14054)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_14051),U_14053),U_14054))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14051,tc_HOL_Obool),tc_fun(U_14051,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14051,tc_HOL_Obool),tc_fun(U_14051,tc_HOL_Obool),tc_fun(U_14051,tc_HOL_Obool)),c_Set_OCollect(U_14051)),U_14052))
| U_14050 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14051,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14051,tc_HOL_Obool),tc_fun(U_14051,tc_HOL_Obool),tc_fun(U_14051,tc_HOL_Obool)),c_Set_OCollect(U_14051)),U_14052)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK359]),skolemize(U_14049,sK359(U_14054,U_14053,U_14052,U_14051,U_14050))],[f_3573_2]) ).
cnf(f_3573_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_14051),sK359(U_14054,U_14053,U_14052,U_14051,U_14050)),U_14054))
| hBOOL(hAPP(hAPP(c_member(U_14051),U_14053),U_14050))
| ~ hBOOL(hAPP(hAPP(c_member(U_14051),U_14053),U_14054))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14051,tc_HOL_Obool),tc_fun(U_14051,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14051,tc_HOL_Obool),tc_fun(U_14051,tc_HOL_Obool),tc_fun(U_14051,tc_HOL_Obool)),c_Set_OCollect(U_14051)),U_14052))
| U_14050 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14051,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14051,tc_HOL_Obool),tc_fun(U_14051,tc_HOL_Obool),tc_fun(U_14051,tc_HOL_Obool)),c_Set_OCollect(U_14051)),U_14052)) ),
inference(clausify,[status(thm)],[f_3573_3]) ).
cnf(f_3573_5,plain,
( ~ hBOOL(hAPP(hAPP(U_14052,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14051,tc_HOL_Obool)),U_14054),U_14050)),sK359(U_14054,U_14053,U_14052,U_14051,U_14050)))
| hBOOL(hAPP(hAPP(c_member(U_14051),U_14053),U_14050))
| ~ hBOOL(hAPP(hAPP(c_member(U_14051),U_14053),U_14054))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14051,tc_HOL_Obool),tc_fun(U_14051,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14051,tc_HOL_Obool),tc_fun(U_14051,tc_HOL_Obool),tc_fun(U_14051,tc_HOL_Obool)),c_Set_OCollect(U_14051)),U_14052))
| U_14050 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14051,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14051,tc_HOL_Obool),tc_fun(U_14051,tc_HOL_Obool),tc_fun(U_14051,tc_HOL_Obool)),c_Set_OCollect(U_14051)),U_14052)) ),
inference(clausify,[status(thm)],[f_3573_3]) ).
fof(f_3574_1,plain,
! [V_A_2,V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_A_2)),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lfp__lowerbound]) ).
fof(f_3574_2,plain,
! [U_14057,U_14056,U_14055] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14055),c_Inductive_Ocomplete__lattice__class_Olfp(U_14055,U_14056)),U_14057))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14055),hAPP(U_14056,U_14057)),U_14057))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14055) ),
inference(variable_rename,[status(thm)],[f_3574_1]) ).
cnf(f_3574_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14055),c_Inductive_Ocomplete__lattice__class_Olfp(U_14055,U_14056)),U_14057))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14055),hAPP(U_14056,U_14057)),U_14057))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14055) ),
inference(clausify,[status(thm)],[f_3574_2]) ).
fof(f_3575_1,plain,
! [V_t_2,T_b] :
( c_Inductive_Ocomplete__lattice__class_Olfp(T_b,hAPP(c_COMBK(T_b,T_b),V_t_2)) = V_t_2
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lfp__const]) ).
fof(f_3575_2,plain,
! [U_14059,U_14058] :
( c_Inductive_Ocomplete__lattice__class_Olfp(U_14058,hAPP(c_COMBK(U_14058,U_14058),U_14059)) = U_14059
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14058) ),
inference(variable_rename,[status(thm)],[f_3575_1]) ).
cnf(f_3575_3,plain,
( c_Inductive_Ocomplete__lattice__class_Olfp(U_14058,hAPP(c_COMBK(U_14058,U_14058),U_14059)) = U_14059
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14058) ),
inference(clausify,[status(thm)],[f_3575_2]) ).
fof(f_3576_1,plain,
! [V_f_2,T_b] :
( c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2) = hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lfp__unfold]) ).
fof(f_3576_2,plain,
! [U_14061,U_14060] :
( c_Inductive_Ocomplete__lattice__class_Olfp(U_14060,U_14061) = hAPP(U_14061,c_Inductive_Ocomplete__lattice__class_Olfp(U_14060,U_14061))
| ~ c_Orderings_Oorder__class_Omono(U_14060,U_14060,U_14061)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14060) ),
inference(variable_rename,[status(thm)],[f_3576_1]) ).
cnf(f_3576_3,plain,
( c_Inductive_Ocomplete__lattice__class_Olfp(U_14060,U_14061) = hAPP(U_14061,c_Inductive_Ocomplete__lattice__class_Olfp(U_14060,U_14061))
| ~ c_Orderings_Oorder__class_Omono(U_14060,U_14060,U_14061)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14060) ),
inference(clausify,[status(thm)],[f_3576_2]) ).
fof(f_3577_1,plain,
! [V_f_2,V_h_2,T_b] :
( V_h_2 = hAPP(V_f_2,V_h_2)
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| V_h_2 != c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_def__lfp__unfold]) ).
fof(f_3577_2,plain,
! [U_14064,U_14063,U_14062] :
( U_14063 = hAPP(U_14064,U_14063)
| ~ c_Orderings_Oorder__class_Omono(U_14062,U_14062,U_14064)
| U_14063 != c_Inductive_Ocomplete__lattice__class_Olfp(U_14062,U_14064)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14062) ),
inference(variable_rename,[status(thm)],[f_3577_1]) ).
cnf(f_3577_3,plain,
( U_14063 = hAPP(U_14064,U_14063)
| ~ c_Orderings_Oorder__class_Omono(U_14062,U_14062,U_14064)
| U_14063 != c_Inductive_Ocomplete__lattice__class_Olfp(U_14062,U_14064)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14062) ),
inference(clausify,[status(thm)],[f_3577_2]) ).
fof(f_3578_1,plain,
! [V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2))),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lfp__lemma2]) ).
fof(f_3578_2,plain,
! [U_14066,U_14065] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14065),hAPP(U_14066,c_Inductive_Ocomplete__lattice__class_Olfp(U_14065,U_14066))),c_Inductive_Ocomplete__lattice__class_Olfp(U_14065,U_14066)))
| ~ c_Orderings_Oorder__class_Omono(U_14065,U_14065,U_14066)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14065) ),
inference(variable_rename,[status(thm)],[f_3578_1]) ).
cnf(f_3578_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14065),hAPP(U_14066,c_Inductive_Ocomplete__lattice__class_Olfp(U_14065,U_14066))),c_Inductive_Ocomplete__lattice__class_Olfp(U_14065,U_14066)))
| ~ c_Orderings_Oorder__class_Omono(U_14065,U_14065,U_14066)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14065) ),
inference(clausify,[status(thm)],[f_3578_2]) ).
fof(f_3579_1,plain,
! [V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2))))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lfp__lemma3]) ).
fof(f_3579_2,plain,
! [U_14068,U_14067] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14067),c_Inductive_Ocomplete__lattice__class_Olfp(U_14067,U_14068)),hAPP(U_14068,c_Inductive_Ocomplete__lattice__class_Olfp(U_14067,U_14068))))
| ~ c_Orderings_Oorder__class_Omono(U_14067,U_14067,U_14068)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14067) ),
inference(variable_rename,[status(thm)],[f_3579_1]) ).
cnf(f_3579_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14067),c_Inductive_Ocomplete__lattice__class_Olfp(U_14067,U_14068)),hAPP(U_14068,c_Inductive_Ocomplete__lattice__class_Olfp(U_14067,U_14068))))
| ~ c_Orderings_Oorder__class_Omono(U_14067,U_14067,U_14068)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14067) ),
inference(clausify,[status(thm)],[f_3579_2]) ).
fof(f_3580_1,plain,
! [V_P_2,V_f_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_A_2),V_P_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_A_2),V_P_2))),V_P_2))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| V_A_2 != c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_def__lfp__induct]) ).
fof(f_3580_2,plain,
! [U_14072,U_14071,U_14070,U_14069] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14069),U_14070),U_14072))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14069),hAPP(U_14071,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14069),U_14070),U_14072))),U_14072))
| ~ c_Orderings_Oorder__class_Omono(U_14069,U_14069,U_14071)
| U_14070 != c_Inductive_Ocomplete__lattice__class_Olfp(U_14069,U_14071)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14069) ),
inference(variable_rename,[status(thm)],[f_3580_1]) ).
cnf(f_3580_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14069),U_14070),U_14072))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14069),hAPP(U_14071,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14069),U_14070),U_14072))),U_14072))
| ~ c_Orderings_Oorder__class_Omono(U_14069,U_14069,U_14071)
| U_14070 != c_Inductive_Ocomplete__lattice__class_Olfp(U_14069,U_14071)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14069) ),
inference(clausify,[status(thm)],[f_3580_2]) ).
fof(f_3581_1,plain,
! [V_P_2,V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),V_P_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),V_P_2))),V_P_2))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lfp__induct]) ).
fof(f_3581_2,plain,
! [U_14075,U_14074,U_14073] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14073),c_Inductive_Ocomplete__lattice__class_Olfp(U_14073,U_14074)),U_14075))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14073),hAPP(U_14074,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14073),c_Inductive_Ocomplete__lattice__class_Olfp(U_14073,U_14074)),U_14075))),U_14075))
| ~ c_Orderings_Oorder__class_Omono(U_14073,U_14073,U_14074)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14073) ),
inference(variable_rename,[status(thm)],[f_3581_1]) ).
cnf(f_3581_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14073),c_Inductive_Ocomplete__lattice__class_Olfp(U_14073,U_14074)),U_14075))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14073),hAPP(U_14074,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14073),c_Inductive_Ocomplete__lattice__class_Olfp(U_14073,U_14074)),U_14075))),U_14075))
| ~ c_Orderings_Oorder__class_Omono(U_14073,U_14073,U_14074)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_14073) ),
inference(clausify,[status(thm)],[f_3581_2]) ).
fof(f_3582_1,plain,
! [V_f_2,V_X_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))))))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))))) ),
inference(fof_nnf,[status(thm)],[fact_coinduct3__lemma]) ).
fof(f_3582_2,plain,
! [U_14078,U_14077,U_14076] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14076,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14076,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14076,tc_HOL_Obool),tc_fun(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool)),tc_fun(U_14076,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14076,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14076,tc_HOL_Obool),tc_fun(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool)),tc_fun(U_14076,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14076,tc_HOL_Obool))),U_14078)),U_14077))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14076,tc_HOL_Obool),U_14078)))),hAPP(U_14078,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14076,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14076,tc_HOL_Obool),tc_fun(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool)),tc_fun(U_14076,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14076,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14076,tc_HOL_Obool),tc_fun(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool)),tc_fun(U_14076,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14076,tc_HOL_Obool))),U_14078)),U_14077))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14076,tc_HOL_Obool),U_14078))))))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool),U_14078)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14076,tc_HOL_Obool)),U_14077),hAPP(U_14078,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14076,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14076,tc_HOL_Obool),tc_fun(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool)),tc_fun(U_14076,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14076,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14076,tc_HOL_Obool),tc_fun(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool)),tc_fun(U_14076,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14076,tc_HOL_Obool))),U_14078)),U_14077))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14076,tc_HOL_Obool),U_14078)))))) ),
inference(variable_rename,[status(thm)],[f_3582_1]) ).
cnf(f_3582_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14076,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14076,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14076,tc_HOL_Obool),tc_fun(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool)),tc_fun(U_14076,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14076,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14076,tc_HOL_Obool),tc_fun(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool)),tc_fun(U_14076,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14076,tc_HOL_Obool))),U_14078)),U_14077))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14076,tc_HOL_Obool),U_14078)))),hAPP(U_14078,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14076,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14076,tc_HOL_Obool),tc_fun(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool)),tc_fun(U_14076,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14076,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14076,tc_HOL_Obool),tc_fun(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool)),tc_fun(U_14076,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14076,tc_HOL_Obool))),U_14078)),U_14077))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14076,tc_HOL_Obool),U_14078))))))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool),U_14078)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14076,tc_HOL_Obool)),U_14077),hAPP(U_14078,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14076,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14076,tc_HOL_Obool),tc_fun(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool)),tc_fun(U_14076,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14076,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14076,tc_HOL_Obool),tc_fun(tc_fun(U_14076,tc_HOL_Obool),tc_fun(U_14076,tc_HOL_Obool)),tc_fun(U_14076,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14076,tc_HOL_Obool))),U_14078)),U_14077))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14076,tc_HOL_Obool),U_14078)))))) ),
inference(clausify,[status(thm)],[f_3582_2]) ).
fof(f_3583_1,plain,
! [V_P_2,V_a_2,V_f_2,T_b,V_A_2] :
( hBOOL(hAPP(V_P_2,V_a_2))
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))))) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
| V_A_2 != c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_def__lfp__induct__set]) ).
fof(f_3583_2,plain,
! [U_14084,U_14083,U_14082,U_14081,U_14080] :
( hBOOL(hAPP(U_14084,U_14083))
| ? [U_14079] :
( ~ hBOOL(hAPP(U_14084,U_14079))
& hBOOL(hAPP(hAPP(c_member(U_14081),U_14079),hAPP(U_14082,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14081,tc_HOL_Obool)),U_14080),hAPP(c_Set_OCollect(U_14081),U_14084))))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_14081),U_14083),U_14080))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14081,tc_HOL_Obool),tc_fun(U_14081,tc_HOL_Obool),U_14082)
| U_14080 != c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14081,tc_HOL_Obool),U_14082) ),
inference(variable_rename,[status(thm)],[f_3583_1]) ).
fof(f_3583_3,plain,
! [U_14084,U_14083,U_14082,U_14081,U_14080] :
( hBOOL(hAPP(U_14084,U_14083))
| ( ~ hBOOL(hAPP(U_14084,sK360(U_14084,U_14083,U_14082,U_14081,U_14080)))
& hBOOL(hAPP(hAPP(c_member(U_14081),sK360(U_14084,U_14083,U_14082,U_14081,U_14080)),hAPP(U_14082,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14081,tc_HOL_Obool)),U_14080),hAPP(c_Set_OCollect(U_14081),U_14084))))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_14081),U_14083),U_14080))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14081,tc_HOL_Obool),tc_fun(U_14081,tc_HOL_Obool),U_14082)
| U_14080 != c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14081,tc_HOL_Obool),U_14082) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK360]),skolemize(U_14079,sK360(U_14084,U_14083,U_14082,U_14081,U_14080))],[f_3583_2]) ).
cnf(f_3583_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_14081),sK360(U_14084,U_14083,U_14082,U_14081,U_14080)),hAPP(U_14082,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14081,tc_HOL_Obool)),U_14080),hAPP(c_Set_OCollect(U_14081),U_14084)))))
| hBOOL(hAPP(U_14084,U_14083))
| ~ hBOOL(hAPP(hAPP(c_member(U_14081),U_14083),U_14080))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14081,tc_HOL_Obool),tc_fun(U_14081,tc_HOL_Obool),U_14082)
| U_14080 != c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14081,tc_HOL_Obool),U_14082) ),
inference(clausify,[status(thm)],[f_3583_3]) ).
cnf(f_3583_5,plain,
( ~ hBOOL(hAPP(U_14084,sK360(U_14084,U_14083,U_14082,U_14081,U_14080)))
| hBOOL(hAPP(U_14084,U_14083))
| ~ hBOOL(hAPP(hAPP(c_member(U_14081),U_14083),U_14080))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14081,tc_HOL_Obool),tc_fun(U_14081,tc_HOL_Obool),U_14082)
| U_14080 != c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14081,tc_HOL_Obool),U_14082) ),
inference(clausify,[status(thm)],[f_3583_3]) ).
fof(f_3584_1,plain,
! [V_P_2,V_f_2,V_a_2,T_b] :
( hBOOL(hAPP(V_P_2,V_a_2))
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)),hAPP(c_Set_OCollect(T_b),V_P_2))))) )
| ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))) ),
inference(fof_nnf,[status(thm)],[fact_lfp__induct__set]) ).
fof(f_3584_2,plain,
! [U_14089,U_14088,U_14087,U_14086] :
( hBOOL(hAPP(U_14089,U_14087))
| ? [U_14085] :
( ~ hBOOL(hAPP(U_14089,U_14085))
& hBOOL(hAPP(hAPP(c_member(U_14086),U_14085),hAPP(U_14088,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14086,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14086,tc_HOL_Obool),U_14088)),hAPP(c_Set_OCollect(U_14086),U_14089))))) )
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14086,tc_HOL_Obool),tc_fun(U_14086,tc_HOL_Obool),U_14088)
| ~ hBOOL(hAPP(hAPP(c_member(U_14086),U_14087),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14086,tc_HOL_Obool),U_14088))) ),
inference(variable_rename,[status(thm)],[f_3584_1]) ).
fof(f_3584_3,plain,
! [U_14089,U_14088,U_14087,U_14086] :
( hBOOL(hAPP(U_14089,U_14087))
| ( ~ hBOOL(hAPP(U_14089,sK361(U_14089,U_14088,U_14087,U_14086)))
& hBOOL(hAPP(hAPP(c_member(U_14086),sK361(U_14089,U_14088,U_14087,U_14086)),hAPP(U_14088,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14086,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14086,tc_HOL_Obool),U_14088)),hAPP(c_Set_OCollect(U_14086),U_14089))))) )
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14086,tc_HOL_Obool),tc_fun(U_14086,tc_HOL_Obool),U_14088)
| ~ hBOOL(hAPP(hAPP(c_member(U_14086),U_14087),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14086,tc_HOL_Obool),U_14088))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK361]),skolemize(U_14085,sK361(U_14089,U_14088,U_14087,U_14086))],[f_3584_2]) ).
cnf(f_3584_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_14086),sK361(U_14089,U_14088,U_14087,U_14086)),hAPP(U_14088,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14086,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14086,tc_HOL_Obool),U_14088)),hAPP(c_Set_OCollect(U_14086),U_14089)))))
| hBOOL(hAPP(U_14089,U_14087))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14086,tc_HOL_Obool),tc_fun(U_14086,tc_HOL_Obool),U_14088)
| ~ hBOOL(hAPP(hAPP(c_member(U_14086),U_14087),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14086,tc_HOL_Obool),U_14088))) ),
inference(clausify,[status(thm)],[f_3584_3]) ).
cnf(f_3584_5,plain,
( ~ hBOOL(hAPP(U_14089,sK361(U_14089,U_14088,U_14087,U_14086)))
| hBOOL(hAPP(U_14089,U_14087))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14086,tc_HOL_Obool),tc_fun(U_14086,tc_HOL_Obool),U_14088)
| ~ hBOOL(hAPP(hAPP(c_member(U_14086),U_14087),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14086,tc_HOL_Obool),U_14088))) ),
inference(clausify,[status(thm)],[f_3584_3]) ).
fof(f_3585_1,plain,
! [V_P_2,V_f_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(V_P_2,V_a_2),V_b_2))
| ? [B_a,B_b] :
( ~ hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_f_2)),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)))))) )
| ~ c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_f_2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_f_2))) ),
inference(fof_nnf,[status(thm)],[fact_lfp__induct2]) ).
fof(f_3585_2,plain,
! [U_14097,U_14096,U_14095,U_14094,U_14093,U_14092] :
( hBOOL(hAPP(hAPP(U_14097,U_14094),U_14095))
| ? [U_14091,U_14090] :
( ~ hBOOL(hAPP(hAPP(U_14097,U_14091),U_14090))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_14092,U_14093)),hAPP(hAPP(c_Product__Type_OPair(U_14092,U_14093),U_14091),U_14090)),hAPP(U_14096,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14092,U_14093),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_14092,U_14093),tc_HOL_Obool),U_14096)),hAPP(c_Set_OCollect(tc_prod(U_14092,U_14093)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14092,U_14093,tc_HOL_Obool),U_14097)))))) )
| ~ c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(U_14092,U_14093),tc_HOL_Obool),tc_fun(tc_prod(U_14092,U_14093),tc_HOL_Obool),U_14096)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14092,U_14093)),hAPP(hAPP(c_Product__Type_OPair(U_14092,U_14093),U_14094),U_14095)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_14092,U_14093),tc_HOL_Obool),U_14096))) ),
inference(variable_rename,[status(thm)],[f_3585_1]) ).
fof(f_3585_3,plain,
! [U_14097,U_14096,U_14095,U_14094,U_14093,U_14092] :
( hBOOL(hAPP(hAPP(U_14097,U_14094),U_14095))
| ? [U_14090] :
( ~ hBOOL(hAPP(hAPP(U_14097,sK362(U_14097,U_14096,U_14095,U_14094,U_14093,U_14092)),U_14090))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_14092,U_14093)),hAPP(hAPP(c_Product__Type_OPair(U_14092,U_14093),sK362(U_14097,U_14096,U_14095,U_14094,U_14093,U_14092)),U_14090)),hAPP(U_14096,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14092,U_14093),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_14092,U_14093),tc_HOL_Obool),U_14096)),hAPP(c_Set_OCollect(tc_prod(U_14092,U_14093)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14092,U_14093,tc_HOL_Obool),U_14097)))))) )
| ~ c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(U_14092,U_14093),tc_HOL_Obool),tc_fun(tc_prod(U_14092,U_14093),tc_HOL_Obool),U_14096)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14092,U_14093)),hAPP(hAPP(c_Product__Type_OPair(U_14092,U_14093),U_14094),U_14095)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_14092,U_14093),tc_HOL_Obool),U_14096))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK362]),skolemize(U_14091,sK362(U_14097,U_14096,U_14095,U_14094,U_14093,U_14092))],[f_3585_2]) ).
fof(f_3585_4,plain,
! [U_14097,U_14096,U_14095,U_14094,U_14093,U_14092] :
( hBOOL(hAPP(hAPP(U_14097,U_14094),U_14095))
| ( ~ hBOOL(hAPP(hAPP(U_14097,sK362(U_14097,U_14096,U_14095,U_14094,U_14093,U_14092)),sK363(U_14097,U_14096,U_14095,U_14094,U_14093,U_14092)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_14092,U_14093)),hAPP(hAPP(c_Product__Type_OPair(U_14092,U_14093),sK362(U_14097,U_14096,U_14095,U_14094,U_14093,U_14092)),sK363(U_14097,U_14096,U_14095,U_14094,U_14093,U_14092))),hAPP(U_14096,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14092,U_14093),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_14092,U_14093),tc_HOL_Obool),U_14096)),hAPP(c_Set_OCollect(tc_prod(U_14092,U_14093)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14092,U_14093,tc_HOL_Obool),U_14097)))))) )
| ~ c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(U_14092,U_14093),tc_HOL_Obool),tc_fun(tc_prod(U_14092,U_14093),tc_HOL_Obool),U_14096)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14092,U_14093)),hAPP(hAPP(c_Product__Type_OPair(U_14092,U_14093),U_14094),U_14095)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_14092,U_14093),tc_HOL_Obool),U_14096))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK363]),skolemize(U_14090,sK363(U_14097,U_14096,U_14095,U_14094,U_14093,U_14092))],[f_3585_3]) ).
cnf(f_3585_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14092,U_14093)),hAPP(hAPP(c_Product__Type_OPair(U_14092,U_14093),sK362(U_14097,U_14096,U_14095,U_14094,U_14093,U_14092)),sK363(U_14097,U_14096,U_14095,U_14094,U_14093,U_14092))),hAPP(U_14096,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14092,U_14093),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_14092,U_14093),tc_HOL_Obool),U_14096)),hAPP(c_Set_OCollect(tc_prod(U_14092,U_14093)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14092,U_14093,tc_HOL_Obool),U_14097))))))
| hBOOL(hAPP(hAPP(U_14097,U_14094),U_14095))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(U_14092,U_14093),tc_HOL_Obool),tc_fun(tc_prod(U_14092,U_14093),tc_HOL_Obool),U_14096)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14092,U_14093)),hAPP(hAPP(c_Product__Type_OPair(U_14092,U_14093),U_14094),U_14095)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_14092,U_14093),tc_HOL_Obool),U_14096))) ),
inference(clausify,[status(thm)],[f_3585_4]) ).
cnf(f_3585_6,plain,
( ~ hBOOL(hAPP(hAPP(U_14097,sK362(U_14097,U_14096,U_14095,U_14094,U_14093,U_14092)),sK363(U_14097,U_14096,U_14095,U_14094,U_14093,U_14092)))
| hBOOL(hAPP(hAPP(U_14097,U_14094),U_14095))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(U_14092,U_14093),tc_HOL_Obool),tc_fun(tc_prod(U_14092,U_14093),tc_HOL_Obool),U_14096)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14092,U_14093)),hAPP(hAPP(c_Product__Type_OPair(U_14092,U_14093),U_14094),U_14095)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_14092,U_14093),tc_HOL_Obool),U_14096))) ),
inference(clausify,[status(thm)],[f_3585_4]) ).
fof(f_3586_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_3586_2,plain,
! [U_14101,U_14100,U_14099] :
( ? [U_14098] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14099,U_14099)),hAPP(hAPP(c_Product__Type_OPair(U_14099,U_14099),hAPP(U_14101,hAPP(c_Nat_OSuc,U_14098))),hAPP(U_14101,U_14098))),U_14100))
| ~ c_Wellfounded_Owf(U_14099,U_14100) ),
inference(variable_rename,[status(thm)],[f_3586_1]) ).
fof(f_3586_3,plain,
! [U_14101,U_14100,U_14099] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14099,U_14099)),hAPP(hAPP(c_Product__Type_OPair(U_14099,U_14099),hAPP(U_14101,hAPP(c_Nat_OSuc,sK364(U_14101,U_14100,U_14099)))),hAPP(U_14101,sK364(U_14101,U_14100,U_14099)))),U_14100))
| ~ c_Wellfounded_Owf(U_14099,U_14100) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK364]),skolemize(U_14098,sK364(U_14101,U_14100,U_14099))],[f_3586_2]) ).
cnf(f_3586_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14099,U_14099)),hAPP(hAPP(c_Product__Type_OPair(U_14099,U_14099),hAPP(U_14101,hAPP(c_Nat_OSuc,sK364(U_14101,U_14100,U_14099)))),hAPP(U_14101,sK364(U_14101,U_14100,U_14099)))),U_14100))
| ~ c_Wellfounded_Owf(U_14099,U_14100) ),
inference(clausify,[status(thm)],[f_3586_3]) ).
fof(f_3587_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_3587_2,plain,
! [U_14106,U_14105,U_14104,U_14103,U_14102] :
( ( hAPP(c_Random_Oiterate(U_14103,U_14104,U_14102,U_14105),U_14106) = hAPP(hAPP(c_Product__Type_Oscomp(U_14104,U_14103,U_14104,tc_prod(U_14103,U_14104)),hAPP(U_14105,U_14106)),c_Random_Oiterate(U_14103,U_14104,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_14102),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_14105))
| U_14102 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ( hAPP(c_Random_Oiterate(U_14103,U_14104,U_14102,U_14105),U_14106) = hAPP(c_Product__Type_OPair(U_14103,U_14104),U_14106)
| U_14102 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(variable_rename,[status(thm)],[f_3587_1]) ).
fof(f_3587_3,plain,
( ! [U_14116,U_14114,U_14112,U_14110,U_14108] :
( hAPP(c_Random_Oiterate(U_14110,U_14112,U_14108,U_14114),U_14116) = hAPP(hAPP(c_Product__Type_Oscomp(U_14112,U_14110,U_14112,tc_prod(U_14110,U_14112)),hAPP(U_14114,U_14116)),c_Random_Oiterate(U_14110,U_14112,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_14108),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_14114))
| U_14108 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ! [U_14115,U_14113,U_14111,U_14109,U_14107] :
( hAPP(c_Random_Oiterate(U_14109,U_14111,U_14107,U_14113),U_14115) = hAPP(c_Product__Type_OPair(U_14109,U_14111),U_14115)
| U_14107 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(miniscope,[status(thm)],[f_3587_2]) ).
cnf(f_3587_4,plain,
( hAPP(c_Random_Oiterate(U_14109,U_14111,U_14107,U_14113),U_14115) = hAPP(c_Product__Type_OPair(U_14109,U_14111),U_14115)
| U_14107 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_3587_3]) ).
cnf(f_3587_5,plain,
( hAPP(c_Random_Oiterate(U_14110,U_14112,U_14108,U_14114),U_14116) = hAPP(hAPP(c_Product__Type_Oscomp(U_14112,U_14110,U_14112,tc_prod(U_14110,U_14112)),hAPP(U_14114,U_14116)),c_Random_Oiterate(U_14110,U_14112,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_14108),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_14114))
| U_14108 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_3587_3]) ).
fof(f_3588_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_3588_2,plain,
! [U_14123,U_14122,U_14121,U_14120,U_14119,U_14118,U_14117] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_14117,U_14118,U_14119,U_14120),U_14121),U_14122),U_14123) = hAPP(hAPP(U_14122,hAPP(c_Product__Type_Ofst(U_14118,U_14119),hAPP(U_14121,U_14123))),hAPP(c_Product__Type_Osnd(U_14118,U_14119),hAPP(U_14121,U_14123))),
inference(variable_rename,[status(thm)],[f_3588_1]) ).
cnf(f_3588_3,plain,
hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_14117,U_14118,U_14119,U_14120),U_14121),U_14122),U_14123) = hAPP(hAPP(U_14122,hAPP(c_Product__Type_Ofst(U_14118,U_14119),hAPP(U_14121,U_14123))),hAPP(c_Product__Type_Osnd(U_14118,U_14119),hAPP(U_14121,U_14123))),
inference(clausify,[status(thm)],[f_3588_2]) ).
fof(f_3589_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_3589_2,plain,
! [U_14128,U_14127,U_14126,U_14125,U_14124] : hAPP(hAPP(c_Product__Type_Oscomp(U_14124,U_14125,U_14124,U_14126),hAPP(c_Product__Type_OPair(U_14125,U_14124),U_14127)),U_14128) = hAPP(U_14128,U_14127),
inference(variable_rename,[status(thm)],[f_3589_1]) ).
cnf(f_3589_3,plain,
hAPP(hAPP(c_Product__Type_Oscomp(U_14124,U_14125,U_14124,U_14126),hAPP(c_Product__Type_OPair(U_14125,U_14124),U_14127)),U_14128) = hAPP(U_14128,U_14127),
inference(clausify,[status(thm)],[f_3589_2]) ).
fof(f_3590_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_3590_2,plain,
! [U_14132,U_14131,U_14130,U_14129] : hAPP(hAPP(c_Product__Type_Oscomp(U_14129,U_14130,U_14131,tc_prod(U_14130,U_14131)),U_14132),c_Product__Type_OPair(U_14130,U_14131)) = U_14132,
inference(variable_rename,[status(thm)],[f_3590_1]) ).
cnf(f_3590_3,plain,
hAPP(hAPP(c_Product__Type_Oscomp(U_14129,U_14130,U_14131,tc_prod(U_14130,U_14131)),U_14132),c_Product__Type_OPair(U_14130,U_14131)) = U_14132,
inference(clausify,[status(thm)],[f_3590_2]) ).
fof(f_3591_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_3591_2,plain,
! [U_14141,U_14140,U_14139,U_14138,U_14137,U_14136,U_14135,U_14134,U_14133] : hAPP(hAPP(c_Product__Type_Oscomp(U_14133,U_14134,U_14135,U_14136),hAPP(hAPP(c_Product__Type_Oscomp(U_14133,U_14137,U_14138,tc_prod(U_14134,U_14135)),U_14139),U_14140)),U_14141) = hAPP(hAPP(c_Product__Type_Oscomp(U_14133,U_14137,U_14138,U_14136),U_14139),hAPP(hAPP(c_COMBC(U_14137,tc_fun(U_14134,tc_fun(U_14135,U_14136)),tc_fun(U_14138,U_14136)),hAPP(hAPP(c_COMBB(tc_fun(U_14138,tc_prod(U_14134,U_14135)),tc_fun(tc_fun(U_14134,tc_fun(U_14135,U_14136)),tc_fun(U_14138,U_14136)),U_14137),c_Product__Type_Oscomp(U_14138,U_14134,U_14135,U_14136)),U_14140)),U_14141)),
inference(variable_rename,[status(thm)],[f_3591_1]) ).
cnf(f_3591_3,plain,
hAPP(hAPP(c_Product__Type_Oscomp(U_14133,U_14134,U_14135,U_14136),hAPP(hAPP(c_Product__Type_Oscomp(U_14133,U_14137,U_14138,tc_prod(U_14134,U_14135)),U_14139),U_14140)),U_14141) = hAPP(hAPP(c_Product__Type_Oscomp(U_14133,U_14137,U_14138,U_14136),U_14139),hAPP(hAPP(c_COMBC(U_14137,tc_fun(U_14134,tc_fun(U_14135,U_14136)),tc_fun(U_14138,U_14136)),hAPP(hAPP(c_COMBB(tc_fun(U_14138,tc_prod(U_14134,U_14135)),tc_fun(tc_fun(U_14134,tc_fun(U_14135,U_14136)),tc_fun(U_14138,U_14136)),U_14137),c_Product__Type_Oscomp(U_14138,U_14134,U_14135,U_14136)),U_14140)),U_14141)),
inference(clausify,[status(thm)],[f_3591_2]) ).
fof(f_3592_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_3592_2,plain,
! [U_14148,U_14147,U_14146,U_14145,U_14144,U_14143,U_14142] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_14142,U_14143,U_14144,U_14145),U_14146),U_14147),U_14148) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14143,U_14144,U_14145),U_14147),hAPP(U_14146,U_14148)),
inference(variable_rename,[status(thm)],[f_3592_1]) ).
cnf(f_3592_3,plain,
hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_14142,U_14143,U_14144,U_14145),U_14146),U_14147),U_14148) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14143,U_14144,U_14145),U_14147),hAPP(U_14146,U_14148)),
inference(clausify,[status(thm)],[f_3592_2]) ).
fof(f_3593_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_3593_2,plain,
! [U_14155,U_14154,U_14153,U_14152,U_14151,U_14150,U_14149] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_14149,U_14150,U_14151,U_14152),U_14153),U_14154),U_14155) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14150,U_14151,U_14152),U_14154),hAPP(U_14153,U_14155)),
inference(variable_rename,[status(thm)],[f_3593_1]) ).
cnf(f_3593_3,plain,
hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_14149,U_14150,U_14151,U_14152),U_14153),U_14154),U_14155) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14150,U_14151,U_14152),U_14154),hAPP(U_14153,U_14155)),
inference(clausify,[status(thm)],[f_3593_2]) ).
fof(f_3594_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_3594_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_3594_1]) ).
fof(f_3594_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_3594_2]) ).
cnf(f_3594_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_3594_3]) ).
cnf(f_3594_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_3594_3]) ).
fof(f_3595_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_3595_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_3595_1]) ).
fof(f_3595_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_3595_2]) ).
fof(f_3595_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),sK365(U_14174,U_14172,U_14165))),U_14174)) )
& hBOOL(hAPP(hAPP(c_member(U_14172),sK365(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,[sK365]),skolemize(U_14164,sK365(U_14174,U_14172,U_14165))],[f_3595_3]) ).
fof(f_3595_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),sK366(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),sK366(U_14175,U_14173))) )
& ? [U_14166] : hBOOL(hAPP(hAPP(c_member(U_14173),U_14166),sK366(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),sK365(U_14174,U_14172,U_14165))),U_14174)) )
& hBOOL(hAPP(hAPP(c_member(U_14172),sK365(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,[sK366]),skolemize(U_14169,sK366(U_14175,U_14173))],[f_3595_4]) ).
fof(f_3595_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),sK366(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),sK366(U_14175,U_14173))) )
& hBOOL(hAPP(hAPP(c_member(U_14173),sK367(U_14175,U_14173)),sK366(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),sK365(U_14174,U_14172,U_14165))),U_14174)) )
& hBOOL(hAPP(hAPP(c_member(U_14172),sK365(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,[sK367]),skolemize(U_14166,sK367(U_14175,U_14173))],[f_3595_5]) ).
fof(f_3595_7,plain,
( ! [U_14175,U_14173] :
( c_Wellfounded_Owf(U_14173,U_14175)
| ( ! [U_14168] :
( ( hBOOL(hAPP(hAPP(c_member(U_14173),sK368(U_14175,U_14173,U_14168)),sK366(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),sK368(U_14175,U_14173,U_14168)),U_14168)),U_14175)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_14173),U_14168),sK366(U_14175,U_14173))) )
& hBOOL(hAPP(hAPP(c_member(U_14173),sK367(U_14175,U_14173)),sK366(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),sK365(U_14174,U_14172,U_14165))),U_14174)) )
& hBOOL(hAPP(hAPP(c_member(U_14172),sK365(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,[sK368]),skolemize(U_14167,sK368(U_14175,U_14173,U_14168))],[f_3595_6]) ).
cnf(f_3595_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_14172),sK365(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_3595_7]) ).
cnf(f_3595_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),sK365(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_3595_7]) ).
cnf(f_3595_10,plain,
( hBOOL(hAPP(hAPP(c_member(U_14173),sK367(U_14175,U_14173)),sK366(U_14175,U_14173)))
| c_Wellfounded_Owf(U_14173,U_14175) ),
inference(clausify,[status(thm)],[f_3595_7]) ).
cnf(f_3595_11,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14173,U_14173)),hAPP(hAPP(c_Product__Type_OPair(U_14173,U_14173),sK368(U_14175,U_14173,U_14168)),U_14168)),U_14175))
| ~ hBOOL(hAPP(hAPP(c_member(U_14173),U_14168),sK366(U_14175,U_14173)))
| c_Wellfounded_Owf(U_14173,U_14175) ),
inference(clausify,[status(thm)],[f_3595_7]) ).
cnf(f_3595_12,plain,
( hBOOL(hAPP(hAPP(c_member(U_14173),sK368(U_14175,U_14173,U_14168)),sK366(U_14175,U_14173)))
| ~ hBOOL(hAPP(hAPP(c_member(U_14173),U_14168),sK366(U_14175,U_14173)))
| c_Wellfounded_Owf(U_14173,U_14175) ),
inference(clausify,[status(thm)],[f_3595_7]) ).
fof(f_3596_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_3596_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_3596_1]) ).
cnf(f_3596_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_3596_2]) ).
fof(f_3597_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_3597_2,plain,
c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(clausify,[status(thm)],[f_3597_1]) ).
fof(f_3598_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_3598_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_3598_1]) ).
fof(f_3598_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_3598_2]) ).
fof(f_3598_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),sK369(U_14185,U_14183)),sK369(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,[sK369]),skolemize(U_14179,sK369(U_14185,U_14183))],[f_3598_3]) ).
cnf(f_3598_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_3598_4]) ).
cnf(f_3598_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),sK369(U_14185,U_14183)),sK369(U_14185,U_14183))),c_Transitive__Closure_Otrancl(U_14183,U_14185))) ),
inference(clausify,[status(thm)],[f_3598_4]) ).
fof(f_3599_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_3599_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_3599_1]) ).
cnf(f_3599_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_3599_2]) ).
fof(f_3600_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_3600_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_3600_1]) ).
cnf(f_3600_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_3600_2]) ).
fof(f_3601_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_3601_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_3601_1]) ).
cnf(f_3601_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_3601_2]) ).
fof(f_3602_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_3602_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_3602_1]) ).
cnf(f_3602_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_3602_2]) ).
fof(f_3603_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_3603_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_3603_1]) ).
cnf(f_3603_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_3603_2]) ).
fof(f_3604_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_3604_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_3604_1]) ).
cnf(f_3604_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_3604_2]) ).
fof(f_3605_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_3605_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_3605_1]) ).
fof(f_3605_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_3605_2]) ).
cnf(f_3605_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_3605_3]) ).
cnf(f_3605_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_3605_3]) ).
fof(f_3606_1,plain,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),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_3606_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_3606_1]) ).
cnf(f_3606_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_3606_2]) ).
fof(f_3607_1,plain,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_Transitive__Closure_Otrancl__into__trancl]) ).
fof(f_3607_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_3607_1]) ).
cnf(f_3607_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_3607_2]) ).
fof(f_3608_1,plain,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_trancl__into__trancl2]) ).
fof(f_3608_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_3608_1]) ).
cnf(f_3608_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_3608_2]) ).
fof(f_3609_1,plain,
! [V_c_2,V_R_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_R_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_R_2)) ),
inference(fof_nnf,[status(thm)],[fact_r__r__into__trancl]) ).
fof(f_3609_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_3609_1]) ).
cnf(f_3609_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_3609_2]) ).
fof(f_3610_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_3610_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_3610_1]) ).
cnf(f_3610_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_3610_2]) ).
fof(f_3611_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_3611_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_3611_1]) ).
cnf(f_3611_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_3611_2]) ).
fof(f_3612_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_3612_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_3612_1]) ).
cnf(f_3612_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_3612_2]) ).
fof(f_3613_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_3613_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_3613_1]) ).
cnf(f_3613_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_3613_2]) ).
fof(f_3614_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_3614_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_3614_1]) ).
cnf(f_3614_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_3614_2]) ).
fof(f_3615_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_3615_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_3615_1]) ).
fof(f_3615_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_3615_2]) ).
cnf(f_3615_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_3615_3]) ).
cnf(f_3615_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_3615_3]) ).
fof(f_3616_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_3616_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_3616_1]) ).
cnf(f_3616_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_3616_2]) ).
fof(f_3617_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_3617_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_3617_1]) ).
cnf(f_3617_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_3617_2]) ).
fof(f_3618_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_3618_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_3618_1]) ).
cnf(f_3618_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_3618_2]) ).
fof(f_3619_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_3619_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_3619_1]) ).
cnf(f_3619_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_3619_2]) ).
fof(f_3620_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_3620_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_3620_1]) ).
cnf(f_3620_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_3620_2]) ).
fof(f_3621_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_3621_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_3621_1]) ).
cnf(f_3621_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_3621_2]) ).
fof(f_3622_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_3622_2,plain,
! [U_14271,U_14270] : c_Transitive__Closure_Otrancl(U_14270,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14270,U_14270),tc_HOL_Obool)),U_14271),c_Relation_OId(U_14270))) = c_Transitive__Closure_Ortrancl(U_14270,U_14271),
inference(variable_rename,[status(thm)],[f_3622_1]) ).
cnf(f_3622_3,plain,
c_Transitive__Closure_Otrancl(U_14270,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14270,U_14270),tc_HOL_Obool)),U_14271),c_Relation_OId(U_14270))) = c_Transitive__Closure_Ortrancl(U_14270,U_14271),
inference(clausify,[status(thm)],[f_3622_2]) ).
fof(f_3623_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_3623_2,plain,
! [U_14273,U_14272] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14272,U_14272),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14272,U_14273)),c_Relation_OId(U_14272)) = c_Transitive__Closure_Ortrancl(U_14272,U_14273),
inference(variable_rename,[status(thm)],[f_3623_1]) ).
cnf(f_3623_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14272,U_14272),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14272,U_14273)),c_Relation_OId(U_14272)) = c_Transitive__Closure_Ortrancl(U_14272,U_14273),
inference(clausify,[status(thm)],[f_3623_2]) ).
fof(f_3624_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_3624_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_3624_1]) ).
cnf(f_3624_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_3624_2]) ).
fof(f_3625_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_3625_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_3625_1]) ).
cnf(f_3625_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_3625_2]) ).
fof(f_3626_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_3626_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_3626_1]) ).
cnf(f_3626_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_3626_2]) ).
fof(f_3627_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_3627_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_3627_1]) ).
cnf(f_3627_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_3627_2]) ).
fof(f_3628_1,plain,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),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_3628_2,plain,
! [U_14286,U_14285,U_14284,U_14283,U_14282] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14282,U_14282)),hAPP(hAPP(c_Product__Type_OPair(U_14282,U_14282),U_14283),U_14286)),c_Transitive__Closure_Ortrancl(U_14282,U_14285)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14282,U_14282)),hAPP(hAPP(c_Product__Type_OPair(U_14282,U_14282),U_14284),U_14286)),c_Transitive__Closure_Ortrancl(U_14282,U_14285)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14282,U_14282)),hAPP(hAPP(c_Product__Type_OPair(U_14282,U_14282),U_14283),U_14284)),c_Transitive__Closure_Ortrancl(U_14282,U_14285))) ),
inference(variable_rename,[status(thm)],[f_3628_1]) ).
cnf(f_3628_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14282,U_14282)),hAPP(hAPP(c_Product__Type_OPair(U_14282,U_14282),U_14283),U_14286)),c_Transitive__Closure_Ortrancl(U_14282,U_14285)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14282,U_14282)),hAPP(hAPP(c_Product__Type_OPair(U_14282,U_14282),U_14284),U_14286)),c_Transitive__Closure_Ortrancl(U_14282,U_14285)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14282,U_14282)),hAPP(hAPP(c_Product__Type_OPair(U_14282,U_14282),U_14283),U_14284)),c_Transitive__Closure_Ortrancl(U_14282,U_14285))) ),
inference(clausify,[status(thm)],[f_3628_2]) ).
fof(f_3629_1,plain,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_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_3629_2,plain,
! [U_14291,U_14290,U_14289,U_14288,U_14287] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14287,U_14287)),hAPP(hAPP(c_Product__Type_OPair(U_14287,U_14287),U_14288),U_14291)),c_Transitive__Closure_Ortrancl(U_14287,U_14290)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14287,U_14287)),hAPP(hAPP(c_Product__Type_OPair(U_14287,U_14287),U_14289),U_14291)),U_14290))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14287,U_14287)),hAPP(hAPP(c_Product__Type_OPair(U_14287,U_14287),U_14288),U_14289)),c_Transitive__Closure_Ortrancl(U_14287,U_14290))) ),
inference(variable_rename,[status(thm)],[f_3629_1]) ).
cnf(f_3629_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14287,U_14287)),hAPP(hAPP(c_Product__Type_OPair(U_14287,U_14287),U_14288),U_14291)),c_Transitive__Closure_Ortrancl(U_14287,U_14290)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14287,U_14287)),hAPP(hAPP(c_Product__Type_OPair(U_14287,U_14287),U_14289),U_14291)),U_14290))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14287,U_14287)),hAPP(hAPP(c_Product__Type_OPair(U_14287,U_14287),U_14288),U_14289)),c_Transitive__Closure_Ortrancl(U_14287,U_14290))) ),
inference(clausify,[status(thm)],[f_3629_2]) ).
fof(f_3630_1,plain,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__into__rtrancl]) ).
fof(f_3630_2,plain,
! [U_14296,U_14295,U_14294,U_14293,U_14292] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14292,U_14292)),hAPP(hAPP(c_Product__Type_OPair(U_14292,U_14292),U_14293),U_14296)),c_Transitive__Closure_Ortrancl(U_14292,U_14295)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14292,U_14292)),hAPP(hAPP(c_Product__Type_OPair(U_14292,U_14292),U_14294),U_14296)),c_Transitive__Closure_Ortrancl(U_14292,U_14295)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14292,U_14292)),hAPP(hAPP(c_Product__Type_OPair(U_14292,U_14292),U_14293),U_14294)),U_14295)) ),
inference(variable_rename,[status(thm)],[f_3630_1]) ).
cnf(f_3630_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14292,U_14292)),hAPP(hAPP(c_Product__Type_OPair(U_14292,U_14292),U_14293),U_14296)),c_Transitive__Closure_Ortrancl(U_14292,U_14295)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14292,U_14292)),hAPP(hAPP(c_Product__Type_OPair(U_14292,U_14292),U_14294),U_14296)),c_Transitive__Closure_Ortrancl(U_14292,U_14295)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14292,U_14292)),hAPP(hAPP(c_Product__Type_OPair(U_14292,U_14292),U_14293),U_14294)),U_14295)) ),
inference(clausify,[status(thm)],[f_3630_2]) ).
fof(f_3631_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_3631_2,plain,
! [U_14298,U_14297] : c_Transitive__Closure_Ortrancl(U_14297,c_Transitive__Closure_Ortrancl(U_14297,U_14298)) = c_Transitive__Closure_Ortrancl(U_14297,U_14298),
inference(variable_rename,[status(thm)],[f_3631_1]) ).
cnf(f_3631_3,plain,
c_Transitive__Closure_Ortrancl(U_14297,c_Transitive__Closure_Ortrancl(U_14297,U_14298)) = c_Transitive__Closure_Ortrancl(U_14297,U_14298),
inference(clausify,[status(thm)],[f_3631_2]) ).
fof(f_3632_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_3632_2,plain,
! [U_14300,U_14299] : c_Relation_Orefl__on(U_14299,c_Orderings_Otop__class_Otop(tc_fun(U_14299,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14299,U_14300)),
inference(variable_rename,[status(thm)],[f_3632_1]) ).
cnf(f_3632_3,plain,
c_Relation_Orefl__on(U_14299,c_Orderings_Otop__class_Otop(tc_fun(U_14299,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14299,U_14300)),
inference(clausify,[status(thm)],[f_3632_2]) ).
fof(f_3633_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_3633_2,plain,
! [U_14302,U_14301] : c_Transitive__Closure_Ortrancl(U_14301,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14301,U_14301),tc_HOL_Obool)),U_14302),c_Relation_OId(U_14301))) = c_Transitive__Closure_Ortrancl(U_14301,U_14302),
inference(variable_rename,[status(thm)],[f_3633_1]) ).
cnf(f_3633_3,plain,
c_Transitive__Closure_Ortrancl(U_14301,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14301,U_14301),tc_HOL_Obool)),U_14302),c_Relation_OId(U_14301))) = c_Transitive__Closure_Ortrancl(U_14301,U_14302),
inference(clausify,[status(thm)],[f_3633_2]) ).
fof(f_3634_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_3634_2,plain,
! [U_14305,U_14304,U_14303] :
( hAPP(c_Relation_OImage(U_14303,U_14303,c_Transitive__Closure_Ortrancl(U_14303,U_14304)),U_14305) = U_14305
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14303,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14303,U_14303,U_14304),U_14305)),U_14305)) ),
inference(variable_rename,[status(thm)],[f_3634_1]) ).
cnf(f_3634_3,plain,
( hAPP(c_Relation_OImage(U_14303,U_14303,c_Transitive__Closure_Ortrancl(U_14303,U_14304)),U_14305) = U_14305
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14303,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14303,U_14303,U_14304),U_14305)),U_14305)) ),
inference(clausify,[status(thm)],[f_3634_2]) ).
fof(f_3635_1,plain,
! [V_R_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
inference(fof_nnf,[status(thm)],[fact_rtrancl__reflcl__absorb]) ).
fof(f_3635_2,plain,
! [U_14307,U_14306] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14306,U_14306),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14306,U_14307)),c_Relation_OId(U_14306)) = c_Transitive__Closure_Ortrancl(U_14306,U_14307),
inference(variable_rename,[status(thm)],[f_3635_1]) ).
cnf(f_3635_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14306,U_14306),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14306,U_14307)),c_Relation_OId(U_14306)) = c_Transitive__Closure_Ortrancl(U_14306,U_14307),
inference(clausify,[status(thm)],[f_3635_2]) ).
fof(f_3636_1,plain,
! [V_S_2,V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) = c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)),
inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__rtrancl]) ).
fof(f_3636_2,plain,
! [U_14310,U_14309,U_14308] : c_Transitive__Closure_Ortrancl(U_14308,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14308,U_14308),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14308,U_14309)),c_Transitive__Closure_Ortrancl(U_14308,U_14310))) = c_Transitive__Closure_Ortrancl(U_14308,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14308,U_14308),tc_HOL_Obool)),U_14309),U_14310)),
inference(variable_rename,[status(thm)],[f_3636_1]) ).
cnf(f_3636_3,plain,
c_Transitive__Closure_Ortrancl(U_14308,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14308,U_14308),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14308,U_14309)),c_Transitive__Closure_Ortrancl(U_14308,U_14310))) = c_Transitive__Closure_Ortrancl(U_14308,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14308,U_14308),tc_HOL_Obool)),U_14309),U_14310)),
inference(clausify,[status(thm)],[f_3636_2]) ).
fof(f_3637_1,plain,
! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
inference(fof_nnf,[status(thm)],[fact_rtrancl__reflcl]) ).
fof(f_3637_2,plain,
! [U_14312,U_14311] : c_Transitive__Closure_Ortrancl(U_14311,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14311,U_14311),tc_HOL_Obool)),U_14312),c_Relation_OId(U_14311))) = c_Transitive__Closure_Ortrancl(U_14311,U_14312),
inference(variable_rename,[status(thm)],[f_3637_1]) ).
cnf(f_3637_3,plain,
c_Transitive__Closure_Ortrancl(U_14311,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14311,U_14311),tc_HOL_Obool)),U_14312),c_Relation_OId(U_14311))) = c_Transitive__Closure_Ortrancl(U_14311,U_14312),
inference(clausify,[status(thm)],[f_3637_2]) ).
fof(f_3638_1,plain,
! [V_S_2,V_R_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))),
inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__subset]) ).
fof(f_3638_2,plain,
! [U_14315,U_14314,U_14313] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14313,U_14313),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14313,U_14313),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14313,U_14314)),c_Transitive__Closure_Ortrancl(U_14313,U_14315))),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),U_14315)))),
inference(variable_rename,[status(thm)],[f_3638_1]) ).
cnf(f_3638_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14313,U_14313),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14313,U_14313),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14313,U_14314)),c_Transitive__Closure_Ortrancl(U_14313,U_14315))),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),U_14315)))),
inference(clausify,[status(thm)],[f_3638_2]) ).
fof(f_3639_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_3639_2,plain,
! [U_14318,U_14317,U_14316] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14316,U_14316),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14316,U_14317)),c_Transitive__Closure_Ortrancl(U_14316,U_14318)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14316,U_14316),tc_HOL_Obool)),U_14317),U_14318)) ),
inference(variable_rename,[status(thm)],[f_3639_1]) ).
cnf(f_3639_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14316,U_14316),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14316,U_14317)),c_Transitive__Closure_Ortrancl(U_14316,U_14318)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14316,U_14316),tc_HOL_Obool)),U_14317),U_14318)) ),
inference(clausify,[status(thm)],[f_3639_2]) ).
fof(f_3640_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_3640_2,plain,
! [U_14321,U_14320,U_14319] :
( c_Transitive__Closure_Ortrancl(U_14319,U_14321) = c_Transitive__Closure_Ortrancl(U_14319,U_14320)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14319,U_14319),tc_HOL_Obool)),U_14321),c_Transitive__Closure_Ortrancl(U_14319,U_14320)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14319,U_14319),tc_HOL_Obool)),U_14320),U_14321)) ),
inference(variable_rename,[status(thm)],[f_3640_1]) ).
cnf(f_3640_3,plain,
( c_Transitive__Closure_Ortrancl(U_14319,U_14321) = c_Transitive__Closure_Ortrancl(U_14319,U_14320)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14319,U_14319),tc_HOL_Obool)),U_14321),c_Transitive__Closure_Ortrancl(U_14319,U_14320)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14319,U_14319),tc_HOL_Obool)),U_14320),U_14321)) ),
inference(clausify,[status(thm)],[f_3640_2]) ).
fof(f_3641_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_3641_2,plain,
! [U_14324,U_14323,U_14322] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14322,U_14322),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14322,U_14323)),c_Transitive__Closure_Ortrancl(U_14322,U_14324)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14322,U_14322),tc_HOL_Obool)),U_14323),c_Transitive__Closure_Ortrancl(U_14322,U_14324))) ),
inference(variable_rename,[status(thm)],[f_3641_1]) ).
cnf(f_3641_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14322,U_14322),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14322,U_14323)),c_Transitive__Closure_Ortrancl(U_14322,U_14324)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14322,U_14322),tc_HOL_Obool)),U_14323),c_Transitive__Closure_Ortrancl(U_14322,U_14324))) ),
inference(clausify,[status(thm)],[f_3641_2]) ).
fof(f_3642_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_3642_2,plain,
! [U_14328,U_14327,U_14326,U_14325] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14325,U_14325)),U_14326),c_Transitive__Closure_Ortrancl(U_14325,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14325,U_14325),tc_HOL_Obool)),U_14327),U_14328))))
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14325,U_14325)),U_14326),c_Transitive__Closure_Ortrancl(U_14325,U_14328)))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14325,U_14325)),U_14326),c_Transitive__Closure_Ortrancl(U_14325,U_14327))) ) ),
inference(variable_rename,[status(thm)],[f_3642_1]) ).
cnf(f_3642_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14325,U_14325)),U_14326),c_Transitive__Closure_Ortrancl(U_14325,U_14327)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_14325,U_14325)),U_14326),c_Transitive__Closure_Ortrancl(U_14325,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14325,U_14325),tc_HOL_Obool)),U_14327),U_14328)))) ),
inference(clausify,[status(thm)],[f_3642_2]) ).
cnf(f_3642_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14325,U_14325)),U_14326),c_Transitive__Closure_Ortrancl(U_14325,U_14328)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_14325,U_14325)),U_14326),c_Transitive__Closure_Ortrancl(U_14325,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14325,U_14325),tc_HOL_Obool)),U_14327),U_14328)))) ),
inference(clausify,[status(thm)],[f_3642_2]) ).
fof(f_3643_1,plain,
! [V_r_2,V_s_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),V_s_2)) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__Int__subset]) ).
fof(f_3643_2,plain,
! [U_14331,U_14330,U_14329] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14329,U_14329),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14329,U_14331)),U_14330))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14329,U_14329),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14329,U_14329,U_14329),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14329,U_14329),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14329,U_14331)),U_14330)),U_14331)),U_14330))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14329,U_14329),tc_HOL_Obool)),c_Relation_OId(U_14329)),U_14330)) ),
inference(variable_rename,[status(thm)],[f_3643_1]) ).
cnf(f_3643_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14329,U_14329),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14329,U_14331)),U_14330))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14329,U_14329),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14329,U_14329,U_14329),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14329,U_14329),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14329,U_14331)),U_14330)),U_14331)),U_14330))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14329,U_14329),tc_HOL_Obool)),c_Relation_OId(U_14329)),U_14330)) ),
inference(clausify,[status(thm)],[f_3643_2]) ).
fof(f_3644_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_3644_2,plain,
! [U_14333,U_14332] : hAPP(hAPP(c_Relation_Orel__comp(U_14332,U_14332,U_14332),c_Transitive__Closure_Ortrancl(U_14332,U_14333)),c_Transitive__Closure_Ortrancl(U_14332,U_14333)) = c_Transitive__Closure_Ortrancl(U_14332,U_14333),
inference(variable_rename,[status(thm)],[f_3644_1]) ).
cnf(f_3644_3,plain,
hAPP(hAPP(c_Relation_Orel__comp(U_14332,U_14332,U_14332),c_Transitive__Closure_Ortrancl(U_14332,U_14333)),c_Transitive__Closure_Ortrancl(U_14332,U_14333)) = c_Transitive__Closure_Ortrancl(U_14332,U_14333),
inference(clausify,[status(thm)],[f_3644_2]) ).
fof(f_3645_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_3645_2,plain,
! [U_14335,U_14334] : hAPP(hAPP(c_Relation_Orel__comp(U_14334,U_14334,U_14334),U_14335),c_Transitive__Closure_Ortrancl(U_14334,U_14335)) = hAPP(hAPP(c_Relation_Orel__comp(U_14334,U_14334,U_14334),c_Transitive__Closure_Ortrancl(U_14334,U_14335)),U_14335),
inference(variable_rename,[status(thm)],[f_3645_1]) ).
cnf(f_3645_3,plain,
hAPP(hAPP(c_Relation_Orel__comp(U_14334,U_14334,U_14334),U_14335),c_Transitive__Closure_Ortrancl(U_14334,U_14335)) = hAPP(hAPP(c_Relation_Orel__comp(U_14334,U_14334,U_14334),c_Transitive__Closure_Ortrancl(U_14334,U_14335)),U_14335),
inference(clausify,[status(thm)],[f_3645_2]) ).
fof(f_3646_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_3646_2,plain,
! [U_14337,U_14336] : c_Transitive__Closure_Ortrancl(U_14336,U_14337) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14336,U_14336),tc_HOL_Obool)),c_Relation_OId(U_14336)),hAPP(hAPP(c_Relation_Orel__comp(U_14336,U_14336,U_14336),c_Transitive__Closure_Ortrancl(U_14336,U_14337)),U_14337)),
inference(variable_rename,[status(thm)],[f_3646_1]) ).
cnf(f_3646_3,plain,
c_Transitive__Closure_Ortrancl(U_14336,U_14337) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14336,U_14336),tc_HOL_Obool)),c_Relation_OId(U_14336)),hAPP(hAPP(c_Relation_Orel__comp(U_14336,U_14336,U_14336),c_Transitive__Closure_Ortrancl(U_14336,U_14337)),U_14337)),
inference(clausify,[status(thm)],[f_3646_2]) ).
fof(f_3647_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_3647_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_3647_1]) ).
cnf(f_3647_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_3647_2]) ).
fof(f_3648_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_3648_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_3648_1]) ).
cnf(f_3648_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_3648_2]) ).
fof(f_3649_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_3649_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_3649_1]) ).
cnf(f_3649_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_3649_2]) ).
fof(f_3650_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_3650_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_3650_1]) ).
cnf(f_3650_3,plain,
hAPP(c_Relation_OImage(U_14345,U_14345,c_Relation_OId(U_14345)),U_14346) = U_14346,
inference(clausify,[status(thm)],[f_3650_2]) ).
fof(f_3651_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_3651_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_3651_1]) ).
fof(f_3651_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_3651_2]) ).
cnf(f_3651_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_3651_3]) ).
cnf(f_3651_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_3651_3]) ).
fof(f_3652_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_3652_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_3652_1]) ).
cnf(f_3652_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_3652_2]) ).
fof(f_3653_1,plain,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_trancl__rtrancl__trancl]) ).
fof(f_3653_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_3653_1]) ).
cnf(f_3653_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_3653_2]) ).
fof(f_3654_1,plain,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl1]) ).
fof(f_3654_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_3654_1]) ).
cnf(f_3654_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_3654_2]) ).
fof(f_3655_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_3655_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_3655_1]) ).
cnf(f_3655_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_3655_2]) ).
cnf(f_3655_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_3655_2]) ).
fof(f_3656_1,plain,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl2]) ).
fof(f_3656_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_3656_1]) ).
cnf(f_3656_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_3656_2]) ).
fof(f_3657_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_3657_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_3657_1]) ).
fof(f_3657_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_3657_2]) ).
cnf(f_3657_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_3657_3]) ).
cnf(f_3657_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_3657_3]) ).
cnf(f_3657_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_3657_3]) ).
cnf(f_3657_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_3657_3]) ).
fof(f_3658_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_3658_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_3658_1]) ).
cnf(f_3658_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_3658_2]) ).
fof(f_3659_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_3659_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_3659_1]) ).
cnf(f_3659_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_3659_2]) ).
fof(f_3660_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_3660_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_3660_1]) ).
cnf(f_3660_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_3660_2]) ).
fof(f_3661_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_3661_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_3661_1]) ).
fof(f_3662_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_3662_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_3662_1]) ).
cnf(f_3662_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_3662_2]) ).
cnf(f_3662_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_3662_2]) ).
fof(f_3663_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_3663_2,plain,
! [U_14402,U_14401,U_14400,U_14399] :
( hBOOL(hAPP(hAPP(c_member(U_14399),U_14402),c_Wellfounded_Oacc(U_14399,U_14401)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14399,U_14399)),hAPP(hAPP(c_Product__Type_OPair(U_14399,U_14399),U_14402),U_14400)),c_Transitive__Closure_Ortrancl(U_14399,U_14401)))
| ~ hBOOL(hAPP(hAPP(c_member(U_14399),U_14400),c_Wellfounded_Oacc(U_14399,U_14401))) ),
inference(variable_rename,[status(thm)],[f_3663_1]) ).
cnf(f_3663_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_14399),U_14402),c_Wellfounded_Oacc(U_14399,U_14401)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14399,U_14399)),hAPP(hAPP(c_Product__Type_OPair(U_14399,U_14399),U_14402),U_14400)),c_Transitive__Closure_Ortrancl(U_14399,U_14401)))
| ~ hBOOL(hAPP(hAPP(c_member(U_14399),U_14400),c_Wellfounded_Oacc(U_14399,U_14401))) ),
inference(clausify,[status(thm)],[f_3663_2]) ).
fof(f_3664_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_3664_2,plain,
! [U_14406,U_14405,U_14404,U_14403] :
( hBOOL(hAPP(hAPP(c_member(U_14403),U_14404),c_Wellfounded_Oacc(U_14403,U_14406)))
| ~ hBOOL(hAPP(hAPP(c_member(U_14403),U_14405),c_Wellfounded_Oacc(U_14403,U_14406)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14403,U_14403)),hAPP(hAPP(c_Product__Type_OPair(U_14403,U_14403),U_14404),U_14405)),c_Transitive__Closure_Ortrancl(U_14403,U_14406))) ),
inference(variable_rename,[status(thm)],[f_3664_1]) ).
cnf(f_3664_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_14403),U_14404),c_Wellfounded_Oacc(U_14403,U_14406)))
| ~ hBOOL(hAPP(hAPP(c_member(U_14403),U_14405),c_Wellfounded_Oacc(U_14403,U_14406)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14403,U_14403)),hAPP(hAPP(c_Product__Type_OPair(U_14403,U_14403),U_14404),U_14405)),c_Transitive__Closure_Ortrancl(U_14403,U_14406))) ),
inference(clausify,[status(thm)],[f_3664_2]) ).
fof(f_3665_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_3665_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_3665_1]) ).
fof(f_3665_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_3665_2]) ).
cnf(f_3665_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_3665_3]) ).
cnf(f_3665_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_3665_3]) ).
cnf(f_3665_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_3665_3]) ).
fof(f_3666_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_3666_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_3666_1]) ).
fof(f_3666_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_3666_2]) ).
cnf(f_3666_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_3666_3]) ).
cnf(f_3666_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_3666_3]) ).
cnf(f_3666_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_3666_3]) ).
fof(f_3667_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_3667_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_3667_1]) ).
cnf(f_3667_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_3667_2]) ).
fof(f_3668_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_3668_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_3668_1]) ).
cnf(f_3668_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_3668_2]) ).
fof(f_3669_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_3669_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_3669_1]) ).
cnf(f_3669_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_3669_2]) ).
fof(f_3670_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_3670_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_3670_1]) ).
fof(f_3670_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_3670_2]) ).
cnf(f_3670_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_3670_3]) ).
cnf(f_3670_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_3670_3]) ).
fof(f_3671_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_3671_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_3671_1]) ).
cnf(f_3671_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_3671_2]) ).
fof(f_3672_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_3672_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_3672_1]) ).
cnf(f_3672_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_3672_2]) ).
fof(f_3673_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_3673_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_3673_1]) ).
fof(f_3673_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,sK370(U_14455,U_14454,U_14453,U_14452,U_14451)))),hAPP(U_14452,sK370(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,[sK370]),skolemize(U_14450,sK370(U_14455,U_14454,U_14453,U_14452,U_14451))],[f_3673_2]) ).
cnf(f_3673_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,sK370(U_14455,U_14454,U_14453,U_14452,U_14451)))),hAPP(U_14452,sK370(U_14455,U_14454,U_14453,U_14452,U_14451)))),c_Transitive__Closure_Ortrancl(U_14451,U_14453))) ),
inference(clausify,[status(thm)],[f_3673_3]) ).
fof(f_3674_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_3674_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_3674_1]) ).
cnf(f_3674_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_3674_2]) ).
fof(f_3675_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_3675_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_3675_1]) ).
cnf(f_3675_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_3675_2]) ).
fof(f_3676_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_3676_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_3676_1]) ).
fof(f_3676_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_3676_2]) ).
cnf(f_3676_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_3676_3]) ).
cnf(f_3676_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_3676_3]) ).
fof(f_3677_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_3677_2,plain,
! [U_14466,U_14465] : hAPP(c_Relation_OField(U_14465),hAPP(c_Relation_Oconverse(U_14465,U_14465),U_14466)) = hAPP(c_Relation_OField(U_14465),U_14466),
inference(variable_rename,[status(thm)],[f_3677_1]) ).
cnf(f_3677_3,plain,
hAPP(c_Relation_OField(U_14465),hAPP(c_Relation_Oconverse(U_14465,U_14465),U_14466)) = hAPP(c_Relation_OField(U_14465),U_14466),
inference(clausify,[status(thm)],[f_3677_2]) ).
fof(f_3678_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_3678_2,plain,
! [U_14469,U_14468,U_14467] : hAPP(c_Relation_Oconverse(U_14467,U_14468),hAPP(c_Relation_Oconverse(U_14468,U_14467),U_14469)) = U_14469,
inference(variable_rename,[status(thm)],[f_3678_1]) ).
cnf(f_3678_3,plain,
hAPP(c_Relation_Oconverse(U_14467,U_14468),hAPP(c_Relation_Oconverse(U_14468,U_14467),U_14469)) = U_14469,
inference(clausify,[status(thm)],[f_3678_2]) ).
fof(f_3679_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_3679_2,plain,
! [U_14473,U_14472,U_14471,U_14470] : hAPP(c_Relation_Oconverse(U_14470,U_14471),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14470,U_14471),tc_HOL_Obool)),U_14472),U_14473)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14471,U_14470),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_14470,U_14471),U_14472)),hAPP(c_Relation_Oconverse(U_14470,U_14471),U_14473)),
inference(variable_rename,[status(thm)],[f_3679_1]) ).
cnf(f_3679_3,plain,
hAPP(c_Relation_Oconverse(U_14470,U_14471),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14470,U_14471),tc_HOL_Obool)),U_14472),U_14473)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14471,U_14470),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_14470,U_14471),U_14472)),hAPP(c_Relation_Oconverse(U_14470,U_14471),U_14473)),
inference(clausify,[status(thm)],[f_3679_2]) ).
fof(f_3680_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_3680_2,plain,
! [U_14476,U_14475,U_14474] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14474,U_14475)),hAPP(c_Relation_Oconverse(U_14475,U_14474),U_14476)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14475,U_14474)),U_14476)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14475,U_14474)),U_14476))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14474,U_14475)),hAPP(c_Relation_Oconverse(U_14475,U_14474),U_14476))) ) ),
inference(variable_rename,[status(thm)],[f_3680_1]) ).
fof(f_3680_3,plain,
( ! [U_14482,U_14480,U_14478] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14478,U_14480)),hAPP(c_Relation_Oconverse(U_14480,U_14478),U_14482)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14480,U_14478)),U_14482)) )
& ! [U_14481,U_14479,U_14477] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14479,U_14477)),U_14481))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14477,U_14479)),hAPP(c_Relation_Oconverse(U_14479,U_14477),U_14481))) ) ),
inference(miniscope,[status(thm)],[f_3680_2]) ).
cnf(f_3680_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14479,U_14477)),U_14481))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14477,U_14479)),hAPP(c_Relation_Oconverse(U_14479,U_14477),U_14481))) ),
inference(clausify,[status(thm)],[f_3680_3]) ).
cnf(f_3680_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14478,U_14480)),hAPP(c_Relation_Oconverse(U_14480,U_14478),U_14482)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14480,U_14478)),U_14482)) ),
inference(clausify,[status(thm)],[f_3680_3]) ).
fof(f_3681_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_3681_2,plain,
! [U_14486,U_14485,U_14484,U_14483] : hAPP(c_Relation_Oconverse(U_14483,U_14483),hAPP(hAPP(c_Relation_Oinv__image(U_14484,U_14483),U_14485),U_14486)) = hAPP(hAPP(c_Relation_Oinv__image(U_14484,U_14483),hAPP(c_Relation_Oconverse(U_14484,U_14484),U_14485)),U_14486),
inference(variable_rename,[status(thm)],[f_3681_1]) ).
cnf(f_3681_3,plain,
hAPP(c_Relation_Oconverse(U_14483,U_14483),hAPP(hAPP(c_Relation_Oinv__image(U_14484,U_14483),U_14485),U_14486)) = hAPP(hAPP(c_Relation_Oinv__image(U_14484,U_14483),hAPP(c_Relation_Oconverse(U_14484,U_14484),U_14485)),U_14486),
inference(clausify,[status(thm)],[f_3681_2]) ).
fof(f_3682_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_3682_2,plain,
! [U_14488,U_14487] : hAPP(c_Relation_Oconverse(U_14487,U_14487),c_Relation_OId__on(U_14487,U_14488)) = c_Relation_OId__on(U_14487,U_14488),
inference(variable_rename,[status(thm)],[f_3682_1]) ).
cnf(f_3682_3,plain,
hAPP(c_Relation_Oconverse(U_14487,U_14487),c_Relation_OId__on(U_14487,U_14488)) = c_Relation_OId__on(U_14487,U_14488),
inference(clausify,[status(thm)],[f_3682_2]) ).
fof(f_3683_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_3683_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_3683_1]) ).
fof(f_3683_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_3683_2]) ).
cnf(f_3683_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_3683_3]) ).
cnf(f_3683_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_3683_3]) ).
fof(f_3684_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_3684_2,plain,
! [U_14502,U_14501,U_14500,U_14499,U_14498] : hAPP(c_Relation_Oconverse(U_14498,U_14499),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14500,tc_fun(tc_prod(U_14498,U_14499),tc_HOL_Obool)),U_14501),U_14502)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14500,tc_fun(tc_prod(U_14499,U_14498),tc_HOL_Obool)),U_14501),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14498,U_14499),tc_HOL_Obool),tc_fun(tc_prod(U_14499,U_14498),tc_HOL_Obool),U_14500),c_Relation_Oconverse(U_14498,U_14499)),U_14502)),
inference(variable_rename,[status(thm)],[f_3684_1]) ).
cnf(f_3684_3,plain,
hAPP(c_Relation_Oconverse(U_14498,U_14499),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14500,tc_fun(tc_prod(U_14498,U_14499),tc_HOL_Obool)),U_14501),U_14502)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14500,tc_fun(tc_prod(U_14499,U_14498),tc_HOL_Obool)),U_14501),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14498,U_14499),tc_HOL_Obool),tc_fun(tc_prod(U_14499,U_14498),tc_HOL_Obool),U_14500),c_Relation_Oconverse(U_14498,U_14499)),U_14502)),
inference(clausify,[status(thm)],[f_3684_2]) ).
fof(f_3685_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_3685_2,plain,
! [U_14507,U_14506,U_14505,U_14504,U_14503] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14503,U_14504)),hAPP(hAPP(c_Product__Type_OPair(U_14503,U_14504),U_14505),U_14506)),hAPP(c_Relation_Oconverse(U_14504,U_14503),U_14507)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14504,U_14503)),hAPP(hAPP(c_Product__Type_OPair(U_14504,U_14503),U_14506),U_14505)),U_14507)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14504,U_14503)),hAPP(hAPP(c_Product__Type_OPair(U_14504,U_14503),U_14506),U_14505)),U_14507))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14503,U_14504)),hAPP(hAPP(c_Product__Type_OPair(U_14503,U_14504),U_14505),U_14506)),hAPP(c_Relation_Oconverse(U_14504,U_14503),U_14507))) ) ),
inference(variable_rename,[status(thm)],[f_3685_1]) ).
fof(f_3685_3,plain,
( ! [U_14517,U_14515,U_14513,U_14511,U_14509] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14509,U_14511)),hAPP(hAPP(c_Product__Type_OPair(U_14509,U_14511),U_14513),U_14515)),hAPP(c_Relation_Oconverse(U_14511,U_14509),U_14517)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14511,U_14509)),hAPP(hAPP(c_Product__Type_OPair(U_14511,U_14509),U_14515),U_14513)),U_14517)) )
& ! [U_14516,U_14514,U_14512,U_14510,U_14508] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14510,U_14508)),hAPP(hAPP(c_Product__Type_OPair(U_14510,U_14508),U_14514),U_14512)),U_14516))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14508,U_14510)),hAPP(hAPP(c_Product__Type_OPair(U_14508,U_14510),U_14512),U_14514)),hAPP(c_Relation_Oconverse(U_14510,U_14508),U_14516))) ) ),
inference(miniscope,[status(thm)],[f_3685_2]) ).
cnf(f_3685_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14510,U_14508)),hAPP(hAPP(c_Product__Type_OPair(U_14510,U_14508),U_14514),U_14512)),U_14516))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14508,U_14510)),hAPP(hAPP(c_Product__Type_OPair(U_14508,U_14510),U_14512),U_14514)),hAPP(c_Relation_Oconverse(U_14510,U_14508),U_14516))) ),
inference(clausify,[status(thm)],[f_3685_3]) ).
cnf(f_3685_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14509,U_14511)),hAPP(hAPP(c_Product__Type_OPair(U_14509,U_14511),U_14513),U_14515)),hAPP(c_Relation_Oconverse(U_14511,U_14509),U_14517)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14511,U_14509)),hAPP(hAPP(c_Product__Type_OPair(U_14511,U_14509),U_14515),U_14513)),U_14517)) ),
inference(clausify,[status(thm)],[f_3685_3]) ).
fof(f_3686_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_3686_2,plain,
! [U_14522,U_14521,U_14520,U_14519,U_14518] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14519,U_14518)),hAPP(hAPP(c_Product__Type_OPair(U_14519,U_14518),U_14521),U_14520)),hAPP(c_Relation_Oconverse(U_14518,U_14519),U_14522)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14518,U_14519)),hAPP(hAPP(c_Product__Type_OPair(U_14518,U_14519),U_14520),U_14521)),U_14522)) ),
inference(variable_rename,[status(thm)],[f_3686_1]) ).
cnf(f_3686_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14519,U_14518)),hAPP(hAPP(c_Product__Type_OPair(U_14519,U_14518),U_14521),U_14520)),hAPP(c_Relation_Oconverse(U_14518,U_14519),U_14522)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14518,U_14519)),hAPP(hAPP(c_Product__Type_OPair(U_14518,U_14519),U_14520),U_14521)),U_14522)) ),
inference(clausify,[status(thm)],[f_3686_2]) ).
fof(f_3687_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_3687_2,plain,
! [U_14527,U_14526,U_14525,U_14524,U_14523] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14524,U_14523)),hAPP(hAPP(c_Product__Type_OPair(U_14524,U_14523),U_14526),U_14525)),U_14527))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14523,U_14524)),hAPP(hAPP(c_Product__Type_OPair(U_14523,U_14524),U_14525),U_14526)),hAPP(c_Relation_Oconverse(U_14524,U_14523),U_14527))) ),
inference(variable_rename,[status(thm)],[f_3687_1]) ).
cnf(f_3687_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14524,U_14523)),hAPP(hAPP(c_Product__Type_OPair(U_14524,U_14523),U_14526),U_14525)),U_14527))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14523,U_14524)),hAPP(hAPP(c_Product__Type_OPair(U_14523,U_14524),U_14525),U_14526)),hAPP(c_Relation_Oconverse(U_14524,U_14523),U_14527))) ),
inference(clausify,[status(thm)],[f_3687_2]) ).
fof(f_3688_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_3688_2,plain,
! [U_14531,U_14530,U_14529,U_14528] : hAPP(c_Relation_Oconverse(U_14528,U_14529),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14528,U_14529),tc_HOL_Obool)),U_14530),U_14531)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14529,U_14528),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_14528,U_14529),U_14530)),hAPP(c_Relation_Oconverse(U_14528,U_14529),U_14531)),
inference(variable_rename,[status(thm)],[f_3688_1]) ).
cnf(f_3688_3,plain,
hAPP(c_Relation_Oconverse(U_14528,U_14529),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14528,U_14529),tc_HOL_Obool)),U_14530),U_14531)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14529,U_14528),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_14528,U_14529),U_14530)),hAPP(c_Relation_Oconverse(U_14528,U_14529),U_14531)),
inference(clausify,[status(thm)],[f_3688_2]) ).
fof(f_3689_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_3689_2,plain,
! [U_14536,U_14535,U_14534,U_14533,U_14532] : hAPP(c_Relation_Oconverse(U_14532,U_14533),hAPP(hAPP(c_Relation_Orel__comp(U_14532,U_14534,U_14533),U_14535),U_14536)) = hAPP(hAPP(c_Relation_Orel__comp(U_14533,U_14534,U_14532),hAPP(c_Relation_Oconverse(U_14534,U_14533),U_14536)),hAPP(c_Relation_Oconverse(U_14532,U_14534),U_14535)),
inference(variable_rename,[status(thm)],[f_3689_1]) ).
cnf(f_3689_3,plain,
hAPP(c_Relation_Oconverse(U_14532,U_14533),hAPP(hAPP(c_Relation_Orel__comp(U_14532,U_14534,U_14533),U_14535),U_14536)) = hAPP(hAPP(c_Relation_Orel__comp(U_14533,U_14534,U_14532),hAPP(c_Relation_Oconverse(U_14534,U_14533),U_14536)),hAPP(c_Relation_Oconverse(U_14532,U_14534),U_14535)),
inference(clausify,[status(thm)],[f_3689_2]) ).
fof(f_3690_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_3690_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_OSUPR(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_OSUPR(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_3690_1]) ).
cnf(f_3690_3,plain,
hAPP(c_Relation_Oconverse(U_14537,U_14538),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(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_OSUPR(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_3690_2]) ).
fof(f_3691_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_3691_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_3691_1]) ).
cnf(f_3691_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_3691_2]) ).
fof(f_3692_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_3692_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_3692_1]) ).
cnf(f_3692_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_3692_2]) ).
fof(f_3693_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_3693_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_3693_1]) ).
cnf(f_3693_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_3693_2]) ).
fof(f_3694_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_3694_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_3694_1]) ).
cnf(f_3694_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_3694_2]) ).
fof(f_3695_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_3695_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_3695_1]) ).
cnf(f_3695_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_3695_2]) ).
fof(f_3696_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_3696_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_3696_1]) ).
cnf(f_3696_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_3696_2]) ).
fof(f_3697_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_3697_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_3697_1]) ).
cnf(f_3697_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_3697_2]) ).
fof(f_3698_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_3698_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_3698_1]) ).
cnf(f_3698_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_3698_2]) ).
fof(f_3699_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_3699_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_3699_1]) ).
cnf(f_3699_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_3699_2]) ).
fof(f_3700_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_3700_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_3700_1]) ).
cnf(f_3700_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_3700_2]) ).
fof(f_3701_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_3701_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_3701_1]) ).
fof(f_3701_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_3701_2]) ).
cnf(f_3701_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_3701_3]) ).
cnf(f_3701_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_3701_3]) ).
fof(f_3702_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_3702_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_3702_1]) ).
cnf(f_3702_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_3702_2]) ).
fof(f_3703_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_3703_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_3703_1]) ).
cnf(f_3703_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_3703_2]) ).
fof(f_3704_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_3704_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_3704_1]) ).
cnf(f_3704_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_3704_2]) ).
fof(f_3705_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_3705_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_3705_1]) ).
cnf(f_3705_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_3705_2]) ).
fof(f_3706_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_3706_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_3706_1]) ).
cnf(f_3706_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_3706_2]) ).
fof(f_3707_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_3707_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_3707_1]) ).
fof(f_3707_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_3707_2]) ).
cnf(f_3707_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_3707_3]) ).
cnf(f_3707_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_3707_3]) ).
fof(f_3708_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_3708_2,plain,
! [U_14615] : c_Relation_Osingle__valued(U_14615,U_14615,c_Relation_OId(U_14615)),
inference(variable_rename,[status(thm)],[f_3708_1]) ).
cnf(f_3708_3,plain,
c_Relation_Osingle__valued(U_14615,U_14615,c_Relation_OId(U_14615)),
inference(clausify,[status(thm)],[f_3708_2]) ).
fof(f_3709_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_3709_2,plain,
! [U_14619,U_14618,U_14617,U_14616] :
( c_Relation_Osingle__valued(U_14616,U_14617,U_14618)
| ~ c_Relation_Osingle__valued(U_14616,U_14617,U_14619)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14616,U_14617),tc_HOL_Obool)),U_14618),U_14619)) ),
inference(variable_rename,[status(thm)],[f_3709_1]) ).
cnf(f_3709_3,plain,
( c_Relation_Osingle__valued(U_14616,U_14617,U_14618)
| ~ c_Relation_Osingle__valued(U_14616,U_14617,U_14619)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14616,U_14617),tc_HOL_Obool)),U_14618),U_14619)) ),
inference(clausify,[status(thm)],[f_3709_2]) ).
fof(f_3710_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_3710_2,plain,
! [U_14624,U_14623,U_14622,U_14621,U_14620] :
( c_Relation_Osingle__valued(U_14620,U_14623,hAPP(hAPP(c_Relation_Orel__comp(U_14620,U_14621,U_14623),U_14622),U_14624))
| ~ c_Relation_Osingle__valued(U_14621,U_14623,U_14624)
| ~ c_Relation_Osingle__valued(U_14620,U_14621,U_14622) ),
inference(variable_rename,[status(thm)],[f_3710_1]) ).
cnf(f_3710_3,plain,
( c_Relation_Osingle__valued(U_14620,U_14623,hAPP(hAPP(c_Relation_Orel__comp(U_14620,U_14621,U_14623),U_14622),U_14624))
| ~ c_Relation_Osingle__valued(U_14621,U_14623,U_14624)
| ~ c_Relation_Osingle__valued(U_14620,U_14621,U_14622) ),
inference(clausify,[status(thm)],[f_3710_2]) ).
fof(f_3711_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_3711_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_3711_1]) ).
cnf(f_3711_3,plain,
c_Relation_Osingle__valued(U_14625,U_14625,c_Relation_OId__on(U_14625,U_14626)),
inference(clausify,[status(thm)],[f_3711_2]) ).
fof(f_3712_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_3712_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_3712_1]) ).
cnf(f_3712_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_3712_2]) ).
fof(f_3713_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_3713_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_3713_1]) ).
fof(f_3713_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_3713_2]) ).
cnf(f_3713_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_3713_3]) ).
cnf(f_3713_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_3713_3]) ).
fof(f_3714_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_3714_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_3714_1]) ).
cnf(f_3714_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_3714_2]) ).
fof(f_3715_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_3715_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_3715_1]) ).
fof(f_3715_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_3715_2]) ).
fof(f_3715_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),sK371(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),sK371(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,[sK371]),skolemize(U_14649,sK371(U_14658,U_14656,U_14654))],[f_3715_3]) ).
fof(f_3715_5,plain,
( ! [U_14658,U_14656,U_14654] :
( c_Relation_Osingle__valued(U_14654,U_14656,U_14658)
| ( ? [U_14647] :
( sK372(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),sK371(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),sK371(U_14658,U_14656,U_14654)),sK372(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,[sK372]),skolemize(U_14648,sK372(U_14658,U_14656,U_14654))],[f_3715_4]) ).
fof(f_3715_6,plain,
( ! [U_14658,U_14656,U_14654] :
( c_Relation_Osingle__valued(U_14654,U_14656,U_14658)
| ( sK372(U_14658,U_14656,U_14654) != sK373(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),sK371(U_14658,U_14656,U_14654)),sK373(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),sK371(U_14658,U_14656,U_14654)),sK372(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,[sK373]),skolemize(U_14647,sK373(U_14658,U_14656,U_14654))],[f_3715_5]) ).
cnf(f_3715_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_3715_6]) ).
cnf(f_3715_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14654,U_14656)),hAPP(hAPP(c_Product__Type_OPair(U_14654,U_14656),sK371(U_14658,U_14656,U_14654)),sK372(U_14658,U_14656,U_14654))),U_14658))
| c_Relation_Osingle__valued(U_14654,U_14656,U_14658) ),
inference(clausify,[status(thm)],[f_3715_6]) ).
cnf(f_3715_9,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14654,U_14656)),hAPP(hAPP(c_Product__Type_OPair(U_14654,U_14656),sK371(U_14658,U_14656,U_14654)),sK373(U_14658,U_14656,U_14654))),U_14658))
| c_Relation_Osingle__valued(U_14654,U_14656,U_14658) ),
inference(clausify,[status(thm)],[f_3715_6]) ).
cnf(f_3715_10,plain,
( sK372(U_14658,U_14656,U_14654) != sK373(U_14658,U_14656,U_14654)
| c_Relation_Osingle__valued(U_14654,U_14656,U_14658) ),
inference(clausify,[status(thm)],[f_3715_6]) ).
fof(f_3716_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_3716_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_3716_1]) ).
fof(f_3716_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_3716_2]) ).
fof(f_3716_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),sK374(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),sK374(U_14671,U_14669,U_14667)),U_14661)),U_14671))
& sK374(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),sK374(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,[sK374]),skolemize(U_14662,sK374(U_14671,U_14669,U_14667))],[f_3716_3]) ).
fof(f_3716_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),sK375(U_14671,U_14669,U_14667)),sK374(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),sK374(U_14671,U_14669,U_14667)),sK375(U_14671,U_14669,U_14667))),U_14671))
& sK374(U_14671,U_14669,U_14667) != sK375(U_14671,U_14669,U_14667)
& hBOOL(hAPP(hAPP(c_member(U_14667),sK375(U_14671,U_14669,U_14667)),U_14669))
& hBOOL(hAPP(hAPP(c_member(U_14667),sK374(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,[sK375]),skolemize(U_14661,sK375(U_14671,U_14669,U_14667))],[f_3716_4]) ).
cnf(f_3716_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_3716_5]) ).
cnf(f_3716_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_14667),sK374(U_14671,U_14669,U_14667)),U_14669))
| c_Relation_Ototal__on(U_14667,U_14669,U_14671) ),
inference(clausify,[status(thm)],[f_3716_5]) ).
cnf(f_3716_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_14667),sK375(U_14671,U_14669,U_14667)),U_14669))
| c_Relation_Ototal__on(U_14667,U_14669,U_14671) ),
inference(clausify,[status(thm)],[f_3716_5]) ).
cnf(f_3716_9,plain,
( sK374(U_14671,U_14669,U_14667) != sK375(U_14671,U_14669,U_14667)
| c_Relation_Ototal__on(U_14667,U_14669,U_14671) ),
inference(clausify,[status(thm)],[f_3716_5]) ).
cnf(f_3716_10,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14667,U_14667)),hAPP(hAPP(c_Product__Type_OPair(U_14667,U_14667),sK374(U_14671,U_14669,U_14667)),sK375(U_14671,U_14669,U_14667))),U_14671))
| c_Relation_Ototal__on(U_14667,U_14669,U_14671) ),
inference(clausify,[status(thm)],[f_3716_5]) ).
cnf(f_3716_11,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14667,U_14667)),hAPP(hAPP(c_Product__Type_OPair(U_14667,U_14667),sK375(U_14671,U_14669,U_14667)),sK374(U_14671,U_14669,U_14667))),U_14671))
| c_Relation_Ototal__on(U_14667,U_14669,U_14671) ),
inference(clausify,[status(thm)],[f_3716_5]) ).
fof(f_3717_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_3717_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_3717_1]) ).
cnf(f_3717_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_3717_2]) ).
fof(f_3718_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_3718_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_3718_1]) ).
cnf(f_3718_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_3718_2]) ).
fof(f_3719_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_3719_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_3719_1]) ).
cnf(f_3719_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_3719_2]) ).
fof(f_3720_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_3720_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_3720_1]) ).
fof(f_3720_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),sK376(U_14687,U_14686)),sK376(U_14687,U_14686))),c_Transitive__Closure_Otrancl(U_14686,U_14687))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK376]),skolemize(U_14685,sK376(U_14687,U_14686))],[f_3720_2]) ).
cnf(f_3720_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),sK376(U_14687,U_14686)),sK376(U_14687,U_14686))),c_Transitive__Closure_Otrancl(U_14686,U_14687))) ),
inference(clausify,[status(thm)],[f_3720_3]) ).
fof(f_3721_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_3721_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_3721_1]) ).
cnf(f_3721_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_3721_2]) ).
fof(f_3722_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_3722_2,plain,
! [U_14694,U_14693,U_14692,U_14691] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(U_14691,U_14692),tc_fun(U_14691,U_14692)),U_14693),c_Fun_Ocomp(U_14692,U_14692,U_14691,U_14694)) = c_Fun_Ocomp(U_14692,U_14692,U_14691,hAPP(hAPP(c_Nat_Ocompow(U_14692,U_14692),U_14693),U_14694)),
inference(variable_rename,[status(thm)],[f_3722_1]) ).
cnf(f_3722_3,plain,
hAPP(hAPP(c_Nat_Ocompow(tc_fun(U_14691,U_14692),tc_fun(U_14691,U_14692)),U_14693),c_Fun_Ocomp(U_14692,U_14692,U_14691,U_14694)) = c_Fun_Ocomp(U_14692,U_14692,U_14691,hAPP(hAPP(c_Nat_Ocompow(U_14692,U_14692),U_14693),U_14694)),
inference(clausify,[status(thm)],[f_3722_2]) ).
fof(f_3723_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_3723_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_3723_1]) ).
cnf(f_3723_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_3723_2]) ).
fof(f_3724_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_3724_2,plain,
! [U_14702,U_14701,U_14700,U_14699] : hAPP(hAPP(c_Nat_Ocompow(U_14699,U_14699),U_14700),hAPP(hAPP(c_Nat_Ocompow(U_14699,U_14699),U_14701),U_14702)) = hAPP(hAPP(c_Nat_Ocompow(U_14699,U_14699),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_14701),U_14700)),U_14702),
inference(variable_rename,[status(thm)],[f_3724_1]) ).
cnf(f_3724_3,plain,
hAPP(hAPP(c_Nat_Ocompow(U_14699,U_14699),U_14700),hAPP(hAPP(c_Nat_Ocompow(U_14699,U_14699),U_14701),U_14702)) = hAPP(hAPP(c_Nat_Ocompow(U_14699,U_14699),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_14701),U_14700)),U_14702),
inference(clausify,[status(thm)],[f_3724_2]) ).
fof(f_3725_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_3725_2,plain,
! [U_14705,U_14704,U_14703] :
( c_Wellfounded_Owf(U_14703,U_14705)
| ~ c_Wellfounded_Owf(U_14703,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14703,U_14703),tc_HOL_Obool),U_14704),U_14705)) ),
inference(variable_rename,[status(thm)],[f_3725_1]) ).
cnf(f_3725_3,plain,
( c_Wellfounded_Owf(U_14703,U_14705)
| ~ c_Wellfounded_Owf(U_14703,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14703,U_14703),tc_HOL_Obool),U_14704),U_14705)) ),
inference(clausify,[status(thm)],[f_3725_2]) ).
fof(f_3726_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_3726_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_3726_1]) ).
cnf(f_3726_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_3726_2]) ).
fof(f_3727_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_3727_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_3727_1]) ).
cnf(f_3727_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_3727_2]) ).
fof(f_3728_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_3728_2,plain,
! [U_14715,U_14714,U_14713] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14713,U_14713)),U_14714),c_Transitive__Closure_Ortrancl(U_14713,U_14715)))
| ! [U_14712] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14713,U_14713)),U_14714),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14713,U_14713),tc_HOL_Obool),U_14712),U_14715))) )
& ( ? [U_14711] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14713,U_14713)),U_14714),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14713,U_14713),tc_HOL_Obool),U_14711),U_14715)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14713,U_14713)),U_14714),c_Transitive__Closure_Ortrancl(U_14713,U_14715))) ) ),
inference(variable_rename,[status(thm)],[f_3728_1]) ).
fof(f_3728_3,plain,
( ! [U_14721,U_14719,U_14717] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14717,U_14717)),U_14719),c_Transitive__Closure_Ortrancl(U_14717,U_14721)))
| ! [U_14712] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14717,U_14717)),U_14719),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14717,U_14717),tc_HOL_Obool),U_14712),U_14721))) )
& ! [U_14720,U_14718,U_14716] :
( ? [U_14711] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14716,U_14716)),U_14718),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14716,U_14716),tc_HOL_Obool),U_14711),U_14720)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14716,U_14716)),U_14718),c_Transitive__Closure_Ortrancl(U_14716,U_14720))) ) ),
inference(miniscope,[status(thm)],[f_3728_2]) ).
fof(f_3728_4,plain,
( ! [U_14721,U_14719,U_14717] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14717,U_14717)),U_14719),c_Transitive__Closure_Ortrancl(U_14717,U_14721)))
| ! [U_14712] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14717,U_14717)),U_14719),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14717,U_14717),tc_HOL_Obool),U_14712),U_14721))) )
& ! [U_14720,U_14718,U_14716] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14716,U_14716)),U_14718),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14716,U_14716),tc_HOL_Obool),sK377(U_14720,U_14718,U_14716)),U_14720)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14716,U_14716)),U_14718),c_Transitive__Closure_Ortrancl(U_14716,U_14720))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK377]),skolemize(U_14711,sK377(U_14720,U_14718,U_14716))],[f_3728_3]) ).
cnf(f_3728_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14716,U_14716)),U_14718),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14716,U_14716),tc_HOL_Obool),sK377(U_14720,U_14718,U_14716)),U_14720)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14716,U_14716)),U_14718),c_Transitive__Closure_Ortrancl(U_14716,U_14720))) ),
inference(clausify,[status(thm)],[f_3728_4]) ).
cnf(f_3728_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14717,U_14717)),U_14719),c_Transitive__Closure_Ortrancl(U_14717,U_14721)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14717,U_14717)),U_14719),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14717,U_14717),tc_HOL_Obool),U_14712),U_14721))) ),
inference(clausify,[status(thm)],[f_3728_4]) ).
fof(f_3729_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_3729_2,plain,
! [U_14725,U_14724,U_14723,U_14722] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14722,U_14722)),U_14723),c_Transitive__Closure_Ortrancl(U_14722,U_14725)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14722,U_14722)),U_14723),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14722,U_14722),tc_HOL_Obool),U_14724),U_14725))) ),
inference(variable_rename,[status(thm)],[f_3729_1]) ).
cnf(f_3729_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14722,U_14722)),U_14723),c_Transitive__Closure_Ortrancl(U_14722,U_14725)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14722,U_14722)),U_14723),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14722,U_14722),tc_HOL_Obool),U_14724),U_14725))) ),
inference(clausify,[status(thm)],[f_3729_2]) ).
fof(f_3730_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_3730_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_3730_1]) ).
cnf(f_3730_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_3730_2]) ).
fof(f_3731_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_3731_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_3731_1]) ).
cnf(f_3731_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_3731_2]) ).
fof(f_3732_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_3732_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_3732_1]) ).
cnf(f_3732_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_3732_2]) ).
fof(f_3733_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_3733_2,plain,
! [U_14738,U_14737,U_14736,U_14735] :
( U_14736 = U_14737
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14735,U_14735)),hAPP(hAPP(c_Product__Type_OPair(U_14735,U_14735),U_14736),U_14737)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14735,U_14735),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14738))) ),
inference(variable_rename,[status(thm)],[f_3733_1]) ).
fof(f_3733_3,plain,
! [U_14738,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_14737)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14735,U_14735),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14738)))
| U_14736 = U_14737 ),
inference(miniscope,[status(thm)],[f_3733_2]) ).
cnf(f_3733_4,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_14737)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14735,U_14735),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14738)))
| U_14736 = U_14737 ),
inference(clausify,[status(thm)],[f_3733_3]) ).
fof(f_3734_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_3734_2,plain,
! [U_14741,U_14740,U_14739] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14739,U_14739)),hAPP(hAPP(c_Product__Type_OPair(U_14739,U_14739),U_14740),U_14740)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14739,U_14739),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14741))),
inference(variable_rename,[status(thm)],[f_3734_1]) ).
cnf(f_3734_3,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(U_14739,U_14739)),hAPP(hAPP(c_Product__Type_OPair(U_14739,U_14739),U_14740),U_14740)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14739,U_14739),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14741))),
inference(clausify,[status(thm)],[f_3734_2]) ).
fof(f_3735_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_3735_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_14746)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14742,U_14742),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14747)),U_14745)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14742,U_14742)),hAPP(hAPP(c_Product__Type_OPair(U_14742,U_14742),U_14744),U_14746)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14742,U_14742),tc_HOL_Obool),U_14747),U_14745)))
| ~ 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)),U_14745)) ),
inference(variable_rename,[status(thm)],[f_3735_1]) ).
cnf(f_3735_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_14746)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14742,U_14742),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14747)),U_14745)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14742,U_14742)),hAPP(hAPP(c_Product__Type_OPair(U_14742,U_14742),U_14744),U_14746)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14742,U_14742),tc_HOL_Obool),U_14747),U_14745)))
| ~ 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)),U_14745)) ),
inference(clausify,[status(thm)],[f_3735_2]) ).
fof(f_3736_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_3736_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_14753)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14748,U_14748),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14751)),U_14752)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14748,U_14748)),hAPP(hAPP(c_Product__Type_OPair(U_14748,U_14748),U_14750),U_14753)),U_14752))
| ~ 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)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14748,U_14748),tc_HOL_Obool),U_14751),U_14752))) ),
inference(variable_rename,[status(thm)],[f_3736_1]) ).
cnf(f_3736_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_14753)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14748,U_14748),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14751)),U_14752)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14748,U_14748)),hAPP(hAPP(c_Product__Type_OPair(U_14748,U_14748),U_14750),U_14753)),U_14752))
| ~ 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)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14748,U_14748),tc_HOL_Obool),U_14751),U_14752))) ),
inference(clausify,[status(thm)],[f_3736_2]) ).
fof(f_3737_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_3737_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_3737_1]) ).
cnf(f_3737_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_3737_2]) ).
fof(f_3738_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_3738_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_3738_1]) ).
cnf(f_3738_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_3738_2]) ).
fof(f_3739_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_3739_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_3739_1]) ).
cnf(f_3739_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_3739_2]) ).
fof(f_3740_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_3740_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_3740_1]) ).
fof(f_3740_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_3740_2]) ).
fof(f_3740_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),sK378(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)),sK378(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,[sK378]),skolemize(U_14763,sK378(U_14772,U_14770,U_14768))],[f_3740_3]) ).
cnf(f_3740_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK378(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_3740_4]) ).
cnf(f_3740_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),sK378(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_3740_4]) ).
cnf(f_3740_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_3740_4]) ).
fof(f_3741_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_3741_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_3741_1]) ).
cnf(f_3741_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_3741_2]) ).
fof(f_3742_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_3742_2,plain,
! [U_14776] : c_Nat_Ofunpow(U_14776) = c_Nat_Ocompow(U_14776,U_14776),
inference(variable_rename,[status(thm)],[f_3742_1]) ).
cnf(f_3742_3,plain,
c_Nat_Ofunpow(U_14776) = c_Nat_Ocompow(U_14776,U_14776),
inference(clausify,[status(thm)],[f_3742_2]) ).
fof(f_3743_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_3743_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_3743_1]) ).
fof(f_3743_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),sK379(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),sK379(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,[sK379]),skolemize(U_14778,sK379(U_14783,U_14782,U_14781,U_14780,U_14779))],[f_3743_2]) ).
fof(f_3743_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),sK379(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),sK379(U_14783,U_14782,U_14781,U_14780,U_14779))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14779,U_14779),tc_HOL_Obool),sK380(U_14783,U_14782,U_14781,U_14780,U_14779)),U_14783)))
& U_14782 = hAPP(c_Nat_OSuc,sK380(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,[sK380]),skolemize(U_14777,sK380(U_14783,U_14782,U_14781,U_14780,U_14779))],[f_3743_3]) ).
cnf(f_3743_5,plain,
( U_14782 = hAPP(c_Nat_OSuc,sK380(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_3743_4]) ).
cnf(f_3743_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),sK379(U_14783,U_14782,U_14781,U_14780,U_14779))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14779,U_14779),tc_HOL_Obool),sK380(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_3743_4]) ).
cnf(f_3743_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),sK379(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_3743_4]) ).
cnf(f_3743_8,plain,
( U_14782 = hAPP(c_Nat_OSuc,sK380(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_3743_4]) ).
cnf(f_3743_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),sK379(U_14783,U_14782,U_14781,U_14780,U_14779))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14779,U_14779),tc_HOL_Obool),sK380(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_3743_4]) ).
cnf(f_3743_10,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),sK379(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_3743_4]) ).
fof(f_3744_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_3744_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_3744_1]) ).
fof(f_3744_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),sK381(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),sK381(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,[sK381]),skolemize(U_14785,sK381(U_14790,U_14789,U_14788,U_14787,U_14786))],[f_3744_2]) ).
fof(f_3744_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),sK381(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),sK382(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),sK381(U_14790,U_14789,U_14788,U_14787,U_14786))),U_14790))
& U_14789 = hAPP(c_Nat_OSuc,sK382(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,[sK382]),skolemize(U_14784,sK382(U_14790,U_14789,U_14788,U_14787,U_14786))],[f_3744_3]) ).
cnf(f_3744_5,plain,
( U_14789 = hAPP(c_Nat_OSuc,sK382(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_3744_4]) ).
cnf(f_3744_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),sK381(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_3744_4]) ).
cnf(f_3744_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14786,U_14786)),hAPP(hAPP(c_Product__Type_OPair(U_14786,U_14786),sK381(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),sK382(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_3744_4]) ).
cnf(f_3744_8,plain,
( U_14789 = hAPP(c_Nat_OSuc,sK382(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_3744_4]) ).
cnf(f_3744_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),sK381(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_3744_4]) ).
cnf(f_3744_10,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14786,U_14786)),hAPP(hAPP(c_Product__Type_OPair(U_14786,U_14786),sK381(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),sK382(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_3744_4]) ).
fof(f_3745_1,plain,
! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2)))
| ? [B_x] :
( ? [B_y] :
( B_y != B_x
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_Q_2)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2),V_Q_2)))) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__separator__converseE]) ).
fof(f_3745_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_3745_1]) ).
fof(f_3745_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 != sK383(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),sK383(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),sK383(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,[sK383]),skolemize(U_14792,sK383(U_14797,U_14796,U_14795,U_14794,U_14793))],[f_3745_2]) ).
fof(f_3745_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)))
| ( sK384(U_14797,U_14796,U_14795,U_14794,U_14793) != sK383(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),sK384(U_14797,U_14796,U_14795,U_14794,U_14793)),sK383(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),sK383(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,[sK384]),skolemize(U_14791,sK384(U_14797,U_14796,U_14795,U_14794,U_14793))],[f_3745_3]) ).
cnf(f_3745_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14793,U_14793)),hAPP(hAPP(c_Product__Type_OPair(U_14793,U_14793),sK383(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_3745_4]) ).
cnf(f_3745_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14793,U_14793)),hAPP(hAPP(c_Product__Type_OPair(U_14793,U_14793),sK384(U_14797,U_14796,U_14795,U_14794,U_14793)),sK383(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_3745_4]) ).
cnf(f_3745_7,plain,
( sK384(U_14797,U_14796,U_14795,U_14794,U_14793) != sK383(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_3745_4]) ).
fof(f_3746_1,plain,
! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2)))
| ? [B_x] :
( ? [B_y] :
( B_x != B_y
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_Q_2)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_b,V_P_2))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2),V_Q_2)))) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__separatorE]) ).
fof(f_3746_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_3746_1]) ).
fof(f_3746_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] :
( sK385(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),sK385(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),sK385(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,[sK385]),skolemize(U_14799,sK385(U_14804,U_14803,U_14802,U_14801,U_14800))],[f_3746_2]) ).
fof(f_3746_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)))
| ( sK385(U_14804,U_14803,U_14802,U_14801,U_14800) != sK386(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),sK385(U_14804,U_14803,U_14802,U_14801,U_14800)),sK386(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),sK385(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,[sK386]),skolemize(U_14798,sK386(U_14804,U_14803,U_14802,U_14801,U_14800))],[f_3746_3]) ).
cnf(f_3746_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),sK385(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_3746_4]) ).
cnf(f_3746_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14800,U_14800)),hAPP(hAPP(c_Product__Type_OPair(U_14800,U_14800),sK385(U_14804,U_14803,U_14802,U_14801,U_14800)),sK386(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_3746_4]) ).
cnf(f_3746_7,plain,
( sK385(U_14804,U_14803,U_14802,U_14801,U_14800) != sK386(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_3746_4]) ).
fof(f_3747_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_3747_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_3747_1]) ).
fof(f_3747_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),sK387(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),sK387(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,[sK387]),skolemize(U_14805,sK387(U_14810,U_14809,U_14808,U_14807,U_14806))],[f_3747_2]) ).
cnf(f_3747_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),sK387(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_3747_3]) ).
cnf(f_3747_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14806,U_14806)),hAPP(hAPP(c_Product__Type_OPair(U_14806,U_14806),sK387(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_3747_3]) ).
fof(f_3748_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_3748_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_3748_1]) ).
fof(f_3748_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),sK388(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),sK388(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,[sK388]),skolemize(U_14811,sK388(U_14816,U_14815,U_14814,U_14813,U_14812))],[f_3748_2]) ).
cnf(f_3748_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),sK388(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_3748_3]) ).
cnf(f_3748_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14812,U_14812)),hAPP(hAPP(c_Product__Type_OPair(U_14812,U_14812),sK388(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_3748_3]) ).
fof(f_3749_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_3749_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_3749_1]) ).
fof(f_3749_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),sK389(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),sK389(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,[sK389]),skolemize(U_14817,sK389(U_14822,U_14821,U_14820,U_14819,U_14818))],[f_3749_2]) ).
cnf(f_3749_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),sK389(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_3749_3]) ).
cnf(f_3749_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14818,U_14818)),hAPP(hAPP(c_Product__Type_OPair(U_14818,U_14818),sK389(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_3749_3]) ).
fof(f_3750_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_3750_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_3750_1]) ).
fof(f_3750_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),sK390(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),sK390(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,[sK390]),skolemize(U_14823,sK390(U_14827,U_14826,U_14825,U_14824))],[f_3750_2]) ).
cnf(f_3750_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),sK390(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_3750_3]) ).
cnf(f_3750_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14824,U_14824)),hAPP(hAPP(c_Product__Type_OPair(U_14824,U_14824),sK390(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_3750_3]) ).
fof(f_3751_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_3751_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_3751_1]) ).
fof(f_3751_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),sK391(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),sK391(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,[sK391]),skolemize(U_14828,sK391(U_14832,U_14831,U_14830,U_14829))],[f_3751_2]) ).
cnf(f_3751_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),sK391(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_3751_3]) ).
cnf(f_3751_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14829,U_14829)),hAPP(hAPP(c_Product__Type_OPair(U_14829,U_14829),sK391(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_3751_3]) ).
fof(f_3752_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_3752_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_3752_1]) ).
fof(f_3752_3,plain,
! [U_14835,U_14834] :
( U_14835 = hAPP(hAPP(c_Product__Type_OPair(U_14834,U_14834),sK392(U_14835,U_14834)),sK392(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,[sK392]),skolemize(U_14833,sK392(U_14835,U_14834))],[f_3752_2]) ).
cnf(f_3752_4,plain,
( U_14835 = hAPP(hAPP(c_Product__Type_OPair(U_14834,U_14834),sK392(U_14835,U_14834)),sK392(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_3752_3]) ).
fof(f_3753_1,plain,
! [V_P_H_2,V_P_2] :
( hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2))
| ? [B_x] :
( ( ( ~ hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(V_P_H_2,B_x)) )
| ( ~ hBOOL(hAPP(V_P_H_2,B_x))
& hBOOL(hAPP(V_P_2,B_x)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__cong]) ).
fof(f_3753_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_3753_1]) ).
fof(f_3753_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,sK393(U_14838,U_14837)))
& hBOOL(hAPP(U_14838,sK393(U_14838,U_14837))) )
| ( ~ hBOOL(hAPP(U_14838,sK393(U_14838,U_14837)))
& hBOOL(hAPP(U_14837,sK393(U_14838,U_14837))) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK393(U_14838,U_14837))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK393]),skolemize(U_14836,sK393(U_14838,U_14837))],[f_3753_2]) ).
cnf(f_3753_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK393(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_3753_3]) ).
cnf(f_3753_5,plain,
( hBOOL(hAPP(U_14838,sK393(U_14838,U_14837)))
| hBOOL(hAPP(U_14837,sK393(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_3753_3]) ).
cnf(f_3753_6,plain,
( ~ hBOOL(hAPP(U_14837,sK393(U_14838,U_14837)))
| hBOOL(hAPP(U_14837,sK393(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_3753_3]) ).
cnf(f_3753_7,plain,
( hBOOL(hAPP(U_14838,sK393(U_14838,U_14837)))
| ~ hBOOL(hAPP(U_14838,sK393(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_3753_3]) ).
cnf(f_3753_8,plain,
( ~ hBOOL(hAPP(U_14837,sK393(U_14838,U_14837)))
| ~ hBOOL(hAPP(U_14838,sK393(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_3753_3]) ).
fof(f_3754_1,plain,
! [V_Q_2,V_P_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_b),V_Q_2))))
| ? [B_x] :
( ~ hBOOL(hAPP(V_Q_2,B_x))
& hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__Collect__mono]) ).
fof(f_3754_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_3754_1]) ).
fof(f_3754_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,sK394(U_14844,U_14843,U_14842,U_14841,U_14840)))
& hBOOL(hAPP(U_14843,sK394(U_14844,U_14843,U_14842,U_14841,U_14840)))
& hBOOL(hAPP(hAPP(c_member(U_14840),sK394(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,[sK394]),skolemize(U_14839,sK394(U_14844,U_14843,U_14842,U_14841,U_14840))],[f_3754_2]) ).
cnf(f_3754_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_14840),sK394(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_3754_3]) ).
cnf(f_3754_5,plain,
( hBOOL(hAPP(U_14843,sK394(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_3754_3]) ).
cnf(f_3754_6,plain,
( ~ hBOOL(hAPP(U_14844,sK394(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_3754_3]) ).
fof(f_3755_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_3755_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_3755_1]) ).
fof(f_3755_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),sK395(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),sK395(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,[sK395]),skolemize(U_14846,sK395(U_14850,U_14849,U_14848,U_14847))],[f_3755_2]) ).
fof(f_3755_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),sK395(U_14850,U_14849,U_14848,U_14847)),sK396(U_14850,U_14849,U_14848,U_14847))),U_14850))
& U_14849 = hAPP(hAPP(c_Product__Type_OPair(U_14847,U_14848),sK396(U_14850,U_14849,U_14848,U_14847)),sK395(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,[sK396]),skolemize(U_14845,sK396(U_14850,U_14849,U_14848,U_14847))],[f_3755_3]) ).
cnf(f_3755_5,plain,
( U_14849 = hAPP(hAPP(c_Product__Type_OPair(U_14847,U_14848),sK396(U_14850,U_14849,U_14848,U_14847)),sK395(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_3755_4]) ).
cnf(f_3755_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14848,U_14847)),hAPP(hAPP(c_Product__Type_OPair(U_14848,U_14847),sK395(U_14850,U_14849,U_14848,U_14847)),sK396(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_3755_4]) ).
fof(f_3756_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_3756_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_3756_1]) ).
fof(f_3756_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),sK397(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),sK397(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,[sK397]),skolemize(U_14853,sK397(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854))],[f_3756_2]) ).
fof(f_3756_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),sK398(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),sK397(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854)),sK398(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),sK397(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,[sK398]),skolemize(U_14852,sK398(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854))],[f_3756_3]) ).
fof(f_3756_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),sK398(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854)),sK399(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),sK397(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854)),sK398(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),sK397(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854)),sK399(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,[sK399]),skolemize(U_14851,sK399(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854))],[f_3756_4]) ).
cnf(f_3756_6,plain,
( U_14856 = hAPP(hAPP(c_Product__Type_OPair(U_14854,U_14855),sK397(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854)),sK399(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_3756_5]) ).
cnf(f_3756_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14854,U_14857)),hAPP(hAPP(c_Product__Type_OPair(U_14854,U_14857),sK397(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854)),sK398(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_3756_5]) ).
cnf(f_3756_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14857,U_14855)),hAPP(hAPP(c_Product__Type_OPair(U_14857,U_14855),sK398(U_14859,U_14858,U_14857,U_14856,U_14855,U_14854)),sK399(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_3756_5]) ).
fof(f_3757_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_3757_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_3757_1]) ).
cnf(f_3757_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_3757_2]) ).
fof(f_3758_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_3758_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_3758_1]) ).
cnf(f_3758_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_3758_2]) ).
fof(f_3759_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_3759_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_3759_1]) ).
cnf(f_3759_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_3759_2]) ).
fof(f_3760_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_3760_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_3760_1]) ).
cnf(f_3760_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_3760_2]) ).
fof(f_3761_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_3761_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_3761_1]) ).
cnf(f_3761_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_3761_2]) ).
fof(f_3762_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_3762_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_3762_1]) ).
fof(f_3762_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_3762_2]) ).
cnf(f_3762_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_3762_3]) ).
cnf(f_3762_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_3762_3]) ).
fof(f_3763_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_3763_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_3763_1]) ).
fof(f_3763_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_3763_2]) ).
cnf(f_3763_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_3763_3]) ).
cnf(f_3763_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_3763_3]) ).
fof(f_3764_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_3764_2,plain,
! [U_14891] : c_Nitpick_Odenom(U_14891) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_14891,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_14891)),
inference(variable_rename,[status(thm)],[f_3764_1]) ).
cnf(f_3764_3,plain,
c_Nitpick_Odenom(U_14891) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_14891,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_14891)),
inference(clausify,[status(thm)],[f_3764_2]) ).
fof(f_3765_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_3765_2,plain,
! [U_14892] : c_Nitpick_Onum(U_14892) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_14892,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_14892)),
inference(variable_rename,[status(thm)],[f_3765_1]) ).
cnf(f_3765_3,plain,
c_Nitpick_Onum(U_14892) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_14892,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_14892)),
inference(clausify,[status(thm)],[f_3765_2]) ).
fof(f_3766_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_3766_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_3766_1]) ).
cnf(f_3766_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_3766_2]) ).
fof(f_3767_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_3767_2,plain,
c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_3767_1]) ).
fof(f_3768_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_c_2,V_a_2),V_b_2),
inference(fof_nnf,[status(thm)],[fact_internal__split__conv]) ).
fof(f_3768_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_3768_1]) ).
cnf(f_3768_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_3768_2]) ).
fof(f_3769_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_3769_2,plain,
c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_3769_1]) ).
fof(f_3770_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_3770_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_3770_1]) ).
fof(f_3770_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),sK400(U_14904,U_14903)),hAPP(U_14903,sK400(U_14904,U_14903)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK400]),skolemize(U_14902,sK400(U_14904,U_14903))],[f_3770_2]) ).
cnf(f_3770_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),sK400(U_14904,U_14903)),hAPP(U_14903,sK400(U_14904,U_14903)))) ),
inference(clausify,[status(thm)],[f_3770_3]) ).
fof(f_3771_1,plain,
! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(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_3771_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_3771_1]) ).
cnf(f_3771_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_3771_2]) ).
fof(f_3772_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_3772_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_3772_1]) ).
cnf(f_3772_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_3772_2]) ).
cnf(f_3772_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_3772_2]) ).
fof(f_3773_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_3773_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_3773_1]) ).
fof(f_3773_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_3773_2]) ).
cnf(f_3773_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_3773_3]) ).
fof(f_3774_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_3774_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_3774_1]) ).
cnf(f_3774_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_3774_2]) ).
fof(f_3775_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_3775_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_3775_1]) ).
cnf(f_3775_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_3775_2]) ).
fof(f_3776_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_3776_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_3776_1]) ).
cnf(f_3776_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_3776_2]) ).
fof(f_3777_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_3777_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_3777_1]) ).
cnf(f_3777_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_3777_2]) ).
fof(f_3778_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_3778_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_3778_1]) ).
fof(f_3778_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_3778_2]) ).
cnf(f_3778_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_3778_3]) ).
cnf(f_3778_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_3778_3]) ).
cnf(f_3778_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_3778_3]) ).
fof(f_3779_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_3779_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_3779_1]) ).
cnf(f_3779_3,plain,
hAPP(hAPP(c_List_Olist_OCons(U_14942),U_14943),U_14944) != U_14944,
inference(clausify,[status(thm)],[f_3779_2]) ).
fof(f_3780_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_3780_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_3780_1]) ).
cnf(f_3780_3,plain,
U_14945 != hAPP(hAPP(c_List_Olist_OCons(U_14946),U_14947),U_14945),
inference(clausify,[status(thm)],[f_3780_2]) ).
fof(f_3781_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_3781_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_3781_1]) ).
cnf(f_3781_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_3781_2]) ).
fof(f_3782_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_3782_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_3782_1]) ).
fof(f_3782_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_3782_2]) ).
cnf(f_3782_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_3782_3]) ).
cnf(f_3782_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_3782_3]) ).
cnf(f_3782_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_3782_3]) ).
cnf(f_3782_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_3782_3]) ).
cnf(f_3782_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_3782_3]) ).
cnf(f_3782_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_3782_3]) ).
fof(f_3783_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_3783_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_3783_1]) ).
cnf(f_3783_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_3783_2]) ).
fof(f_3784_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_3784_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_3784_1]) ).
fof(f_3784_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_3784_2]) ).
cnf(f_3784_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_3784_3]) ).
cnf(f_3784_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_3784_3]) ).
fof(f_3785_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_3785_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_3785_1]) ).
cnf(f_3785_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_3785_2]) ).
fof(f_3786_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_3786_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_3786_1]) ).
fof(f_3786_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_3786_2]) ).
cnf(f_3786_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_3786_3]) ).
cnf(f_3786_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_3786_3]) ).
cnf(f_3786_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_3786_3]) ).
cnf(f_3786_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_3786_3]) ).
fof(f_3787_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_3787_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_3787_1]) ).
fof(f_3787_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_3787_2]) ).
cnf(f_3787_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_3787_3]) ).
cnf(f_3787_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_3787_3]) ).
cnf(f_3787_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_3787_3]) ).
fof(f_3788_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_3788_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_3788_1]) ).
cnf(f_3788_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_3788_2]) ).
fof(f_3789_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_3789_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_3789_1]) ).
cnf(f_3789_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_3789_2]) ).
fof(f_3790_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_3790_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_3790_1]) ).
cnf(f_3790_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_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_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_3791_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_3791_1]) ).
cnf(f_3791_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_3791_2]) ).
fof(f_3792_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_3792_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_3792_1]) ).
cnf(f_3792_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_3792_2]) ).
fof(f_3793_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_3793_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_3793_1]) ).
cnf(f_3793_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_3793_2]) ).
fof(f_3794_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_3794_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_3794_1]) ).
cnf(f_3794_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_3794_2]) ).
fof(f_3795_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_3795_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_3795_1]) ).
cnf(f_3795_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_3795_2]) ).
fof(f_3796_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_3796_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_3796_1]) ).
cnf(f_3796_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_3796_2]) ).
fof(f_3797_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_3797_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_3797_1]) ).
cnf(f_3797_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_3797_2]) ).
fof(f_3798_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_3798_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_3798_1]) ).
fof(f_3798_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_3798_2]) ).
cnf(f_3798_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_3798_3]) ).
cnf(f_3798_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_3798_3]) ).
fof(f_3799_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_3799_2,plain,
! [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_15072)),hAPP(hAPP(c_List_Olist_OCons(U_15068),U_15070),U_15072))),c_List_Olistrel1(U_15068,U_15071)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15068,U_15068)),hAPP(hAPP(c_Product__Type_OPair(U_15068,U_15068),U_15069),U_15070)),U_15071)) ),
inference(variable_rename,[status(thm)],[f_3799_1]) ).
cnf(f_3799_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15068),tc_List_Olist(U_15068))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15068),tc_List_Olist(U_15068)),hAPP(hAPP(c_List_Olist_OCons(U_15068),U_15069),U_15072)),hAPP(hAPP(c_List_Olist_OCons(U_15068),U_15070),U_15072))),c_List_Olistrel1(U_15068,U_15071)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15068,U_15068)),hAPP(hAPP(c_Product__Type_OPair(U_15068,U_15068),U_15069),U_15070)),U_15071)) ),
inference(clausify,[status(thm)],[f_3799_2]) ).
fof(f_3800_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_3800_2,plain,
! [U_15078,U_15077,U_15076,U_15075,U_15074,U_15073] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15073),tc_List_Olist(U_15073))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15073),tc_List_Olist(U_15073)),hAPP(hAPP(c_List_Olist_OCons(U_15073),U_15074),U_15075)),hAPP(hAPP(c_List_Olist_OCons(U_15073),U_15076),U_15077))),c_List_Olistrel1(U_15073,U_15078)))
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15073),tc_List_Olist(U_15073))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15073),tc_List_Olist(U_15073)),U_15075),U_15077)),c_List_Olistrel1(U_15073,U_15078)))
| U_15074 != U_15076 )
& ( U_15075 != U_15077
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15073,U_15073)),hAPP(hAPP(c_Product__Type_OPair(U_15073,U_15073),U_15074),U_15076)),U_15078)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15073),tc_List_Olist(U_15073))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15073),tc_List_Olist(U_15073)),U_15075),U_15077)),c_List_Olistrel1(U_15073,U_15078)))
& U_15074 = U_15076 )
| ( U_15075 = U_15077
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15073,U_15073)),hAPP(hAPP(c_Product__Type_OPair(U_15073,U_15073),U_15074),U_15076)),U_15078)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15073),tc_List_Olist(U_15073))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15073),tc_List_Olist(U_15073)),hAPP(hAPP(c_List_Olist_OCons(U_15073),U_15074),U_15075)),hAPP(hAPP(c_List_Olist_OCons(U_15073),U_15076),U_15077))),c_List_Olistrel1(U_15073,U_15078))) ) ),
inference(variable_rename,[status(thm)],[f_3800_1]) ).
fof(f_3800_3,plain,
( ! [U_15090,U_15088,U_15086,U_15084,U_15082,U_15080] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15080),tc_List_Olist(U_15080))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15080),tc_List_Olist(U_15080)),hAPP(hAPP(c_List_Olist_OCons(U_15080),U_15082),U_15084)),hAPP(hAPP(c_List_Olist_OCons(U_15080),U_15086),U_15088))),c_List_Olistrel1(U_15080,U_15090)))
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15080),tc_List_Olist(U_15080))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15080),tc_List_Olist(U_15080)),U_15084),U_15088)),c_List_Olistrel1(U_15080,U_15090)))
| U_15082 != U_15086 )
& ( U_15084 != U_15088
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15080,U_15080)),hAPP(hAPP(c_Product__Type_OPair(U_15080,U_15080),U_15082),U_15086)),U_15090)) ) ) )
& ! [U_15089,U_15087,U_15085,U_15083,U_15081,U_15079] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15079),tc_List_Olist(U_15079))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15079),tc_List_Olist(U_15079)),U_15083),U_15087)),c_List_Olistrel1(U_15079,U_15089)))
& U_15081 = U_15085 )
| ( U_15083 = U_15087
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15079,U_15079)),hAPP(hAPP(c_Product__Type_OPair(U_15079,U_15079),U_15081),U_15085)),U_15089)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15079),tc_List_Olist(U_15079))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15079),tc_List_Olist(U_15079)),hAPP(hAPP(c_List_Olist_OCons(U_15079),U_15081),U_15083)),hAPP(hAPP(c_List_Olist_OCons(U_15079),U_15085),U_15087))),c_List_Olistrel1(U_15079,U_15089))) ) ),
inference(miniscope,[status(thm)],[f_3800_2]) ).
cnf(f_3800_4,plain,
( U_15081 = U_15085
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_15079,U_15079)),hAPP(hAPP(c_Product__Type_OPair(U_15079,U_15079),U_15081),U_15085)),U_15089))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15079),tc_List_Olist(U_15079))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15079),tc_List_Olist(U_15079)),hAPP(hAPP(c_List_Olist_OCons(U_15079),U_15081),U_15083)),hAPP(hAPP(c_List_Olist_OCons(U_15079),U_15085),U_15087))),c_List_Olistrel1(U_15079,U_15089))) ),
inference(clausify,[status(thm)],[f_3800_3]) ).
cnf(f_3800_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15079),tc_List_Olist(U_15079))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15079),tc_List_Olist(U_15079)),U_15083),U_15087)),c_List_Olistrel1(U_15079,U_15089)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_15079,U_15079)),hAPP(hAPP(c_Product__Type_OPair(U_15079,U_15079),U_15081),U_15085)),U_15089))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15079),tc_List_Olist(U_15079))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15079),tc_List_Olist(U_15079)),hAPP(hAPP(c_List_Olist_OCons(U_15079),U_15081),U_15083)),hAPP(hAPP(c_List_Olist_OCons(U_15079),U_15085),U_15087))),c_List_Olistrel1(U_15079,U_15089))) ),
inference(clausify,[status(thm)],[f_3800_3]) ).
cnf(f_3800_6,plain,
( U_15081 = U_15085
| U_15083 = U_15087
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15079),tc_List_Olist(U_15079))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15079),tc_List_Olist(U_15079)),hAPP(hAPP(c_List_Olist_OCons(U_15079),U_15081),U_15083)),hAPP(hAPP(c_List_Olist_OCons(U_15079),U_15085),U_15087))),c_List_Olistrel1(U_15079,U_15089))) ),
inference(clausify,[status(thm)],[f_3800_3]) ).
cnf(f_3800_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15079),tc_List_Olist(U_15079))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15079),tc_List_Olist(U_15079)),U_15083),U_15087)),c_List_Olistrel1(U_15079,U_15089)))
| U_15083 = U_15087
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15079),tc_List_Olist(U_15079))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15079),tc_List_Olist(U_15079)),hAPP(hAPP(c_List_Olist_OCons(U_15079),U_15081),U_15083)),hAPP(hAPP(c_List_Olist_OCons(U_15079),U_15085),U_15087))),c_List_Olistrel1(U_15079,U_15089))) ),
inference(clausify,[status(thm)],[f_3800_3]) ).
cnf(f_3800_8,plain,
( U_15084 != U_15088
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15080,U_15080)),hAPP(hAPP(c_Product__Type_OPair(U_15080,U_15080),U_15082),U_15086)),U_15090))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15080),tc_List_Olist(U_15080))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15080),tc_List_Olist(U_15080)),hAPP(hAPP(c_List_Olist_OCons(U_15080),U_15082),U_15084)),hAPP(hAPP(c_List_Olist_OCons(U_15080),U_15086),U_15088))),c_List_Olistrel1(U_15080,U_15090))) ),
inference(clausify,[status(thm)],[f_3800_3]) ).
cnf(f_3800_9,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15080),tc_List_Olist(U_15080))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15080),tc_List_Olist(U_15080)),U_15084),U_15088)),c_List_Olistrel1(U_15080,U_15090)))
| U_15082 != U_15086
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15080),tc_List_Olist(U_15080))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15080),tc_List_Olist(U_15080)),hAPP(hAPP(c_List_Olist_OCons(U_15080),U_15082),U_15084)),hAPP(hAPP(c_List_Olist_OCons(U_15080),U_15086),U_15088))),c_List_Olistrel1(U_15080,U_15090))) ),
inference(clausify,[status(thm)],[f_3800_3]) ).
fof(f_3801_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_3801_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_3801_1]) ).
cnf(f_3801_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_3801_2]) ).
fof(f_3802_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_3802_2,plain,
! [U_15098,U_15097,U_15096] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15096),tc_List_Olist(U_15096))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15096),tc_List_Olist(U_15096)),U_15098),U_15098)),c_List_Olexord(U_15096,U_15097)))
| ? [U_15095] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15096,U_15096)),hAPP(hAPP(c_Product__Type_OPair(U_15096,U_15096),U_15095),U_15095)),U_15097)) ),
inference(variable_rename,[status(thm)],[f_3802_1]) ).
fof(f_3802_3,plain,
! [U_15098,U_15097,U_15096] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15096),tc_List_Olist(U_15096))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15096),tc_List_Olist(U_15096)),U_15098),U_15098)),c_List_Olexord(U_15096,U_15097)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_15096,U_15096)),hAPP(hAPP(c_Product__Type_OPair(U_15096,U_15096),sK401(U_15098,U_15097,U_15096)),sK401(U_15098,U_15097,U_15096))),U_15097)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK401]),skolemize(U_15095,sK401(U_15098,U_15097,U_15096))],[f_3802_2]) ).
cnf(f_3802_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15096),tc_List_Olist(U_15096))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15096),tc_List_Olist(U_15096)),U_15098),U_15098)),c_List_Olexord(U_15096,U_15097)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_15096,U_15096)),hAPP(hAPP(c_Product__Type_OPair(U_15096,U_15096),sK401(U_15098,U_15097,U_15096)),sK401(U_15098,U_15097,U_15096))),U_15097)) ),
inference(clausify,[status(thm)],[f_3802_3]) ).
fof(f_3803_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_3803_2,plain,
! [U_15101,U_15100,U_15099] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15099),tc_List_Olist(U_15099))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15099),tc_List_Olist(U_15099)),U_15100),U_15100)),c_List_Olistrel(U_15099,c_Transitive__Closure_Ortrancl(U_15099,U_15101)))),
inference(variable_rename,[status(thm)],[f_3803_1]) ).
cnf(f_3803_3,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15099),tc_List_Olist(U_15099))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15099),tc_List_Olist(U_15099)),U_15100),U_15100)),c_List_Olistrel(U_15099,c_Transitive__Closure_Ortrancl(U_15099,U_15101)))),
inference(clausify,[status(thm)],[f_3803_2]) ).
fof(f_3804_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_3804_2,plain,
! [U_15104,U_15103,U_15102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15102),tc_List_Olist(U_15102)),tc_HOL_Obool)),c_List_Olistrel(U_15102,U_15103)),c_List_Olistrel(U_15102,U_15104)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15102,U_15102),tc_HOL_Obool)),U_15103),U_15104)) ),
inference(variable_rename,[status(thm)],[f_3804_1]) ).
cnf(f_3804_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15102),tc_List_Olist(U_15102)),tc_HOL_Obool)),c_List_Olistrel(U_15102,U_15103)),c_List_Olistrel(U_15102,U_15104)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15102,U_15102),tc_HOL_Obool)),U_15103),U_15104)) ),
inference(clausify,[status(thm)],[f_3804_2]) ).
fof(f_3805_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_3805_2,plain,
! [U_15106,U_15105] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15105),tc_List_Olist(U_15105)),tc_HOL_Obool)),c_List_Olistrel(U_15105,U_15106)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15105),c_List_Olistrel1(U_15105,U_15106)))),
inference(variable_rename,[status(thm)],[f_3805_1]) ).
cnf(f_3805_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15105),tc_List_Olist(U_15105)),tc_HOL_Obool)),c_List_Olistrel(U_15105,U_15106)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15105),c_List_Olistrel1(U_15105,U_15106)))),
inference(clausify,[status(thm)],[f_3805_2]) ).
fof(f_3806_1,plain,
! [V_r_2,V_ys_2,V_xs_2,T_b] :
( 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_3806_2,plain,
! [U_15110,U_15109,U_15108,U_15107] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15107)),U_15108) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15107)),U_15109)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15107),tc_List_Olist(U_15107))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15107),tc_List_Olist(U_15107)),U_15108),U_15109)),c_List_Olistrel(U_15107,U_15110))) ),
inference(variable_rename,[status(thm)],[f_3806_1]) ).
cnf(f_3806_3,plain,
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15107)),U_15108) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15107)),U_15109)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15107),tc_List_Olist(U_15107))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15107),tc_List_Olist(U_15107)),U_15108),U_15109)),c_List_Olistrel(U_15107,U_15110))) ),
inference(clausify,[status(thm)],[f_3806_2]) ).
fof(f_3807_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_3807_2,plain,
! [U_15115,U_15114,U_15113,U_15112,U_15111] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15111),tc_List_Olist(U_15111))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15111),tc_List_Olist(U_15111)),U_15112),U_15115)),c_List_Olistrel(U_15111,c_Transitive__Closure_Ortrancl(U_15111,U_15114))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15111),tc_List_Olist(U_15111))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15111),tc_List_Olist(U_15111)),U_15113),U_15115)),c_List_Olistrel(U_15111,c_Transitive__Closure_Ortrancl(U_15111,U_15114))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15111),tc_List_Olist(U_15111))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15111),tc_List_Olist(U_15111)),U_15112),U_15113)),c_List_Olistrel(U_15111,c_Transitive__Closure_Ortrancl(U_15111,U_15114)))) ),
inference(variable_rename,[status(thm)],[f_3807_1]) ).
cnf(f_3807_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15111),tc_List_Olist(U_15111))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15111),tc_List_Olist(U_15111)),U_15112),U_15115)),c_List_Olistrel(U_15111,c_Transitive__Closure_Ortrancl(U_15111,U_15114))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15111),tc_List_Olist(U_15111))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15111),tc_List_Olist(U_15111)),U_15113),U_15115)),c_List_Olistrel(U_15111,c_Transitive__Closure_Ortrancl(U_15111,U_15114))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15111),tc_List_Olist(U_15111))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15111),tc_List_Olist(U_15111)),U_15112),U_15113)),c_List_Olistrel(U_15111,c_Transitive__Closure_Ortrancl(U_15111,U_15114)))) ),
inference(clausify,[status(thm)],[f_3807_2]) ).
fof(f_3808_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_3808_2,plain,
! [U_15117,U_15116] : c_List_Olistrel(U_15116,c_Transitive__Closure_Ortrancl(U_15116,U_15117)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15116),c_List_Olistrel1(U_15116,U_15117)),
inference(variable_rename,[status(thm)],[f_3808_1]) ).
cnf(f_3808_3,plain,
c_List_Olistrel(U_15116,c_Transitive__Closure_Ortrancl(U_15116,U_15117)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15116),c_List_Olistrel1(U_15116,U_15117)),
inference(clausify,[status(thm)],[f_3808_2]) ).
fof(f_3809_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_3809_2,plain,
! [U_15121,U_15120,U_15119,U_15118] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15118),tc_List_Olist(U_15118))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15118),tc_List_Olist(U_15118)),U_15119),U_15120)),c_List_Olistrel(U_15118,c_Transitive__Closure_Ortrancl(U_15118,U_15121))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15118),tc_List_Olist(U_15118))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15118),tc_List_Olist(U_15118)),U_15119),U_15120)),c_List_Olistrel1(U_15118,U_15121))) ),
inference(variable_rename,[status(thm)],[f_3809_1]) ).
cnf(f_3809_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15118),tc_List_Olist(U_15118))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15118),tc_List_Olist(U_15118)),U_15119),U_15120)),c_List_Olistrel(U_15118,c_Transitive__Closure_Ortrancl(U_15118,U_15121))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15118),tc_List_Olist(U_15118))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15118),tc_List_Olist(U_15118)),U_15119),U_15120)),c_List_Olistrel1(U_15118,U_15121))) ),
inference(clausify,[status(thm)],[f_3809_2]) ).
fof(f_3810_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_3810_2,plain,
! [U_15124,U_15123,U_15122] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15122),tc_List_Olist(U_15122)),tc_HOL_Obool)),c_List_Olistrel1(U_15122,U_15123)),c_List_Olistrel(U_15122,U_15124)))
| ~ c_Relation_Orefl__on(U_15122,c_Orderings_Otop__class_Otop(tc_fun(U_15122,tc_HOL_Obool)),U_15124)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15122,U_15122),tc_HOL_Obool)),U_15123),U_15124)) ),
inference(variable_rename,[status(thm)],[f_3810_1]) ).
cnf(f_3810_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15122),tc_List_Olist(U_15122)),tc_HOL_Obool)),c_List_Olistrel1(U_15122,U_15123)),c_List_Olistrel(U_15122,U_15124)))
| ~ c_Relation_Orefl__on(U_15122,c_Orderings_Otop__class_Otop(tc_fun(U_15122,tc_HOL_Obool)),U_15124)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15122,U_15122),tc_HOL_Obool)),U_15123),U_15124)) ),
inference(clausify,[status(thm)],[f_3810_2]) ).
fof(f_3811_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_3811_2,plain,
! [U_15128,U_15127,U_15126,U_15125] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15125),tc_List_Olist(U_15125))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15125),tc_List_Olist(U_15125)),U_15126),U_15127)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15125),c_List_Olistrel1(U_15125,U_15128))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15125),tc_List_Olist(U_15125))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15125),tc_List_Olist(U_15125)),U_15126),U_15127)),c_List_Olistrel(U_15125,U_15128))) ),
inference(variable_rename,[status(thm)],[f_3811_1]) ).
cnf(f_3811_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15125),tc_List_Olist(U_15125))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15125),tc_List_Olist(U_15125)),U_15126),U_15127)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15125),c_List_Olistrel1(U_15125,U_15128))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15125),tc_List_Olist(U_15125))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15125),tc_List_Olist(U_15125)),U_15126),U_15127)),c_List_Olistrel(U_15125,U_15128))) ),
inference(clausify,[status(thm)],[f_3811_2]) ).
fof(f_3812_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_3812_2,plain,
! [U_15134,U_15133,U_15132,U_15131,U_15130,U_15129] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15129),tc_List_Olist(U_15129))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15129),tc_List_Olist(U_15129)),hAPP(hAPP(c_List_Olist_OCons(U_15129),U_15130),U_15133)),hAPP(hAPP(c_List_Olist_OCons(U_15129),U_15131),U_15134))),c_List_Olistrel(U_15129,U_15132)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15129),tc_List_Olist(U_15129))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15129),tc_List_Olist(U_15129)),U_15133),U_15134)),c_List_Olistrel(U_15129,U_15132)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15129,U_15129)),hAPP(hAPP(c_Product__Type_OPair(U_15129,U_15129),U_15130),U_15131)),U_15132)) ),
inference(variable_rename,[status(thm)],[f_3812_1]) ).
cnf(f_3812_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15129),tc_List_Olist(U_15129))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15129),tc_List_Olist(U_15129)),hAPP(hAPP(c_List_Olist_OCons(U_15129),U_15130),U_15133)),hAPP(hAPP(c_List_Olist_OCons(U_15129),U_15131),U_15134))),c_List_Olistrel(U_15129,U_15132)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15129),tc_List_Olist(U_15129))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15129),tc_List_Olist(U_15129)),U_15133),U_15134)),c_List_Olistrel(U_15129,U_15132)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15129,U_15129)),hAPP(hAPP(c_Product__Type_OPair(U_15129,U_15129),U_15130),U_15131)),U_15132)) ),
inference(clausify,[status(thm)],[f_3812_2]) ).
fof(f_3813_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_3813_2,plain,
! [U_15138,U_15137,U_15136,U_15135] :
( ( c_List_Olistrelp(U_15135,hAPP(hAPP(c_COMBC(U_15135,tc_fun(tc_prod(U_15135,U_15135),tc_HOL_Obool),tc_fun(U_15135,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15135,tc_fun(tc_fun(tc_prod(U_15135,U_15135),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15135,U_15135),tc_HOL_Obool),tc_fun(U_15135,tc_HOL_Obool)),U_15135),c_COMBC(U_15135,tc_fun(tc_prod(U_15135,U_15135),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15135,tc_prod(U_15135,U_15135)),tc_fun(U_15135,tc_fun(tc_fun(tc_prod(U_15135,U_15135),tc_HOL_Obool),tc_HOL_Obool)),U_15135),hAPP(c_COMBB(tc_prod(U_15135,U_15135),tc_fun(tc_fun(tc_prod(U_15135,U_15135),tc_HOL_Obool),tc_HOL_Obool),U_15135),c_member(tc_prod(U_15135,U_15135)))),c_Product__Type_OPair(U_15135,U_15135)))),U_15136),U_15137,U_15138)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15135),tc_List_Olist(U_15135))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15135),tc_List_Olist(U_15135)),U_15137),U_15138)),c_List_Olistrel(U_15135,U_15136))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15135),tc_List_Olist(U_15135))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15135),tc_List_Olist(U_15135)),U_15137),U_15138)),c_List_Olistrel(U_15135,U_15136)))
| ~ c_List_Olistrelp(U_15135,hAPP(hAPP(c_COMBC(U_15135,tc_fun(tc_prod(U_15135,U_15135),tc_HOL_Obool),tc_fun(U_15135,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15135,tc_fun(tc_fun(tc_prod(U_15135,U_15135),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15135,U_15135),tc_HOL_Obool),tc_fun(U_15135,tc_HOL_Obool)),U_15135),c_COMBC(U_15135,tc_fun(tc_prod(U_15135,U_15135),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15135,tc_prod(U_15135,U_15135)),tc_fun(U_15135,tc_fun(tc_fun(tc_prod(U_15135,U_15135),tc_HOL_Obool),tc_HOL_Obool)),U_15135),hAPP(c_COMBB(tc_prod(U_15135,U_15135),tc_fun(tc_fun(tc_prod(U_15135,U_15135),tc_HOL_Obool),tc_HOL_Obool),U_15135),c_member(tc_prod(U_15135,U_15135)))),c_Product__Type_OPair(U_15135,U_15135)))),U_15136),U_15137,U_15138) ) ),
inference(variable_rename,[status(thm)],[f_3813_1]) ).
fof(f_3813_3,plain,
( ! [U_15146,U_15144,U_15142,U_15140] :
( c_List_Olistrelp(U_15140,hAPP(hAPP(c_COMBC(U_15140,tc_fun(tc_prod(U_15140,U_15140),tc_HOL_Obool),tc_fun(U_15140,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15140,tc_fun(tc_fun(tc_prod(U_15140,U_15140),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15140,U_15140),tc_HOL_Obool),tc_fun(U_15140,tc_HOL_Obool)),U_15140),c_COMBC(U_15140,tc_fun(tc_prod(U_15140,U_15140),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15140,tc_prod(U_15140,U_15140)),tc_fun(U_15140,tc_fun(tc_fun(tc_prod(U_15140,U_15140),tc_HOL_Obool),tc_HOL_Obool)),U_15140),hAPP(c_COMBB(tc_prod(U_15140,U_15140),tc_fun(tc_fun(tc_prod(U_15140,U_15140),tc_HOL_Obool),tc_HOL_Obool),U_15140),c_member(tc_prod(U_15140,U_15140)))),c_Product__Type_OPair(U_15140,U_15140)))),U_15142),U_15144,U_15146)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15140),tc_List_Olist(U_15140))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15140),tc_List_Olist(U_15140)),U_15144),U_15146)),c_List_Olistrel(U_15140,U_15142))) )
& ! [U_15145,U_15143,U_15141,U_15139] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15139),tc_List_Olist(U_15139))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15139),tc_List_Olist(U_15139)),U_15143),U_15145)),c_List_Olistrel(U_15139,U_15141)))
| ~ c_List_Olistrelp(U_15139,hAPP(hAPP(c_COMBC(U_15139,tc_fun(tc_prod(U_15139,U_15139),tc_HOL_Obool),tc_fun(U_15139,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15139,tc_fun(tc_fun(tc_prod(U_15139,U_15139),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15139,U_15139),tc_HOL_Obool),tc_fun(U_15139,tc_HOL_Obool)),U_15139),c_COMBC(U_15139,tc_fun(tc_prod(U_15139,U_15139),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15139,tc_prod(U_15139,U_15139)),tc_fun(U_15139,tc_fun(tc_fun(tc_prod(U_15139,U_15139),tc_HOL_Obool),tc_HOL_Obool)),U_15139),hAPP(c_COMBB(tc_prod(U_15139,U_15139),tc_fun(tc_fun(tc_prod(U_15139,U_15139),tc_HOL_Obool),tc_HOL_Obool),U_15139),c_member(tc_prod(U_15139,U_15139)))),c_Product__Type_OPair(U_15139,U_15139)))),U_15141),U_15143,U_15145) ) ),
inference(miniscope,[status(thm)],[f_3813_2]) ).
cnf(f_3813_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15139),tc_List_Olist(U_15139))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15139),tc_List_Olist(U_15139)),U_15143),U_15145)),c_List_Olistrel(U_15139,U_15141)))
| ~ c_List_Olistrelp(U_15139,hAPP(hAPP(c_COMBC(U_15139,tc_fun(tc_prod(U_15139,U_15139),tc_HOL_Obool),tc_fun(U_15139,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15139,tc_fun(tc_fun(tc_prod(U_15139,U_15139),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15139,U_15139),tc_HOL_Obool),tc_fun(U_15139,tc_HOL_Obool)),U_15139),c_COMBC(U_15139,tc_fun(tc_prod(U_15139,U_15139),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15139,tc_prod(U_15139,U_15139)),tc_fun(U_15139,tc_fun(tc_fun(tc_prod(U_15139,U_15139),tc_HOL_Obool),tc_HOL_Obool)),U_15139),hAPP(c_COMBB(tc_prod(U_15139,U_15139),tc_fun(tc_fun(tc_prod(U_15139,U_15139),tc_HOL_Obool),tc_HOL_Obool),U_15139),c_member(tc_prod(U_15139,U_15139)))),c_Product__Type_OPair(U_15139,U_15139)))),U_15141),U_15143,U_15145) ),
inference(clausify,[status(thm)],[f_3813_3]) ).
cnf(f_3813_5,plain,
( c_List_Olistrelp(U_15140,hAPP(hAPP(c_COMBC(U_15140,tc_fun(tc_prod(U_15140,U_15140),tc_HOL_Obool),tc_fun(U_15140,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15140,tc_fun(tc_fun(tc_prod(U_15140,U_15140),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15140,U_15140),tc_HOL_Obool),tc_fun(U_15140,tc_HOL_Obool)),U_15140),c_COMBC(U_15140,tc_fun(tc_prod(U_15140,U_15140),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15140,tc_prod(U_15140,U_15140)),tc_fun(U_15140,tc_fun(tc_fun(tc_prod(U_15140,U_15140),tc_HOL_Obool),tc_HOL_Obool)),U_15140),hAPP(c_COMBB(tc_prod(U_15140,U_15140),tc_fun(tc_fun(tc_prod(U_15140,U_15140),tc_HOL_Obool),tc_HOL_Obool),U_15140),c_member(tc_prod(U_15140,U_15140)))),c_Product__Type_OPair(U_15140,U_15140)))),U_15142),U_15144,U_15146)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15140),tc_List_Olist(U_15140))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15140),tc_List_Olist(U_15140)),U_15144),U_15146)),c_List_Olistrel(U_15140,U_15142))) ),
inference(clausify,[status(thm)],[f_3813_3]) ).
fof(f_3814_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_3814_2,plain,
! [U_15153,U_15152,U_15151,U_15150,U_15149] :
( ? [U_15148,U_15147] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15149),tc_List_Olist(U_15149))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15149),tc_List_Olist(U_15149)),U_15147),U_15152)),c_List_Olistrel(U_15149,U_15153)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15149,U_15149)),hAPP(hAPP(c_Product__Type_OPair(U_15149,U_15149),U_15148),U_15151)),U_15153))
& U_15150 = hAPP(hAPP(c_List_Olist_OCons(U_15149),U_15148),U_15147) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15149),tc_List_Olist(U_15149))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15149),tc_List_Olist(U_15149)),U_15150),hAPP(hAPP(c_List_Olist_OCons(U_15149),U_15151),U_15152))),c_List_Olistrel(U_15149,U_15153))) ),
inference(variable_rename,[status(thm)],[f_3814_1]) ).
fof(f_3814_3,plain,
! [U_15153,U_15152,U_15151,U_15150,U_15149] :
( ? [U_15147] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15149),tc_List_Olist(U_15149))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15149),tc_List_Olist(U_15149)),U_15147),U_15152)),c_List_Olistrel(U_15149,U_15153)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15149,U_15149)),hAPP(hAPP(c_Product__Type_OPair(U_15149,U_15149),sK402(U_15153,U_15152,U_15151,U_15150,U_15149)),U_15151)),U_15153))
& U_15150 = hAPP(hAPP(c_List_Olist_OCons(U_15149),sK402(U_15153,U_15152,U_15151,U_15150,U_15149)),U_15147) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15149),tc_List_Olist(U_15149))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15149),tc_List_Olist(U_15149)),U_15150),hAPP(hAPP(c_List_Olist_OCons(U_15149),U_15151),U_15152))),c_List_Olistrel(U_15149,U_15153))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK402]),skolemize(U_15148,sK402(U_15153,U_15152,U_15151,U_15150,U_15149))],[f_3814_2]) ).
fof(f_3814_4,plain,
! [U_15153,U_15152,U_15151,U_15150,U_15149] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15149),tc_List_Olist(U_15149))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15149),tc_List_Olist(U_15149)),sK403(U_15153,U_15152,U_15151,U_15150,U_15149)),U_15152)),c_List_Olistrel(U_15149,U_15153)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15149,U_15149)),hAPP(hAPP(c_Product__Type_OPair(U_15149,U_15149),sK402(U_15153,U_15152,U_15151,U_15150,U_15149)),U_15151)),U_15153))
& U_15150 = hAPP(hAPP(c_List_Olist_OCons(U_15149),sK402(U_15153,U_15152,U_15151,U_15150,U_15149)),sK403(U_15153,U_15152,U_15151,U_15150,U_15149)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15149),tc_List_Olist(U_15149))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15149),tc_List_Olist(U_15149)),U_15150),hAPP(hAPP(c_List_Olist_OCons(U_15149),U_15151),U_15152))),c_List_Olistrel(U_15149,U_15153))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK403]),skolemize(U_15147,sK403(U_15153,U_15152,U_15151,U_15150,U_15149))],[f_3814_3]) ).
cnf(f_3814_5,plain,
( U_15150 = hAPP(hAPP(c_List_Olist_OCons(U_15149),sK402(U_15153,U_15152,U_15151,U_15150,U_15149)),sK403(U_15153,U_15152,U_15151,U_15150,U_15149))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15149),tc_List_Olist(U_15149))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15149),tc_List_Olist(U_15149)),U_15150),hAPP(hAPP(c_List_Olist_OCons(U_15149),U_15151),U_15152))),c_List_Olistrel(U_15149,U_15153))) ),
inference(clausify,[status(thm)],[f_3814_4]) ).
cnf(f_3814_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15149,U_15149)),hAPP(hAPP(c_Product__Type_OPair(U_15149,U_15149),sK402(U_15153,U_15152,U_15151,U_15150,U_15149)),U_15151)),U_15153))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15149),tc_List_Olist(U_15149))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15149),tc_List_Olist(U_15149)),U_15150),hAPP(hAPP(c_List_Olist_OCons(U_15149),U_15151),U_15152))),c_List_Olistrel(U_15149,U_15153))) ),
inference(clausify,[status(thm)],[f_3814_4]) ).
cnf(f_3814_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15149),tc_List_Olist(U_15149))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15149),tc_List_Olist(U_15149)),sK403(U_15153,U_15152,U_15151,U_15150,U_15149)),U_15152)),c_List_Olistrel(U_15149,U_15153)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15149),tc_List_Olist(U_15149))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15149),tc_List_Olist(U_15149)),U_15150),hAPP(hAPP(c_List_Olist_OCons(U_15149),U_15151),U_15152))),c_List_Olistrel(U_15149,U_15153))) ),
inference(clausify,[status(thm)],[f_3814_4]) ).
fof(f_3815_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_3815_2,plain,
! [U_15159,U_15158,U_15157,U_15156,U_15155,U_15154] :
( ( c_List_Olistrelp(U_15154,U_15155,hAPP(hAPP(c_List_Olist_OCons(U_15154),U_15156),U_15157),hAPP(hAPP(c_List_Olist_OCons(U_15154),U_15158),U_15159))
| ~ c_List_Olistrelp(U_15154,U_15155,U_15157,U_15159)
| ~ hBOOL(hAPP(hAPP(U_15155,U_15156),U_15158)) )
& ( ( c_List_Olistrelp(U_15154,U_15155,U_15157,U_15159)
& hBOOL(hAPP(hAPP(U_15155,U_15156),U_15158)) )
| ~ c_List_Olistrelp(U_15154,U_15155,hAPP(hAPP(c_List_Olist_OCons(U_15154),U_15156),U_15157),hAPP(hAPP(c_List_Olist_OCons(U_15154),U_15158),U_15159)) ) ),
inference(variable_rename,[status(thm)],[f_3815_1]) ).
fof(f_3815_3,plain,
( ! [U_15171,U_15169,U_15167,U_15165,U_15163,U_15161] :
( c_List_Olistrelp(U_15161,U_15163,hAPP(hAPP(c_List_Olist_OCons(U_15161),U_15165),U_15167),hAPP(hAPP(c_List_Olist_OCons(U_15161),U_15169),U_15171))
| ~ c_List_Olistrelp(U_15161,U_15163,U_15167,U_15171)
| ~ hBOOL(hAPP(hAPP(U_15163,U_15165),U_15169)) )
& ! [U_15170,U_15168,U_15166,U_15164,U_15162,U_15160] :
( ( c_List_Olistrelp(U_15160,U_15162,U_15166,U_15170)
& hBOOL(hAPP(hAPP(U_15162,U_15164),U_15168)) )
| ~ c_List_Olistrelp(U_15160,U_15162,hAPP(hAPP(c_List_Olist_OCons(U_15160),U_15164),U_15166),hAPP(hAPP(c_List_Olist_OCons(U_15160),U_15168),U_15170)) ) ),
inference(miniscope,[status(thm)],[f_3815_2]) ).
cnf(f_3815_4,plain,
( hBOOL(hAPP(hAPP(U_15162,U_15164),U_15168))
| ~ c_List_Olistrelp(U_15160,U_15162,hAPP(hAPP(c_List_Olist_OCons(U_15160),U_15164),U_15166),hAPP(hAPP(c_List_Olist_OCons(U_15160),U_15168),U_15170)) ),
inference(clausify,[status(thm)],[f_3815_3]) ).
cnf(f_3815_5,plain,
( c_List_Olistrelp(U_15160,U_15162,U_15166,U_15170)
| ~ c_List_Olistrelp(U_15160,U_15162,hAPP(hAPP(c_List_Olist_OCons(U_15160),U_15164),U_15166),hAPP(hAPP(c_List_Olist_OCons(U_15160),U_15168),U_15170)) ),
inference(clausify,[status(thm)],[f_3815_3]) ).
cnf(f_3815_6,plain,
( c_List_Olistrelp(U_15161,U_15163,hAPP(hAPP(c_List_Olist_OCons(U_15161),U_15165),U_15167),hAPP(hAPP(c_List_Olist_OCons(U_15161),U_15169),U_15171))
| ~ c_List_Olistrelp(U_15161,U_15163,U_15167,U_15171)
| ~ hBOOL(hAPP(hAPP(U_15163,U_15165),U_15169)) ),
inference(clausify,[status(thm)],[f_3815_3]) ).
fof(f_3816_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_3816_2,plain,
! [U_15177,U_15176,U_15175,U_15174,U_15173,U_15172] :
( c_List_Olistrelp(U_15175,U_15172,hAPP(hAPP(c_List_Olist_OCons(U_15175),U_15173),U_15176),hAPP(hAPP(c_List_Olist_OCons(U_15175),U_15174),U_15177))
| ~ c_List_Olistrelp(U_15175,U_15172,U_15176,U_15177)
| ~ hBOOL(hAPP(hAPP(U_15172,U_15173),U_15174)) ),
inference(variable_rename,[status(thm)],[f_3816_1]) ).
cnf(f_3816_3,plain,
( c_List_Olistrelp(U_15175,U_15172,hAPP(hAPP(c_List_Olist_OCons(U_15175),U_15173),U_15176),hAPP(hAPP(c_List_Olist_OCons(U_15175),U_15174),U_15177))
| ~ c_List_Olistrelp(U_15175,U_15172,U_15176,U_15177)
| ~ hBOOL(hAPP(hAPP(U_15172,U_15173),U_15174)) ),
inference(clausify,[status(thm)],[f_3816_2]) ).
fof(f_3817_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_3817_2,plain,
! [U_15184,U_15183,U_15182,U_15181,U_15180] :
( ? [U_15179,U_15178] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15180),tc_List_Olist(U_15180))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15180),tc_List_Olist(U_15180)),U_15182),U_15178)),c_List_Olistrel(U_15180,U_15184)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15180,U_15180)),hAPP(hAPP(c_Product__Type_OPair(U_15180,U_15180),U_15181),U_15179)),U_15184))
& U_15183 = hAPP(hAPP(c_List_Olist_OCons(U_15180),U_15179),U_15178) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15180),tc_List_Olist(U_15180))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15180),tc_List_Olist(U_15180)),hAPP(hAPP(c_List_Olist_OCons(U_15180),U_15181),U_15182)),U_15183)),c_List_Olistrel(U_15180,U_15184))) ),
inference(variable_rename,[status(thm)],[f_3817_1]) ).
fof(f_3817_3,plain,
! [U_15184,U_15183,U_15182,U_15181,U_15180] :
( ? [U_15178] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15180),tc_List_Olist(U_15180))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15180),tc_List_Olist(U_15180)),U_15182),U_15178)),c_List_Olistrel(U_15180,U_15184)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15180,U_15180)),hAPP(hAPP(c_Product__Type_OPair(U_15180,U_15180),U_15181),sK404(U_15184,U_15183,U_15182,U_15181,U_15180))),U_15184))
& U_15183 = hAPP(hAPP(c_List_Olist_OCons(U_15180),sK404(U_15184,U_15183,U_15182,U_15181,U_15180)),U_15178) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15180),tc_List_Olist(U_15180))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15180),tc_List_Olist(U_15180)),hAPP(hAPP(c_List_Olist_OCons(U_15180),U_15181),U_15182)),U_15183)),c_List_Olistrel(U_15180,U_15184))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK404]),skolemize(U_15179,sK404(U_15184,U_15183,U_15182,U_15181,U_15180))],[f_3817_2]) ).
fof(f_3817_4,plain,
! [U_15184,U_15183,U_15182,U_15181,U_15180] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15180),tc_List_Olist(U_15180))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15180),tc_List_Olist(U_15180)),U_15182),sK405(U_15184,U_15183,U_15182,U_15181,U_15180))),c_List_Olistrel(U_15180,U_15184)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15180,U_15180)),hAPP(hAPP(c_Product__Type_OPair(U_15180,U_15180),U_15181),sK404(U_15184,U_15183,U_15182,U_15181,U_15180))),U_15184))
& U_15183 = hAPP(hAPP(c_List_Olist_OCons(U_15180),sK404(U_15184,U_15183,U_15182,U_15181,U_15180)),sK405(U_15184,U_15183,U_15182,U_15181,U_15180)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15180),tc_List_Olist(U_15180))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15180),tc_List_Olist(U_15180)),hAPP(hAPP(c_List_Olist_OCons(U_15180),U_15181),U_15182)),U_15183)),c_List_Olistrel(U_15180,U_15184))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK405]),skolemize(U_15178,sK405(U_15184,U_15183,U_15182,U_15181,U_15180))],[f_3817_3]) ).
cnf(f_3817_5,plain,
( U_15183 = hAPP(hAPP(c_List_Olist_OCons(U_15180),sK404(U_15184,U_15183,U_15182,U_15181,U_15180)),sK405(U_15184,U_15183,U_15182,U_15181,U_15180))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15180),tc_List_Olist(U_15180))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15180),tc_List_Olist(U_15180)),hAPP(hAPP(c_List_Olist_OCons(U_15180),U_15181),U_15182)),U_15183)),c_List_Olistrel(U_15180,U_15184))) ),
inference(clausify,[status(thm)],[f_3817_4]) ).
cnf(f_3817_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15180,U_15180)),hAPP(hAPP(c_Product__Type_OPair(U_15180,U_15180),U_15181),sK404(U_15184,U_15183,U_15182,U_15181,U_15180))),U_15184))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15180),tc_List_Olist(U_15180))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15180),tc_List_Olist(U_15180)),hAPP(hAPP(c_List_Olist_OCons(U_15180),U_15181),U_15182)),U_15183)),c_List_Olistrel(U_15180,U_15184))) ),
inference(clausify,[status(thm)],[f_3817_4]) ).
cnf(f_3817_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15180),tc_List_Olist(U_15180))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15180),tc_List_Olist(U_15180)),U_15182),sK405(U_15184,U_15183,U_15182,U_15181,U_15180))),c_List_Olistrel(U_15180,U_15184)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15180),tc_List_Olist(U_15180))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15180),tc_List_Olist(U_15180)),hAPP(hAPP(c_List_Olist_OCons(U_15180),U_15181),U_15182)),U_15183)),c_List_Olistrel(U_15180,U_15184))) ),
inference(clausify,[status(thm)],[f_3817_4]) ).
fof(f_3818_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_3818_2,plain,
! [U_15187,U_15186,U_15185] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15185),tc_List_Olist(U_15185)),tc_HOL_Obool)),c_List_Olistrel(U_15185,U_15186)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(U_15185),tc_List_Olist(U_15185)),c_List_Olists(U_15185,U_15187)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_15185),tc_HOL_Obool),tc_List_Olist(U_15185)),c_List_Olists(U_15185,U_15187)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15185,U_15185),tc_HOL_Obool)),U_15186),hAPP(hAPP(c_Product__Type_OSigma(U_15185,U_15185),U_15187),hAPP(c_COMBK(tc_fun(U_15185,tc_HOL_Obool),U_15185),U_15187)))) ),
inference(variable_rename,[status(thm)],[f_3818_1]) ).
cnf(f_3818_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15185),tc_List_Olist(U_15185)),tc_HOL_Obool)),c_List_Olistrel(U_15185,U_15186)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(U_15185),tc_List_Olist(U_15185)),c_List_Olists(U_15185,U_15187)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_15185),tc_HOL_Obool),tc_List_Olist(U_15185)),c_List_Olists(U_15185,U_15187)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15185,U_15185),tc_HOL_Obool)),U_15186),hAPP(hAPP(c_Product__Type_OSigma(U_15185,U_15185),U_15187),hAPP(c_COMBK(tc_fun(U_15185,tc_HOL_Obool),U_15185),U_15187)))) ),
inference(clausify,[status(thm)],[f_3818_2]) ).
fof(f_3819_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_3819_2,plain,
! [U_15188] : c_List_Olists(U_15188,c_Orderings_Otop__class_Otop(tc_fun(U_15188,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_15188),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3819_1]) ).
cnf(f_3819_3,plain,
c_List_Olists(U_15188,c_Orderings_Otop__class_Otop(tc_fun(U_15188,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_15188),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3819_2]) ).
fof(f_3820_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_3820_2,plain,
! [U_15191,U_15190,U_15189] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(U_15189),tc_HOL_Obool)),c_List_Olists(U_15189,U_15190)),c_List_Olists(U_15189,U_15191)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15189,tc_HOL_Obool)),U_15190),U_15191)) ),
inference(variable_rename,[status(thm)],[f_3820_1]) ).
cnf(f_3820_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(U_15189),tc_HOL_Obool)),c_List_Olists(U_15189,U_15190)),c_List_Olists(U_15189,U_15191)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15189,tc_HOL_Obool)),U_15190),U_15191)) ),
inference(clausify,[status(thm)],[f_3820_2]) ).
fof(f_3821_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_3821_2,plain,
! [U_15194,U_15193,U_15192] :
( c_Equiv__Relations_Oequiv(tc_List_Olist(U_15192),c_List_Olists(U_15192,U_15193),c_List_Olistrel(U_15192,U_15194))
| ~ c_Equiv__Relations_Oequiv(U_15192,U_15193,U_15194) ),
inference(variable_rename,[status(thm)],[f_3821_1]) ).
cnf(f_3821_3,plain,
( c_Equiv__Relations_Oequiv(tc_List_Olist(U_15192),c_List_Olists(U_15192,U_15193),c_List_Olistrel(U_15192,U_15194))
| ~ c_Equiv__Relations_Oequiv(U_15192,U_15193,U_15194) ),
inference(clausify,[status(thm)],[f_3821_2]) ).
fof(f_3822_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_3822_2,plain,
! [U_15197,U_15196,U_15195] :
( c_Relation_Orefl__on(tc_List_Olist(U_15195),c_List_Olists(U_15195,U_15196),c_List_Olistrel(U_15195,U_15197))
| ~ c_Relation_Orefl__on(U_15195,U_15196,U_15197) ),
inference(variable_rename,[status(thm)],[f_3822_1]) ).
cnf(f_3822_3,plain,
( c_Relation_Orefl__on(tc_List_Olist(U_15195),c_List_Olists(U_15195,U_15196),c_List_Olistrel(U_15195,U_15197))
| ~ c_Relation_Orefl__on(U_15195,U_15196,U_15197) ),
inference(clausify,[status(thm)],[f_3822_2]) ).
fof(f_3823_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_3823_2,plain,
! [U_15201,U_15200,U_15199,U_15198] :
( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15198)),hAPP(hAPP(c_List_Olist_OCons(U_15198),U_15199),U_15200)),c_List_Olists(U_15198,U_15201)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15198)),U_15200),c_List_Olists(U_15198,U_15201)))
| ~ hBOOL(hAPP(hAPP(c_member(U_15198),U_15199),U_15201)) )
& ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15198)),U_15200),c_List_Olists(U_15198,U_15201)))
& hBOOL(hAPP(hAPP(c_member(U_15198),U_15199),U_15201)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15198)),hAPP(hAPP(c_List_Olist_OCons(U_15198),U_15199),U_15200)),c_List_Olists(U_15198,U_15201))) ) ),
inference(variable_rename,[status(thm)],[f_3823_1]) ).
fof(f_3823_3,plain,
( ! [U_15209,U_15207,U_15205,U_15203] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15203)),hAPP(hAPP(c_List_Olist_OCons(U_15203),U_15205),U_15207)),c_List_Olists(U_15203,U_15209)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15203)),U_15207),c_List_Olists(U_15203,U_15209)))
| ~ hBOOL(hAPP(hAPP(c_member(U_15203),U_15205),U_15209)) )
& ! [U_15208,U_15206,U_15204,U_15202] :
( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15202)),U_15206),c_List_Olists(U_15202,U_15208)))
& hBOOL(hAPP(hAPP(c_member(U_15202),U_15204),U_15208)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15202)),hAPP(hAPP(c_List_Olist_OCons(U_15202),U_15204),U_15206)),c_List_Olists(U_15202,U_15208))) ) ),
inference(miniscope,[status(thm)],[f_3823_2]) ).
cnf(f_3823_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_15202),U_15204),U_15208))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15202)),hAPP(hAPP(c_List_Olist_OCons(U_15202),U_15204),U_15206)),c_List_Olists(U_15202,U_15208))) ),
inference(clausify,[status(thm)],[f_3823_3]) ).
cnf(f_3823_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15202)),U_15206),c_List_Olists(U_15202,U_15208)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15202)),hAPP(hAPP(c_List_Olist_OCons(U_15202),U_15204),U_15206)),c_List_Olists(U_15202,U_15208))) ),
inference(clausify,[status(thm)],[f_3823_3]) ).
cnf(f_3823_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15203)),hAPP(hAPP(c_List_Olist_OCons(U_15203),U_15205),U_15207)),c_List_Olists(U_15203,U_15209)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15203)),U_15207),c_List_Olists(U_15203,U_15209)))
| ~ hBOOL(hAPP(hAPP(c_member(U_15203),U_15205),U_15209)) ),
inference(clausify,[status(thm)],[f_3823_3]) ).
fof(f_3824_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_3824_2,plain,
! [U_15212,U_15211,U_15210] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15210)),U_15211),c_List_Olists(U_15210,c_Wellfounded_Oacc(U_15210,U_15212))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15210)),U_15211),c_Wellfounded_Oacc(tc_List_Olist(U_15210),c_List_Olistrel1(U_15210,U_15212)))) ),
inference(variable_rename,[status(thm)],[f_3824_1]) ).
cnf(f_3824_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15210)),U_15211),c_List_Olists(U_15210,c_Wellfounded_Oacc(U_15210,U_15212))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15210)),U_15211),c_Wellfounded_Oacc(tc_List_Olist(U_15210),c_List_Olistrel1(U_15210,U_15212)))) ),
inference(clausify,[status(thm)],[f_3824_2]) ).
fof(f_3825_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_3825_2,plain,
! [U_15215,U_15214,U_15213] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15213)),U_15214),c_Wellfounded_Oacc(tc_List_Olist(U_15213),c_List_Olistrel1(U_15213,U_15215))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15213)),U_15214),c_List_Olists(U_15213,c_Wellfounded_Oacc(U_15213,U_15215)))) ),
inference(variable_rename,[status(thm)],[f_3825_1]) ).
cnf(f_3825_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15213)),U_15214),c_Wellfounded_Oacc(tc_List_Olist(U_15213),c_List_Olistrel1(U_15213,U_15215))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15213)),U_15214),c_List_Olists(U_15213,c_Wellfounded_Oacc(U_15213,U_15215)))) ),
inference(clausify,[status(thm)],[f_3825_2]) ).
fof(f_3826_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_3826_2,plain,
! [U_15221,U_15220,U_15219,U_15218] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15218),tc_List_Olist(U_15218))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15218),tc_List_Olist(U_15218)),U_15219),U_15220)),c_List_Olistrel(U_15218,U_15221)))
| ? [U_15217] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15218,U_15218)),hAPP(hAPP(c_Product__Type_OPair(U_15218,U_15218),hAPP(hAPP(c_List_Onth(U_15218),U_15219),U_15217)),hAPP(hAPP(c_List_Onth(U_15218),U_15220),U_15217))),U_15221))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15217),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15218)),U_15219))) )
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15218)),U_15219) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15218)),U_15220) )
& ( ( ! [U_15216] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15218,U_15218)),hAPP(hAPP(c_Product__Type_OPair(U_15218,U_15218),hAPP(hAPP(c_List_Onth(U_15218),U_15219),U_15216)),hAPP(hAPP(c_List_Onth(U_15218),U_15220),U_15216))),U_15221))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15216),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15218)),U_15219))) )
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15218)),U_15219) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15218)),U_15220) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15218),tc_List_Olist(U_15218))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15218),tc_List_Olist(U_15218)),U_15219),U_15220)),c_List_Olistrel(U_15218,U_15221))) ) ),
inference(variable_rename,[status(thm)],[f_3826_1]) ).
fof(f_3826_3,plain,
( ! [U_15229,U_15227,U_15225,U_15223] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15223),tc_List_Olist(U_15223))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15223),tc_List_Olist(U_15223)),U_15225),U_15227)),c_List_Olistrel(U_15223,U_15229)))
| ? [U_15217] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15223,U_15223)),hAPP(hAPP(c_Product__Type_OPair(U_15223,U_15223),hAPP(hAPP(c_List_Onth(U_15223),U_15225),U_15217)),hAPP(hAPP(c_List_Onth(U_15223),U_15227),U_15217))),U_15229))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15217),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15223)),U_15225))) )
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15223)),U_15225) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15223)),U_15227) )
& ! [U_15228,U_15226,U_15224,U_15222] :
( ( ! [U_15216] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15222,U_15222)),hAPP(hAPP(c_Product__Type_OPair(U_15222,U_15222),hAPP(hAPP(c_List_Onth(U_15222),U_15224),U_15216)),hAPP(hAPP(c_List_Onth(U_15222),U_15226),U_15216))),U_15228))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15216),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15222)),U_15224))) )
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15222)),U_15224) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15222)),U_15226) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15222),tc_List_Olist(U_15222))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15222),tc_List_Olist(U_15222)),U_15224),U_15226)),c_List_Olistrel(U_15222,U_15228))) ) ),
inference(miniscope,[status(thm)],[f_3826_2]) ).
fof(f_3826_4,plain,
( ! [U_15229,U_15227,U_15225,U_15223] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15223),tc_List_Olist(U_15223))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15223),tc_List_Olist(U_15223)),U_15225),U_15227)),c_List_Olistrel(U_15223,U_15229)))
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15223,U_15223)),hAPP(hAPP(c_Product__Type_OPair(U_15223,U_15223),hAPP(hAPP(c_List_Onth(U_15223),U_15225),sK406(U_15229,U_15227,U_15225,U_15223))),hAPP(hAPP(c_List_Onth(U_15223),U_15227),sK406(U_15229,U_15227,U_15225,U_15223)))),U_15229))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK406(U_15229,U_15227,U_15225,U_15223)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15223)),U_15225))) )
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15223)),U_15225) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15223)),U_15227) )
& ! [U_15228,U_15226,U_15224,U_15222] :
( ( ! [U_15216] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15222,U_15222)),hAPP(hAPP(c_Product__Type_OPair(U_15222,U_15222),hAPP(hAPP(c_List_Onth(U_15222),U_15224),U_15216)),hAPP(hAPP(c_List_Onth(U_15222),U_15226),U_15216))),U_15228))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15216),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15222)),U_15224))) )
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15222)),U_15224) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15222)),U_15226) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15222),tc_List_Olist(U_15222))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15222),tc_List_Olist(U_15222)),U_15224),U_15226)),c_List_Olistrel(U_15222,U_15228))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK406]),skolemize(U_15217,sK406(U_15229,U_15227,U_15225,U_15223))],[f_3826_3]) ).
cnf(f_3826_5,plain,
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15222)),U_15224) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15222)),U_15226)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15222),tc_List_Olist(U_15222))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15222),tc_List_Olist(U_15222)),U_15224),U_15226)),c_List_Olistrel(U_15222,U_15228))) ),
inference(clausify,[status(thm)],[f_3826_4]) ).
cnf(f_3826_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15222,U_15222)),hAPP(hAPP(c_Product__Type_OPair(U_15222,U_15222),hAPP(hAPP(c_List_Onth(U_15222),U_15224),U_15216)),hAPP(hAPP(c_List_Onth(U_15222),U_15226),U_15216))),U_15228))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15216),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15222)),U_15224)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15222),tc_List_Olist(U_15222))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15222),tc_List_Olist(U_15222)),U_15224),U_15226)),c_List_Olistrel(U_15222,U_15228))) ),
inference(clausify,[status(thm)],[f_3826_4]) ).
cnf(f_3826_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK406(U_15229,U_15227,U_15225,U_15223)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15223)),U_15225)))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15223)),U_15225) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15223)),U_15227)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15223),tc_List_Olist(U_15223))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15223),tc_List_Olist(U_15223)),U_15225),U_15227)),c_List_Olistrel(U_15223,U_15229))) ),
inference(clausify,[status(thm)],[f_3826_4]) ).
cnf(f_3826_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15223,U_15223)),hAPP(hAPP(c_Product__Type_OPair(U_15223,U_15223),hAPP(hAPP(c_List_Onth(U_15223),U_15225),sK406(U_15229,U_15227,U_15225,U_15223))),hAPP(hAPP(c_List_Onth(U_15223),U_15227),sK406(U_15229,U_15227,U_15225,U_15223)))),U_15229))
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15223)),U_15225) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15223)),U_15227)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15223),tc_List_Olist(U_15223))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15223),tc_List_Olist(U_15223)),U_15225),U_15227)),c_List_Olistrel(U_15223,U_15229))) ),
inference(clausify,[status(thm)],[f_3826_4]) ).
fof(f_3827_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_3827_2,plain,
! [U_15235,U_15234,U_15233,U_15232] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15232),tc_List_Olist(U_15232))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15232),tc_List_Olist(U_15232)),U_15235),U_15234)),c_List_Olexord(U_15232,U_15233)))
| U_15234 = U_15235
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15232),tc_List_Olist(U_15232))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15232),tc_List_Olist(U_15232)),U_15234),U_15235)),c_List_Olexord(U_15232,U_15233)))
| ? [U_15231,U_15230] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15232,U_15232)),hAPP(hAPP(c_Product__Type_OPair(U_15232,U_15232),U_15230),U_15231)),U_15233))
& U_15231 != U_15230
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15232,U_15232)),hAPP(hAPP(c_Product__Type_OPair(U_15232,U_15232),U_15231),U_15230)),U_15233)) ) ),
inference(variable_rename,[status(thm)],[f_3827_1]) ).
fof(f_3827_3,plain,
! [U_15235,U_15234,U_15233,U_15232] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15232),tc_List_Olist(U_15232))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15232),tc_List_Olist(U_15232)),U_15235),U_15234)),c_List_Olexord(U_15232,U_15233)))
| U_15234 = U_15235
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15232),tc_List_Olist(U_15232))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15232),tc_List_Olist(U_15232)),U_15234),U_15235)),c_List_Olexord(U_15232,U_15233)))
| ? [U_15230] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15232,U_15232)),hAPP(hAPP(c_Product__Type_OPair(U_15232,U_15232),U_15230),sK407(U_15235,U_15234,U_15233,U_15232))),U_15233))
& sK407(U_15235,U_15234,U_15233,U_15232) != U_15230
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15232,U_15232)),hAPP(hAPP(c_Product__Type_OPair(U_15232,U_15232),sK407(U_15235,U_15234,U_15233,U_15232)),U_15230)),U_15233)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK407]),skolemize(U_15231,sK407(U_15235,U_15234,U_15233,U_15232))],[f_3827_2]) ).
fof(f_3827_4,plain,
! [U_15235,U_15234,U_15233,U_15232] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15232),tc_List_Olist(U_15232))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15232),tc_List_Olist(U_15232)),U_15235),U_15234)),c_List_Olexord(U_15232,U_15233)))
| U_15234 = U_15235
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15232),tc_List_Olist(U_15232))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15232),tc_List_Olist(U_15232)),U_15234),U_15235)),c_List_Olexord(U_15232,U_15233)))
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15232,U_15232)),hAPP(hAPP(c_Product__Type_OPair(U_15232,U_15232),sK408(U_15235,U_15234,U_15233,U_15232)),sK407(U_15235,U_15234,U_15233,U_15232))),U_15233))
& sK407(U_15235,U_15234,U_15233,U_15232) != sK408(U_15235,U_15234,U_15233,U_15232)
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15232,U_15232)),hAPP(hAPP(c_Product__Type_OPair(U_15232,U_15232),sK407(U_15235,U_15234,U_15233,U_15232)),sK408(U_15235,U_15234,U_15233,U_15232))),U_15233)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK408]),skolemize(U_15230,sK408(U_15235,U_15234,U_15233,U_15232))],[f_3827_3]) ).
cnf(f_3827_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15232,U_15232)),hAPP(hAPP(c_Product__Type_OPair(U_15232,U_15232),sK407(U_15235,U_15234,U_15233,U_15232)),sK408(U_15235,U_15234,U_15233,U_15232))),U_15233))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15232),tc_List_Olist(U_15232))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15232),tc_List_Olist(U_15232)),U_15235),U_15234)),c_List_Olexord(U_15232,U_15233)))
| U_15234 = U_15235
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15232),tc_List_Olist(U_15232))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15232),tc_List_Olist(U_15232)),U_15234),U_15235)),c_List_Olexord(U_15232,U_15233))) ),
inference(clausify,[status(thm)],[f_3827_4]) ).
cnf(f_3827_6,plain,
( sK407(U_15235,U_15234,U_15233,U_15232) != sK408(U_15235,U_15234,U_15233,U_15232)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15232),tc_List_Olist(U_15232))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15232),tc_List_Olist(U_15232)),U_15235),U_15234)),c_List_Olexord(U_15232,U_15233)))
| U_15234 = U_15235
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15232),tc_List_Olist(U_15232))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15232),tc_List_Olist(U_15232)),U_15234),U_15235)),c_List_Olexord(U_15232,U_15233))) ),
inference(clausify,[status(thm)],[f_3827_4]) ).
cnf(f_3827_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15232,U_15232)),hAPP(hAPP(c_Product__Type_OPair(U_15232,U_15232),sK408(U_15235,U_15234,U_15233,U_15232)),sK407(U_15235,U_15234,U_15233,U_15232))),U_15233))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15232),tc_List_Olist(U_15232))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15232),tc_List_Olist(U_15232)),U_15235),U_15234)),c_List_Olexord(U_15232,U_15233)))
| U_15234 = U_15235
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15232),tc_List_Olist(U_15232))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15232),tc_List_Olist(U_15232)),U_15234),U_15235)),c_List_Olexord(U_15232,U_15233))) ),
inference(clausify,[status(thm)],[f_3827_4]) ).
fof(f_3828_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_3828_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_3828_1]) ).
cnf(f_3828_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_3828_2]) ).
fof(f_3829_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_3829_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_3829_1]) ).
fof(f_3829_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_3829_2]) ).
fof(f_3829_4,plain,
( ! [U_15247,U_15245,U_15243] :
( U_15243 = U_15245
| ( hAPP(hAPP(c_List_Onth(U_15247),U_15243),sK409(U_15247,U_15245,U_15243)) != hAPP(hAPP(c_List_Onth(U_15247),U_15245),sK409(U_15247,U_15245,U_15243))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK409(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,[sK409]),skolemize(U_15238,sK409(U_15247,U_15245,U_15243))],[f_3829_3]) ).
cnf(f_3829_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_3829_4]) ).
cnf(f_3829_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_3829_4]) ).
cnf(f_3829_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK409(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_3829_4]) ).
cnf(f_3829_8,plain,
( hAPP(hAPP(c_List_Onth(U_15247),U_15243),sK409(U_15247,U_15245,U_15243)) != hAPP(hAPP(c_List_Onth(U_15247),U_15245),sK409(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_3829_4]) ).
fof(f_3830_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_3830_2,plain,
! [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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_15249,
inference(variable_rename,[status(thm)],[f_3830_1]) ).
cnf(f_3830_3,plain,
hAPP(hAPP(c_List_Onth(U_15248),hAPP(hAPP(c_List_Olist_OCons(U_15248),U_15249),U_15250)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_15249,
inference(clausify,[status(thm)],[f_3830_2]) ).
fof(f_3831_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_3831_2,plain,
! [U_15254,U_15253,U_15252,U_15251] : hAPP(hAPP(c_List_Onth(U_15251),hAPP(hAPP(c_List_Olist_OCons(U_15251),U_15252),U_15253)),hAPP(c_Nat_OSuc,U_15254)) = hAPP(hAPP(c_List_Onth(U_15251),U_15253),U_15254),
inference(variable_rename,[status(thm)],[f_3831_1]) ).
cnf(f_3831_3,plain,
hAPP(hAPP(c_List_Onth(U_15251),hAPP(hAPP(c_List_Olist_OCons(U_15251),U_15252),U_15253)),hAPP(c_Nat_OSuc,U_15254)) = hAPP(hAPP(c_List_Onth(U_15251),U_15253),U_15254),
inference(clausify,[status(thm)],[f_3831_2]) ).
fof(f_3832_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_3832_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_3832_1]) ).
cnf(f_3832_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_3832_2]) ).
fof(f_3833_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_3833_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_3833_1]) ).
fof(f_3833_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_3833_2]) ).
cnf(f_3833_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_3833_3]) ).
cnf(f_3833_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_3833_3]) ).
fof(f_3834_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_3834_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_3834_1]) ).
fof(f_3834_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_3834_2]) ).
cnf(f_3834_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_3834_3]) ).
cnf(f_3834_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_3834_3]) ).
fof(f_3835_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_3835_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_3835_1]) ).
fof(f_3835_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_3835_2]) ).
fof(f_3835_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),sK410(U_15295,U_15293,U_15291,U_15289))),hAPP(hAPP(c_List_Onth(U_15289),U_15293),sK410(U_15295,U_15293,U_15291,U_15289)))),U_15295))
& hAPP(hAPP(c_List_Otake(U_15289),sK410(U_15295,U_15293,U_15291,U_15289)),U_15291) = hAPP(hAPP(c_List_Otake(U_15289),sK410(U_15295,U_15293,U_15291,U_15289)),U_15293)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK410(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,[sK410]),skolemize(U_15283,sK410(U_15295,U_15293,U_15291,U_15289))],[f_3835_3]) ).
cnf(f_3835_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK410(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_3835_4]) ).
cnf(f_3835_6,plain,
( hAPP(hAPP(c_List_Otake(U_15289),sK410(U_15295,U_15293,U_15291,U_15289)),U_15291) = hAPP(hAPP(c_List_Otake(U_15289),sK410(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_3835_4]) ).
cnf(f_3835_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),sK410(U_15295,U_15293,U_15291,U_15289))),hAPP(hAPP(c_List_Onth(U_15289),U_15293),sK410(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_3835_4]) ).
cnf(f_3835_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK410(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_3835_4]) ).
cnf(f_3835_9,plain,
( hAPP(hAPP(c_List_Otake(U_15289),sK410(U_15295,U_15293,U_15291,U_15289)),U_15291) = hAPP(hAPP(c_List_Otake(U_15289),sK410(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_3835_4]) ).
cnf(f_3835_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),sK410(U_15295,U_15293,U_15291,U_15289))),hAPP(hAPP(c_List_Onth(U_15289),U_15293),sK410(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_3835_4]) ).
cnf(f_3835_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_3835_4]) ).
cnf(f_3835_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_3835_4]) ).
fof(f_3836_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_3836_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_3836_1]) ).
cnf(f_3836_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_3836_2]) ).
fof(f_3837_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_3837_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_3837_1]) ).
cnf(f_3837_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(U_15300),hAPP(c_List_Oset(U_15300),U_15301))),
inference(clausify,[status(thm)],[f_3837_2]) ).
fof(f_3838_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_3838_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_3838_1]) ).
cnf(f_3838_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15302,tc_HOL_Obool)),hAPP(c_List_Oset(U_15302),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_3838_2]) ).
fof(f_3839_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_3839_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_3839_1]) ).
cnf(f_3839_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_3839_2]) ).
fof(f_3840_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_3840_2,plain,
! [U_15311,U_15310,U_15309,U_15308] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15310,tc_HOL_Obool)),hAPP(c_List_Oset(U_15310),hAPP(hAPP(c_List_Otake(U_15310),U_15308),U_15311))),hAPP(c_List_Oset(U_15310),hAPP(hAPP(c_List_Otake(U_15310),U_15309),U_15311))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15308),U_15309)) ),
inference(variable_rename,[status(thm)],[f_3840_1]) ).
cnf(f_3840_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15310,tc_HOL_Obool)),hAPP(c_List_Oset(U_15310),hAPP(hAPP(c_List_Otake(U_15310),U_15308),U_15311))),hAPP(c_List_Oset(U_15310),hAPP(hAPP(c_List_Otake(U_15310),U_15309),U_15311))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15308),U_15309)) ),
inference(clausify,[status(thm)],[f_3840_2]) ).
fof(f_3841_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_3841_2,plain,
! [U_15314,U_15313,U_15312] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15312,tc_HOL_Obool)),hAPP(c_List_Oset(U_15312),hAPP(hAPP(c_List_Otake(U_15312),U_15313),U_15314))),hAPP(c_List_Oset(U_15312),U_15314))),
inference(variable_rename,[status(thm)],[f_3841_1]) ).
cnf(f_3841_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15312,tc_HOL_Obool)),hAPP(c_List_Oset(U_15312),hAPP(hAPP(c_List_Otake(U_15312),U_15313),U_15314))),hAPP(c_List_Oset(U_15312),U_15314))),
inference(clausify,[status(thm)],[f_3841_2]) ).
fof(f_3842_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_3842_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_3842_1]) ).
cnf(f_3842_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_3842_2]) ).
fof(f_3843_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_3843_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_3843_1]) ).
cnf(f_3843_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_3843_2]) ).
fof(f_3844_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_3844_2,plain,
! [U_15325,U_15324,U_15323,U_15322] : hAPP(hAPP(c_List_Otake(U_15322),hAPP(c_Nat_OSuc,U_15323)),hAPP(hAPP(c_List_Olist_OCons(U_15322),U_15324),U_15325)) = hAPP(hAPP(c_List_Olist_OCons(U_15322),U_15324),hAPP(hAPP(c_List_Otake(U_15322),U_15323),U_15325)),
inference(variable_rename,[status(thm)],[f_3844_1]) ).
cnf(f_3844_3,plain,
hAPP(hAPP(c_List_Otake(U_15322),hAPP(c_Nat_OSuc,U_15323)),hAPP(hAPP(c_List_Olist_OCons(U_15322),U_15324),U_15325)) = hAPP(hAPP(c_List_Olist_OCons(U_15322),U_15324),hAPP(hAPP(c_List_Otake(U_15322),U_15323),U_15325)),
inference(clausify,[status(thm)],[f_3844_2]) ).
fof(f_3845_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_3845_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_15329)))
| U_15327 = U_15328
| ~ hBOOL(hAPP(hAPP(c_member(U_15326),U_15327),hAPP(c_List_Oset(U_15326),hAPP(hAPP(c_List_Olist_OCons(U_15326),U_15328),U_15329)))) ),
inference(variable_rename,[status(thm)],[f_3845_1]) ).
cnf(f_3845_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_15326),U_15327),hAPP(c_List_Oset(U_15326),U_15329)))
| U_15327 = U_15328
| ~ hBOOL(hAPP(hAPP(c_member(U_15326),U_15327),hAPP(c_List_Oset(U_15326),hAPP(hAPP(c_List_Olist_OCons(U_15326),U_15328),U_15329)))) ),
inference(clausify,[status(thm)],[f_3845_2]) ).
fof(f_3846_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_3846_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_15332)))
| ~ hBOOL(hAPP(hAPP(c_member(U_15330),U_15331),hAPP(c_List_Oset(U_15330),c_List_Osublist(U_15330,U_15332,U_15333)))) ),
inference(variable_rename,[status(thm)],[f_3846_1]) ).
cnf(f_3846_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_15330),U_15331),hAPP(c_List_Oset(U_15330),U_15332)))
| ~ hBOOL(hAPP(hAPP(c_member(U_15330),U_15331),hAPP(c_List_Oset(U_15330),c_List_Osublist(U_15330,U_15332,U_15333)))) ),
inference(clausify,[status(thm)],[f_3846_2]) ).
fof(f_3847_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_3847_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),U_15337)))
| ~ hBOOL(hAPP(hAPP(c_member(U_15334),U_15335),hAPP(c_List_Oset(U_15334),hAPP(hAPP(c_List_Otake(U_15334),U_15336),U_15337)))) ),
inference(variable_rename,[status(thm)],[f_3847_1]) ).
cnf(f_3847_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_15334),U_15335),hAPP(c_List_Oset(U_15334),U_15337)))
| ~ hBOOL(hAPP(hAPP(c_member(U_15334),U_15335),hAPP(c_List_Oset(U_15334),hAPP(hAPP(c_List_Otake(U_15334),U_15336),U_15337)))) ),
inference(clausify,[status(thm)],[f_3847_2]) ).
fof(f_3848_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_3848_2,plain,
! [U_15341,U_15340,U_15339,U_15338] :
( ~ hBOOL(hAPP(hAPP(c_member(U_15338),U_15339),hAPP(c_List_Oset(U_15338),c_List_Osublist(U_15338,U_15340,U_15341))))
| hBOOL(hAPP(hAPP(c_member(U_15338),U_15339),hAPP(c_List_Oset(U_15338),U_15340))) ),
inference(variable_rename,[status(thm)],[f_3848_1]) ).
cnf(f_3848_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_15338),U_15339),hAPP(c_List_Oset(U_15338),c_List_Osublist(U_15338,U_15340,U_15341))))
| hBOOL(hAPP(hAPP(c_member(U_15338),U_15339),hAPP(c_List_Oset(U_15338),U_15340))) ),
inference(clausify,[status(thm)],[f_3848_2]) ).
fof(f_3849_1,plain,
! [V_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_3849_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_3849_1]) ).
cnf(f_3849_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_3849_2]) ).
fof(f_3850_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_3850_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_3850_1]) ).
cnf(f_3850_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_3850_2]) ).
fof(f_3851_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_3851_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_3851_1]) ).
cnf(f_3851_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_3851_2]) ).
fof(f_3852_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_3852_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_3852_1]) ).
cnf(f_3852_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_3852_2]) ).
fof(f_3853_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_3853_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_3853_1]) ).
cnf(f_3853_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_3853_2]) ).
fof(f_3854_1,plain,
! [V_P_2,V_xs_2,T_b] :
( ( ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
| ? [B_i] :
( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) )
& ( ! [B_i] :
( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ),
inference(fof_nnf,[status(thm)],[fact_all__set__conv__all__nth]) ).
fof(f_3854_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_3854_1]) ).
fof(f_3854_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_3854_2]) ).
fof(f_3854_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,sK411(U_15368,U_15366,U_15364)))
& hBOOL(hAPP(hAPP(c_member(U_15364),sK411(U_15368,U_15366,U_15364)),hAPP(c_List_Oset(U_15364),U_15366))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK411]),skolemize(U_15357,sK411(U_15368,U_15366,U_15364))],[f_3854_3]) ).
fof(f_3854_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),sK412(U_15369,U_15367,U_15365))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK412(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,sK411(U_15368,U_15366,U_15364)))
& hBOOL(hAPP(hAPP(c_member(U_15364),sK411(U_15368,U_15366,U_15364)),hAPP(c_List_Oset(U_15364),U_15366))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK412]),skolemize(U_15359,sK412(U_15369,U_15367,U_15365))],[f_3854_4]) ).
cnf(f_3854_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_15364),sK411(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_3854_5]) ).
cnf(f_3854_7,plain,
( ~ hBOOL(hAPP(U_15368,sK411(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_3854_5]) ).
cnf(f_3854_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK412(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_3854_5]) ).
cnf(f_3854_9,plain,
( ~ hBOOL(hAPP(U_15369,hAPP(hAPP(c_List_Onth(U_15365),U_15367),sK412(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_3854_5]) ).
fof(f_3855_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_3855_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_3855_1]) ).
cnf(f_3855_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_3855_2]) ).
fof(f_3856_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_3856_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_3856_1]) ).
cnf(f_3856_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_3856_2]) ).
fof(f_3857_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_3857_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_3857_1]) ).
fof(f_3857_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_3857_2]) ).
fof(f_3857_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),sK413(U_15390,U_15388,U_15386)),U_15390))
& hBOOL(hAPP(hAPP(c_member(U_15386),sK413(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,[sK413]),skolemize(U_15381,sK413(U_15390,U_15388,U_15386))],[f_3857_3]) ).
cnf(f_3857_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_3857_4]) ).
cnf(f_3857_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_15386),sK413(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_3857_4]) ).
cnf(f_3857_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_15386),sK413(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_3857_4]) ).
fof(f_3858_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_3858_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_3858_1]) ).
cnf(f_3858_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_3858_2]) ).
fof(f_3859_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_3859_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_3859_1]) ).
cnf(f_3859_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_3859_2]) ).
fof(f_3860_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_3860_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_3860_1]) ).
fof(f_3860_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_3860_2]) ).
fof(f_3860_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),sK414(U_15406,U_15404,U_15402)) = U_15404
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK414(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,[sK414]),skolemize(U_15397,sK414(U_15406,U_15404,U_15402))],[f_3860_3]) ).
cnf(f_3860_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK414(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_3860_4]) ).
cnf(f_3860_6,plain,
( hAPP(hAPP(c_List_Onth(U_15402),U_15406),sK414(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_3860_4]) ).
cnf(f_3860_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_3860_4]) ).
fof(f_3861_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_3861_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_3861_1]) ).
cnf(f_3861_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_3861_2]) ).
fof(f_3862_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_3862_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_3862_1]) ).
cnf(f_3862_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_3862_2]) ).
fof(f_3863_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_3863_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_3863_1]) ).
cnf(f_3863_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_3863_2]) ).
fof(f_3864_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_3864_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_3864_1]) ).
cnf(f_3864_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_3864_2]) ).
fof(f_3865_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_3865_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_3865_1]) ).
fof(f_3865_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_3865_2]) ).
fof(f_3865_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)),sK415(U_15431,U_15429,U_15427,U_15425)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15425,U_15425)),sK415(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,[sK415]),skolemize(U_15419,sK415(U_15431,U_15429,U_15427,U_15425))],[f_3865_3]) ).
cnf(f_3865_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_3865_4]) ).
cnf(f_3865_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_3865_4]) ).
cnf(f_3865_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15425,U_15425)),sK415(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_3865_4]) ).
cnf(f_3865_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)),sK415(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_3865_4]) ).
fof(f_3866_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_3866_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_3866_1]) ).
cnf(f_3866_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_3866_2]) ).
fof(f_3867_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_3867_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_3867_1]) ).
cnf(f_3867_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_3867_2]) ).
fof(f_3868_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_3868_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_3868_1]) ).
cnf(f_3868_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_3868_2]) ).
fof(f_3869_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_3869_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_3869_1]) ).
cnf(f_3869_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_3869_2]) ).
fof(f_3870_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_3870_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_3870_1]) ).
fof(f_3870_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_3870_2]) ).
fof(f_3870_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),sK416(U_15461,U_15459,U_15457)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15461,U_15461)),sK416(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,[sK416]),skolemize(U_15452,sK416(U_15461,U_15459,U_15457))],[f_3870_3]) ).
cnf(f_3870_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_3870_4]) ).
cnf(f_3870_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_3870_4]) ).
cnf(f_3870_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15461,U_15461)),sK416(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_3870_4]) ).
cnf(f_3870_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15461,U_15461,tc_HOL_Obool),c_fequal),sK416(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_3870_4]) ).
fof(f_3871_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_3871_2,plain,
! [U_15465,U_15464,U_15463,U_15462] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15462,U_15462)),hAPP(hAPP(c_Product__Type_OPair(U_15462,U_15462),U_15463),U_15464)),hAPP(c_List_Oset(tc_prod(U_15462,U_15462)),hAPP(hAPP(c_List_Ozip(U_15462,U_15462),U_15465),U_15465))))
| U_15463 != U_15464
| ~ hBOOL(hAPP(hAPP(c_member(U_15462),U_15463),hAPP(c_List_Oset(U_15462),U_15465))) )
& ( ( U_15463 = U_15464
& hBOOL(hAPP(hAPP(c_member(U_15462),U_15463),hAPP(c_List_Oset(U_15462),U_15465))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15462,U_15462)),hAPP(hAPP(c_Product__Type_OPair(U_15462,U_15462),U_15463),U_15464)),hAPP(c_List_Oset(tc_prod(U_15462,U_15462)),hAPP(hAPP(c_List_Ozip(U_15462,U_15462),U_15465),U_15465)))) ) ),
inference(variable_rename,[status(thm)],[f_3871_1]) ).
fof(f_3871_3,plain,
( ! [U_15473,U_15471,U_15469,U_15467] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15467,U_15467)),hAPP(hAPP(c_Product__Type_OPair(U_15467,U_15467),U_15469),U_15471)),hAPP(c_List_Oset(tc_prod(U_15467,U_15467)),hAPP(hAPP(c_List_Ozip(U_15467,U_15467),U_15473),U_15473))))
| U_15469 != U_15471
| ~ hBOOL(hAPP(hAPP(c_member(U_15467),U_15469),hAPP(c_List_Oset(U_15467),U_15473))) )
& ! [U_15472,U_15470,U_15468,U_15466] :
( ( U_15468 = U_15470
& hBOOL(hAPP(hAPP(c_member(U_15466),U_15468),hAPP(c_List_Oset(U_15466),U_15472))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15466,U_15466)),hAPP(hAPP(c_Product__Type_OPair(U_15466,U_15466),U_15468),U_15470)),hAPP(c_List_Oset(tc_prod(U_15466,U_15466)),hAPP(hAPP(c_List_Ozip(U_15466,U_15466),U_15472),U_15472)))) ) ),
inference(miniscope,[status(thm)],[f_3871_2]) ).
cnf(f_3871_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_15466),U_15468),hAPP(c_List_Oset(U_15466),U_15472)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15466,U_15466)),hAPP(hAPP(c_Product__Type_OPair(U_15466,U_15466),U_15468),U_15470)),hAPP(c_List_Oset(tc_prod(U_15466,U_15466)),hAPP(hAPP(c_List_Ozip(U_15466,U_15466),U_15472),U_15472)))) ),
inference(clausify,[status(thm)],[f_3871_3]) ).
cnf(f_3871_5,plain,
( U_15468 = U_15470
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15466,U_15466)),hAPP(hAPP(c_Product__Type_OPair(U_15466,U_15466),U_15468),U_15470)),hAPP(c_List_Oset(tc_prod(U_15466,U_15466)),hAPP(hAPP(c_List_Ozip(U_15466,U_15466),U_15472),U_15472)))) ),
inference(clausify,[status(thm)],[f_3871_3]) ).
cnf(f_3871_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15467,U_15467)),hAPP(hAPP(c_Product__Type_OPair(U_15467,U_15467),U_15469),U_15471)),hAPP(c_List_Oset(tc_prod(U_15467,U_15467)),hAPP(hAPP(c_List_Ozip(U_15467,U_15467),U_15473),U_15473))))
| U_15469 != U_15471
| ~ hBOOL(hAPP(hAPP(c_member(U_15467),U_15469),hAPP(c_List_Oset(U_15467),U_15473))) ),
inference(clausify,[status(thm)],[f_3871_3]) ).
fof(f_3872_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_3872_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_3872_1]) ).
cnf(f_3872_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_3872_2]) ).
fof(f_3873_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_3873_2,plain,
! [U_15485,U_15484,U_15483,U_15482,U_15481,U_15480] :
( hBOOL(hAPP(hAPP(c_member(U_15481),U_15483),hAPP(c_List_Oset(U_15481),U_15485)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15480,U_15481)),hAPP(hAPP(c_Product__Type_OPair(U_15480,U_15481),U_15482),U_15483)),hAPP(c_List_Oset(tc_prod(U_15480,U_15481)),hAPP(hAPP(c_List_Ozip(U_15480,U_15481),U_15484),U_15485)))) ),
inference(variable_rename,[status(thm)],[f_3873_1]) ).
fof(f_3873_3,plain,
! [U_15485,U_15484,U_15483,U_15482,U_15481] :
( ! [U_15480] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15480,U_15481)),hAPP(hAPP(c_Product__Type_OPair(U_15480,U_15481),U_15482),U_15483)),hAPP(c_List_Oset(tc_prod(U_15480,U_15481)),hAPP(hAPP(c_List_Ozip(U_15480,U_15481),U_15484),U_15485))))
| hBOOL(hAPP(hAPP(c_member(U_15481),U_15483),hAPP(c_List_Oset(U_15481),U_15485))) ),
inference(miniscope,[status(thm)],[f_3873_2]) ).
cnf(f_3873_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15480,U_15481)),hAPP(hAPP(c_Product__Type_OPair(U_15480,U_15481),U_15482),U_15483)),hAPP(c_List_Oset(tc_prod(U_15480,U_15481)),hAPP(hAPP(c_List_Ozip(U_15480,U_15481),U_15484),U_15485))))
| hBOOL(hAPP(hAPP(c_member(U_15481),U_15483),hAPP(c_List_Oset(U_15481),U_15485))) ),
inference(clausify,[status(thm)],[f_3873_3]) ).
fof(f_3874_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_3874_2,plain,
! [U_15491,U_15490,U_15489,U_15488,U_15487,U_15486] :
( ( hBOOL(hAPP(hAPP(c_member(U_15487),U_15489),hAPP(c_List_Oset(U_15487),U_15491)))
& hBOOL(hAPP(hAPP(c_member(U_15486),U_15488),hAPP(c_List_Oset(U_15486),U_15490))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15486,U_15487)),hAPP(hAPP(c_Product__Type_OPair(U_15486,U_15487),U_15488),U_15489)),hAPP(c_List_Oset(tc_prod(U_15486,U_15487)),hAPP(hAPP(c_List_Ozip(U_15486,U_15487),U_15490),U_15491)))) ),
inference(variable_rename,[status(thm)],[f_3874_1]) ).
cnf(f_3874_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_15486),U_15488),hAPP(c_List_Oset(U_15486),U_15490)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15486,U_15487)),hAPP(hAPP(c_Product__Type_OPair(U_15486,U_15487),U_15488),U_15489)),hAPP(c_List_Oset(tc_prod(U_15486,U_15487)),hAPP(hAPP(c_List_Ozip(U_15486,U_15487),U_15490),U_15491)))) ),
inference(clausify,[status(thm)],[f_3874_2]) ).
cnf(f_3874_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_15487),U_15489),hAPP(c_List_Oset(U_15487),U_15491)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15486,U_15487)),hAPP(hAPP(c_Product__Type_OPair(U_15486,U_15487),U_15488),U_15489)),hAPP(c_List_Oset(tc_prod(U_15486,U_15487)),hAPP(hAPP(c_List_Ozip(U_15486,U_15487),U_15490),U_15491)))) ),
inference(clausify,[status(thm)],[f_3874_2]) ).
fof(f_3875_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_3875_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_3875_1]) ).
cnf(f_3875_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_3875_2]) ).
fof(f_3876_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_3876_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_3876_1]) ).
cnf(f_3876_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_3876_2]) ).
fof(f_3877_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_3877_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_3877_1]) ).
cnf(f_3877_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_3877_2]) ).
fof(f_3878_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_3878_2,plain,
! [U_15502,U_15501] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_15501,U_15502)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_15501,U_15502),
inference(variable_rename,[status(thm)],[f_3878_1]) ).
cnf(f_3878_3,plain,
hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_15501,U_15502)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_15501,U_15502),
inference(clausify,[status(thm)],[f_3878_2]) ).
fof(f_3879_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_3879_2,plain,
! [U_15504,U_15503] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_15503,U_15504) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_15503,U_15504)),
inference(variable_rename,[status(thm)],[f_3879_1]) ).
cnf(f_3879_3,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_15503,U_15504) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_15503,U_15504)),
inference(clausify,[status(thm)],[f_3879_2]) ).
fof(f_3880_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_3880_2,plain,
! [U_15507] :
( ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15507) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [U_15506] :
( U_15506 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_15506),hAPP(c_List_Oset(tc_Nat_Onat),U_15507))) ) )
& ( ! [U_15505] :
( U_15505 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_15505),hAPP(c_List_Oset(tc_Nat_Onat),U_15507))) )
| hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15507) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_3880_1]) ).
fof(f_3880_3,plain,
( ! [U_15509] :
( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15509) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [U_15506] :
( U_15506 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_15506),hAPP(c_List_Oset(tc_Nat_Onat),U_15509))) ) )
& ! [U_15508] :
( ! [U_15505] :
( U_15505 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_15505),hAPP(c_List_Oset(tc_Nat_Onat),U_15508))) )
| hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15508) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_3880_2]) ).
fof(f_3880_4,plain,
( ! [U_15509] :
( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15509) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( sK417(U_15509) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK417(U_15509)),hAPP(c_List_Oset(tc_Nat_Onat),U_15509))) ) )
& ! [U_15508] :
( ! [U_15505] :
( U_15505 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_15505),hAPP(c_List_Oset(tc_Nat_Onat),U_15508))) )
| hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15508) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK417]),skolemize(U_15506,sK417(U_15509))],[f_3880_3]) ).
cnf(f_3880_5,plain,
( U_15505 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_15505),hAPP(c_List_Oset(tc_Nat_Onat),U_15508)))
| hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15508) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_3880_4]) ).
cnf(f_3880_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK417(U_15509)),hAPP(c_List_Oset(tc_Nat_Onat),U_15509)))
| hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15509) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_3880_4]) ).
cnf(f_3880_7,plain,
( sK417(U_15509) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15509) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_3880_4]) ).
fof(f_3881_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_3881_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_3881_1]) ).
cnf(f_3881_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_3881_2]) ).
fof(f_3882_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_3882_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_3882_1]) ).
cnf(f_3882_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_3882_2]) ).
fof(f_3883_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_3883_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_3883_1]) ).
cnf(f_3883_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_3883_2]) ).
fof(f_3884_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_3884_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_3884_1]) ).
cnf(f_3884_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_3884_2]) ).
fof(f_3885_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_3885_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_3885_1]) ).
fof(f_3885_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_3885_2]) ).
cnf(f_3885_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_3885_3]) ).
cnf(f_3885_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_3885_3]) ).
fof(f_3886_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_3886_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_3886_1]) ).
fof(f_3886_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,sK418(U_15526,U_15525,U_15524,U_15523))),hAPP(U_15526,sK418(U_15526,U_15525,U_15524,U_15523))))
& hBOOL(hAPP(hAPP(c_member(U_15523),sK418(U_15526,U_15525,U_15524,U_15523)),hAPP(c_List_Oset(U_15523),U_15524))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK418]),skolemize(U_15522,sK418(U_15526,U_15525,U_15524,U_15523))],[f_3886_2]) ).
cnf(f_3886_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_15523),sK418(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_3886_3]) ).
cnf(f_3886_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_15525,sK418(U_15526,U_15525,U_15524,U_15523))),hAPP(U_15526,sK418(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_3886_3]) ).
fof(f_3887_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_3887_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_3887_1]) ).
cnf(f_3887_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_3887_2]) ).
fof(f_3888_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_3888_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_3888_1]) ).
cnf(f_3888_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_3888_2]) ).
fof(f_3889_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_3889_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_3889_1]) ).
cnf(f_3889_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_3889_2]) ).
fof(f_3890_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_3890_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_3890_1]) ).
cnf(f_3890_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_3890_2]) ).
fof(f_3891_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_3891_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_3891_1]) ).
cnf(f_3891_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_3891_2]) ).
fof(f_3892_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_3892_2,plain,
! [U_15548,U_15547,U_15546,U_15545] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15545)),hAPP(hAPP(c_List_Olist__update(U_15545,U_15546),U_15547),U_15548)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15545)),U_15546),
inference(variable_rename,[status(thm)],[f_3892_1]) ).
cnf(f_3892_3,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15545)),hAPP(hAPP(c_List_Olist__update(U_15545,U_15546),U_15547),U_15548)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15545)),U_15546),
inference(clausify,[status(thm)],[f_3892_2]) ).
fof(f_3893_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_3893_2,plain,
! [U_15552,U_15551,U_15550,U_15549] :
( ( c_List_Obutlast(U_15550,hAPP(hAPP(c_List_Olist__update(U_15550,U_15551),U_15549),U_15552)) = hAPP(hAPP(c_List_Olist__update(U_15550,c_List_Obutlast(U_15550,U_15551)),U_15549),U_15552)
| U_15549 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15550)),U_15551)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
& ( c_List_Obutlast(U_15550,hAPP(hAPP(c_List_Olist__update(U_15550,U_15551),U_15549),U_15552)) = c_List_Obutlast(U_15550,U_15551)
| U_15549 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15550)),U_15551)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_3893_1]) ).
fof(f_3893_3,plain,
( ! [U_15560,U_15558,U_15556,U_15554] :
( c_List_Obutlast(U_15556,hAPP(hAPP(c_List_Olist__update(U_15556,U_15558),U_15554),U_15560)) = hAPP(hAPP(c_List_Olist__update(U_15556,c_List_Obutlast(U_15556,U_15558)),U_15554),U_15560)
| U_15554 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15556)),U_15558)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
& ! [U_15559,U_15557,U_15555,U_15553] :
( c_List_Obutlast(U_15555,hAPP(hAPP(c_List_Olist__update(U_15555,U_15557),U_15553),U_15559)) = c_List_Obutlast(U_15555,U_15557)
| U_15553 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15555)),U_15557)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_3893_2]) ).
cnf(f_3893_4,plain,
( c_List_Obutlast(U_15555,hAPP(hAPP(c_List_Olist__update(U_15555,U_15557),U_15553),U_15559)) = c_List_Obutlast(U_15555,U_15557)
| U_15553 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15555)),U_15557)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_3893_3]) ).
cnf(f_3893_5,plain,
( c_List_Obutlast(U_15556,hAPP(hAPP(c_List_Olist__update(U_15556,U_15558),U_15554),U_15560)) = hAPP(hAPP(c_List_Olist__update(U_15556,c_List_Obutlast(U_15556,U_15558)),U_15554),U_15560)
| U_15554 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15556)),U_15558)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_3893_3]) ).
fof(f_3894_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_3894_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_3894_1]) ).
cnf(f_3894_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_3894_2]) ).
fof(f_3895_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_3895_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_3895_1]) ).
cnf(f_3895_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_3895_2]) ).
fof(f_3896_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_3896_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_3896_1]) ).
cnf(f_3896_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_3896_2]) ).
fof(f_3897_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_3897_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_3897_1]) ).
cnf(f_3897_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_3897_2]) ).
fof(f_3898_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_3898_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)),U_15588),U_15589) = c_Nat_Onat_Onat__case(tc_List_Olist(U_15585),hAPP(hAPP(c_List_Olist_OCons(U_15585),U_15589),U_15587),hAPP(hAPP(c_COMBB(tc_List_Olist(U_15585),tc_List_Olist(U_15585),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_15585),U_15586)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_15585,tc_List_Olist(U_15585)),c_List_Olist__update(U_15585,U_15587)),U_15589)),U_15588),
inference(variable_rename,[status(thm)],[f_3898_1]) ).
cnf(f_3898_3,plain,
hAPP(hAPP(c_List_Olist__update(U_15585,hAPP(hAPP(c_List_Olist_OCons(U_15585),U_15586),U_15587)),U_15588),U_15589) = c_Nat_Onat_Onat__case(tc_List_Olist(U_15585),hAPP(hAPP(c_List_Olist_OCons(U_15585),U_15589),U_15587),hAPP(hAPP(c_COMBB(tc_List_Olist(U_15585),tc_List_Olist(U_15585),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_15585),U_15586)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_15585,tc_List_Olist(U_15585)),c_List_Olist__update(U_15585,U_15587)),U_15589)),U_15588),
inference(clausify,[status(thm)],[f_3898_2]) ).
fof(f_3899_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_3899_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_3899_1]) ).
cnf(f_3899_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_3899_2]) ).
fof(f_3900_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_3900_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)),hAPP(c_Nat_OSuc,U_15597)),U_15598) = hAPP(hAPP(c_List_Olist_OCons(U_15594),U_15595),hAPP(hAPP(c_List_Olist__update(U_15594,U_15596),U_15597),U_15598)),
inference(variable_rename,[status(thm)],[f_3900_1]) ).
cnf(f_3900_3,plain,
hAPP(hAPP(c_List_Olist__update(U_15594,hAPP(hAPP(c_List_Olist_OCons(U_15594),U_15595),U_15596)),hAPP(c_Nat_OSuc,U_15597)),U_15598) = hAPP(hAPP(c_List_Olist_OCons(U_15594),U_15595),hAPP(hAPP(c_List_Olist__update(U_15594,U_15596),U_15597),U_15598)),
inference(clausify,[status(thm)],[f_3900_2]) ).
fof(f_3901_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_3901_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_3901_1]) ).
cnf(f_3901_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_3901_2]) ).
fof(f_3902_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_3902_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_3902_1]) ).
cnf(f_3902_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_3902_2]) ).
fof(f_3903_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_3903_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_3903_1]) ).
cnf(f_3903_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_3903_2]) ).
fof(f_3904_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_3904_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_3904_1]) ).
cnf(f_3904_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_3904_2]) ).
fof(f_3905_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_3905_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_3905_1]) ).
cnf(f_3905_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_3905_2]) ).
cnf(f_3905_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_3905_2]) ).
fof(f_3906_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_3906_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_3906_1]) ).
cnf(f_3906_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_3906_2]) ).
cnf(f_3906_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_3906_2]) ).
fof(f_3907_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_3907_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_3907_1]) ).
cnf(f_3907_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_3907_2]) ).
fof(f_3908_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_3908_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_3908_1]) ).
cnf(f_3908_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_3908_2]) ).
fof(f_3909_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_3909_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_3909_1]) ).
cnf(f_3909_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_3909_2]) ).
fof(f_3910_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_3910_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_3910_1]) ).
cnf(f_3910_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_3910_2]) ).
fof(f_3911_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_3911_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_3911_1]) ).
fof(f_3911_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_3911_2]) ).
fof(f_3911_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),sK419(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)),sK419(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,[sK419]),skolemize(U_15636,sK419(U_15649,U_15647,U_15645,U_15643))],[f_3911_3]) ).
fof(f_3911_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),sK420(U_15649,U_15647,U_15645,U_15643)),sK419(U_15649,U_15647,U_15645,U_15643))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK420(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),sK420(U_15649,U_15647,U_15645,U_15643))),sK419(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,[sK420]),skolemize(U_15635,sK420(U_15649,U_15647,U_15645,U_15643))],[f_3911_4]) ).
cnf(f_3911_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),sK420(U_15649,U_15647,U_15645,U_15643))),sK419(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_3911_5]) ).
cnf(f_3911_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK420(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_3911_5]) ).
cnf(f_3911_8,plain,
( U_15647 = hAPP(hAPP(c_List_Olist__update(U_15643,U_15645),sK420(U_15649,U_15647,U_15645,U_15643)),sK419(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_3911_5]) ).
cnf(f_3911_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_3911_5]) ).
fof(f_3912_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_3912_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_3912_1]) ).
cnf(f_3912_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_3912_2]) ).
fof(f_3913_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_3913_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_3913_1]) ).
cnf(f_3913_3,plain,
hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(U_15655,U_15656))),
inference(clausify,[status(thm)],[f_3913_2]) ).
fof(f_3914_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_3914_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_3914_1]) ).
cnf(f_3914_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_3914_2]) ).
fof(f_3915_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_3915_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_3915_1]) ).
cnf(f_3915_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_3915_2]) ).
fof(f_3916_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_3916_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_3916_1]) ).
cnf(f_3916_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_3916_2]) ).
fof(f_3917_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_3917_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_3917_1]) ).
cnf(f_3917_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_3917_2]) ).
fof(f_3918_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_3918_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_3918_1]) ).
fof(f_3918_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_3918_2]) ).
cnf(f_3918_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_3918_3]) ).
cnf(f_3918_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_3918_3]) ).
cnf(f_3918_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_3918_3]) ).
fof(f_3919_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_3919_2,plain,
! [U_15681,U_15680] :
( hBOOL(hAPP(c_List_Odistinct(U_15680),U_15681))
| 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) ),
inference(variable_rename,[status(thm)],[f_3919_1]) ).
cnf(f_3919_3,plain,
( hBOOL(hAPP(c_List_Odistinct(U_15680),U_15681))
| 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) ),
inference(clausify,[status(thm)],[f_3919_2]) ).
fof(f_3920_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_3920_2,plain,
! [U_15683,U_15682] :
( 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)
| ~ hBOOL(hAPP(c_List_Odistinct(U_15682),U_15683)) ),
inference(variable_rename,[status(thm)],[f_3920_1]) ).
cnf(f_3920_3,plain,
( 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)
| ~ hBOOL(hAPP(c_List_Odistinct(U_15682),U_15683)) ),
inference(clausify,[status(thm)],[f_3920_2]) ).
fof(f_3921_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_3921_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_3921_1]) ).
cnf(f_3921_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_3921_2]) ).
cnf(f_3921_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_3921_2]) ).
fof(f_3922_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_3922_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_3922_1]) ).
fof(f_3922_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_3922_2]) ).
fof(f_3922_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),sK421(U_15697,U_15695)) = hAPP(hAPP(c_List_Onth(U_15695),U_15697),U_15690)
& sK421(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),sK421(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,[sK421]),skolemize(U_15691,sK421(U_15697,U_15695))],[f_3922_3]) ).
fof(f_3922_5,plain,
( ! [U_15697,U_15695] :
( hBOOL(hAPP(c_List_Odistinct(U_15695),U_15697))
| ( hAPP(hAPP(c_List_Onth(U_15695),U_15697),sK421(U_15697,U_15695)) = hAPP(hAPP(c_List_Onth(U_15695),U_15697),sK422(U_15697,U_15695))
& sK421(U_15697,U_15695) != sK422(U_15697,U_15695)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK422(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),sK421(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,[sK422]),skolemize(U_15690,sK422(U_15697,U_15695))],[f_3922_4]) ).
cnf(f_3922_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_3922_5]) ).
cnf(f_3922_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK421(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_3922_5]) ).
cnf(f_3922_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK422(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_3922_5]) ).
cnf(f_3922_9,plain,
( sK421(U_15697,U_15695) != sK422(U_15697,U_15695)
| hBOOL(hAPP(c_List_Odistinct(U_15695),U_15697)) ),
inference(clausify,[status(thm)],[f_3922_5]) ).
cnf(f_3922_10,plain,
( hAPP(hAPP(c_List_Onth(U_15695),U_15697),sK421(U_15697,U_15695)) = hAPP(hAPP(c_List_Onth(U_15695),U_15697),sK422(U_15697,U_15695))
| hBOOL(hAPP(c_List_Odistinct(U_15695),U_15697)) ),
inference(clausify,[status(thm)],[f_3922_5]) ).
fof(f_3923_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_3923_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_3923_1]) ).
cnf(f_3923_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_3923_2]) ).
fof(f_3924_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_3924_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_3924_1]) ).
fof(f_3924_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_3924_2]) ).
cnf(f_3924_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_3924_3]) ).
cnf(f_3924_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_3924_3]) ).
fof(f_3925_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_3925_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_3925_1]) ).
fof(f_3925_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),sK423(U_15710,U_15709,U_15708,U_15707)) != hAPP(hAPP(c_List_Onth(U_15708),U_15710),sK423(U_15710,U_15709,U_15708,U_15707))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK423(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,[sK423]),skolemize(U_15706,sK423(U_15710,U_15709,U_15708,U_15707))],[f_3925_2]) ).
cnf(f_3925_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK423(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_3925_3]) ).
cnf(f_3925_5,plain,
( hAPP(hAPP(c_List_Onth(U_15708),U_15709),sK423(U_15710,U_15709,U_15708,U_15707)) != hAPP(hAPP(c_List_Onth(U_15708),U_15710),sK423(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_3925_3]) ).
fof(f_3926_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_3926_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_3926_1]) ).
cnf(f_3926_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_3926_2]) ).
fof(f_3927_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_3927_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_3927_1]) ).
fof(f_3927_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_3927_2]) ).
cnf(f_3927_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_3927_3]) ).
cnf(f_3927_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_3927_3]) ).
fof(f_3928_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_3928_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_3928_1]) ).
cnf(f_3928_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_3928_2]) ).
fof(f_3929_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_3929_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)),c_List_Olist_ONil(U_15728)),U_15729)),c_List_Olistrel(U_15728,U_15730))) ),
inference(variable_rename,[status(thm)],[f_3929_1]) ).
cnf(f_3929_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)),c_List_Olist_ONil(U_15728)),U_15729)),c_List_Olistrel(U_15728,U_15730))) ),
inference(clausify,[status(thm)],[f_3929_2]) ).
fof(f_3930_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_3930_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)),U_15732),c_List_Olist_ONil(U_15731))),c_List_Olistrel(U_15731,U_15733))) ),
inference(variable_rename,[status(thm)],[f_3930_1]) ).
cnf(f_3930_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)),U_15732),c_List_Olist_ONil(U_15731))),c_List_Olistrel(U_15731,U_15733))) ),
inference(clausify,[status(thm)],[f_3930_2]) ).
fof(f_3931_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_3931_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_3931_1]) ).
cnf(f_3931_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_3931_2]) ).
fof(f_3932_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_3932_2,plain,
! [U_15736] : hBOOL(hAPP(c_List_Odistinct(U_15736),c_List_Olist_ONil(U_15736))),
inference(variable_rename,[status(thm)],[f_3932_1]) ).
cnf(f_3932_3,plain,
hBOOL(hAPP(c_List_Odistinct(U_15736),c_List_Olist_ONil(U_15736))),
inference(clausify,[status(thm)],[f_3932_2]) ).
fof(f_3933_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_3933_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_3933_1]) ).
cnf(f_3933_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_3933_2]) ).
fof(f_3934_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_3934_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_3934_1]) ).
cnf(f_3934_3,plain,
c_List_Obutlast(U_15740,c_List_Olist_ONil(U_15740)) = c_List_Olist_ONil(U_15740),
inference(clausify,[status(thm)],[f_3934_2]) ).
fof(f_3935_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_3935_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_3935_1]) ).
fof(f_3935_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_3935_2]) ).
cnf(f_3935_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_3935_3]) ).
cnf(f_3935_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_3935_3]) ).
fof(f_3936_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_3936_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_3936_1]) ).
fof(f_3936_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_3936_2]) ).
cnf(f_3936_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_3936_3]) ).
cnf(f_3936_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_3936_3]) ).
fof(f_3937_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_3937_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_3937_1]) ).
cnf(f_3937_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_3937_2]) ).
fof(f_3938_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_3938_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_3938_1]) ).
cnf(f_3938_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_3938_2]) ).
fof(f_3939_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_3939_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_3939_1]) ).
cnf(f_3939_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_3939_2]) ).
fof(f_3940_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_3940_2,plain,
! [U_15772,U_15771,U_15770] :
( ( hAPP(hAPP(c_List_Otake(U_15770),U_15771),U_15772) = c_List_Olist_ONil(U_15770)
| ( U_15772 != c_List_Olist_ONil(U_15770)
& U_15771 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_15772 = c_List_Olist_ONil(U_15770)
| U_15771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Otake(U_15770),U_15771),U_15772) != c_List_Olist_ONil(U_15770) ) ),
inference(variable_rename,[status(thm)],[f_3940_1]) ).
fof(f_3940_3,plain,
( ! [U_15778,U_15776,U_15774] :
( hAPP(hAPP(c_List_Otake(U_15774),U_15776),U_15778) = c_List_Olist_ONil(U_15774)
| ( U_15778 != c_List_Olist_ONil(U_15774)
& U_15776 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_15777,U_15775,U_15773] :
( U_15777 = c_List_Olist_ONil(U_15773)
| U_15775 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Otake(U_15773),U_15775),U_15777) != c_List_Olist_ONil(U_15773) ) ),
inference(miniscope,[status(thm)],[f_3940_2]) ).
cnf(f_3940_4,plain,
( U_15777 = c_List_Olist_ONil(U_15773)
| U_15775 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Otake(U_15773),U_15775),U_15777) != c_List_Olist_ONil(U_15773) ),
inference(clausify,[status(thm)],[f_3940_3]) ).
cnf(f_3940_5,plain,
( U_15776 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_List_Otake(U_15774),U_15776),U_15778) = c_List_Olist_ONil(U_15774) ),
inference(clausify,[status(thm)],[f_3940_3]) ).
cnf(f_3940_6,plain,
( U_15778 != c_List_Olist_ONil(U_15774)
| hAPP(hAPP(c_List_Otake(U_15774),U_15776),U_15778) = c_List_Olist_ONil(U_15774) ),
inference(clausify,[status(thm)],[f_3940_3]) ).
fof(f_3941_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_3941_2,plain,
! [U_15780,U_15779] : hAPP(hAPP(c_List_Otake(U_15779),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15780) = c_List_Olist_ONil(U_15779),
inference(variable_rename,[status(thm)],[f_3941_1]) ).
cnf(f_3941_3,plain,
hAPP(hAPP(c_List_Otake(U_15779),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15780) = c_List_Olist_ONil(U_15779),
inference(clausify,[status(thm)],[f_3941_2]) ).
fof(f_3942_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_3942_2,plain,
! [U_15782,U_15781] : hAPP(hAPP(c_List_Otake(U_15781),U_15782),c_List_Olist_ONil(U_15781)) = c_List_Olist_ONil(U_15781),
inference(variable_rename,[status(thm)],[f_3942_1]) ).
cnf(f_3942_3,plain,
hAPP(hAPP(c_List_Otake(U_15781),U_15782),c_List_Olist_ONil(U_15781)) = c_List_Olist_ONil(U_15781),
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_15784,U_15783] : c_List_Olist_Olist__size(U_15783,U_15784,c_List_Olist_ONil(U_15783)) = 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_15783,U_15784,c_List_Olist_ONil(U_15783)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_3943_2]) ).
fof(f_3944_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_3944_2,plain,
! [U_15786,U_15785] : c_List_Osublist(U_15785,c_List_Olist_ONil(U_15785),U_15786) = c_List_Olist_ONil(U_15785),
inference(variable_rename,[status(thm)],[f_3944_1]) ).
cnf(f_3944_3,plain,
c_List_Osublist(U_15785,c_List_Olist_ONil(U_15785),U_15786) = c_List_Olist_ONil(U_15785),
inference(clausify,[status(thm)],[f_3944_2]) ).
fof(f_3945_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_3945_2,plain,
! [U_15788,U_15787] : c_List_Oremove1(U_15787,U_15788,c_List_Olist_ONil(U_15787)) = c_List_Olist_ONil(U_15787),
inference(variable_rename,[status(thm)],[f_3945_1]) ).
cnf(f_3945_3,plain,
c_List_Oremove1(U_15787,U_15788,c_List_Olist_ONil(U_15787)) = c_List_Olist_ONil(U_15787),
inference(clausify,[status(thm)],[f_3945_2]) ).
fof(f_3946_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_3946_2,plain,
! [U_15792,U_15791,U_15790,U_15789] : c_List_Oremove1(U_15789,U_15790,c_List_Oremove1(U_15789,U_15791,U_15792)) = c_List_Oremove1(U_15789,U_15791,c_List_Oremove1(U_15789,U_15790,U_15792)),
inference(variable_rename,[status(thm)],[f_3946_1]) ).
cnf(f_3946_3,plain,
c_List_Oremove1(U_15789,U_15790,c_List_Oremove1(U_15789,U_15791,U_15792)) = c_List_Oremove1(U_15789,U_15791,c_List_Oremove1(U_15789,U_15790,U_15792)),
inference(clausify,[status(thm)],[f_3946_2]) ).
fof(f_3947_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_3947_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_3947_1]) ).
cnf(f_3947_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_3947_2]) ).
fof(f_3948_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_3948_2,plain,
! [U_15796,U_15795] : c_List_Olistrelp(U_15795,U_15796,c_List_Olist_ONil(U_15795),c_List_Olist_ONil(U_15795)),
inference(variable_rename,[status(thm)],[f_3948_1]) ).
cnf(f_3948_3,plain,
c_List_Olistrelp(U_15795,U_15796,c_List_Olist_ONil(U_15795),c_List_Olist_ONil(U_15795)),
inference(clausify,[status(thm)],[f_3948_2]) ).
fof(f_3949_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_3949_2,plain,
! [U_15799,U_15798,U_15797] : hAPP(hAPP(c_List_Ozip(U_15797,U_15798),U_15799),c_List_Olist_ONil(U_15798)) = c_List_Olist_ONil(tc_prod(U_15797,U_15798)),
inference(variable_rename,[status(thm)],[f_3949_1]) ).
cnf(f_3949_3,plain,
hAPP(hAPP(c_List_Ozip(U_15797,U_15798),U_15799),c_List_Olist_ONil(U_15798)) = c_List_Olist_ONil(tc_prod(U_15797,U_15798)),
inference(clausify,[status(thm)],[f_3949_2]) ).
fof(f_3950_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_3950_2,plain,
! [U_15802,U_15801,U_15800] : hAPP(hAPP(c_List_Ozip(U_15800,U_15801),c_List_Olist_ONil(U_15800)),U_15802) = c_List_Olist_ONil(tc_prod(U_15800,U_15801)),
inference(variable_rename,[status(thm)],[f_3950_1]) ).
cnf(f_3950_3,plain,
hAPP(hAPP(c_List_Ozip(U_15800,U_15801),c_List_Olist_ONil(U_15800)),U_15802) = c_List_Olist_ONil(tc_prod(U_15800,U_15801)),
inference(clausify,[status(thm)],[f_3950_2]) ).
fof(f_3951_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_3951_2,plain,
! [U_15803] :
( hAPP(c_List_Omonoid__add__class_Olistsum(U_15803),c_List_Olist_ONil(U_15803)) = c_Groups_Ozero__class_Ozero(U_15803)
| ~ class_Groups_Omonoid__add(U_15803) ),
inference(variable_rename,[status(thm)],[f_3951_1]) ).
cnf(f_3951_3,plain,
( hAPP(c_List_Omonoid__add__class_Olistsum(U_15803),c_List_Olist_ONil(U_15803)) = c_Groups_Ozero__class_Ozero(U_15803)
| ~ class_Groups_Omonoid__add(U_15803) ),
inference(clausify,[status(thm)],[f_3951_2]) ).
fof(f_3952_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_3952_2,plain,
! [U_15805,U_15804] :
( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15804)),U_15805) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_15805 != c_List_Olist_ONil(U_15804) )
& ( U_15805 = c_List_Olist_ONil(U_15804)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15804)),U_15805) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_3952_1]) ).
fof(f_3952_3,plain,
( ! [U_15809,U_15807] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15807)),U_15809) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_15809 != c_List_Olist_ONil(U_15807) )
& ! [U_15808,U_15806] :
( U_15808 = c_List_Olist_ONil(U_15806)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15806)),U_15808) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_3952_2]) ).
cnf(f_3952_4,plain,
( U_15808 = c_List_Olist_ONil(U_15806)
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15806)),U_15808) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_3952_3]) ).
cnf(f_3952_5,plain,
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15807)),U_15809) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_15809 != c_List_Olist_ONil(U_15807) ),
inference(clausify,[status(thm)],[f_3952_3]) ).
fof(f_3953_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_3953_2,plain,
! [U_15810] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15810)),c_List_Olist_ONil(U_15810)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_3953_1]) ).
cnf(f_3953_3,plain,
hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15810)),c_List_Olist_ONil(U_15810)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_3953_2]) ).
fof(f_3954_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_3954_2,plain,
! [U_15812,U_15811] :
( ( hAPP(c_List_Oset(U_15811),U_15812) = c_Orderings_Obot__class_Obot(tc_fun(U_15811,tc_HOL_Obool))
| U_15812 != c_List_Olist_ONil(U_15811) )
& ( U_15812 = c_List_Olist_ONil(U_15811)
| hAPP(c_List_Oset(U_15811),U_15812) != c_Orderings_Obot__class_Obot(tc_fun(U_15811,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_3954_1]) ).
fof(f_3954_3,plain,
( ! [U_15816,U_15814] :
( hAPP(c_List_Oset(U_15814),U_15816) = c_Orderings_Obot__class_Obot(tc_fun(U_15814,tc_HOL_Obool))
| U_15816 != c_List_Olist_ONil(U_15814) )
& ! [U_15815,U_15813] :
( U_15815 = c_List_Olist_ONil(U_15813)
| hAPP(c_List_Oset(U_15813),U_15815) != c_Orderings_Obot__class_Obot(tc_fun(U_15813,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_3954_2]) ).
cnf(f_3954_4,plain,
( U_15815 = c_List_Olist_ONil(U_15813)
| hAPP(c_List_Oset(U_15813),U_15815) != c_Orderings_Obot__class_Obot(tc_fun(U_15813,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3954_3]) ).
cnf(f_3954_5,plain,
( hAPP(c_List_Oset(U_15814),U_15816) = c_Orderings_Obot__class_Obot(tc_fun(U_15814,tc_HOL_Obool))
| U_15816 != c_List_Olist_ONil(U_15814) ),
inference(clausify,[status(thm)],[f_3954_3]) ).
fof(f_3955_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_3955_2,plain,
! [U_15818,U_15817] :
( ( c_Orderings_Obot__class_Obot(tc_fun(U_15817,tc_HOL_Obool)) = hAPP(c_List_Oset(U_15817),U_15818)
| U_15818 != c_List_Olist_ONil(U_15817) )
& ( U_15818 = 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_15818) ) ),
inference(variable_rename,[status(thm)],[f_3955_1]) ).
fof(f_3955_3,plain,
( ! [U_15822,U_15820] :
( c_Orderings_Obot__class_Obot(tc_fun(U_15820,tc_HOL_Obool)) = hAPP(c_List_Oset(U_15820),U_15822)
| U_15822 != c_List_Olist_ONil(U_15820) )
& ! [U_15821,U_15819] :
( U_15821 = c_List_Olist_ONil(U_15819)
| c_Orderings_Obot__class_Obot(tc_fun(U_15819,tc_HOL_Obool)) != hAPP(c_List_Oset(U_15819),U_15821) ) ),
inference(miniscope,[status(thm)],[f_3955_2]) ).
cnf(f_3955_4,plain,
( U_15821 = c_List_Olist_ONil(U_15819)
| c_Orderings_Obot__class_Obot(tc_fun(U_15819,tc_HOL_Obool)) != hAPP(c_List_Oset(U_15819),U_15821) ),
inference(clausify,[status(thm)],[f_3955_3]) ).
cnf(f_3955_5,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_15820,tc_HOL_Obool)) = hAPP(c_List_Oset(U_15820),U_15822)
| U_15822 != c_List_Olist_ONil(U_15820) ),
inference(clausify,[status(thm)],[f_3955_3]) ).
fof(f_3956_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_3956_2,plain,
! [U_15823] : hAPP(c_List_Oset(U_15823),c_List_Olist_ONil(U_15823)) = c_Orderings_Obot__class_Obot(tc_fun(U_15823,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3956_1]) ).
cnf(f_3956_3,plain,
hAPP(c_List_Oset(U_15823),c_List_Olist_ONil(U_15823)) = c_Orderings_Obot__class_Obot(tc_fun(U_15823,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3956_2]) ).
fof(f_3957_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_3957_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_3957_1]) ).
fof(f_3957_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_3957_2]) ).
cnf(f_3957_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_3957_3]) ).
cnf(f_3957_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_3957_3]) ).
fof(f_3958_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_3958_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_3958_1]) ).
cnf(f_3958_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_3958_2]) ).
fof(f_3959_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_3959_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_3959_1]) ).
cnf(f_3959_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_3959_2]) ).
fof(f_3960_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_3960_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_3960_1]) ).
cnf(f_3960_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_3960_2]) ).
cnf(f_3960_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_3960_2]) ).
fof(f_3961_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_3961_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_3961_1]) ).
cnf(f_3961_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_3961_2]) ).
fof(f_3962_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_3962_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_3962_1]) ).
cnf(f_3962_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_3962_2]) ).
fof(f_3963_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_3963_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_3963_1]) ).
cnf(f_3963_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_3963_2]) ).
fof(f_3964_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_3964_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_3964_1]) ).
cnf(f_3964_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_3964_2]) ).
fof(f_3965_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_3965_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_3965_1]) ).
fof(f_3965_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_3965_2]) ).
cnf(f_3965_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_3965_3]) ).
cnf(f_3965_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_3965_3]) ).
fof(f_3966_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_3966_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_3966_1]) ).
cnf(f_3966_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_3966_2]) ).
fof(f_3967_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_3967_2,plain,
! [U_15869,U_15868,U_15867] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15867),tc_List_Olist(U_15867))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15867),tc_List_Olist(U_15867)),c_List_Olist_ONil(U_15867)),U_15868)),c_List_Olistrel1(U_15867,U_15869))),
inference(variable_rename,[status(thm)],[f_3967_1]) ).
cnf(f_3967_3,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15867),tc_List_Olist(U_15867))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15867),tc_List_Olist(U_15867)),c_List_Olist_ONil(U_15867)),U_15868)),c_List_Olistrel1(U_15867,U_15869))),
inference(clausify,[status(thm)],[f_3967_2]) ).
fof(f_3968_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_3968_2,plain,
! [U_15872,U_15871,U_15870] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15870),tc_List_Olist(U_15870))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15870),tc_List_Olist(U_15870)),U_15871),c_List_Olist_ONil(U_15870))),c_List_Olistrel1(U_15870,U_15872))),
inference(variable_rename,[status(thm)],[f_3968_1]) ).
cnf(f_3968_3,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15870),tc_List_Olist(U_15870))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15870),tc_List_Olist(U_15870)),U_15871),c_List_Olist_ONil(U_15870))),c_List_Olistrel1(U_15870,U_15872))),
inference(clausify,[status(thm)],[f_3968_2]) ).
fof(f_3969_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_3969_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_3969_1]) ).
cnf(f_3969_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_3969_2]) ).
fof(f_3970_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_3970_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_3970_1]) ).
cnf(f_3970_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_3970_2]) ).
fof(f_3971_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_3971_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)),c_List_Olist_ONil(U_15878)),U_15879)),c_List_Olex(U_15878,U_15880))),
inference(variable_rename,[status(thm)],[f_3971_1]) ).
cnf(f_3971_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)),c_List_Olist_ONil(U_15878)),U_15879)),c_List_Olex(U_15878,U_15880))),
inference(clausify,[status(thm)],[f_3971_2]) ).
fof(f_3972_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_3972_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)),U_15882),c_List_Olist_ONil(U_15881))),c_List_Olex(U_15881,U_15883))),
inference(variable_rename,[status(thm)],[f_3972_1]) ).
cnf(f_3972_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)),U_15882),c_List_Olist_ONil(U_15881))),c_List_Olex(U_15881,U_15883))),
inference(clausify,[status(thm)],[f_3972_2]) ).
fof(f_3973_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_3973_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_3973_1]) ).
cnf(f_3973_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_3973_2]) ).
fof(f_3974_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_3974_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_3974_1]) ).
fof(f_3974_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_3974_2]) ).
cnf(f_3974_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_3974_3]) ).
cnf(f_3974_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_3974_3]) ).
fof(f_3975_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_3975_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_3975_1]) ).
fof(f_3975_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_3975_2]) ).
cnf(f_3975_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_3975_3]) ).
cnf(f_3975_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_3975_3]) ).
fof(f_3976_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_3976_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_3976_1]) ).
cnf(f_3976_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_3976_2]) ).
fof(f_3977_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_3977_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_3977_1]) ).
fof(f_3977_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_3977_2]) ).
cnf(f_3977_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_3977_3]) ).
cnf(f_3977_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_3977_3]) ).
fof(f_3978_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_3978_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_3978_1]) ).
fof(f_3978_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_3978_2]) ).
cnf(f_3978_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_3978_3]) ).
cnf(f_3978_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_3978_3]) ).
fof(f_3979_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_3979_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_3979_1]) ).
cnf(f_3979_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_3979_2]) ).
fof(f_3980_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_3980_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_3980_1]) ).
cnf(f_3980_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_3980_2]) ).
fof(f_3981_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_3981_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_3981_1]) ).
fof(f_3981_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_3981_2]) ).
cnf(f_3981_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_3981_3]) ).
cnf(f_3981_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_3981_3]) ).
fof(f_3982_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_3982_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_3982_1]) ).
cnf(f_3982_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_3982_2]) ).
cnf(f_3982_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_3982_2]) ).
fof(f_3983_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_3983_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_3983_1]) ).
cnf(f_3983_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_3983_2]) ).
fof(f_3984_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_3984_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_3984_1]) ).
cnf(f_3984_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_3984_2]) ).
fof(f_3985_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_3985_2,plain,
! [U_15945,U_15944,U_15943,U_15942,U_15941] : hAPP(hAPP(c_List_Ozip(U_15941,U_15942),hAPP(hAPP(c_List_Olist_OCons(U_15941),U_15943),U_15944)),U_15945) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_15941,U_15942)),U_15942,c_List_Olist_ONil(tc_prod(U_15941,U_15942)),hAPP(hAPP(c_COMBC(U_15942,tc_fun(tc_List_Olist(U_15942),tc_List_Olist(tc_prod(U_15941,U_15942))),tc_fun(tc_List_Olist(U_15942),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_15942),tc_List_Olist(tc_prod(U_15941,U_15942))),tc_fun(tc_List_Olist(U_15942),tc_List_Olist(tc_prod(U_15941,U_15942)))),U_15942),c_COMBB(tc_List_Olist(tc_prod(U_15941,U_15942)),tc_List_Olist(tc_prod(U_15941,U_15942)),tc_List_Olist(U_15942))),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_15942),c_List_Olist_OCons(tc_prod(U_15941,U_15942))),hAPP(c_Product__Type_OPair(U_15941,U_15942),U_15943)))),hAPP(c_List_Ozip(U_15941,U_15942),U_15944))),U_15945),
inference(variable_rename,[status(thm)],[f_3985_1]) ).
cnf(f_3985_3,plain,
hAPP(hAPP(c_List_Ozip(U_15941,U_15942),hAPP(hAPP(c_List_Olist_OCons(U_15941),U_15943),U_15944)),U_15945) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_15941,U_15942)),U_15942,c_List_Olist_ONil(tc_prod(U_15941,U_15942)),hAPP(hAPP(c_COMBC(U_15942,tc_fun(tc_List_Olist(U_15942),tc_List_Olist(tc_prod(U_15941,U_15942))),tc_fun(tc_List_Olist(U_15942),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_15942),tc_List_Olist(tc_prod(U_15941,U_15942))),tc_fun(tc_List_Olist(U_15942),tc_List_Olist(tc_prod(U_15941,U_15942)))),U_15942),c_COMBB(tc_List_Olist(tc_prod(U_15941,U_15942)),tc_List_Olist(tc_prod(U_15941,U_15942)),tc_List_Olist(U_15942))),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_15942),c_List_Olist_OCons(tc_prod(U_15941,U_15942))),hAPP(c_Product__Type_OPair(U_15941,U_15942),U_15943)))),hAPP(c_List_Ozip(U_15941,U_15942),U_15944))),U_15945),
inference(clausify,[status(thm)],[f_3985_2]) ).
fof(f_3986_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_3986_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_3986_1]) ).
cnf(f_3986_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_3986_2]) ).
fof(f_3987_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_3987_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_3987_1]) ).
cnf(f_3987_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_3987_2]) ).
fof(f_3988_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_3988_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_3988_1]) ).
cnf(f_3988_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_3988_2]) ).
fof(f_3989_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_3989_2,plain,
! [U_15963,U_15962,U_15961,U_15960,U_15959] : hAPP(hAPP(c_List_Ozip(U_15959,U_15960),U_15961),hAPP(hAPP(c_List_Olist_OCons(U_15960),U_15962),U_15963)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_15959,U_15960)),U_15959,c_List_Olist_ONil(tc_prod(U_15959,U_15960)),hAPP(hAPP(c_COMBC(U_15959,tc_fun(tc_List_Olist(U_15959),tc_List_Olist(tc_prod(U_15959,U_15960))),tc_fun(tc_List_Olist(U_15959),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_15959),tc_List_Olist(tc_prod(U_15959,U_15960))),tc_fun(tc_List_Olist(U_15959),tc_List_Olist(tc_prod(U_15959,U_15960)))),U_15959),c_COMBB(tc_List_Olist(tc_prod(U_15959,U_15960)),tc_List_Olist(tc_prod(U_15959,U_15960)),tc_List_Olist(U_15959))),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_15959),c_List_Olist_OCons(tc_prod(U_15959,U_15960))),hAPP(hAPP(c_COMBC(U_15959,U_15960,tc_prod(U_15959,U_15960)),c_Product__Type_OPair(U_15959,U_15960)),U_15962)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15959),tc_List_Olist(U_15960),tc_List_Olist(tc_prod(U_15959,U_15960))),c_List_Ozip(U_15959,U_15960)),U_15963))),U_15961),
inference(variable_rename,[status(thm)],[f_3989_1]) ).
cnf(f_3989_3,plain,
hAPP(hAPP(c_List_Ozip(U_15959,U_15960),U_15961),hAPP(hAPP(c_List_Olist_OCons(U_15960),U_15962),U_15963)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_15959,U_15960)),U_15959,c_List_Olist_ONil(tc_prod(U_15959,U_15960)),hAPP(hAPP(c_COMBC(U_15959,tc_fun(tc_List_Olist(U_15959),tc_List_Olist(tc_prod(U_15959,U_15960))),tc_fun(tc_List_Olist(U_15959),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_15959),tc_List_Olist(tc_prod(U_15959,U_15960))),tc_fun(tc_List_Olist(U_15959),tc_List_Olist(tc_prod(U_15959,U_15960)))),U_15959),c_COMBB(tc_List_Olist(tc_prod(U_15959,U_15960)),tc_List_Olist(tc_prod(U_15959,U_15960)),tc_List_Olist(U_15959))),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_15959),c_List_Olist_OCons(tc_prod(U_15959,U_15960))),hAPP(hAPP(c_COMBC(U_15959,U_15960,tc_prod(U_15959,U_15960)),c_Product__Type_OPair(U_15959,U_15960)),U_15962)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15959),tc_List_Olist(U_15960),tc_List_Olist(tc_prod(U_15959,U_15960))),c_List_Ozip(U_15959,U_15960)),U_15963))),U_15961),
inference(clausify,[status(thm)],[f_3989_2]) ).
fof(f_3990_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_3990_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_3990_1]) ).
cnf(f_3990_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_3990_2]) ).
fof(f_3991_1,plain,
! [V_P_2,V_a1_2,V_a0_2] :
( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
| ? [B_i,B_j] :
( ~ hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
& ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) )
& hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_i),B_j))) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) ),
inference(fof_nnf,[status(thm)],[fact_upto_Opinduct]) ).
fof(f_3991_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_3991_1]) ).
fof(f_3991_3,plain,
! [U_15971,U_15970,U_15969] :
( hBOOL(hAPP(hAPP(U_15971,U_15969),U_15970))
| ? [U_15967] :
( ~ hBOOL(hAPP(hAPP(U_15971,sK424(U_15971,U_15970,U_15969)),U_15967))
& ( hBOOL(hAPP(hAPP(U_15971,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK424(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),sK424(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),sK424(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,[sK424]),skolemize(U_15968,sK424(U_15971,U_15970,U_15969))],[f_3991_2]) ).
fof(f_3991_4,plain,
! [U_15971,U_15970,U_15969] :
( hBOOL(hAPP(hAPP(U_15971,U_15969),U_15970))
| ( ~ hBOOL(hAPP(hAPP(U_15971,sK424(U_15971,U_15970,U_15969)),sK425(U_15971,U_15970,U_15969)))
& ( hBOOL(hAPP(hAPP(U_15971,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK424(U_15971,U_15970,U_15969)),c_Groups_Oone__class_Oone(tc_Int_Oint))),sK425(U_15971,U_15970,U_15969)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK424(U_15971,U_15970,U_15969)),sK425(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),sK424(U_15971,U_15970,U_15969)),sK425(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,[sK425]),skolemize(U_15967,sK425(U_15971,U_15970,U_15969))],[f_3991_3]) ).
cnf(f_3991_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),sK424(U_15971,U_15970,U_15969)),sK425(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_3991_4]) ).
cnf(f_3991_6,plain,
( hBOOL(hAPP(hAPP(U_15971,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK424(U_15971,U_15970,U_15969)),c_Groups_Oone__class_Oone(tc_Int_Oint))),sK425(U_15971,U_15970,U_15969)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK424(U_15971,U_15970,U_15969)),sK425(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_3991_4]) ).
cnf(f_3991_7,plain,
( ~ hBOOL(hAPP(hAPP(U_15971,sK424(U_15971,U_15970,U_15969)),sK425(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_3991_4]) ).
fof(f_3992_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_3992_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_3992_1]) ).
cnf(f_3992_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_3992_2]) ).
fof(f_3993_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_3993_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_3993_1]) ).
fof(f_3993_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_3993_2]) ).
cnf(f_3993_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_3993_3]) ).
cnf(f_3993_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_3993_3]) ).
fof(f_3994_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_3994_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_3994_1]) ).
cnf(f_3994_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_3994_2]) ).
fof(f_3995_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_3995_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_3995_1]) ).
fof(f_3995_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_3995_2]) ).
cnf(f_3995_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_3995_3]) ).
cnf(f_3995_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_3995_3]) ).
cnf(f_3995_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_3995_3]) ).
fof(f_3996_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_3996_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_3996_1]) ).
fof(f_3996_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_3996_2]) ).
fof(f_3996_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),sK426(U_16022,U_16020,U_16018,U_16016,U_16014)),U_16022)
& hAPP(hAPP(c_List_Olist_OCons(U_16014),U_16016),sK426(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,[sK426]),skolemize(U_16007,sK426(U_16022,U_16020,U_16018,U_16016,U_16014))],[f_3996_3]) ).
cnf(f_3996_5,plain,
( hAPP(hAPP(c_List_Olist_OCons(U_16014),U_16016),sK426(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_3996_4]) ).
cnf(f_3996_6,plain,
( U_16018 = hAPP(hAPP(c_List_Oappend(U_16014),sK426(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_3996_4]) ).
cnf(f_3996_7,plain,
( hAPP(hAPP(c_List_Olist_OCons(U_16014),U_16016),sK426(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_3996_4]) ).
cnf(f_3996_8,plain,
( U_16018 = hAPP(hAPP(c_List_Oappend(U_16014),sK426(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_3996_4]) ).
cnf(f_3996_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_3996_4]) ).
cnf(f_3996_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_3996_4]) ).
fof(f_3997_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_3997_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_3997_1]) ).
fof(f_3997_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_3997_2]) ).
fof(f_3997_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),sK427(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),sK427(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,[sK427]),skolemize(U_16024,sK427(U_16039,U_16037,U_16035,U_16033,U_16031))],[f_3997_3]) ).
cnf(f_3997_5,plain,
( U_16033 = hAPP(hAPP(c_List_Olist_OCons(U_16031),U_16037),sK427(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_3997_4]) ).
cnf(f_3997_6,plain,
( hAPP(hAPP(c_List_Oappend(U_16031),sK427(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_3997_4]) ).
cnf(f_3997_7,plain,
( U_16033 = hAPP(hAPP(c_List_Olist_OCons(U_16031),U_16037),sK427(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_3997_4]) ).
cnf(f_3997_8,plain,
( hAPP(hAPP(c_List_Oappend(U_16031),sK427(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_3997_4]) ).
cnf(f_3997_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_3997_4]) ).
cnf(f_3997_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_3997_4]) ).
fof(f_3998_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_3998_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_3998_1]) ).
cnf(f_3998_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_3998_2]) ).
fof(f_3999_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_3999_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_3999_1]) ).
cnf(f_3999_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_3999_2]) ).
fof(f_4000_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_4000_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_4000_1]) ).
fof(f_4000_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_4000_2]) ).
cnf(f_4000_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_4000_3]) ).
cnf(f_4000_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_4000_3]) ).
cnf(f_4000_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_4000_3]) ).
fof(f_4001_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_4001_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_4001_1]) ).
cnf(f_4001_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_4001_2]) ).
fof(f_4002_1,plain,
! [V_tsa_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
( ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_tsa_2)
| ! [B_us] :
( ( V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),V_tsa_2)
| hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) != V_zs_2 )
& ( hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) != V_tsa_2
| V_xs_2 != hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us) ) ) )
& ( ? [B_us] :
( ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_tsa_2)
& hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2 )
| ( hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_tsa_2
& V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us) ) )
| hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) != hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_tsa_2) ) ),
inference(fof_nnf,[status(thm)],[fact_append__eq__append__conv2]) ).
fof(f_4002_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_4002_1]) ).
fof(f_4002_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_4002_2]) ).
fof(f_4002_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),sK428(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),sK428(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,[sK428]),skolemize(U_16074,sK428(U_16086,U_16084,U_16082,U_16080,U_16078))],[f_4002_3]) ).
fof(f_4002_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),sK429(U_16086,U_16084,U_16082,U_16080,U_16078)),U_16086)
& hAPP(hAPP(c_List_Oappend(U_16078),U_16080),sK429(U_16086,U_16084,U_16082,U_16080,U_16078)) = U_16084 )
| ( hAPP(hAPP(c_List_Oappend(U_16078),sK428(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),sK428(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,[sK429]),skolemize(U_16075,sK429(U_16086,U_16084,U_16082,U_16080,U_16078))],[f_4002_4]) ).
cnf(f_4002_6,plain,
( hAPP(hAPP(c_List_Oappend(U_16078),U_16080),sK429(U_16086,U_16084,U_16082,U_16080,U_16078)) = U_16084
| U_16080 = hAPP(hAPP(c_List_Oappend(U_16078),U_16084),sK428(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_4002_5]) ).
cnf(f_4002_7,plain,
( U_16082 = hAPP(hAPP(c_List_Oappend(U_16078),sK429(U_16086,U_16084,U_16082,U_16080,U_16078)),U_16086)
| U_16080 = hAPP(hAPP(c_List_Oappend(U_16078),U_16084),sK428(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_4002_5]) ).
cnf(f_4002_8,plain,
( hAPP(hAPP(c_List_Oappend(U_16078),U_16080),sK429(U_16086,U_16084,U_16082,U_16080,U_16078)) = U_16084
| hAPP(hAPP(c_List_Oappend(U_16078),sK428(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_4002_5]) ).
cnf(f_4002_9,plain,
( U_16082 = hAPP(hAPP(c_List_Oappend(U_16078),sK429(U_16086,U_16084,U_16082,U_16080,U_16078)),U_16086)
| hAPP(hAPP(c_List_Oappend(U_16078),sK428(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_4002_5]) ).
cnf(f_4002_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_4002_5]) ).
cnf(f_4002_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_4002_5]) ).
fof(f_4003_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_4003_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_4003_1]) ).
fof(f_4003_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_4003_2]) ).
cnf(f_4003_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_4003_3]) ).
cnf(f_4003_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_4003_3]) ).
fof(f_4004_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_4004_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_4004_1]) ).
fof(f_4004_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 )
&